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Diffstat (limited to 'info')
815 files changed, 9483 insertions, 18479 deletions
diff --git a/info/asy-overview/asy/jh.asy b/info/asy-overview/asy/jh.asy index a6bd31400f..94bc1fa560 100644 --- a/info/asy-overview/asy/jh.asy +++ b/info/asy-overview/asy/jh.asy @@ -1,15 +1,12 @@ // Common definitions for asy_tut -// Function to call the texpreamble() function -void define_texpreamble() { - texpreamble("\usepackage{mathtools} - \usepackage[utf8]{inputenc} - \usepackage[osf,scaled=.92,loosest]{heuristica} - \usepackage[heuristica,vvarbb,bigdelims]{newtxmath} - \usepackage[T1]{fontenc} - \renewcommand*\oldstylenums[1]{\textosf{#1}}"); -} - +// Set up LaTeX for each label +texpreamble("\usepackage{mathtools} + \usepackage[utf8]{inputenc} + \usepackage[osf,scaled=.92,loosest]{heuristica} + \usepackage[heuristica,vvarbb,bigdelims]{newtxmath} + \usepackage[T1]{fontenc} + \renewcommand*\oldstylenums[1]{\textosf{#1}}"); // Change default size of fonts import fontsize; defaultpen(fontsize(9pt)); // Like LaTeX \small diff --git a/info/asy-overview/asy_overview.pdf b/info/asy-overview/asy_overview.pdf Binary files differindex 7a7b8a1341..524c6c53e6 100644 --- a/info/asy-overview/asy_overview.pdf +++ b/info/asy-overview/asy_overview.pdf diff --git a/info/asy-overview/src/appendix/appendix.tex b/info/asy-overview/src/appendix/appendix.tex index f4016f9cd6..1c21dc0bfa 100644 --- a/info/asy-overview/src/appendix/appendix.tex +++ b/info/asy-overview/src/appendix/appendix.tex @@ -4,19 +4,20 @@ Rather than copy and paste code common across graphics, we can put them in a separate file and import them. In the earlier \Asy{} sources the lines \begin{minted}{Asymptote} -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; \end{minted} -will first run the commands in the file \path{../../../asy/jh.asy}, -and then run the function defined in that file. +will run the commands in the file \path{../../../asy/jh.asy} +and also make available the routines and data defined there. -Here is the file. -Its first few lines define the command to set the fonts, +Here is the file's contents. +First, it sets the fonts and changes the default font size. -(This change leaves more room for graphic elements and -also helps the graphics have a visually cohesive identity.) +(The smaller size leaves more room for graphic elements and +also helps the graphics have a visually cohesive identity distinct from +the document's body.) Then it defines a color scheme.\footnote{% - Thank you to \protect\texttt{color.adobe.com} user Michelle Delapenha.} -Lastly, it defines the + Credit to \protect\texttt{color.adobe.com} user Michelle Delapenha for this scheme.} +Last, it gives the \mintinline{Asymptote}{material} defaults for 3D graphics. \begin{center} diff --git a/info/asy-overview/src/asy_tut.tex b/info/asy-overview/src/asy_tut.tex index fc88e07b2b..c90d49037e 100644 --- a/info/asy-overview/src/asy_tut.tex +++ b/info/asy-overview/src/asy_tut.tex @@ -5,8 +5,8 @@ % See: https://github.com/vectorgraphics/asymptote/blob/master/doc/externalprc.tex % Compile .asy files with asy -inlineimage <fn> \RequirePackage{asymptote} -\def\asydir{chapter4/asy/} -\graphicspath{{asy/}} +\def\asydir{chapter4/asy} +\graphicspath{ {asy/} {chapter4/asy/} } % uncomment for 3D graphics: \input chapter4/asy/vectors.pre \input chapter4/asy/planes.pre diff --git a/info/asy-overview/src/chapter1/chapter1.tex b/info/asy-overview/src/chapter1/chapter1.tex index 40c4ecb1be..bc7946a58d 100644 --- a/info/asy-overview/src/chapter1/chapter1.tex +++ b/info/asy-overview/src/chapter1/chapter1.tex @@ -3,7 +3,7 @@ Making an \Asy{} input file is like making a \LaTeX{} input file, so you already have a feel for the basics. To start, -in your favorite editor open an \Asy{} input file \path{asy/unit_circle.asy}. +use your favorite editor to open a file \path{asy/unit_circle.asy}. \begin{minted}{Bash} jim@millstone:~/Documents/asy_tut/src$ cd asy jim@millstone:~/Documents/asy_tut/src/asy$ emacs unit_circle.asy @@ -88,7 +88,7 @@ for a list of the options.) Second, the dot showing the generic point on the unit circle is too big. In the revised source below we've adjusted the size by inserting -\mintinline{Asymptote}{dotfactor = 4} in line~23 +\mintinline{Asymptote}{dotfactor = 4} in line~22 (the default factor is $6$). Finally, the $(\cos\theta,\sin\theta)$ label is in a different font than diff --git a/info/asy-overview/src/chapter1/main.tex b/info/asy-overview/src/chapter1/main.tex index 4617cd0c20..4ca0d66228 100644 --- a/info/asy-overview/src/chapter1/main.tex +++ b/info/asy-overview/src/chapter1/main.tex @@ -11,6 +11,6 @@ include the output PDF in your \LaTeX{} file. \includegraphics{asy/unit_circle_after.pdf} % Can instead include the .asy source in the text body. % \asyinclude{asy/unit_circle_after.asy} - % There is also an environment where you type the .asy source directly. + % There is also an environment where you type the Asy source directly. \end{center} \end{document} diff --git a/info/asy-overview/src/chapter2/asy/cos.asy b/info/asy-overview/src/chapter2/asy/cos.asy index bc053d3bf4..2e4ca0e5b3 100644 --- a/info/asy-overview/src/chapter2/asy/cos.asy +++ b/info/asy-overview/src/chapter2/asy/cos.asy @@ -1,6 +1,6 @@ // cos.asy settings.outformat="pdf"; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph; diff --git a/info/asy-overview/src/chapter2/asy/exponential.asy b/info/asy-overview/src/chapter2/asy/exponential.asy index e81c9545b5..b9d1f2f26c 100644 --- a/info/asy-overview/src/chapter2/asy/exponential.asy +++ b/info/asy-overview/src/chapter2/asy/exponential.asy @@ -1,6 +1,6 @@ // exponential.asy settings.outformat="pdf"; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph; @@ -25,7 +25,7 @@ dot(Label("$(\ln(2),2)$",filltype=Fill(white)), (log(2),2), 2*E); // Axes making graph paper pen GRAPHPAPERPEN=(0.25*LIGHT_COLOR+0.75*white) - +squarecap; // Make graph paper lines + +squarecap; // For graph paper lines xaxis(axis=YEquals(ymax+0.2), xmin=xmin-0.5, xmax=xmax+0.5, diff --git a/info/asy-overview/src/chapter2/asy/plot.asy b/info/asy-overview/src/chapter2/asy/plot.asy index 77ad978bc5..3893038233 100644 --- a/info/asy-overview/src/chapter2/asy/plot.asy +++ b/info/asy-overview/src/chapter2/asy/plot.asy @@ -7,7 +7,7 @@ texpreamble("\usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \renewcommand*\oldstylenums[1]{\textosf{#1}}"); -import graph; // Access plotting routines +import graph; // Function to be plotted real fcn(real x) { diff --git a/info/asy-overview/src/chapter2/asy/plot_after.asy b/info/asy-overview/src/chapter2/asy/plot_after.asy index 0d5ab883c6..09f131a02e 100644 --- a/info/asy-overview/src/chapter2/asy/plot_after.asy +++ b/info/asy-overview/src/chapter2/asy/plot_after.asy @@ -1,7 +1,8 @@ // plot_after.asy -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +settings.outformat="pdf"; +import "../../../asy/jh.asy" as jh; -import graph; // Access plotting routines +import graph; // Function to be plotted real fcn(real x) { diff --git a/info/asy-overview/src/chapter2/chapter2.tex b/info/asy-overview/src/chapter2/chapter2.tex index 658d4c3896..ae454e7cb9 100644 --- a/info/asy-overview/src/chapter2/chapter2.tex +++ b/info/asy-overview/src/chapter2/chapter2.tex @@ -9,8 +9,8 @@ we can't ask \Asy{} to plot all $x$'s. We will instead plot the $x$'s where the associated $y$'s are between $-5$ and~$5$. To find these -we can use \textit{Sage} to solve -$5=x+(1/(x-1))$ and $-5=x+(1/(x-1))$. +we can use a computer algebra system such as \textit{Sage} to solve +$5=x+1/(x-1)$ and $-5=x+1/(x-1)$. \begin{minted}{Python} sage: x = var('x') sage: solve( [5==x+(1/(x-1))], x ) @@ -51,24 +51,25 @@ We make the $y$~unit height be half of the $x$ unit width by adding this command \begin{minted}{Asymptote} scale(Linear, Linear(0.5)) \end{minted} -(the \mintinline{Asymptote}{Linear} is in contrast with -\mintinline{Asymptote}{Logarithmic}). +(\mintinline{Asymptote}{Linear} is in contrast with a +\mintinline{Asymptote}{Logarithmic} scale). The axes and graph now come out rescaled but we must also adjust the location of points, the ones defining the vertical asymptote line, using for example -line~29's \mintinline{Asymptote}{Scale((1,ymin))}. +line~26's \mintinline{Asymptote}{Scale((1,ymin))}. -That tweak of the $y$~axis causes the tick labels to be scrunched together, -so we arrange that \Asy{} lists only every fifth label. +That tweak of the $y$~axis causes its tick labels to be scrunched together, +so we arrange that \Asy{} labels only every fifth tick +(the labeled ones are called major ticks and the others are minor ticks). \begin{minted}{Asymptote} yaxis(ymin=ymin-0.4, ymax=ymax+0.4, LeftTicks(Step=5, step=1, OmitTick(0), Size=3pt, size=2pt), Arrows(TeXHead)); \end{minted} -That command also sets the length of the major and minor ticks. +That command also sets the length of these major and minor ticks. -Here is \path{asy/plot_after.asy} -(more on the first couple of lines in the next section). +Here is \path{asy/plot_after.asy}. +An explanation of line~3 is in the next section. \begin{center} \inputminted{Asymptote}{chapter2/asy/plot_after.asy} \end{center} @@ -82,9 +83,16 @@ Here is the output. \section{Defaults} Rather than copy and paste elements common across graphics such as the font commands or colors, -we can put them in a separate file \path{jh.asy} and import them, -as in the prior source's line~2. -That file's source is in the Appendix. +we can put them in a separate file and import them, +as in the prior source's line~3. +The source of that file, \path{jh.asy}, is in the Appendix. +(About the +\mintinline{Asymptote}{"../../../asy/"} +directory stuff:~usually we set up \Asy{} with a directory for common files +and then just say \mintinline{Asymptote}{import jh}. +But for this document we want that a user can compile without setup +so the relative path is in the source.) + \section{Ticks} @@ -108,10 +116,10 @@ Note line~25's \mintinline{Asymptote}{NW}, which prints the $3\pi/2$ northwest of its tick. Our other tick example has a graph paper effect, -where ticks in a light color extending across the graph. +with lines in a light color extending across the graph. (I sometimes use this for lectures; here, -to estimate by eye that the slope of the tangent line -at $y=2$ is $2$.) +to estimate by eye that at $y=2$ the slope of the tangent line +is~$2$.) \begin{center} \includegraphics{chapter2/asy/exponential.pdf} \end{center} @@ -120,28 +128,32 @@ The source has a number of interesting features. \begin{center} \inputminted{Asymptote}{chapter2/asy/exponential.asy} \end{center} -The graph paper effect is due to the input in lines 30 through~46. +The graph paper effect is due to the input in lines 26 through~46. The horizontal lines are a little clearer so we will cover them. -They are created by the first two \mintinline{Asymptote}{yaxis(..)} commands, -which produce two vertical axes, one on the left and one on the right, -These are drawn with a \mintinline{Asymptote}{nullpen} so we don't see -vertical black lines at those locations. +They are created by the \mintinline{Asymptote}{yaxis(..)} commands +in lines 39--46. +These two vertical axes, one on the left and one on the right, +are drawn with a \mintinline{Asymptote}{nullpen} so we don't see +vertical black lines at \mintinline{Asymptote}{xmin-0.2} +and \mintinline{Asymptote}{xmax+0.2}. What we do see are -the ticks extending back and forth between them in the color given by +the ticks for those axes, +extending back and forth between them in the color given by \mintinline{Asymptote}{GRAPHPAPERPEN}, because of the \mintinline{Asymptote}{extend=true}. These ticks have a null label because of the \LaTeX{} comment character~\mintinline{Asymptote}{"%"}. -(The $y$~axis on the left produces the horizontal +The $y$~axis on the left produces the horizontal graph paper marks between -$x=\text{\mintinline{Asymptote}{xmin-0.2}}$ and the third $y$~axis at +$x=\text{\mintinline{Asymptote}{xmin-0.2}}$ and $x=0$, while the one on the right generates the marks -from $x=0$ to $x=\text{\mintinline{Asymptote}{xmax+0.2}}$.) +from $x=0$ to $x=\text{\mintinline{Asymptote}{xmax+0.2}}$. +(The $x=0$ comes from the $y$~axis in lines 52--54.) -The commands from line~49 to the end produce the black line axes. +The commands from line~49 to the end produce the axes shown in black. % Note that \mintinline{Asymptote}{yaxis(..)} produces only one arrow. -This is a long file but we will discuss a few finer points. +This is a long file but we will discuss a few fine points. One is that the $(\ln(2),2)$ label has a white background obscuring some of the graph paper lines, from the \mintinline{Asymptote}{Label("$(\ln(2),2)$",filltype=Fill(white))} @@ -152,7 +164,7 @@ is there because \Asy{} draws the graph by connecting dots that evaluate \mintinline{Asymptote}{fcn} at a finite number of points, and the default was too small so that -the graphic had jaggies on the left. +the graphic had visible jaggies. Finally, lines 18 and~19 as well as lines 27 and~28 make clear that essential to understanding \Asy{} is understanding the ideas of diff --git a/info/asy-overview/src/chapter3/asy/integral.asy b/info/asy-overview/src/chapter3/asy/integral.asy index 1b756c0404..ccc2249a17 100644 --- a/info/asy-overview/src/chapter3/asy/integral.asy +++ b/info/asy-overview/src/chapter3/asy/integral.asy @@ -1,6 +1,6 @@ // integral.asy settings.outformat="pdf"; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph; diff --git a/info/asy-overview/src/chapter3/asy/zoom.asy b/info/asy-overview/src/chapter3/asy/zoom.asy index 462bf9d048..8c45316b58 100644 --- a/info/asy-overview/src/chapter3/asy/zoom.asy +++ b/info/asy-overview/src/chapter3/asy/zoom.asy @@ -1,6 +1,6 @@ // zoom.asy settings.outformat="pdf"; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph; diff --git a/info/asy-overview/src/chapter3/asy/zoom_iterate.asy b/info/asy-overview/src/chapter3/asy/zoom_iterate.asy index 2c6268fa8c..3ecf6d9c86 100644 --- a/info/asy-overview/src/chapter3/asy/zoom_iterate.asy +++ b/info/asy-overview/src/chapter3/asy/zoom_iterate.asy @@ -1,12 +1,18 @@ // zoom_iterate.asy settings.outformat="pdf"; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph; path f = GENERIC_FCN_PLOT; // Shorter to type real c = 3.1; +// Find f(c) on f and get f'(c) +real c_time = times(f, c)[0]; +pair c_point = point(f,c_time); +pair d = dir(f, c_time); +real t_line_fcn(real x) { return (d.y/d.x)*(x-c_point.x) + c_point.y; } + string OUTPUT_FN = "zoom_iterate%03d"; for (int i=0; i<4; ++i) { picture pic; // Generate a new picture @@ -16,20 +22,14 @@ for (int i=0; i<4; ++i) { real delta = 1/2^(i); real xmin = c-delta; real xmax = c+delta; - // Find f(c) on f, and get f'(c) as a pair - real c_time = times(f, c)[0]; - pair c_point = point(f,c_time); - pair d = dir(f, c_time); - real t_line_fcn(real x) { return (d.y/d.x)*(x-c_point.x) + c_point.y; } - path t_line = graph(t_line_fcn, xmin, xmax); - - // Limits of f to show + // Limits of f and tangent line to show real left_time = times(f, xmin)[0]; real right_time = times(f, xmax)[0]; path f_shown = subpath(f, left_time, right_time); + path t_line = graph(t_line_fcn, xmin, xmax); - // Draw f and tangent line - transform f_trans = shift(0, 0.5*delta)*shift(0, -1*c_point.y); // Shift f close to axis + // Shift f and tangent line close to x-axis, then draw + transform f_trans = shift(0, 0.5*delta)*shift(0, -1*c_point.y); draw(pic, f_trans*f_shown, BOLD_COLOR); draw(pic, f_trans*t_line, HIGHLIGHT_COLOR); dotfactor = 3; diff --git a/info/asy-overview/src/chapter3/asy/zoom_times.asy b/info/asy-overview/src/chapter3/asy/zoom_times.asy index a3d3964883..d7d4628b29 100644 --- a/info/asy-overview/src/chapter3/asy/zoom_times.asy +++ b/info/asy-overview/src/chapter3/asy/zoom_times.asy @@ -1,6 +1,6 @@ // zoom_times.asy settings.outformat="pdf"; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph; diff --git a/info/asy-overview/src/chapter3/chapter3.tex b/info/asy-overview/src/chapter3/chapter3.tex index 162ef87df7..d592b69c22 100644 --- a/info/asy-overview/src/chapter3/chapter3.tex +++ b/info/asy-overview/src/chapter3/chapter3.tex @@ -2,12 +2,13 @@ \chapter{Paths and pens} \section{Paths} -This plots a function that is generic in that it isn't $f(x)=x^2$ or some -other function derived from a simple expression. -We will use this it for the classic Calculus -lesson of zooming in on a point of tangency to -illustrate that -the curve is locally well-approximated by the line. +This plots a function that is generic in that it isn't +derived from a simple expression such as $\cos x$ or $x+(1/(x-1))$. +We will use it for the classic Calculus +lesson +illustrating that +the curve is locally well-approximated by the line, +by zooming in on a point of tangency. \begin{center} \includegraphics{chapter3/asy/zoom.pdf} \end{center} @@ -24,6 +25,7 @@ so I included a copy in \path{jh.asy} as \mintinline{Asymptote}{GENERIC_FCN_PLOT}.) Earlier, when we drew a vertical asymptote line we instead connected two points with a \mintinline{Asymptote}{--} operator, which gives a line segment. +There are other connectors but these two are the most common. In line~17, \Asy's \mintinline{Asymptote}{dir(..)} command gives the direction of the @@ -40,7 +42,7 @@ As to line~15's \mintinline{Asymptote}{c_time = times(f, c)[0]}, just as \MF{} and \MP{} do. These curves are parametrized by a variable called `time'. -By definition, the initial point $(0,-25)$ is at time~$0$, the next point +By definition, the initial point $(0,-0.25)$ is at time~$0$, the next point $(1,0.35)$ is at time~$1$, etc. (To forestall any confusion:~the time has nothing to do with the first coordinate, it comes from when the point is specified in the @@ -51,7 +53,7 @@ This illustrates, showing some times. \includegraphics{chapter3/asy/zoom_times.pdf} \end{center} The \mintinline{Asymptote}{times(..)} command returns an array of times -where the path it intersects the vertical line +where the path intersects the vertical line $x=\text{\mintinline{Asymptote}{c}}$. We extract the first one (in this case the only one) with the \mintinline{Asymptote}{[0]}. @@ -66,11 +68,11 @@ The source for the prior graphic shows two useful aspects of \begin{center} \inputminted{Asymptote}{chapter3/asy/zoom_times.asy} \end{center} -The first aspect is in line~19. +The first of those is in line~19. The \mintinline{Asymptote}{format("$%0.02f$",t)} turns the floating point number~$t$ into the string used in the label. -A larger point is in lines~17 through~20, where the code has an iteration. +The other is in lines~17 through~20, where the code has an iteration. One strength of \Asy{} is that it is a standard programming language, with clean constructs that are like those you use in other languages in your daily work. @@ -98,8 +100,8 @@ is more complex than the others that we have seen. One reason is that this one file produces four pictures, so that we needn't maintain four separate \path{.asy} files with lots of overlap. -The four output files are produced in the loop between lines~11 and~47. -Line~12 creates a new +The four output files are produced in the loop between lines~17 and~47. +Line~18 creates a new \mintinline{Asymptote}{picture} and line~46 outputs it. The files are named @@ -112,15 +114,15 @@ form of that name is given by the string Besides using a single input to create multiple output files, there are two other things that are new here. -One is line~13's +One is line~19's \mintinline{Asymptote}{size(pic, 3cm, 0)}. -This makes each output graphic be three centimeters wide, and as tall as +This makes each output graphic be three centimeters wide and as tall as required, setting the size of the $x$ and~$y$ units as needed to get that width. The result is a zooming-in on successively shorter intervals of the $x$~axis. The other new thing -is that when the $x$~axis interval is small, rescaling the units to make the +is that rescaling the units to make the entire figure three centimeters wide would put the plotted function very far above the $x$~axis. @@ -128,8 +130,8 @@ So we have moved the function down near the axis. This transformation applies not just to the function but also to the tangent line and to the point $(c,f(c))$, so we have broken this transformation out as a separate thing, -line~32's -\mintinline{Asymptote}{transform f_trans = shift(0,0.5*delta)*shift(0,-1*c_point.y)}. +in line~32. +%\mintinline{Asymptote}{transform f_trans = shift(0,0.5*delta)*shift(0,-1*c_point.y)}. Transformations are applied with the star operator, as on lines~33, 34, and~36. @@ -158,8 +160,8 @@ Here is the resulting graphic. The \mintinline{Asymptote}{buildcycle(left_side, f, right_side, bottom)} on line~20 is new. -It takes the paths surrounding the region of interest and -constructs the path that is its boundary. +It takes paths surrounding the region of interest and +constructs the path that is the region's boundary. (A more common way to make a cyclic path is to end with \mintinline{Asymptote}{cycle}, as with \mintinline{Asymptote}{path triangle = (0,0)--(0,1)--(1,0)--cycle}.) @@ -167,7 +169,7 @@ constructs the path that is its boundary. Then line~23's \mintinline{Asymptote}{fill(region, NEUTRAL_COLOR+opacity(0.5))} covers the region using a pen that, in addition to its color, allows some of the material behind it to show through. -Note that some PDF viewers have trouble with opacity so your results may vary, +Note that some PDF viewers have trouble with opacity so your results may vary but one viewer that gives good results is Adobe's Reader. The \Asy{} reference gives many options for pens. diff --git a/info/asy-overview/src/chapter4/asy/planes.asy b/info/asy-overview/src/chapter4/asy/planes.asy index 6f7d6efc9e..b5b0ea81dc 100644 --- a/info/asy-overview/src/chapter4/asy/planes.asy +++ b/info/asy-overview/src/chapter4/asy/planes.asy @@ -3,7 +3,7 @@ settings.outformat="pdf"; settings.tex="pdflatex"; settings.prc = true; settings.render = 0; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph3; projection default_projection = orthographic(3,1.5,0.5,up=Z); diff --git a/info/asy-overview/src/chapter4/asy/vectors.asy b/info/asy-overview/src/chapter4/asy/vectors.asy index b1f2ad1700..a0c965a823 100644 --- a/info/asy-overview/src/chapter4/asy/vectors.asy +++ b/info/asy-overview/src/chapter4/asy/vectors.asy @@ -3,7 +3,7 @@ settings.outformat = "pdf"; settings.tex = "pdflatex"; // For compiling in-pic text settings.prc = true; // Manipulable in a PDF file settings.render = 0; // Needed for "poster" image, i.e., picture to click on -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import fontsize; diff --git a/info/asy-overview/src/chapter4/asy/washer.asy b/info/asy-overview/src/chapter4/asy/washer.asy index c74f6c0d16..1f071aad17 100644 --- a/info/asy-overview/src/chapter4/asy/washer.asy +++ b/info/asy-overview/src/chapter4/asy/washer.asy @@ -3,7 +3,7 @@ settings.tex = "pdflatex"; settings.outformat = "pdf"; settings.render = 8; // Tweaked this until poster pic looked better settings.prc = true; -cd("../../../asy"); import jh; cd(""); define_texpreamble(); +import "../../../asy/jh.asy" as jh; import graph3; projection default_projection = orthographic(3,1.5,0.5,up=Z); diff --git a/info/asy-overview/src/chapter4/chapter4.tex b/info/asy-overview/src/chapter4/chapter4.tex index ff1f3064f4..4e12c76957 100644 --- a/info/asy-overview/src/chapter4/chapter4.tex +++ b/info/asy-overview/src/chapter4/chapter4.tex @@ -1,9 +1,10 @@ % Chapter 4 from Asymptote tutorial Jim Hefferon -\def\asydir{chapter4/asy/} +\def\asydir{chapter4/asy} \chapter{3D} A strength of \Asy{} is its ability in three dimensions. -It can easily draw what you want to draw, including +It can easily draw what you want to draw. +That includes % that it extends to three dimensions constructs for good-looking paths % that come from two-dimensional \MF{} and \MP. doing projections, which can be tricky to get right by eye. @@ -11,16 +12,15 @@ doing projections, which can be tricky to get right by eye. In addition, you can choose to make these graphics manipulable, so that you can use your mouse to turn them around or peek under them, and in general have an explore. -This is great for a Calculus lecture so its what I'm showing here. - -Note that only some PDF viewers let you manipulate. -For instance, Adobe's Reader works but the readers embedded in web +This is great for a Calculus lecture so it is what I'm showing here. +(Note that only some PDF viewers let you manipulate. +For instance, Adobe's Reader works but the ones embedded in web browsers do not. To test your reader just click on the graphic below. -(You may be asked to let the reader +You may be asked to let the reader run the code that does the manipulation.) -We start with a picture showing the vector of displacements $(2,1,1)$ at a +We start with a picture showing the displacement vector $(2,1,1)$ at a number of initial points. % \begin{center} % \asyinclude{chapter4/asy/vectors} @@ -29,8 +29,8 @@ number of initial points. \input chapter4/asy/vectors.tex \end{center} -The input code has two different things going on. -First, so that the vectors are scattered about, +The input code shows two new things. +First, to scatter the vectors about, in lines 34--36 they get a randomly-chosen initial point. The randomization uses the seed from line~24. To find that number I uncommented lines 21--23 and commented out line~24, @@ -43,7 +43,7 @@ until there are such eight vectors. \begin{center} \inputminted{Asymptote}{chapter4/asy/vectors.asy} \end{center} -The other thing in the code is the 3D stuff. +However, the really new stuff is the 3D stuff. It is surprisingly like the 2D constructs that we have seen. Line~10's \mintinline{Asymptote}{import graph3} gives access to @@ -57,10 +57,15 @@ and instead of you say \mintinline{Asymptote}{xaxis3(..)}. But much of it is at least similar. +(Lines~11 and~12 give the projection, +essentially setting the location of the camera +that is taking this picture. +Even if we use a reader that allows us to manipulate the image, +we still need a starting view.) -The next graphic shows surfaces, -which are genuinely different than what we saw in 2D. -It illustrates that the angle between two +We next see something +genuinely different from a 2D context, surfaces. +This graphic illustrates that the angle between two intersecting planes is the same as the angle between their normal vectors. % \begin{center} @@ -69,15 +74,11 @@ vectors. \begin{center} \vcenteredhbox{\input chapter4/asy/planes.tex }% \end{center} -We can imagine that lines~19 and~20 set the location of the camera -that is taking this picture. -Even if we use a reader where the image is manipulable, -we need a starting view. \begin{center} \inputminted{Asymptote}{chapter4/asy/planes.asy} \end{center} -This graphic's code +This code spotlights the power of transforms. We don't have to give the equations of the planes or specify their normals. Instead, in line~17 we define the edge of @@ -91,12 +92,12 @@ The new plane with its edge and its normal vector then comes from applying that transform to the horizontal plane, its edge, and its normal. -To color the surfaces, in lines~24 and~26 we use -\mintinline{Asymptote}{figure material}. -We will reuse these later so the definition is in \path{jh.sty}; -see lines~28--35 in the Appendix. -This coloring involves \mintinline{Asymptote}{opacity(..)} and -note that you can indeed see through the planes to some extent. +In lines~24 and~26 we use +\mintinline{Asymptote}{figure_material} to give the surfaces color. +We will reuse this later so the definition is in \path{jh.sty}; +see lines~26--32 in the Appendix. +This involves \mintinline{Asymptote}{opacity(..)} and +note that you can indeed see through the planes. Finally, in lines~40--46 we take advantage of one of \Asy's many helper functions to find and draw the arc of the angle between the planes and the normals. @@ -144,8 +145,9 @@ Here is a shot of the output. \framebox{\includegraphics[page=1,scale=0.325,trim=0.25in 5in 0.25in 0.25in]{chapter4/main_3d.pdf}} \end{center} In that output PDF, -you should be able to click on the graphic and move it around -(of course, your reader must supports this). +you should be able to click on the poster graphic to bring up +the manipulable graphic, +if your reader supports that. diff --git a/info/asy-overview/src/chapter4/main_3d.tex b/info/asy-overview/src/chapter4/main_3d.tex index 9af013d4ff..40fe635435 100644 --- a/info/asy-overview/src/chapter4/main_3d.tex +++ b/info/asy-overview/src/chapter4/main_3d.tex @@ -1,14 +1,15 @@ % main_3d.tex LaTeX demonstraton file showing Asymptote 3D, Jim Hefferon \documentclass{article} \usepackage{graphicx} -\graphicspath{ {asy/} } % Trailing slash, dirs in curly braces +\graphicspath{ {asy/} } % Path to poster graphic; dirs in curly braces, trailing slash \usepackage{asymptote} \def\asydir{asy} % No trailing slash % For non-manipulable 3D figures, just compile with "asy vectors" and % include the PDF output as with 2D figures. % For manipulable 3D figures: -% (1) Compile .asy file with "asy -inlineimage vectors". -% It outputs a number of files, including .tex and .pre files. +% (1) Compile the .asy file with "asy -inlineimage vectors". +% It outputs a number of files, including .tex and .pre files, +% and the .pdf "poster" that you click on to start the manipulation. % (2) Include the .pre line here along with one of the lines in center below \input asy/vectors.pre @@ -19,6 +20,6 @@ Include the output graphic directly in the text body. \input asy/vectors.tex % \end{center} If you use the commented-out way then run -\texttt{asy -inlinimage <latex-fn>-1} +\texttt{asy -inlineimage <latex-fn>-1} between a pair of \LaTeX{} runs of this file. \end{document} diff --git a/info/asy-overview/src/preface/preface.tex b/info/asy-overview/src/preface/preface.tex index 8a2cb9cdbf..f3e5a6209e 100644 --- a/info/asy-overview/src/preface/preface.tex +++ b/info/asy-overview/src/preface/preface.tex @@ -49,5 +49,5 @@ Showing only one option is just a question of going shorter. \begin{flushleft} Jim Hef{}feron \\ University of Vermont \\ -2024-May-26 +2024-Sep-29 \end{flushleft}
\ No newline at end of file diff --git a/info/biblio/font.bib b/info/biblio/font.bib index 287032abf9..65c446021c 100644 --- a/info/biblio/font.bib +++ b/info/biblio/font.bib @@ -2,9 +2,9 @@ %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", -%%% version = "1.127", -%%% date = "08 May 2024", -%%% time = "07:47:15 MST", +%%% version = "1.129", +%%% date = "03 August 2024", +%%% time = "16:28:35 MDT", %%% filename = "font.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB @@ -14,7 +14,7 @@ %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", -%%% checksum = "18065 25010 114533 1094663", +%%% checksum = "28623 25116 115060 1099457", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", @@ -24,7 +24,7 @@ %%% docstring = "This bibliography records publications about %%% typographic fonts. %%% -%%% At version 1.127, the year coverage looked +%%% At version 1.129, the year coverage looked %%% like this: %%% %%% 1785 ( 1) 1865 ( 0) 1945 ( 0) @@ -88,14 +88,14 @@ %%% 1859 ( 0) 1939 ( 0) 2019 ( 5) %%% 1860 ( 0) 1940 ( 1) 2020 ( 1) %%% 1861 ( 0) 1941 ( 0) 2021 ( 1) -%%% 1862 ( 0) 1942 ( 0) 2022 ( 1) -%%% 1863 ( 0) 1943 ( 0) 2023 ( 2) -%%% 1864 ( 0) 1944 ( 0) 2024 ( 1) +%%% 1862 ( 0) 1942 ( 0) 2022 ( 2) +%%% 1863 ( 0) 1943 ( 0) 2023 ( 3) +%%% 1864 ( 0) 1944 ( 0) 2024 ( 3) %%% 19xx ( 3) %%% 20xx ( 2) %%% -%%% Article: 531 -%%% Book: 167 +%%% Article: 532 +%%% Book: 170 %%% Booklet: 4 %%% InCollection: 5 %%% InProceedings: 71 @@ -108,7 +108,7 @@ %%% TechReport: 30 %%% Unpublished: 1 %%% -%%% Total entries: 990 +%%% Total entries: 994 %%% %%% This bibliography has been collected from %%% bibliographies in the author's personal @@ -24056,6 +24056,44 @@ keywords = "Adobe Systems co-founder", } +@Book{Cheung:2022:TLB, + editor = "Victor Cheung", + booktitle = "From Type to Logo: the Best Logotypes from Around the + World", + title = "From Type to Logo: the Best Logotypes from Around the + World", + publisher = "Victionary", + address = "Hong Kong", + pages = "269 + 3", + year = "2022", + ISBN = "988-756-659-4 (hardcover)", + ISBN-13 = "978-988-756-659-5 (hardcover)", + LCCN = "NC1002.L63 F76 2022", + bibdate = "Sat Aug 3 16:23:22 MDT 2024", + bibsource = "fsz3950.oclc.org:210/WorldCat; + https://www.math.utah.edu/pub/tex/bib/font.bib", + abstract = "``When it comes to building a brand, logo design is + often one of the first few important steps in the + creative journey. With so much more competition to + contend with today, how can designers help start-ups + and evolving brands put their best foot forward + visually? A key branding element used by many of the + biggest companies around the world, a logotype revolves + around a company's name or initials and features + typography as the main design approach. From Type to + Logo details the processes of combining the two + distinct design disciplines in a compelling book of + case studies that make an inspiring reference point for + budding and working branding professionals alike.", + acknowledgement = ack-nhfb, + tableofcontents = "Foreword \\ + Preface \\ + Logotypes \\ + Feature Stories \\ + Showcase \\ + Biography", +} + @Article{Durazzi:2022:RTM, author = "Allison Durazzi", title = "Review of {``\booktitle{Type Matters: The Rhetoricity @@ -24158,6 +24196,56 @@ Computerized typesetting.", } +@Book{Anonymous:2024:SUC, + author = "Anonymous", + title = "Serif in Use: a Collection of Serif Typefaces", + publisher = "Victionary", + address = "Hong Kong", + pages = "531 + 45", + year = "2024", + ISBN = "988-768-443-0 (hardcover)", + ISBN-13 = "978-988-768-443-5 (hardcover)", + LCCN = "Z250.5.S47 S47 2024", + bibdate = "Fri Aug 02 10:58:16 2024", + bibsource = "https://www.math.utah.edu/pub/tex/bib/font.bib", + acknowledgement = ack-nhfb, +} + +@Book{Cheung:2023:SUC, + author = "Victor Cheung", + title = "Sans in Use: Creative Typefaces and Their + Applications. From {A} to {Z}. {Book A}", + publisher = "Victionary", + address = "North Point, Hong Kong", + pages = "576", + remark = "Covers 93 typefaces.", + year = "2023", + ISBN = "988-768-442-2", + ISBN-13 = "978-988-768-442-8", + LCCN = "Z250.5.S24 S24 2024", + bibdate = "Sat Aug 3 14:46:34 MDT 2024", + bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/font.bib", + acknowledgement = ack-nhfb, + abstract = "In the world of typography, it is not uncommon to see + combinations of serif and sans serif typefaces in the + same design. However, it takes skill to combine them in + a way to avoid unwanted graphic tension or clashing + fonts, and ensure maximum legibility of the text in the + design. From font weights to classifications, each + typeface has its own distinct personality, and should + be carefully paired to convey the right tone and mood + of the design. Featuring a selection of type specimens, + their design applications, and the thoughts that go + behind the craft, \booktitle{Sans in Use}\slash + \booktitle{Serif in Use} collects the best combinations + of both categories and serves as a reference point for + inspiration-seeking designers and typographers + alike. Through examples and interviews with + internationally renowned type foundries, typography + designers and type experts, the future of typeface + creation is laid bare.", +} + @Article{Hossain:2024:TSR, author = "Anushah Hossain", title = "Text Standards for the ``Rest of World'': The Making @@ -24186,6 +24274,24 @@ Writing", } +@Article{Lovenheim:2024:SRS, + author = "Peter Lovenheim", + title = "Seeing {Rochester} signs through {Chuck Bigelow}'s + eyes", + journal = "Rochester Beacon", + volume = "??", + number = "??", + pages = "??--??", + day = "29", + month = jul, + year = "2024", + bibdate = "Fri Aug 02 09:04:12 2024", + bibsource = "https://www.math.utah.edu/pub/tex/bib/font.bib", + URL = "https://rochesterbeacon.com/2024/07/29/seeing-rochester-signs-through-chuck-bigelows-eyes/", + acknowledgement = ack-nhfb, + keywords = "Chuck Bigelow; Kris Holmes", +} + @Misc{Anonymous:20xx:W, author = "Anonymous", title = "{WhatTheFont}", diff --git a/info/biblio/font.ltx b/info/biblio/font.ltx index f05b486605..9d1647a027 100644 --- a/info/biblio/font.ltx +++ b/info/biblio/font.ltx @@ -2,9 +2,9 @@ %%% ==================================================================== %%% @LaTeX-file{ %%% author = "Nelson H. F. Beebe", -%%% version = "1.127", -%%% date = "08 May 2024", -%%% time = "07:47:28 MST", +%%% version = "1.129", +%%% date = "03 August 2024", +%%% time = "16:28:39 MDT", %%% filename = "font.ltx", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB @@ -14,7 +14,7 @@ %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", -%%% checksum = "44652 81 290 3038", +%%% checksum = "37061 81 290 3044", %%% email = "beebe@math.utah.edu, beebe@acm.org, %%% beebe@computer.org (Internet)", %%% codetable = "ISO/ASCII", @@ -62,8 +62,8 @@ WWW URL: \protect\path=https://www.math.utah.edu/~beebe/= } -\date{08 May 2024 \\ -Version 1.127} +\date{03 August 2024 \\ +Version 1.129} \begin{document} \maketitle \nocite{*} diff --git a/info/drawing-with-metapost/Drawing-with-Metapost.pdf b/info/drawing-with-metapost/Drawing-with-Metapost.pdf Binary files differindex 780071b759..0216380d7d 100644 --- a/info/drawing-with-metapost/Drawing-with-Metapost.pdf +++ b/info/drawing-with-metapost/Drawing-with-Metapost.pdf diff --git a/info/drawing-with-metapost/README.md b/info/drawing-with-metapost/README.md index 5b84892242..29fb143f8d 100644 --- a/info/drawing-with-metapost/README.md +++ b/info/drawing-with-metapost/README.md @@ -1,37 +1,45 @@ # Drawing-with-Metapost +Toby Thurston -- 31 Oct 2024 + This project provides a document that discusses how to draw technical diagrams -with John Hobby's Metapost language. It includes over 200 illustrations -created with Metapost, complete with source code as inspiration and examples. -The intended level is for intermediate to advanced users rather than complete -beginners. For introductions, tutorials, and other articles about Metapost, -see http://www.tug.org/metapost.html +with John Hobby's Metapost language. It includes over 200 illustrations created +with Metapost, complete with source code as inspiration and examples. The +intended level is for intermediate to advanced users rather than complete +beginners. For introductions, tutorials, and other articles about Metapost, see +http://www.tug.org/metapost.html -Start with "Drawing-with-Metapost.pdf" in the top directory. +Start with `Drawing-with-Metapost.pdf` in the top directory. The `src` directory contains - the TeX source for the main document - the style file used for marking up Metapost source code - the Metapost source for each illustration used in the main document -- the corresponding PDF file created from the MP source +- the corresponding PDF files created from each MP source file + +The text includes a discussion of the techniques used for drawing the +illustrations, and includes complete or partial listings for most of them. +These listings are included directly from the source code used, so in all cases +the output should exactly match what you see on the page. You might like to read the main document first, but you might also like to -browse through the PDFs in the src directory, and when you find one that is +browse through the PDFs in the `src` directory, and when you find one that is interesting, have a look at the corresponding MP source file. There is a one-to-one match between the PDF names and the MP source names, so -"apollonius.pdf" is created from "apollonius.mp". The src directory contains -a few drawings that are not (yet) included in the main document. +`geometry-apollonius.pdf` is created from `geometry-apollonius.mp`. The `src` +directory contains a few drawings that are not included in the main document. To update the main PDF document I follow these steps - build any new or updated Metapost source files with `lualatex` to create PDFs in the src directory -- build the main tex file with `lualatex -output-directory=.. -recorder Drawing-with-Metapost` -- run a Python script to read the .fls and `git add` all the files used +- build the main tex file with `lualatex -recorder Drawing-with-Metapost` +- run a Python script to read the `.fls` and `git add` all the files used - git commit and push -Toby Thurston -- 14 Apr 2023 +If you find any errors, or have any suggestions for improvement, please raise an +issue or submit a pull request on Github. -Copyright (c) 2023 by Toby Thurston. This material may be distributed only +Copyright (c) 2024 by Toby Thurston. This material may be distributed only subject to the terms and conditions set forth in the Open Publication License, v1.0 or later (the latest version is presently available at http://www.opencontent.org/openpub/). diff --git a/info/drawing-with-metapost/src/Drawing-with-Metapost.tex b/info/drawing-with-metapost/src/Drawing-with-Metapost.tex index e7143f4333..d90f56683c 100644 --- a/info/drawing-with-metapost/src/Drawing-with-Metapost.tex +++ b/info/drawing-with-metapost/src/Drawing-with-Metapost.tex @@ -1,14 +1,18 @@ -% Copyright (c) 2023 by Toby Thurston. This material may be distributed only +% Copyright (c) 2024 by Toby Thurston. This material may be distributed only % subject to the terms and conditions set forth in the Open Publication License, % v1.0 or later (the latest version is presently available at % http://www.opencontent.org/openpub/). + +\loop\iftrue +\errmessage{This manual is copyrighted and should not be compiled as is.} +\repeat \documentclass[a4paper,landscape]{article} \usepackage{luamplib} \mplibtextextlabel{enable} +\everymplib{beginfig(0);} \everyendmplib{endfig;} \usepackage{fontspec} \newfontfamily{\demo}{TeX Gyre Pagella} \DeclareTextFontCommand{\textdemo}{\demo} -\usepackage{unicode-math} \usepackage[inner=1in,textwidth=5in,textheight=6in, marginparsep=0.5in, marginparwidth=4.2in]{geometry} \usepackage{sectsty} \allsectionsfont{\normalfont\sffamily\bfseries} @@ -17,34 +21,45 @@ \def\mfbook{\textsl{The \MF\kern1pt book}} \def\texbook{\textsl{The \TeX\kern1pt book}} \usepackage{shortvrb}\MakeShortVerb{"} +\usepackage{enumitem} \usepackage{dwmpcode} \title{Drawing with Metapost} \author{Toby Thurston} -\date{March 2017 – April 2023} +\date{March 2017 – October 2024} \overfullrule=2pt -\def\kw#1{\begingroup\def\_{\kern.04em - \vbox{\hrule width.3em height .6pt}\kern.08em}% -\ifmmode\mathop{\textbf{#1}}\else\hbox{\bf#1\/}\fi\endgroup} -\def\op#1{\begingroup\def\_{\kern.04em - \vbox{\hrule width.3em height .6pt}\kern.08em}% -\ifmmode\mathop{\textrm{#1}}\else\hbox{\rm#1\/}\fi\endgroup} -\def\id#1{\begingroup\def\_{\kern.04em - \vbox{\hrule width.3em height .6pt}\kern.08em}% -\ifmmode\mathop{\textit{#1}}\else\hbox{\it#1\/}\fi\endgroup} -\def\cycle{{\rm cycle}} +\def\kw#1{\begingroup\def\_{\kern.04em\vbox{\hrule width.3em height .6pt}\kern.08em}% +\ifmmode\mathop{\textbf{#1}}\else\textbf{#1}\fi\endgroup} +\def\op#1{\begingroup\def\_{\kern.04em\vbox{\hrule width.3em height .6pt}\kern.08em}% +\ifmmode\mathop{\textrm{#1}}\else\textrm{#1}\fi\endgroup} +\def\id#1{\begingroup\def\_{\kern.04em\vbox{\hrule width.3em height .6pt}\kern.08em}% +\ifmmode\mathop{\textit{#1}}\else\textit{#1}\fi\endgroup} +\def\cycle{\textrm{cycle}} \def\vpic#1#2{\moveright5.5in\vbox to 0pt{\hsize4in\vskip#1\centerline{\includegraphics{#2}}\vss}} \def\mpic#1#2{\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip#1\centerline{\includegraphics{#2}}\vss}}} -\def\mnote#1#2{\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip#1\noindent #2\par\vss}}} \def\mwpic#1#2{\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip#1\centerline{\includegraphics[width=4in]{#2}}\vss}}} -\def\mxpic#1#2#3{\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip#1\centerline{\includegraphics[width=#2]{#3}}\vss}}} -\def\nb{$\vcenter{\begin{mplibcode}beginfig(1); +\def\mnote#1#2{\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip#1\noindent #2\par\vss}}} +\def\nb{$\vcenter{\begin{mplibcode} for t=0 upto 3: fill unitsquare scaled 4 shifted right shifted up rotated 45 rotated 90t; -endfor currentpicture := currentpicture scaled 1/2; endfig;\end{mplibcode}}$\ } +endfor currentpicture := currentpicture scaled 1/2; \end{mplibcode}}$\ } \def\unit#1{\ifmmode\,\else\thinspace\fi\hbox{#1}} \def\to{\mathrel{\ldotp\ldotp}} \def\<#1>{\ensuremath{\langle\hbox{#1}\rangle}} -\newfontface\ding{Zapf Dingbats} -\def\hey{\llap{\ding ☞\ }} +\usepackage{pifont} +\def\hey{\llap{{\ding{43}}\ }} +\newcommand\fleuron{\begin{mplibcode} + -z1 = z4 = 7 dir 8; + y2 - y1 = y4 - y3 = 3(y4 - y1); + z2 - z1 = z4 - z3 = whatever * dir 50; + draw z1 .. controls z2 and z3 .. z4 + withpen pencircle xscaled 1.2 yscaled 0.2 rotated 50; + currentpicture := currentpicture rotated - angle z4; +\end{mplibcode}} +\newcommand\continued{\moveright 296pt\vbox to 0pt{\vskip -36pt +\begin{mplibcode} + ahangle := 30; + drawarrow origin {right} .. {dir 60} 42 dir 60; + label.lft("\small \dots continued", origin); +\end{mplibcode}\vss}} % \begin{document} \let\folio\thepage @@ -57,7 +72,7 @@ endfor currentpicture := currentpicture scaled 1/2; endfig;\end{mplibcode}}$\ } 0pt{\vskip23pt\noindent\sffamily{\Large\bfseries\@title}\par\bigskip \noindent\@author\ --- \@date\par \bigskip\noindent - \includegraphics{archimedes.pdf} + \includegraphics{tiling-archimedes} \vss} \makeatother \thispagestyle{empty} @@ -67,7 +82,7 @@ This document contains a collection of ideas and techniques for producing attrac technical drawings with John Hobby’s \MP\ language. I’m assuming that you already know the basics of the language, that you have it installed as part of your up to date \TeX\ ecosystem, and that you have established a reasonable workflow that -let’s you write a Metapost program, compile it, and include the results in your +let’s you write a \MP\ program, compile it, and include the results in your \TeX\ document. If not, you might like to start at the \MP\ page on CTAN, and read some of the excellent tutorials, including "mpintro.pdf". If you have already done this, please read on. @@ -86,12 +101,21 @@ be useful and then see how it’s done. And when I say \textit{plain} \MP\ I mean \MP\ with the default format (as defined in the file "plain.mp") loaded and only a few simple external packages (like -"boxes.mp" occasionally). Nearly all of the examples here are supposed to be self +"colorbrewer") occasionally. Nearly all of the examples here are supposed to be self contained, and any macros are defined locally so you can get to grips with what’s going on. \MP\ is a very subtle language, and it’s possible to do some very clever -and completely inscrutable things with it; in contrast I’ve tried to be as clear as +and completely inscrutable things with it; but here I have tried to be as clear as possible in my examples. +\vbox to 0pt{ +\vskip 1in +\noindent +\begingroup\footnotesize\blue{ +Copyright \copyright\ 2024 by Toby Thurston. This material may be distributed only +subject to the terms and conditions set forth in the Open Publication License,~v1.0 +or later (the latest version is presently available at +"http://www.opencontent.org/openpub/").}\endgroup\par\vss} + \newpage \section{Some features of the syntax} @@ -100,7 +124,7 @@ possible in my examples. current scopeâ€; the assignment "a:=3;" means “update the value of "a" to the value "3" immediatelyâ€. The difference becomes apparent when you try to update a variable in the same scope. - \mwpic{0pt}{tiling} + \mwpic{-64pt}{tiling-arch-hexagon} This difference also lets you write linear equations like "a=-b;". After this, as soon as you give a value to "a", \MP\ immediately works @@ -165,7 +189,7 @@ simple, and since the basic tutorials can go out of date, here are descriptions my own workflows that you might find helpful. You might also think I'm being really inefficient; if so please drop me a line and suggest an improvement. -The common features of each of these workflows are: mac os, the MacVim editor to +The common features of each of these workflows are: Mac~OS, the MacVim editor to edit \MP\ source code, and Skim.app to view PostScript and PDF files. I have the complete MacTeX distribution installed; any commands mentioned below are supplied by MacTeX. @@ -191,26 +215,26 @@ line means that the output will be written to files with an extension that match the chosen output format, which will be "png", "svg", or more usually "eps", which is the default (and suggests that the output is Encapsulated PostScript). +\smallskip + I then add drawing and label commands, using all the traditional facilities for typesetting labels described in section \ref{sec:trad-labels}. I compile the source with "mpost". I usually do this from within MacVim using the command line ":!mpost %" where "!" means “this is an external command†and the "%" picks up the current file name. Usually I need several attempts to get a diagram right, so I open Skim to preview the -output with ":!open -a Skim %:r1.eps". I have Skim set up so that when I recompile -the source, it automatically updates the view of the PostScript output. +output. \vadjust{\moveright5.4in\vbox to 0pt{\vss\hsize 4in\noindent -$$\includegraphics[width=4in]{workflow-plain.pdf}$$ -If I want to use the diagram in a \LaTeX\ document I can include the EPS file -directly with -\begin{texcode} - \includegraphics{some-diagram1.eps} -\end{texcode} -but usually I prefer to convert the EPS to PDF using "epstopdf" rather than rely on -the automatic conversion. This is mainly because the PDFs are generally more useful -files to have about (I can include them in presentations etc). Sometimes I do this -manually but usually I use a small Python script to automate this process: run +$$\includegraphics[width=4in]{workflow-plain}$$ +Until recent (2024) versions of Mac~OS, it was possible to get Skim to view the +PostScript output directly, with automatic updates on recompile, +but the conversion from PostScript no longer works properly, so +I now prefer to convert the EPS to PDF using "epstopdf". This +slightly complicates the edit, compile, and preview loop. On the other hand +the PDFs are generally more useful files to create, so it is worth the extra effort. + +I use a small Python script to automate the process: run "mpost" with the "-recorder" option; scan the list of files to see what got -produced; check which ones are PostScript; call "esptopdf" to make each one into a +produced; check which ones are PostScript; call "epstopdf" to make each one into a PDF file; remove each EPS file if successful. Your mileage may vary.\par }} @@ -226,8 +250,8 @@ the template I use: \begin{texcode} \documentclass[border=5mm]{standalone} \usepackage{luamplib} -\begin{document} \mplibtextextlabel{enable} +\begin{document} \begin{mplibcode} \end{texcode} \vskip-12pt @@ -246,11 +270,16 @@ using the \texttt{standalone} class, which automatically adjusts the page size t fit the contents of document, so is ideal for single diagrams. One small disadvantage is that you can only produce a single PDF output file, so you need to have a separate file for each picture, but the good news is that you get a much simpler and -more effective integration with \LaTeX, in particular with the font environment. -Since this only works with "lualatex" you have to use the "fontspec" package, as -explained in section \ref{sec:neo-labels}. +more effective integration with \LaTeX, in particular with the font environment, but +as this only works with "lualatex" you have to use the "fontspec" package, as +explained in section \ref{sec:neo-labels}.\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize 4in\noindent +\hey\small If you like the fancier \MP\ format provided with ConTexT, you can use it directly with this +"luamplib" approach. Just add this option to your preamble: +\begin{texcode} +\mplibsetformat{metafun} +\end{texcode}}} -\subsection{Integrated graphics with Lua\LaTeX} +\subsection{Integrated graphics with Lua\LaTeX}\label{sec:lua-integrated} If you are ready to use "lualatex" for processing your entire document, then you can directly embed your \MP\ drawings in a series of "mplibcode" environments. Each one @@ -264,26 +293,26 @@ modern machine this is not really an issue any more. \label{plain-shapes} In \MP\ there are two sorts of paths: open and closed. -\mpic{-12pt}{closed-triangles} +\mpic{-12pt}{paths-triangles} A closed path is called a cycle, and is created with the \mpl{cycle} primitive like this: \begin{code} path t; t = origin -- (55,0) -- (55,34) -- cycle; \end{code} You can think of \mpl{cycle} as meaning ‘connect back to the start and close the path’. -Note that you have explicitly put \mpl{cycle} to make a closed path. If you wrote +Note that you have explicitly put \mpl{cycle} to make a closed path. If you wrote \begin{code}[xrightmargin=-32pt] path u; u = origin {right} .. (55,0) .. (55,34) .. {-2,-1} origin; \end{code} then $u$ would be an open path even though the last point is the same as the first. Any path that does not have \mpl{cycle} at the end is an open -path.\mpic{-12pt}{open-triangle} +path.\mpic{-12pt}{paths-open-triangle} You can use \mpl{draw} with either sort of path, but you can only use \mpl{fill} with a cycle. This concept is common to most drawing languages but it’s often hidden: an open path might be automatically closed for you when you try to fill it. \MP\ takes a more cautious approach; if you pass an open path to \mpl{fill} you will get an error that says ‘Not a cycle’, even if the first and last points are the same like path -$u$ above. +$u$ above. If you want to write a macro that deals differently with the two types of path, then you can use \mpl{cycle} in a boolean context to test @@ -306,7 +335,7 @@ quite sure what the five joiners do, $\longrightarrow$\marginpar{% --&straight line\cr ---&tense line\cr \&&splice.\cr}\vss}} or you would like to bone up on exactly what \mpl{curl} and -\mpl{tension} are for, then you are recommended to review Chapter 14 of \mfbook. +\mpl{tension} are for, then you are recommended to review Chapter 14 of \mfbook. \vfill\noindent Most of the examples in this document use only the two simple joiners \mpl{--} and @@ -317,47 +346,48 @@ point. \subsection{Predefined closed paths} There are several closed paths defined for you in plain \MP. -\mpic{0pt}{closed-standards} +\mpic{-36pt}{paths-standards} \begin{itemize} \item "unitsquare" is defined as the path \mpl{(0,0)--(1,0)--(1,1)--(0,1)--cycle}. It runs counter-clockwise from the origin, and you can use it to draw any rectangle with appropriate use of \mpl{xscaled} and \mpl{yscaled}, or a parallelogram with \mpl{slanted}, or a diamond with \mpl{rotated} --- but note that the definition means - that is it centred on point \mpl{(1/2, 1/2)} so you might want to + that is it centred on point \mpl{(1/2, 1/2)} so you might want to shift it by \mpl{-(1/2,1/2)} before you transform it. \item "fullcircle" which you can use to draw any circle or ellipse with appropriate use of \mpl{xscaled} and \mpl{yscaled}. Unlike the square, it is defined so that it is centred at the origin. But beware that it has unit \textit{diameter}, so its radius is $0.5\unit{bp}$ long. The path runs counter-clockwise and starts at 3 - o’clock; which means \mpl{point 0 of fullcircle = 1/2 right} is true. + o’clock; which means \mpl{point 0 of fullcircle = 1/2 right} is true. \item "superellipse()" which creates the shape beloved of the Danish designer Piet Hein. Unlike the other two, this one is defined as a function rather than a \<path> constant, so you need to call it like this: \begin{code} -path s; -s = superellipse(1/2 right, 1/2 up, 1/2 left, 1/2 down, .8); +path s; +s = superellipse(1/2 right, 1/2 up, 1/2 left, 1/2 down, 13/16); \end{code} - to create a ‘unit’ shape that matches \mpl{fullcircle} as shown on the right. - The fifth parameter is the ‘superness’: the value - 1 makes it look almost square, 0.8 is about right, 0.5 gives you a diamond, - and values outside the range $(0.5,1)$ give you rather weird propeller + to create a ‘unit’ shape that matches \mpl{fullcircle} as shown above. + The fifth parameter is the ‘superness’: the value \mpic{-132pt}{paths-superellipses} + 1 makes it look almost square; $\frac12$ gives you a diamond; a value somewhere + between $\frac34$ and $\frac78$ looks about right.\quad$\longrightarrow$\\ + Values outside the range $(0.5,1)$ give you rather weird propeller shapes. - Note that, unaccountably, $\id{superellipse}()$ is defined -in \texttt{plain.mp} with a \kw{def} rather than a \kw{vardef}. -This means you need to enclose it in a group before you can -transform it in any way. One way to do this is to use parentheses; or you -can assign it to a \<path> variable, as shown above. + \nb Note that, unaccountably, $\id{superellipse}()$ is defined in + \texttt{plain.mp} with a \kw{def} rather than a \kw{vardef}. This means you + need to enclose it in a group before you can transform it in any way. One + way to do this is to use parentheses; or you can assign it to a \<path> + variable, as shown above. \end{itemize} \newpage\subsection{Points on the standard closed paths} -\noindent\mpic{-10pt}{closed-points}% +\noindent\mpic{-10pt}{paths-points}% \textsc{Here are the three shapes} centred on the origin and labelled to show the points along them. \textbf{Note} that the \textit{unitsquare} shape has been shifted so that it is centred on the origin in all of these examples. The small red circle marks the @@ -384,15 +414,15 @@ could try center p -- subpath(0,1/5 length p) of p -- cycle \end{code} Clearly this works rather better with more circular shapes. Indeed for a circle you -can convert directly between circumference angle and points along the path. So -you have defined path $c$ to be scaled copy of \mpl{fullcircle}, then -\mpl{point 1 of c} is $45^\circ$ round and 1~radian is \mpl{point 1.27324 of c}, (because -$4/\pi \simeq 1.27324$). +can convert directly between circumference angle and points along the path. So you +have defined path $c$ to be scaled copy of \mpl{fullcircle}, then \mpl{point 1 of c} +is $45^\circ$ round and 1~radian is \mpl{point 1.27324 of c}, (because $4/\pi \simeq +1.27324$). \vfill\noindent In a closed path, the point numbering in \MP\ wraps round: so in a circle, point $n$ is the same as point $n+8$; and in general point $n$ is the same as -point $n+\hbox{\bf length }p$. This works with negative numbers too, so we could use +point $n+\kw{length} p$. This works with negative numbers too, so we could use \begin{code} center p -- subpath(-1,1) of p -- cycle \end{code} @@ -405,17 +435,17 @@ drawarrow subpath(1/2, length p + 1/2) of p; \newpage \subsection{Regular polygons of a given radius}\label{polygons} -\noindent\mpic{-10pt}{closed-polygons}% +\noindent\mpic{-10pt}{paths-polygons}% \textsc{Regular polygons} with a given radius can be defined or drawn directly with a simple inline loop: -\vadjust{\moveright -60pt \vbox to 0pt{\vskip-3pt\includegraphics{little-hexagon.pdf}\vss}} +\vadjust{\moveright -60pt \vbox to 0pt{\vskip-3pt\includegraphics{paths-little-hexagon}\vss}} \begin{code} draw for i=0 upto 5: 20 dir 60i -- endfor cycle; \end{code} which works because \mpl{dir d} expands to \mpl{right rotated d}. But you might prefer to make a macro: \begin{code} -vardef polygon(expr n, r) = - for i=0 upto n-1: (r, 0) rotated (360/n * i) -- endfor cycle +vardef polygon(expr n, r) = + for i=0 upto n-1: (r, 0) rotated (360/n * i) -- endfor cycle enddef; \end{code} This produces a closed path to represent an $n$-sided polygon that fits in a circle @@ -425,64 +455,42 @@ previous segment chart.\rlap{\ $\rightarrow$}\\ If you need polygon paths that start at the top, you can just swap the coordinates: \begin{code} -vardef polygon(expr n, r) = - for i=0 upto n-1: (0, r) rotated (360/n * i) -- endfor cycle +vardef polygon(expr n, r) = + for i=0 upto n-1: (0, r) rotated (360/n * i) -- endfor cycle enddef; \end{code} -$$\includegraphics[width=0.66\textwidth]{closed-polygon-tops.pdf}$$ +$$\includegraphics[width=0.66\textwidth]{paths-polygon-tops}$$ \hey Note also that some extra care is required to find the centres of these shapes. The \mpl{center} macro defined in "plain.mp" gives you the centre of the bounding box, but this is not the same as the centre of the polygon when the number of sides is -odd. What you need instead is the geometric median: +odd. What you need instead is the geometric center or \textit{centroid}: \begin{code} -vardef median primary p = +vardef centroid primary p = origin for i=1 upto length p: + point i of p / length p endfor enddef; \end{code} -This should work for any closed path, not just regular polygons. +This should work for any closed path, not just regular polygons. For ways to +label the vertices neatly, as shown above, see §\ref{sec:new-dynamic}. \newpage \subsection{Regular polygons of a given side length}\label{polygons-given-side} But you might want a polygon with a fixed side instead of a fixed radius. This needs -a little trigonometry, using the sine rule:\mpic{-42pt}{closed-fixed-polygon} -\begin{code} -vardef polygon_with_side(expr n, s) = - save a, b, r; numeric a, b, r; - a * n = 360; a + 2b = 180; r = s * sind(b) / sind(a); - for i = 0 upto n-1: (0, r) rotated (a * i) -- endfor cycle -enddef; -\end{code} -Which you can use like this to produce a nest of polygons $\rightarrow$ -\begin{smallcode} -for n = 11 downto 3: path p; p = polygon_with_side(n, 72); - fill p withcolor (n/32)[white, 3/4 if odd n: red else: blue fi]; - draw p; -endfor -\end{smallcode} +a little trigonometry, using the sine rule:\mpic{-60pt}{paths-fixed-polygon} +\smallmpexternal[firstline=7, lastline=11]{paths-fixed-polygon.mp} +\noindent +Which you can use like this to produce a nest of polygons \rightarrowfill +\smallmpexternal[firstline=12, lastline=16]{paths-fixed-polygon.mp} + +\vfill +\noindent These polygon paths are centred on $(0, 0)$ but sometimes it is more convenient to construct a polygon on a known segment -rather than working out how to rotate and shift it into place. -$$\includegraphics[width=0.9\textwidth]{closed-polygon-chain.pdf}$$ -Here is a way to do that using the \mpl{of} syntax in the macro construction -$\longrightarrow$ +rather than working out how to rotate and shift it into place. +$$\includegraphics[width=0.9\textwidth]{paths-polygon-chain}$$ +Here is a way to do that using the “\mpl{of}†syntax in the macro construction \rightarrowfill \vadjust{\moveright 384pt\vbox to 0pt{\vss -\begin{smallcode} -vardef poly expr n of p = save x, y; - z0 = point 0 of p; z1 = point 1 of p; - for i=2 upto n-1: - z[i] = z[i-2] rotatedabout(z[i-1], 180(2/n-1)); - endfor - for i=0 upto n-1: z[i] -- endfor cycle -enddef; -path P[]; P3 = for i=0 upto 2: 6 up rotated 120i -- endfor cycle; -fill P3 withcolor 3/4 red; draw P3; -for n = 4 upto 23: - numeric m; m = floor(n / 2); - P[n] = poly n of subpath (m, m-1) of P[n-1]; - fill P[n] withcolor (n/32)[3/4 if odd n: red else: blue fi, white]; - draw P[n]; label(decimal n, median(P[n])); -endfor -\end{smallcode}\vskip -12pt}} +\smallmpexternal[firstline=6,lastline=22]{paths-polygon-chain.mp} +\vskip -42pt}} \newpage\subsection{Curved polygons} @@ -491,11 +499,11 @@ endfor \mpl{..} you would get a circle, and contrariwise, if you try \mpl{tensepath(fullcircle scaled 20)} you will get a regular octagon. But we can also adjust the directions at the corners to make a variety of closed polygon shapes -with closed edges. +with closed edges. One of the most pleasing is the Reuleaux polygon, with circular arcs for edges. -$$\includegraphics[width=0.9\textwidth]{closed-reuleaux-set.pdf}$$ -The figure on the right attempts to explain the geometry.\mwpic{-160pt}{closed-reuleaux-geometry} +$$\includegraphics[width=0.9\textwidth]{paths-reuleaux-set}$$ +The figure on the right attempts to explain the geometry.\mwpic{-160pt}{paths-reuleaux-geometry} \begin{code} vardef reuleaux(expr n, r) = save a; numeric a; a = 90/n; @@ -506,38 +514,16 @@ enddef; \end{code} If you swap the directions at each point you get shapes that are not quite like hypocycloids; play about a bit more to get flower shapes or windmills. -$$\includegraphics[width=0.9\textwidth]{closed-antireuleaux-set.pdf}$$ +$$\includegraphics[width=0.9\textwidth]{paths-antireuleaux-set}$$ \newpage \subsection{A triangle of Schläfli polygons}\label{sec:gcd} Apart from the curious polygon patterns in the display, the main \MP\ point of interest -is the recursive "gcd" macro to find the greatest common divisor.\mpic{-108pt}{gons} - -\begin{code} -input colorbrewer-rgb +is the recursive "gcd" macro to find the greatest common +divisor.\mpic{-108pt}{paths-schlafli-polygons} -vardef gcd(expr a, b) = - if b = 0: a else: gcd(b, a mod b) fi -enddef; - -beginfig(1); -for n=2 upto 24: - for s=1 upto floor n/2: - pair p; p = (12n - 24s, -24n); - path gon; gon = - for t=0 upto n/gcd(s,n) - 1: - 10 up rotated (360/n * s * t) -- - endfor cycle; - if (n mod s = 0): - fill gon shifted p withcolor Blues 9 2; - label("$" & decimal (n/s) & "$", p); - fi - draw gon shifted p withpen pencircle scaled 1/8; - endfor -endfor -endfig; -\end{code} +\mpexternal[firstline=6,lastline=26]{paths-schlafli-polygons.mp} \noindent The macro also leads directly to an efficient way to find the least common multiple: @@ -553,39 +539,38 @@ overflow. Plain \MP\ has a built-in function to compute the intersection points of two paths, and there’s a handy high level function called "buildcycle" that uses this function to create an arbitrary closed path. -\mpic{0pt}{area-under-graph} +\mpic{-36pt}{paths-area-under-graph} The arguments to the function are just a list of paths, and providing the paths all intersect sensibly, it returns a closed path that can be filled or drawn. This is often used for colouring an area under a function in a graph. Here is an example. The red line has been defined -as path "f" and the two axes as paths "xx", and "yy". The blue area was defined +as path "f" and the two axes as paths "xx", and "yy". The light blue area was defined with -\begin{code} -buildcycle(yy shifted (1u,0), f, yy shifted (2.71828u,0), xx) -\end{code} +\mpexternal[firstline=18,lastline=18]{paths-area-under-graph.mp} +\noindent Note the re-use of the $y$-axis path shifted along by different amounts. -\smallskip\noindent +\vfill\noindent There are similar examples in the \MP\ manual, but "buildcycle" can also be useful in more creative graphics. Here’s a second example that uses closed paths to give an illusion of depth to a simple graphic of the planet Saturn. -\mpic{0pt}{saturn} +\mpic{0pt}{paths-saturn} \marginpar{\hbox{}\vskip1.3in\raggedright\noindent\textbf{Notes}\begin{itemize} - \item The first five paths are just circles and ellipses based on "fullcircle". - \item The drawing is done inside an "image" simply so that the final result can + \item The first five paths are just circles and ellipses based on \mpl{fullcircle}. + \item The drawing is done inside an \mpl{image} simply so that the final result can be drawn at an angle - \item "unfill gap" is shorthand for "fill gap withcolor background" - \item The subpaths passed to "buildcycle" are chosen carefully to make sure we + \item \mpl{unfill gap} means: \mpl{fill gap withcolor background} + \item The subpaths passed to \mpl{buildcycle} are chosen carefully to make sure we get the intersections at the right points and so that the component paths - all run in the same direction. Note that "subpath (8,4) of globe" runs + all run in the same direction. Note that \mpl{subpath (8,4) of globe} runs clockwise (that is backwards) from point 8 to point 4. \end{itemize}} -\mpexternal{saturn-code.mp} +\mpexternal[firstline=7,lastline=23]{paths-saturn.mp} \newpage\subsection{The implementation of \texttt{buildcycle}} -\textsc{The implementation} of "buildcycle" in plain \MP\ is interesting for a number of +\textsc{The implementation} of \mpl{buildcycle} in plain \MP\ is interesting for a number of reasons. Here it is copied from "plain.mp" (with minor simplifications) $\longrightarrow$ \vadjust{\moveright5.5in\vbox to 0pt{\kern-1cm% \begin{code} @@ -614,19 +599,19 @@ enddef; Notice how freely the indentation can vary; this is both a blessing (because you can line up things clearly) and a curse (because the syntax may not be very obvious at first glance). Notice also the different ways we can use a -$\kw{for}$-loop. The first two are used at the ‘outer’ level to repeat complete +\mpl{for}-loop. The first two are used at the ‘outer’ level to repeat complete statements (that end with semi-colons); the third one is used at the ‘inner’ level to build up a single statement. -The use of a "text" parameter allows us to pass a comma-separated list as an +The use of a \mpl{text} parameter allows us to pass a comma-separated list as an argument; in this case the list is supposed to be a list of path expressions that -(we hope) will make up a cycle. The first "for" loop provides us with a standard +(we hope) will make up a cycle. The first \mpl{for} loop provides us with a standard idiom to split a list; in this case the comma-separated value of "input_path_list" is separated into into a more convenient array of paths called "pp" indexed by "k". -Note that the declaration of the array as "path" forces the argument to be a list of +Note that the declaration of the array as \<path> forces the argument to be a list of paths. -The second "for" loop steps through this array of paths looking for intersections. +The second \mpl{for} loop steps through this array of paths looking for intersections. The index "j" is set to be "k" when "i=1", and then set to the previous value of "i" at the end of the loop; in this way "pp[j]" is the path before "pp[i]" in what is supposed to be a cycle. @@ -638,14 +623,12 @@ by reversing the previous path and setting the $b$-point indirectly by subtracti the time returned from the length of the path. If all has gone well, then "ta" will hold all the start points of the desired -subpaths, and "tb" all the corresponding end -points. -The third and final "for" loop assumes that this is indeed the case, and tries to -connect them all together. Note that it uses ".." rather than "&" just in case the -points are not quite co-incident; finally it finishes with a -\mpl{cycle} to close the path even though point "tb" of path "k" should be identical (or -at least very close) to -point "ta" of path "0". +subpaths, and "tb" all the corresponding end points. The third and final \mpl{for} +loop assumes that this is indeed the case, and tries to connect them all together. +Note that it uses \mpl{..} rather than \mpl{&} just in case the points are not quite +co-incident; finally it finishes with a \mpl{cycle} to close the path even though +point \mpl{tb[k] of pp[k]} should be identical (or at least very close) to point +\mpl{ta[0] of pp[0]}. This implementation of \mpl{buildcycle} works well in most cases, provided that there are enough components to the cycle of paths. If you only have two paths, then the @@ -656,16 +639,10 @@ be contained within the other. This is explored in the next section. \subsection{Strange behaviour of \texttt{buildcycle} with two closed paths} The implementation of "buildcycle" in plain \MP\ can get confused if you use it with -just two paths. Consider the following example: \mpic{0pt}{overlaps-missing-filler} -\begin{code} -beginfig(1); - path A, B; - A = fullcircle scaled 2.5cm; - B = fullcircle scaled 1.8cm shifted (1cm,0); - fill buildcycle(A,B) withcolor .8[blue,white]; - drawarrow A; drawarrow B; -endfig; -\end{code} +just two paths. Consider the following example: \mpic{0pt}{paths-overlaps-missing-filler} + +\mpexternal[firstline=7,lastline=14]{paths-overlaps-missing-filler.mp} + When we compile this example, we get no error message from "buildcycle", but there is no fill colour visible in the output. The problem is that the points found by "buildcycle" are the same both times that it steps through the middle loop, so @@ -673,12 +650,12 @@ the closed path it returns consists of two identical (or very close) points and so the fill has zero area. Now observe what happens when we rotate and reverse each of the paths in -turn.\mpic{-24pt}{overlaps-default-fillers} +turn.\mpic{-24pt}{paths-overlaps-default-fillers} Number 1 corresponds to the example shown above; point~0 of~$A$ is inside the closed path $B$. In~2 we have rotated path $A$ by 180° so that the start of path~$A$ is no longer inside $B$, and now "buildcycle" works ‘properly’ --- but this is the only time it does so. In~3, we've rotated $B$ by 180° as well, so that $B$ starts inside -$A$ and as expected "buildcycle" fails. In 4 we've rotated $A$ back to it's +$A$ and as expected "buildcycle" fails. In 4 we've rotated $A$ back to its original position, so that both paths start inside each other; and we get the union of the two shapes. In 5--8, we've repeated the exercise with path $A$ reversed, and "buildcycle" fails in yet more interesting ways. @@ -743,116 +720,12 @@ vardef overlap(expr a, b) = enddef; \end{smallcode} Using this "overlap" macro in place of "buildcycle" produces less surprising -results.\mpic{-2in}{overlaps} - -\newpage -\subsection{Fitting dashed lines to a path} - -\textsc{This one is} perhaps for perfectionists, but also shows how simple it -is to make useful adjustments in \MP. As you will know, plain \MP\ provides two -built-in dash patterns, so that you can draw a path \mpl{dashed withdots} or -\mpl{dashed evenly}. -\vadjust{% -\moveright384pt\vbox to 0pt{\vskip-46pt\hsize 4.2in\small -$$ -\begin{mplibcode} -vardef exactly(expr a) = - save m; numeric m; 2m = (a-6) / round(a/6); - dashpattern(on m off m) -enddef; -vardef gooddots(expr a) = - save m; numeric m; 2m = (a-5) / round(a/5); - dashpattern(off m on 0 off m) -enddef; - beginfig(1); - for i=2 upto 8: - path c[]; - c1 = fullcircle scaled 16i shifted 80 left; - c2 = fullcircle scaled 16i shifted 80 right; - draw c1 dashed evenly withcolor 2/3 blue; - draw c2 dashed exactly(arclength c2) withcolor 1/2 red; - %draw c1 shifted 160 down dashed withdots withcolor 2/3 blue; - %draw c2 shifted 160 down dashed gooddots(arclength c2) withcolor 1/2 red; - endfor - endfig; -\end{mplibcode} -$$ - -\noindent -The blue circles on the left were drawn with \mpl{dashed evenly}, and the uneven -gaps are noticeable at the “three o’clock†positions where the paths begin and end. -As you can see the default dash spacing looks fine at some sizes but bad on others. On the right you can see the -same circular paths coloured red, and drawn with \mpl{dashed exactly(arclength c, -6)}. - -$$ -\begin{mplibcode} -vardef exactly(expr a, u) = - save m; numeric m; 2m = a / round(a/u); - dashpattern(on m off m) -enddef; - beginfig(1); - for i=2 upto 8: - path c[]; - c1 = unitsquare shifted -(1/2, 1/2) scaled 16i shifted 80 left; - c2 = unitsquare shifted -(1/2, 1/2) scaled 16i shifted 80 right; - draw c1 dashed evenly withcolor 2/3 blue; - draw c2 dashed (exactly(arclength c2, 8) shifted 6 right) withcolor 1/2 red; - endfor - endfig; -\end{mplibcode} -$$ -Other paths may require a bit more ingenuity and thought. Because the square paths -have four equal sides, they work better with a target dash length that is a multiple -of 4. Here the blue squares on the left use the default \mpl{dashed evenly}, and the -red on the right, \mpl{exactly(arclength c2, 8)} \mpl{shifted 6 right}. The shift makes -the corners look better. - - -\vss}} - -The keyword \mpl{dashed} gives you access to the PostScript "setdash" command, its -argument is a special \<picture> defined with the \MP\ \mpl{dashpattern} function. -If you look in "plain.mp" you will find these declarations: -\begin{code} -picture evenly,withdots; -evenly = dashpattern(on 3 off 3); % dashed evenly -withdots = dashpattern(off 2.5 on 0 off 2.5); % dashed withdots -\end{code} -The detailed syntax is explained in §9.4 of the \MP\ manual, but essentially -\mpl{withdots} creates a unit 5 points long with a dot in the middle, and -\mpl{evenly} creates a unit 6 points long with the dashes 3pt long (plus the round -bit at the end of each dash, unless you have changed \mpl{linecap}) and gaps 3pt -long (minus any round bits). - -You probably also know that you can adjust these sizes by applying a suitable -scaling, so that \mpl{dashed withdots scaled 1/2} gives a rather denser dotted line, -and \mpl{dashed evenly scaled 4} will give you very long dashes. But you may also -notice that the dash patterns (particularly the longer ones) do not always fit your -paths exactly -- this is especially noticeable with closed paths, where you may end -up with one unsightly long dash or a very short gap a the point where the path -begins and ends. - -Fortunately there is a very simple solution: adjust the length of the dash pattern -so that an integer number of dash units exactly fit your path. -\begin{code} -vardef exactly(expr a, u) = - save m; numeric m; 2m = (a-u) / round(a/u); - dashpattern(on m off m) -enddef; -\end{code} -Here "a" is supposed to be the \mpl{arclength} of your path, and "u" the desired -unit size, so you can use it like this: -\begin{code} -path c; c = fullcircle scaled 200; -draw c dashed exactly(arclength c, 6); -\end{code} -to get a close approximation to \mpl{dashed evenly} that exactly fits the path. +results.\mpic{-2in}{paths-overlaps} \newpage \section{Numbers} -This section discusses plain \MP's scalar numeric variables +This section discusses plain \MP\ scalar numeric variables and what you can do with them. \MP\ inherits its unusual native system of scaled numbers from \MF; like many of Knuth's creations it is slightly quirky, but works very well once you get the hang @@ -872,19 +745,16 @@ implications: choose fractional step-values in a "for" loop; the errors can accumulate so that you may miss your expected terminal value.\vadjust{\moveright5.5in\vbox to 0pt{\kern-2in\hsize4in\noindent - Compare the following two snippets: + Compare the following two snippets: $$\vbox{\halign{#\hfil\quad&#\hfil\cr Code&Output\cr\noalign{\smallskip\hrule\bigskip} - \vtop{\parindent0pt\hsize2.2in - \bgroup\obeylines - $\kw{for}$ $i=0$ \kw{step} $1/10$ \kw{until} $1$: - \quad$\kw{show}$ $i$; - $\kw{endfor}$ - \egroup - -} +\vtop{\begin{code}[xleftmargin=0pt, xrightmargin=160pt] +for i = 0 step 1/10 until 1: + show i; +endfor +\end{code}} & - \vtop{\parindent0pt\parskip-2pt\obeylines\hsize60pt\tt + \vtop{\parindent0pt\parskip-2pt\obeylines\hsize60pt\ttfamily >> 0 >> 0.1 >> 0.20001 @@ -897,15 +767,13 @@ implications: >> 0.90005 } \cr\noalign{\bigskip} - \vtop{\parindent0pt\hsize2.2in - \bgroup\obeylines - $\kw{for}$ $i=0$ \kw{step} $1$ \kw{until} $10$: - \quad$\kw{show}$ $i/10$; - $\kw{endfor}$ - \egroup -} +\vtop{\begin{code}[xleftmargin=0pt, xrightmargin=160pt] +for i = 0 step 1 until 10: + show i/10; +endfor +\end{code}} & - \vtop{\parindent0pt\parskip-2pt\obeylines\hsize60pt\tt + \vtop{\parindent0pt\parskip-2pt\obeylines\hsize60pt\ttfamily >> 0 >> 0.1 >> 0.2 @@ -919,7 +787,8 @@ implications: >> 1 }\cr\noalign{\bigskip\hrule}\cr }}$$ -You get 11 iterations in the second but only 10 with the first. +Unless you run this with "-numbersystem=decimal", you will get +11 iterations in the second but only 10 with the first. \vss}} \item The system limits you to numbers that are less than 4096 in absolute value. @@ -951,7 +820,7 @@ and \id{eps}: \begin{itemize} \item $\id{eps}$ is defined to be a small amount that is noticeable to \MF’s rounding algorithms, namely -${32\over65536}={1\over2048}\simeq 0.00049$. As a distance on the page or screen it's invisible at +${32\over65536}={1\over2048}\simeq 0.00049$. As a distance on the page or screen, it's invisible at any resolution less than 150,000 dots per square inch. If you were designing fonts in \MF, $\id{eps}$ could help you avoid bad choices of pixels at low resolutions, but in \MP\ it's only really useful in comparisons that might suffer from rounding errors. @@ -974,9 +843,9 @@ have. \vadjust{\moveright5.5in\vbox to 0pt{\kern-221pt\hsize 4.25in \noindent Running the toy program: -\par\bigskip -$\kw{show} \id{numbersystem}, \id{eps}, \id{epsilon}, \id{infinity}; \kw{end}\!.$ -\par\bigskip\noindent +\begin{code} +show numbersystem, eps, epsilon, infinity; end. +\end{code} gives the following results with the different number systems: @@ -1109,54 +978,15 @@ Note that $\kw{mod}$ preserves any fractional part, so $355/113 \mathrel{\kw{mod \smallskip \parshape=1 0pt 3.4in This behaviour is usually what you want. -\vadjust{\moveright 266pt \vbox to 0pt{\noindent +\vadjust{\moveright 266pt \vbox to 0pt{\noindent \begin{mplibcode} input clocks -beginfig(1); draw clock(hour, minute) scaled 0.8; endfig; +draw clock(hour, minute) scaled 0.8; \end{mplibcode}\vss}} For example we can use it to turn the time of day into an appropriate rotation for the hands of a clock.% \vadjust{\moveright 384pt\vbox to 0pt{\kern-196pt -\begin{code} -path hand[]; -hand1 = origin .. (.257,1/50) .. (.377,1/60) - & (.377,1/60) {up} .. (.40,3/50) - .. (.60, 1/40) .. {right} (.75,0); -hand1 := (hand1 .. reverse hand1 reflectedabout(left,right) - .. cycle) scaled 50; -hand2 = origin .. (.60, 1/64) .. {right} (.925,0); -hand2 := (hand2 .. reverse hand2 reflectedabout(left,right) - .. cycle) scaled 50; - -% hour of the day to degrees -vardef htod(expr hours) = 30*((15-hours) mod 12) enddef; -vardef mtod(expr minutes) = 6*((75-minutes) mod 60) enddef; - -vardef clock(expr hours, minutes) = image( - % face and outer ring - fill fullcircle scaled 100 withcolor 1/256(240, 240, 230); - draw fullcircle scaled 99 withcolor .8 white; - draw fullcircle scaled 100 withpen pencircle scaled 7/8; - % numerals - for h=1 upto 12: - label( decimal h infont "bchr8r", (40,0) rotated htod(h)); - endfor - % hour and minute marks - for t=0 step 6 until 359: - draw ((48,0)--(49,0)) rotated t; - endfor - drawoptions(withpen pencircle scaled 7/8); - for t=0 step 30 until 359: - draw ((47,0)--(49,0)) rotated t; - endfor - % hands rotated to the given time - filldraw hand1 rotated htod(hours+minutes/60); - filldraw hand2 rotated mtod(minutes); - % draw the center on top - fill fullcircle scaled 5; - fill fullcircle scaled 3 withcolor .4 white; -) enddef; -\end{code} +\mpexternal[firstline=9,lastline=46,xleftmargin=0pt]{clocks.mp} \vss}} In the program given on the right, this idea is used to define functions that convert from hours and minutes @@ -1170,9 +1000,9 @@ to give a sort of graphical time stamp. \vfill There is also a "round" function that rounds a number to the nearest integer. It is -essentially defined as $\mathop{\kw{floor}}(x+0.5)$ except that it is enhanced to -deal with $\kw{pair}$ variables as well. If you round a pair the $x$-part and -the $y$-part are rounded separately, so that $\mathop{\kw{round}}(3.14159, 2.71828) +essentially defined as $\kw{floor}(x+0.5)$ except that it is enhanced to +deal with \<pair> variables as well. If you round a pair the $x$-part and +the $y$-part are rounded separately, so that $\kw{round}(3.14159, 2.71828) = (3,3)$. The "round" function only takes a single argument, but you can use it to round to a @@ -1185,12 +1015,11 @@ must remain less than 32767 if you are using the default number system. \newpage \subsection{Integer powers} -\textsc{Even if you use} one of the new number systems, you may occasionally get -caught out by the \mpl{**} operator. As the table on the right shows, you may get +\textsc{Occasionally} you might get +caught out by the implementation of the \mpl{**} operator. As the table on the right shows, you may get an approximate answer from \mpl{x ** y} even when $x$ and $y$ are both integers. \vadjust{\moveright 384pt\vbox to 0pt{\kern -2pt $$\begin{mplibcode} -beginfig(0); %primarydef x ** y = 1 for n=1 upto y: * x endfor enddef; for x=1 upto 19: for y = 1 upto 7: @@ -1206,32 +1035,31 @@ endfor label.lft("Results of \mpl{x**y} for small values, using", lrcorner currentpicture shifted 36 up); label.lft("the default \mpl{scaled} number system", lrcorner currentpicture shifted 24 up); currentpicture := currentpicture scaled 0.8; -endfig; \end{mplibcode}$$\vss}} Note that the squares are all integers, and the powers of two appear to be ok (although if the page was wider you would see that \mpl{2**9} is $512.00002$), but -that with a couple of exceptions cubes and higher powers are slightly off. Changing -the number system makes it worse; even $x^1$ is not always an integer. The reason +that with a couple of exceptions cubes and higher powers are all slightly off. Changing +to one of the new number systems makes it worse; even $x^1$ is not always an integer. The reason can be found in the way that the \mpl{**} operator is defined in "plain.mp". \begin{smallcode}[xleftmargin=0pt, xrightmargin=-36pt] primarydef x ** y = if y = 2: x * x else: takepower y of x fi enddef; def takepower expr y of x = - if x > 0: + if x > 0: mexp(y * mlog x) - elseif (x = 0) and (y > 0): + elseif (x = 0) and (y > 0): 0 - else: + else: if y = floor y: if y >= 0: 1 for n=1 upto y: * x endfor else: 1 for n=-1 downto y: / x endfor fi - else: + else: hide(errmessage "Undefined power: " & decimal x & "**" & decimal y) - fi - fi + fi + fi enddef; \end{smallcode} -This is inherited direction from plain \MF, and as it says in the \mfbook, it is +This is inherited directly from plain \MF, and as it says in the \mfbook, it is optimized for $x^2$ and takes care to handle correctly negative numbers and zeros. But for all positive values of $x$ other than 2 it is implemented using logs, and the results are therefore only approximate. To avoid confusion where this might @@ -1246,7 +1074,7 @@ primarydef x ** y = 1 for n=1 upto y: * x endfor enddef; \newpage \section{Pairs, triples, and other tuples} -\vpic{7pt}{random-selection} +\vpic{7pt}{pairs-random-selection} \noindent \MP\ inherits a generalized concept of number from \MF\ that includes ordered pairs. @@ -1311,7 +1139,7 @@ vardef z@#=(x@#,y@#) enddef; which you can use to find orthogonal points. \bigskip\noindent -\includegraphics{random-function} +\includegraphics{pairs-random-function} \vss}}% The deceptively simple definition of $\id{z}$ as a subscripted macro allows you to write "z1 = (10,20);" and have it automatically expanded into the equivalent of @@ -1387,34 +1215,8 @@ However \MP\ does let you add (and subtract) two pairs, so complex addition and subtraction are just done with the normal operators. \vadjust{\moveright 384pt\vbox to 0pt{\vskip -3.74in -$$\includegraphics{complex-operators}$$ -\begin{code} -beginfig(1); - numeric u; u = 1cm; - z1 = 2 dir 15; z2 = 1.2 dir 60; - z3 = z1+z2; z4 = z1 zscaled z2; z5 = (x1,-y1); - drawoptions(withcolor 2/3 white); - draw (1/2 left -- 3 right) scaled u ; - draw (1/2 down -- 3 up ) scaled u ; - draw subpath (0,3) of fullcircle scaled 2u rotated -22.5; - drawoptions(); - dotlabel.lrt (btex $\scriptstyle 1$ etex, (u,0)); - dotlabel.ulft(btex $\scriptstyle i$ etex, (0,u)); - interim ahangle := 30; - forsuffixes @=1,2,3,4,5: - x@ := x@ * u; y@ := y@ * u; - drawarrow origin -- z@ - cutafter fullcircle scaled 5 shifted z@ - withcolor 2/3 if @ < 3: blue else: red fi; - endfor - fill fullcircle scaled dotlabeldiam; - dotlabel.rt (btex $A$ etex, z1); - dotlabel.urt(btex $B$ etex, z2); - dotlabel.top(btex $A+B$ etex, z3); - dotlabel.top(btex $A \times B$ etex, z4); - dotlabel.rt (btex $\bar{A}$ etex, z5); -endfig; -\end{code} +$$\includegraphics{pairs-complex-operators}$$ +\mpexternal[firstline=6,lastline=30]{pairs-complex-operators.mp} \vss}}% To get the complex conjugate you could use "reflectedabout(left,right)", but it's probably easier just to write @@ -1442,23 +1244,11 @@ usual operations when they are required\dots Since multiplication by $z$ can be thought of as a transformation consisting of rotation by the argument of $z$ and scaling by $|z|$, you can define the complex inverse and complex square root simply using \mpl{angle} and \mpl{abs}. -\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip -24pt -\centerline{\includegraphics{complex-inverse-and-sqrt}} -The interesting part of the left hand figure was drawn as follows: -\begin{smallcode} -input colorbrewer-rgb -for i=1 upto 3: - z[i] = (3/2 + 1/4 normaldeviate) * dir (16 i + normaldeviate); - path a; - a = z[i] scaled 42 -- origin -- zinverse(z[i]) scaled 42; - drawarrow a cutafter fullcircle scaled 5 shifted point 2 of a - withcolor SetTwo[7][2+i]; - drawdot point 0 of a withpen pencircle scaled dotlabeldiam; - drawdot point 2 of a withpen pencircle scaled dotlabeldiam; - drawdot point 2 of a withpen pencircle scaled 2 withcolor white; -endfor -\end{smallcode} -The only difference on the right is that the drawing used "zsqrt()". +\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip -84pt +\centerline{\includegraphics{pairs-complex-inverse-and-sqrt}} +\noindent +The drawing uses the two functions defined on the left. +\smallmpexternal[firstline=11,lastline=44,xleftmargin=0pt]{pairs-complex-inverse-and-sqrt.mp} \vss}} \smallskip\noindent @@ -1470,9 +1260,9 @@ z zscaled zinverse(z) = (1,0) In other words you need to find a complex number with an argument that is the negative of the argument of $z$ and a modulus that will scale $|z|$ to 1. You can use the polar notation with "dir" to write this directly: -\begin{code} -vardef zinverse(expr z) = 1/abs z * dir - angle z enddef; -\end{code} + +\mpexternal[firstline=6,lastline=6]{pairs-complex-inverse-and-sqrt.mp} + The complex division, $z/w$, can now be done as: \mpl{z zscaled zinverse(w)}. The only difficulty with this function is how it deals with zero, or rather with the point $(0,0)$. Since `\mpl{abs (0,0)}' gives $0$, the function will give you @@ -1491,11 +1281,7 @@ def zsqrt(expr z) = sqrt(abs z) * dir 1/2 angle z enddef; This function also has a difficulty with the point $(0,0)$, because "angle (0,0)" is not well defined, and so \MP\ throws an error. If you want a function that correctly returns $(0,0)$ as its own square root, then try something like this: -\begin{code} -def zsqrt(expr z) = - if abs z > 0: sqrt(abs z) * dir 1/2 angle fi z -enddef; -\end{code} +\mpexternal[firstline=7,lastline=9]{pairs-complex-inverse-and-sqrt.mp} \newpage \subsubsection{Using complex numbers to draw fractals} @@ -1503,57 +1289,10 @@ enddef; As an example of what you can do with complex arithmetic, here is a version of the diagram from §4.1 of Knuth's \textsl{Seminumerical Algorithms} showing $S$, the set of all points that can be written as $\sum_{k\ge1}a_k(i-1)^{-k}$. -\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip -81pt -\begin{smallcode} -vardef fizz(expr X) = - pair m, n; - m = right; - n = origin; - numeric a, x; - x = X; - forever: - exitif x = 0; - m := m zscaled zinverse((-1, 1)); - a := x mod 2; - n := n + a * m; - x := x div 2; - endfor - n -enddef; -input colorbrewer-rgb -color shade[]; -shade0 = Reds 5 4; shade1 = Oranges 5 4; -shade2 = Greens 5 4; shade3 = Blues 5 4; - -beginfig(1); - numeric s, t; s = 256; t = 4; - for n=0 upto (s/t*s/t-1): - numeric h, v; - h = floor 1/8 (n mod 32); - v = n mod 4; - fill fullcircle scaled t shifted (fizz(n) scaled s) - withcolor (1/2 + 1/8 v)[white, shade[h]]; - endfor; - - path xx, yy; - xx = (left--right) scaled (s+8); - yy = xx rotated 90; - for i=-1 upto 1: - draw xx shifted (0, s*i) withpen pencircle scaled 1/8; - draw yy shifted (s*i, 0) withpen pencircle scaled 1/8; - endfor - dotlabel.lrt(btex $-1-i$ etex, (-1, -1) scaled s); - dotlabel.lrt(btex $-1$ etex, (-1, 0) scaled s); - dotlabel.lrt(btex $-1+i$ etex, (-1, 1) scaled s); - dotlabel.lrt(btex $-i$ etex, (0, -1) scaled s); - dotlabel.lrt(btex $+i$ etex, (0, 1) scaled s); - dotlabel.lrt(btex $+1-i$ etex, (1, -1) scaled s); - dotlabel.lrt(btex $+1$ etex, (1, 0) scaled s); - dotlabel.lrt(btex $+1+i$ etex, (1, 1) scaled s); -endfig; -\end{smallcode} +\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip -36pt +\mpexternal[firstline=7,lastline=42,xleftmargin=0pt]{pairs-double-dragon.mp} \vss}} -$$\includegraphics[width=\textwidth]{double-dragon.pdf}$$ +$$\includegraphics[width=\textwidth]{pairs-double-dragon}$$ \vbox to 0pt{\noindent\small\textbf{Note}: you can adjust the “resolution†with the parameter $t$, but don't make it smaller than 1 if you are using the default number system; the diagram looks a bit strange unless $t$ is an integer power of 2.\vss} @@ -1584,25 +1323,26 @@ or, slightly more idiomatically: As you can see, you can apply implicit multiplication to a \mpl{color}, so after the declaration above "2 brg" would be a valid colour, although you have to think a bit to know what that means in terms of colour in your drawings. -\vadjust{\moveright 384pt\vbox to 0pt{\kern-72pt +\vadjust{\moveright 396pt\vbox to 0pt{\kern-144pt\noindent To use RGB hex strings, you'll need to write a function: \begin{code} vardef hexrgb(expr Spec) = - save r, g, b; - numeric r, g, b; - r = hex(substring (1,3) of Spec); - g = hex(substring (3,5) of Spec); - b = hex(substring (5,7) of Spec); - 1/256(r,g,b) + save r, g, b; + numeric r, g, b; + r = hex substring (1,3) of Spec; + g = hex substring (3,5) of Spec; + b = hex substring (5,7) of Spec; + 1/256(r,g,b) enddef; brg = hexrgb("#014225"); pbr = hexrgb("#df3439"); \end{code} +\noindent\hey The \mpl{hex} function is a built-in primitive operation. \vss}}% Plain \MP\ defines five basic colour constants: \mpl{red}, \mpl{green}, \mpl{blue}, \mpl{white}, \mpl{black}. These are quite useful with leading -fractions: \mpl{2/3 red} gives a nice dark red, that's good for drawing lines you +fractions: \mpl{2/3 red} gives a nice dark red, that is good for drawing lines you want to emphasize; \mpl{1/2 white} gives you a shade of grey; and so on. But since \mpl{black} is defined as \mpl{(0,0,0)}, \mpl{1/2 black} just gives you \mpl{black}. @@ -1612,21 +1352,9 @@ easier to read. Much more usefully, you can use the mediation notation to get a colour that is part way between two others. So \mpl{1/2[red, white]} gives you a shade of pink, and \mpl{2/3[blue, white]} a sort of sky blue. You can also use this idea to vary colour with data, as in \mpl{(r)[red, blue]} where \mpl{r} is some -calculated value. \vadjust{\moveright 384pt\vbox to 0pt{\kern-36pt -\begin{code} -color brg; brg = 1/256 (1, 66, 37); -color pbr; pbr = 1/256 (223, 52, 57); -N = 5; n = 0; -for y=1 upto N: - for x=1 upto N: - fill fullcircle scaled 16 shifted 20(x,y) - withpen pencircle scaled 2 - withcolor (n/N/N)[pbr, brg]; - label(decimal incr n infont "phvr8r", 20(x,y)) - withcolor white; - endfor -endfor -\end{code}\vss}} +calculated value. \vadjust{\moveright 396pt\vbox to 0pt{\kern-64pt +\mpexternal[firstline=6,lastline=18]{color-blend-toy.mp} +\vss}} Here's a toy example: \vbox to 0pt{\centerline{\includegraphics[scale=0.8]{color-blend-toy}}\vss} @@ -1635,78 +1363,34 @@ Here's a toy example: \subsection{CMYK colours} \MP\ also implements a CMYK colour model, using tuples of four numerics. -This is more or less a direct mapping onto the PostScript "cmykcolor" functions. In this model the four components represent cyan, magenta, yellow, and black. White is \mpl{(0,0,0,0)} and black is anything where the last component is 1. -Beware however that the constants, \mpl{white} and \mpl{black} are defined in -"plain.mp" as RGB colours, and you can't mix the two models, so anything like -\mpl{1/2[(1,1,0,0), white]} will not work. If you want to do lots of work with CMYK colours -you might like to redefine the color constants. -$$\includegraphics[width=0.7\textwidth]{blended-color-circles}$$ + +Beware that the five colour constants defined in "plain.mp" are defined as RGB +colours, and you can't mix colour models, so anything like \mpl{1/2[(1,1,0,0), +white]} will not work, unless you redefine the color constants as CMYK colours: +\begin{smallcode} +cmykcolor black, white, red, green, blue; +black = (0,0,0,1); white = (0,0,0,0); +red = (0,1,1,0); green = (1,0,1,0); blue = (1,1,0,0); +\end{smallcode} +$$\includegraphics[width=0.7\textwidth]{color-blended-circles}$$ \hey The apparent blending of colours here is done by calculating the overlaps -and filling them in order. In plain \MP, there is no support for transparency in any of the -colour models; this is because they are inherited directly from PostScript. +and filling them in order. With plain "mpost", there is no support for transparency in any of the +colour models; but "luamplib" gives you access to PDF transparency, see +§\ref{sec:transparent}. \moveright 384pt\vbox to 0pt{\vss -\begin{code} -% the illusion of blended colours is helped by buildcycle - -path C[], B[]; - -% arrange each circle so that point 0 is outside the others -C1 = fullcircle scaled 120 rotated 90 shifted 40 up; -C2 = C1 rotated 120; -C3 = C2 rotated 120; - -B0 = buildcycle(C1, C2, C3); -B1 = buildcycle(C1, C2); -B2 = buildcycle(C2, C3); -B3 = buildcycle(C3, C1); - -picture P; -for x=0 upto 1: - for y=0 upto 1: - P := image( - s := 1/4 + x/2; - k := 0 + y/4; - fill C1 withcolor s*(1,0,0,k); - fill C2 withcolor s*(0,1,0,k); - fill C3 withcolor s*(0,0,1,k); - fill B3 withcolor s*(1,0,1,k); - fill B2 withcolor s*(0,1,1,k); - fill B1 withcolor s*(1,1,0,k); - fill B0 withcolor s*(1,1,1,k); - undraw C1; undraw C2; undraw C3; - ) shifted -(200x, 200y); - draw P; - label.bot(("shade: " & decimal s & ", k: " & decimal k) - infont "phvr8r", point 1/2 of bbox P); - endfor -endfor -\end{code}} - +\mpexternal[firstline=9,lastline=41]{color-blended-circles.mp} +} \newpage \subsection{HSV colours} HSV colours are colours defined by a triple of hue, saturation, and value. Unlike RGB and CMYK colours there is no native support in \MP\ but it is possible to write a routine that maps HSV triples into RGB colours: -\begin{code} -vardef hsv_color(expr h,s,v) = - save chroma, hh, x, m; - chroma = v*s; - hh = h/60; - x = chroma * (1-abs(hh mod 2 - 1)); - m = v - chroma; - if hh < 1: (chroma,x,0)+(m,m,m) - elseif hh < 2: (x,chroma,0)+(m,m,m) - elseif hh < 3: (0,chroma,x)+(m,m,m) - elseif hh < 4: (0,x,chroma)+(m,m,m) - elseif hh < 5: (x,0,chroma)+(m,m,m) - else: (chroma,0,x)+(m,m,m) - fi -enddef; -\end{code} +\mpexternal{color-hsv-macro.mp} +\noindent This is based on information from the Wikipedia article on on “HSL and HSVâ€. @@ -1719,110 +1403,22 @@ darker. Once you get the hang of them, they make choosing colours rather easier You can produce ranges of colour by changing hue, or make gradations of a single colour by changing the saturation or value. -\moveright 384pt\vbox to 0pt{\vss -\begin{code} -defaultfont := "phvr8r"; - -numeric s[], v[]; -s0 = 1/2; v0 = 7/8; -s1 = 7/8; v1 = 7/8; -s2 = 7/8; v2 = 1/2; -for y=0 upto 2: - for h=0 step 15 until 360: - fill fullcircle scaled 24 shifted (h, -32y) - withcolor hsv_color(h, s[y], v[y]); - draw fullcircle scaled 24 shifted (h, -32y) - withcolor white; - if y=1: - label(decimal h infont defaultfont scaled 1/2, (h,-16)); - fi - endfor -endfor - -label.urt("Less saturation", (-20,12)); -label.lrt("Lower value", (-20,-76)); - -drawarrow (-15, -12) -- (-15,12); -drawarrow (-15, -52) -- (-15,-76); -\end{code}} +\moveright 376pt\vbox to 0pt{\vss +\mpexternal[firstline=5,lastline=31]{color-hsv-gamut.mp}} \newpage -\subsubsection{An HSV example of a graduated scale} +\subsection*{An HSV example of a graduated scale} \noindent -This example requires the \mpl{hsv_color} routine from the previous page. -\mpic{12pt}{color-hsv-bathymetric} -\begin{code}[xleftmargin=0pt] -defaultfont := "phvr8r"; defaultscale := 3/4; -path h,d,b; numeric n; n = 10; -h = ((-2,0)--(0,0)--(-1,3)--(-2,3)--cycle) scaled 60; -d = h rotated 180; -b = subpath (0,1) of h -- point 1+1/n of d -- - (xpart point 0 of h, ypart point 1+1/n of d) -- cycle; -fill b withcolor hsv_color(123, 1/8, 7/8); -draw subpath (2.13,4) of b; -for i=1 upto n: - fill point 4-(i-1)/n of h -- point 1+(i-1)/n of h - -- point 1+i/n of h -- point 4-i/n of h -- cycle - withcolor hsv_color(42, 1/4 + 3/4 * i/n, 1 - i/3n); - fill point 4-(i-1)/n of d -- point 1+(i-1)/n of d - -- point 1+i/n of d -- point 4-i/n of d -- cycle - withcolor hsv_color(200, i/n - 1/n, 1 - i/3n); -endfor -string s; -for i=1 upto n-1: - draw point 4-i/n of h -- point 1+i/n of h; - draw point 4-i/n of d -- point 1+i/n of d; - s := decimal if i < 4: (i**2+1) else: (10 + (i-3)*10) fi & "00"; - label.rt(s, point 1+i/n of h); - label.lft(s, point 1+i/n of d); -endfor -label.rt("Metres", point 2 of h); -label.lft("Metres", point 2 of d); -label.lft("Hypsometric tints" infont defaultfont - scaled defaultscale rotated 90, point 7/2 of h); -label.rt("Bathymetric tints" infont defaultfont - scaled defaultscale rotated -90, point 7/2 of d); -label.lft("sea level", point 0 of h); -label("areas below sea level", center b); -draw h; draw d; -\end{code} - - +This example requires the \mpl{hsv_color} macro from the previous page. +\mpic{2pt}{color-hsv-bathymetric} +\mpexternal[firstline=7,lastline=39, xleftmargin=0pt]{color-hsv-bathymetric.mp} \newpage \subsection{Grey scale} -\moveright5.5in\vbox to 0pt{\vskip6pt -\begin{code}[xleftmargin=0pt] -numeric s; s = 13; -path atom; -atom = origin - -- (2s,0) rotated -30 -- (2s,0) rotated -30 + (0,s) - -- ( s,0) rotated 30 -- ( s,0) rotated 30 + (0,s) - -- (0,2s) -- cycle; - -picture p[]; -for i=0 upto 2: - p[i] = image( - fill atom rotated -120i withcolor (7/8 - 1/8i) ; - draw atom rotated -120i; - ); -endfor - -n = 13; -for i=-n upto n: - for j=-n upto n: - forsuffixes $=0,1,2: - draw p$ shifted ((3i*s,0) rotated -30 - + (0,floor(1/2i)*3s + 3j*s)); - endfor - endfor -endfor - -clip currentpicture to (unitsquare shifted -(1/2,1/2) - xscaled 55.425s yscaled 30s); -\end{code} +\moveright5.4in\vbox to 0pt{\vskip6pt +\mpexternal[firstline=5,lastline=36,xleftmargin=0pt]{color-grey-escher.mp} \vss} \noindent The \mpl{withcolor} command will also take a single \mpl{numeric} instead of a 3-tuple or @@ -1833,9 +1429,8 @@ number in plain \MP\ is: $\id{epsilon} = 1/256/256;$ then you can have at most 6 between. Grey scale is appropriate for some printed media, and can make effective textures -and patterns. -The code on the right was used to produce this: -$$\includegraphics[width=\textwidth]{escher}$$ +and patterns. The pattern below was produced by this program \rightarrowfill +$$\includegraphics{color-grey-escher}$$ First a basic path (named $\id{atom}$) is defined, then in the first loop three picture variables, $p_1$, $p_2$, and $p_3$, are defined, each one rotated 120° from the previous and filled with a slightly darker shade of grey. @@ -1843,49 +1438,23 @@ The double loop then draws the three versions of the shape on an up-and-down gri Finally the picture is clipped to a neat rectangle. \newpage -\subsubsection{Drawing algorithmic shadows} -\moveright5.5in\vbox to 0pt{\vskip6pt -\begin{code}[xleftmargin=0pt] -path b, w; -b = ((-3,-4)--(3,-2)--(3,+2)--(-3,4)--cycle) scaled 5; -w = b reflectedabout(up, down); - -numeric n; -n = 128; - -picture B, W; -B = image(for i=0 step 1/n until 1: - draw point 4-i of b -- point 1+i**2 of b - withcolor 1-i**8; - endfor); - - W = image(for i=0 step 1/n until 1: - draw point 4-i of w -- point 1+i**2 of w - withcolor 3/4-i**8; - endfor); - -for i=-9 upto 9: - for j=-4 upto 4: - draw if odd (i+j): W else: B fi shifted (i*30,j*30); - endfor -endfor - -clip currentpicture to bbox currentpicture yscaled 7/8; -\end{code} +\subsection*{Drawing algorithmic shadows} +\moveright5.25in\vbox to 0pt{\vskip6pt +\mpexternal[firstline=5,lastline=32]{color-grey-shadows.mp} \vss} \noindent Here is a more complex pattern, showing one way to create an illusion of shadows with multiple fine lines. -$$\includegraphics[width=\textwidth]{shadows}$$ +$$\includegraphics{color-grey-shadows}$$ The first part defines two wedge-shaped closed paths, $\id{w}$ being the mirror image of $\id{b}$. Like the standard \id{unitsquare} path, the path $\id{b}$ is defined so that point 0 is the bottom left corner. -The two $\kw{picture}$ variables are produced -by drawing lines across the shapes from bottom to top. By setting $n$ high enough, -these multiple lines blend smoothly to give an even colour. And by using higher -powers of the index variable, an effective shadow can be drawn ‘bunched up’ into the -top of each shape. +The two \<picture> variables are produced by drawing lines across the shapes from +bottom to top. If you set the loop step small enough, these multiple lines blend smoothly to +give an even colour. And by using higher powers of the index variable, an effective +shadow can be drawn ‘bunched up’ into the top of each shape. Note that \MP\ likes +integer powers of two. By repeating them alternately in a grid, we get an effective texture, which is clipped at the end to a neat rectangle again. @@ -1896,24 +1465,15 @@ clipped at the end to a neat rectangle again. \moveright 384pt\vbox to 0pt{\vskip144pt\raggedright\hsize4in\noindent This map shows the "RdYlBu[9]" palette in action on a map of the Brexit vote in -London. The outlines are the 33 London boroughs, and the colours show how we voted, -faded by turnout. The data and the outlines are from publicly-available UK -government sources. They were prepared for \MP\ using various Python scripts, and -they are available in the source for this document. +London. The outlines are the 33 London boroughs, and the colours show how we voted. +The size of the labels shows the turnout. The data and the outlines are from +public domain sources. They were prepared for \MP\ using various scripts, +and they are available in the source for this document. -\vskip 72pt +\vskip 48pt Here is the code for the palette used as the legend: -\begin{smallcode} -input colorbrewer-rgb -numeric s; s = 10; -for i = 1 upto 9: - fill unitsquare scaled s shifted (i*s, 0) withcolor RdYlBu[9][i]; - if i > 1: draw (i*s, 0) -- (i*s, s); fi -endfor -draw unitsquare xscaled 9s yscaled s shifted (s,0); -label.top("Leave" infont "phvr8r", (s, s)); -label.top("Remain" infont "phvr8r", (10s, s)); -\end{smallcode} +\mpexternal[firstline=9,lastline=9]{color-brexit-map.mp} +\mpexternal[firstline=11,lastline=19]{color-brexit-map.mp} \vss} \noindent @@ -1926,7 +1486,7 @@ otherwise you can get it from "https://ctan.org/pkg/metapost-colorbrewer". The package provides two files that define all the colour ranges; one for CMYK and another for RGB; an example of usage is shown below on the right. -$$\includegraphics[width=\textwidth]{brexit-map.pdf}$$ +$$\includegraphics[width=\textwidth]{color-brexit-map.pdf}$$ %-------------------------------------------- @@ -1934,46 +1494,9 @@ $$\includegraphics[width=\textwidth]{brexit-map.pdf}$$ \section{Random numbers} \MP\ provides us with two built-in functions to generate random numbers. -\vadjust{\moveright 384pt\vbox to 0pt{\kern-24pt -\begin{code} -vardef dice(expr pip_count, pip_color) = - save d,r,p, ul, ur, lr, ll; - r=1/8; path d; picture p; - d = for i=0 upto 3: - quartercircle scaled 3 shifted (15,15) rotated 90i -- - endfor cycle; - p = image(draw fullcircle scaled 6; - fill fullcircle scaled 6 withcolor pip_color); - pair ul, ur, ll, lr; - ul = 1/5[ulcorner d, lrcorner d]; - lr = 4/5[ulcorner d, lrcorner d]; - ur = 1/5[urcorner d, llcorner d]; - ll = 4/5[urcorner d, llcorner d]; - image(fill d withcolor background; draw d; - if odd(pip_count): - draw p shifted center d; - fi; - if pip_count > 1: - draw p shifted ul; draw p shifted lr; - fi; - if pip_count > 3: - draw p shifted ur; draw p shifted ll; - fi; - if pip_count = 6: - draw p shifted 1/2[ul,ur]; - draw p shifted 1/2[ll,lr]; - fi) -enddef; - -beginfig(1); -for i=0 upto 4: - draw dice(1+floor uniformdeviate 6, red) - rotated (2 normaldeviate) - shifted (36i,0); -endfor -endfig; -\end{code} - $$\includegraphics{dice}$$ +\vadjust{\moveright 372pt\vbox to 0pt{\kern-24pt +\mpexternal[firstline=5,lastline=39,xrightmargin=-36pt]{random-dice.mp} +$$\includegraphics{random-dice}$$ \vss}} \begin{itemize} \item `$\kw{uniformdeviate}\,n$' generates a random real number between $0$ and @@ -2003,7 +1526,7 @@ endfig; about 68.3\%; between $-2$ and 2, about 95.4\%. \vadjust{\moveright 3.6in\vbox to 0pt{\hsize 1.6in \vskip21pt \noindent \small 10000 samples suggest\\\kw{normaldeviate} works.\par\vss}} - $$\includegraphics[width=4.6in]{gaussian}$$ + $$\includegraphics[width=4.6in]{random-gaussian}$$ To relocate the mean, just add a constant. To rescale the distribution, multiply by the desired standard deviation (the square root of the desired variance). @@ -2018,85 +1541,39 @@ The \kw{normaldeviate} function is provided as a primitive \MP\ operation. The implementation is based on the `Ratio method' presented in \textsl{The Art of Computer Programming}, section~3.4.1. It turns out to be very straightforward to implement the algorithm for this method as a user-level program $\longrightarrow$ -\vadjust{\moveright5.5in\vbox to 0pt{\kern -64pt -\begin{smallcode} -vardef normaldeviate = - save u, v, xa; - forever: - forever: - u := uniformdeviate 1; - exitif (u>1/64); - endfor - v := sqrt(8/mexp(256)) * ( -1/2 + uniformdeviate 1 ); - xa := v/u; - exitif ( xa**2 <= -mlog(u)/64 ); - endfor - xa -enddef; - -vardef exponentialdeviate = - save u; - forever: - u := uniformdeviate 1; - exitif (u>0); - endfor - -mlog(u)/256 -enddef; - -vardef gammadeviate(expr a,b) = - save y, x, v, s, accept; boolean accept; - s = sqrt(2a-1); - forever: - forever: - y := tand(uniformdeviate 180); - exitif y<64; - endfor - x := s * y + a - 1; - accept := false; - if x>0: - v := uniformdeviate 1; - if (v <= (1+y**2)*mexp((a-1)*mlog(x/(a-1))-(256*s*y))): - accept := true; - fi - fi - exitif accept; - endfor - x/b - enddef; -\end{smallcode} +\vadjust{\moveright5.5in\vbox to 0pt{\kern -112pt +\smallmpexternal{random-other-distributions.mp} \vss}}% -There are a couple points here. First, the inner loop around the assignment to $u$ is -designed to avoid very small values that would cause $v/u$ to be larger than 64, and -hence make "xa**2" overflow. This is a useful general technique, and justified in -terms of the algorithm since large values of $v/u$ are rejected anyway. Secondly, -the expression "sqrt(8/mexp(256))" is a constant ($ \sqrt{8/e} \simeq 1.71553 $) and could be -replaced by it's value, but this does not make an appreciable improvement to the +This version of \mpl{normaldeviate} is of academic interest only, in all real code +you should use the primitive operation, but there are a couple of programming notes. +If you put ‘\mpl{u = uniformdeviate 1}’, then you have $0 \le u < 1$, so $v/u$ might +give you a divides-by-zero error; using ‘\mpl{u = 1 - uniformdeviate 63/64}’ ensures +that $1/64 < u \le 1$, which not only avoids the possibility of a divide-by-zero +error, but also ensures that $|(v/u)| < 64$, so that you can square it without +overflow. This is a useful general technique, and justified in terms of the +algorithm since large values of $v/u$ are rejected anyway. Secondly, the expression +\mpl{sqrt(8/mexp(256))} is a constant ($ \sqrt{8/e} \simeq 1.71553 $) and could be +replaced by its value, but this does not make an appreciable improvement to the speed of the routine. On a modern machine, this routine is only very slightly slower than using the primitive function. +\medskip\noindent It is also fairly straightforward to implement random number generators that follow other statistical distributions. The mathematical details are in the section of \textsl{TOACP} referenced above. Two examples, for the exponential distribution and the gamma distribution, are shown on the right. In both cases, note the care required to avoid -arithmetic overflow (and see section~\ref{trig} for the "tand" function). +arithmetic overflow with the default scaled number system. \medskip\label{mexp}\noindent You can also see the special nature of \MP's \kw{mexp} and \kw{mlog} functions. They are defined so that $\kw{mexp} x = \exp(x/256)$ and $\kw{mlog} x =256\log(x)$. This is another artefact of the scaled number system. \MP\ computes $x^y$ using the -formula "mexp(y*mlog(x))", and the adjusted log values give more accurate results. +formula \mpl{mexp(y*mlog(x))}, and the adjusted log values give more accurate results. Note that this means that you have $e=\kw{mexp}(256)$. -\medskip\noindent -At the start of each job, \MP\ automatically sets a new seed for the random number -generator, so that the sequence of numbers is different each time. But you can set -this yourself if you need the same sequence each time. At the start of your program -you should put "randomseed:=3.14;" (or whatever value you prefer). According to -\textsl{The Metafont Book}, the default value is -$\id{day}+\id{time}\ast\id{epsilon}$, but in \MP\ the exact value used depends on -the resolution of the timers available on your system; essentially the value -should be different every time you run \MP. +It is sometimes useful to define macros for the usual versions of $\exp$ and $\log$ +as shown on the right. This not only helps you make fewer programming mistakes, and \newpage\subsection{Random walks} @@ -2104,34 +1581,9 @@ should be different every time you run \MP. You can use the random number generation routines to produce visualizations of random walks, with various levels of analysis. \vadjust{\moveright5.5in\vbox to 0pt{\hsize 4.4in\kern -2\baselineskip -\begin{code} -beginfig(1); -numeric w, h, n; w = 377; h = 80; n = 500; -draw (origin--right) scaled w; -draw (origin--right) scaled w shifted (0,+h/2) withcolor 3/4; -draw (origin--right) scaled w shifted (0,-h/2) withcolor 3/4; -pair zenith, nadir; zenith = nadir = origin; -path walk[]; -for i=1 upto 8: - numeric y; y = 0; - walk[i] = origin for x=w/n step w/n until w: - hide( - y := y if uniformdeviate 1 < 1/2: + else: - fi 1; - if y > ypart zenith: zenith := (x,y) ; fi - if y < ypart nadir: nadir := (x,y) ; fi - ) - -- (x,y) - endfor; - undraw walk[i] withpen pencircle scaled 3/4; - draw walk[i] withcolor (1/2+y/h)[red, blue] -endfor -drawarrow (12 up -- 2 up) shifted zenith withcolor blue; -drawarrow (12 down -- 2 down) shifted nadir withcolor red; -endfig; -\end{code} - +\mpexternal[firstline=5,lastline=31,xleftmargin=0pt]{random-walks-red-blue.mp} \smallskip\noindent -\hey Note the \mpl{undraw} line using a slightly thicker pen; this makes it +\hey Note the \mpl{undraw} line using a slightly thicker pen; this makes it easier to follow the lines as they cross each other. \vss}} $$\includegraphics[width=\textwidth]{random-walks-red-blue}$$ @@ -2150,32 +1602,40 @@ set this delta value, for example by using a different type of random variate, o the value, or changing the odds in favour of one direction or the other. For example: \begin{code} -y := y if uniformdeviate 1 < p: + 2 else: - 1 fi; +y := y if uniformdeviate 1 < p: + 2 else: - 1 fi; \end{code} will set the delta to $+2$ with probability $p$ and and to $-1$ with probability $1-p$. -\newpage\subsection{Brownian motion} +\newpage +\subsubsection{Random walks with different constraints} -A random walk is normally constrained to move one unit at a time, but if you relax +\textsc{Formally}, a random walk is constrained to move one unit at a time, but if you relax that constraint and use `\kw{normaldeviate}' in place of `\kw{uniformdeviate}' you -can get rather more interesting patterns.\vadjust{\moveright5.5in\vbox to 0pt{ -\hsize4in\kern -20pt -\begin{code} -beginfig(2); -for n=1 upto 4: - x:=y:=0; - draw (x,y) for i=1 upto 2000: - hide(x:=x+4normaldeviate; y:=y+4normaldeviate;) - .. (x,y) - endfor withcolor ((n+2)/9)[blue,white]; - fill fullcircle scaled 3 shifted (x,y) withcolor red; -endfor -% mark the origin -fill fullcircle scaled 3 withcolor green; -endfig; -\end{code} +may get more “realistic†patterns. +\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4.2in\kern2\baselineskip\noindent +The drawing here is much the same as the previous page, except that the definition of +\id{walk} in the central loop is simplified to this: +\mpexternal[firstline=15,lastline=18,xleftmargin=0pt]{random-walks-normal.mp} +}} +$$\includegraphics[width=\textwidth]{random-walks-normal}$$ +Alternatively you could add an extra constraint that the final value should be zero +(or some other desired target value); this is the so-called “Brownian bridgeâ€. +$$\includegraphics[width=\textwidth]{random-walks-normal-bridge}$$ +To do this, you make a random walk path, as above, with \id{n} points, and then copy +it into a new path where the $i$-th point is adjusted by $i/n\times(t-y)$ where $t$ +is the target value, and $y$ is the $y$-value of the last point on the walk path. +\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4.2in\vss +\mpexternal[firstline=7,lastline=23,xleftmargin=0pt]{random-walks-normal-bridge.mp} +}} -\kern 120pt +\newpage\subsection{Brownian motion} + +Relaxing all the constraints, can give you even more +interesting patterns.\vadjust{\moveright5.5in\vbox to 0pt{ +\hsize4.2in\vskip -32pt +\mpexternal[firstline=6,lastline=20,xleftmargin=0pt]{random-two-dimensional-brownian.mp} + +\kern 84pt \noindent Using these random number generators means that the output is different each time because \MP\ produces a different sequence of numbers. You may @@ -2188,16 +1648,17 @@ using a random number at the top of your program. randomseed := uniformdeviate infinity; \end{code} Now \MP\ writes the (random) value used in the log for you to copy. Note that if you are using -"luamplib" you need to add the "\mplibshowlog{enable}" option. +"luamplib" you need to add the "\mplibshowlog{enable}" option to get this value in +the log. \vss}} If you also allow the $x$-coordinates to wander at random as well as the $y$-coordinates you get two-dimensional random patterns. And if you replace the straight line segments "--" with ".." so that \MP\ -draws a smooth curve through the points, as well as vary the colour each time -you draw a new curve, then the result is almost artistic. +draws a smooth curve through the points, then the result is almost artistic. -\medskip\noindent -\hbox to \textwidth{\includegraphics[width=1.2\textwidth]{brown3a}\hss} +\vbox to 0pt{\noindent +\hbox to \textwidth{\includegraphics[width=1.2\textwidth]{random-two-dimensional-brownian}\hss} +\vss} \newpage\subsection{Drawing freehand} @@ -2207,45 +1668,7 @@ examples there are all in French (including all the names of the custom macros), perhaps it would be better to say `translated' rather than `stolen'; moreover my implementations are easier to use with plain \MP.\vadjust{\moveright5.5in\vbox to 0pt{ \hsize4in\kern -5.5\baselineskip -\begin{smallcode} -def freehand_segment(expr p) = - point 0 of p {direction 0 of p rotated (4+normaldeviate)} .. - point 1 of p {direction 1 of p rotated (4+normaldeviate)} -enddef; -def freehand_path(expr p) = - freehand_segment(subpath(0,1) of p) - for i=1 upto length(p)-1: - & freehand_segment(subpath(i,i+1) of p) - endfor - if cycle p: & cycle fi -enddef; -defaultfont := "eurm10"; -color sepia; sepia = (0.44, 0.26, 0.08); -picture marker; marker = image(for s=-1/2, 1/2: - draw (left--right) scaled 2 rotated 60 shifted (s,0); -endfor); -def moved_along expr x of p = rotated angle direction x of p - shifted point x of p enddef; - -beginfig(1); -pair A, B, C, D; -A = (0,-30); B = (180,0); C = (120,90); -D = (1/2 + 1/40 normaldeviate)[A, B]; -path triangle, circumcircle, bisector; -triangle = freehand_path(A--D--B--C--cycle); -bisector = freehand_segment(C--D); -circumcircle = freehand_path(A..B..C..cycle); -draw triangle; -draw bisector; -draw circumcircle withcolor .67 red; -draw marker moved_along 1/2 of triangle withcolor .67 red; -draw marker moved_along 3/2 of triangle withcolor .67 red; -label.lft("A", A); -label.rt ("B", B); -label.top("C", C); -label.bot("D", D); -endfig; -\end{smallcode} +\smallmpexternal[firstline=5,lastline=42,xleftmargin=0pt]{random-freehand-circumcircle.mp} \vss}} \subsubsection{Making curves and straight lines look hand drawn} @@ -2269,48 +1692,11 @@ you might find that a little of this type of decoration goes a long way. This second freehand figure uses a macro to draw a wonky line through two points with a bit of overlap at each end. The overlap size is given using the suffix -syntax. The lines are drawn in sepia ink to enhance the hand-drawn look. The angle +syntax. The lines are drawn in sepia ink to enhance the hand-drawn look. The angle labels are positioned on invisible arcs between neighbouring wonky lines. \vadjust{\moveright5.5in\vbox to 0pt{ \hsize4in\kern -4.5\baselineskip -\begin{code}[xleftmargin=0pt] -vardef freehand_through@#(expr a, b) = - save t; pair t; - t = @# * unitvector(b - a) rotated (4 + normaldeviate); - a - t .. a {t} .. b {t} .. b + t -enddef; - -vardef mid_arc@#(expr p, a, b) = - save c; path c; - c = fullcircle scaled (2*@#) shifted p cutbefore a cutafter b; - point arctime 1/2 arclength c of c of c -enddef; - -beginfig(1); -defaultfont := "eurm10"; color sepia; sepia = (0.44, 0.26, 0.08); -pair A, B, C; A = (0,-30); B = (180,0); C = (120,90); - -path a, b, c; -a = freehand_through 7 (A, B); -b = freehand_through 8 (B, C); -c = freehand_through 6 (C, A); - -drawoptions(withcolor sepia); -draw a; draw b; draw c; - -drawoptions(withcolor .67 blue); -label.bot ("a", point 3/2 of a); -label.rt ("b", point 3/2 of b); -label.ulft("c", point 3/2 of c); - -drawoptions(withcolor .5 red); -label(char 11, mid_arc 16 (A, a, c)); -label(char 12, mid_arc 14 (B, b, a)); -label(char 13, mid_arc 14 (C, c, b)); - -drawoptions(); -endfig; -\end{code} +\mpexternal[firstline=5,lastline=41,xleftmargin=0pt]{random-freehand-through.mp} \vss}} $$\includegraphics{random-freehand-through}$$ @@ -2319,8 +1705,8 @@ $$\includegraphics{random-freehand-through}$$ \noindent\llap{\nb\ }The AMS Euler font available to \MP\ as "eurm10" is encoded as a subset of the \TeX\ math italic layout --- essentially it has all the Greek letters but none of the arrows, nor the musical notation. -$$\includegraphics{euler-sampler}$$ -If you can't get the upper case $\Gamma$ at \mpl{char 0}, then you might be running +$$\includegraphics{trad-euler-sampler}$$ +If you can't get the upper case $\Gamma$ at \mpl{char 0}, then you might be running an old out-of-date version of "luamplib". \newpage\subsection{Increasingly random shapes of the same size} @@ -2331,26 +1717,7 @@ $$\hbox to \textwidth{\includegraphics{random-shapes}\hss}$$ For these shapes the objective was to make them increasingly random, but to keep them all the same length.\vadjust{\moveright5.5in\vbox to 0pt{ \hsize4in -\begin{code} -beginfig(1); -numeric desired_length, n, s; -desired_length = 180; n = 30; s = 80; - -for r=0 upto 8: - - path shape; - shape = for i=1 upto n: - (s + r * normaldeviate, 0) rotated (360/n*i) .. - endfor cycle; - - shape := shape scaled (desired_length/arclength shape); - - draw shape shifted (r*s, 0) withcolor (r/8)[black,red]; - label(decimal r, (r*s, 0)); - -endfor -endfig; -\end{code} +\mpexternal[firstline=6,lastline=21,xleftmargin=0pt]{random-shapes.mp} \vss}} Each time round the outer loop the \id{shape} is redeclared to clear it, and then redefined by an inline-loop with $n$ steps like @@ -2373,101 +1740,45 @@ you need to have defined \id{shape} before you can refer to it. \newpage\subsection{Explosions and splashes} Random numbers are also useful to make eye catching banners for posters, -presentations, and infographics. Here are two simple example shapes: $\to$ -\mpic{18pt}{explode} - -\begin{smallcode} -string heavy_font; -heavy_font = "PlayfairDisplay-Black-osf-t1--base"; - -randomseed:=2128.5073; - -beginfig(1); -n = 40; r = 10; s = 50; -path explosion, splash; -explosion = for i=1 upto n: - (s if odd(i): - else: + fi r + uniformdeviate r,0) rotated (i*360/n) -- -endfor cycle; - -splash = for i=1 upto n: - (s if odd(i): - else: + fi r + uniformdeviate r,0) rotated (i*360/n) .. -endfor cycle; -splash := splash shifted (3s,0); - -fill explosion withcolor 1/2 green + red; -draw explosion withpen pencircle scaled 2 withcolor 2/3 red; -label("BOOM!" infont heavy_font scaled 2, center explosion) - withcolor red; -fill splash withcolor 1/2 green + blue; -draw splash withpen pencircle scaled 2 withcolor 2/3 blue; -label("SPLAT!" infont heavy_font scaled 2, center splash) - withcolor blue; -endfig; -\end{smallcode} - +presentations, and infographics. Here are two simple example shapes \rightarrowfill +\mwpic{0pt}{random-explosions} +\mpexternal[firstline=8,lastline=29,xleftmargin=0pt]{random-explosions.mp} \noindent -In this figure "n" is the number of points in the shape, "r" is the amount of -randomness, and :"s" is the radius used. -In order to get a clear zig-zag outline, the loop alternately adds or subtracts "r"; -and then adds a random amount on top to make it look random. -Notice that the only difference between the "explosion" and "splash" is that how -the connecting lines are constrained to be straight or allowed to make smooth -curves.\vadjust{\moveright5.5in\vtop to -2pt{\hsize 4in\vss\noindent -The display font used here is one of the gems hidden away in "psfonts.map". +In this figure $n$ is the number of points in the shape, $s$ is the radius, and $r$ +is the amount of randomness added to or removed from $s$. In order to get a clear +zig-zag outline, the loop alternately adds or subtracts $r$; and then adds a random +amount on top to make it look random. Notice that the only difference between the +"explosion" and "splash" is that how the connecting lines are constrained to be +straight or allowed to make smooth curves. +\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent\small +The display font used here is Playfair Display Black. If you have it installed +as a system font, you can use "fontspec" and "luamplib" with "lualatex" as described +in §\ref{sec:sa-lua-flow}, but if you are still using +plain "mpost", then you need to hunt for it in your local "psfonts.map". If you run \MP\ with the "-recorder" option, it will create a list of all the files used, with the current job name and an extension of ".fls". This file will include a line which tells you exactly which version of "psfonts.map" is being used. - The DVIPS documentation explains the format of the file, but for \MP's purposes the -first word of each non-comment line defines a font name you can try. However beware -that just because a name is defined in your map file, does not necessarily mean that -you actually have the required PostScript font files installed as well. But if you have a -full TexLive installation you will find that very many of them are already -installed.\strut -}} +first word of each non-comment line defines a font name you can try. When you find +it you can add something like this to the top of the example: +\begin{smallcode} +defaultfont = "PlayfairDisplay-Black-osf-t1--base"; +defaultscale = 3; +\end{smallcode}}} \newpage\subsection{Simulating jagged edges or rough surfaces} You can use the idea of adding a little bit of noise to simulate a rough surface. -$$\includegraphics[width=0.95\textwidth]{qed}$$ +\vadjust{\moveright5.25in\vbox to 0pt{\hsize 4in\vskip-12pt +\smallmpexternal[firstline=6,lastline=37,xleftmargin=0pt]{random-qed.mp} +\vss}} +$$\includegraphics[width=0.95\textwidth]{random-qed}$$ These diagrams are supposed to represent light rays reflecting from a surface: on the left the surface is smooth ($r=0$) and on the right it's rough ($r=0.42$). The parameter $r$ is used in the \MP\ program as a scaling factor for the random noise added to each point along the rough surface; the only difference in the code to produce the two figures was the value of $r$.% -\vadjust{\moveright5.5in\vbox to - 0pt{\hsize 4in\vss -\begin{smallcode} -def perpendicular expr t of p = - direction t of p rotated 90 shifted point t of p - enddef; - -beginfig(1); -u = 5mm; r = 0.42; n = 32; s = 8u; theta = -45; - -path base; -base = origin - for i=1 upto n-1: -- (i/n*s,r*normaldeviate) endfor - -- (s,0) -- (s,-u) -- (0,-u) -- cycle; -fill base withcolor .8[blue,white]; -draw base withcolor .67 blue; - -path ray[]; -for i=2 upto 6: - ray[i] = (left--right) scaled 2/3 s rotated theta shifted (i*u,0); - b := ypart (ray[i] intersectiontimes base); - ray[i] := point 0 of ray[i] - -- point b of base - -- point 0 of ray[i] - reflectedabout(point b of base, perpendicular b of base); - drawarrow ray[i]; -endfor - -label("r=" & decimal r, center base); -endfig; -\end{smallcode} -\vss}} First the base block is created with some noise on the upper side. Then five rays are created. Applying \mpl{ypart} to the pair of times returned by \mpl{intersectiontimes} gives us the point of the base where the incident ray hits @@ -2487,45 +1798,21 @@ sometimes this can create unexpected loops. It's also possible to use a random walk approach so that each random step takes account of the previous one to avoid any big jumps. Here's one way to do that. -$$\includegraphics{torn-edge-straight}$$ -\begin{code} -path t; numeric x, y; -x = 0; y=0; -t = (x, -20) -- (x, y) for i=1 upto 288: - -- (incr x, walkr y) - endfor -- (x, -20) -- cycle; -draw t withcolor .67 blue; -\end{code} +$$\includegraphics{random-torn-straight-edge}$$ +\mpexternal[firstline=6,lastline=12]{random-torn-straight-edge.mp} + +\noindent The "walkr" routine works like the "incr" and "decr" commands; it updates the value of the argument. The idea is that the further away from zero you are, the more likely is that the next value will take you back towards zero. -\begin{code} -vardef walkr suffix $ = - $ := $ if uniformdeviate 1 < (2**-abs($)): + else: - fi - signr $; $ - enddef; -vardef signr suffix $ = - if $<0: - else: + fi uniformdeviate 1 - enddef; -\end{code} +\mpexternal{random-torn-edge.mp} You can use this to produce more realistic torn edges. You can also apply this as a form of jitter to a curved path, by adding a suitably rotated vector to enough -points along the path. +points along the path, as shown in the example on the right.\rightarrowfill \moveright5.5in\vbox to 0pt{\kern-4in -\begin{code} -path c; c = fullcircle scaled 200; -draw c withcolor .8 white; - -y=0; n = 600; -path t; t = for i=0 upto n-1: - point i/n*length(c) of c - + (0, walkr y) rotated angle direction i/n*length(c) of c - -- -endfor cycle; -draw t withcolor .67 red; -\end{code} -$$\includegraphics{torn-edge-circle}$$ +\mpexternal[firstline=6,lastline=16]{random-torn-edge-circle.mp} +$$\includegraphics{random-torn-edge-circle}$$ \vss} @@ -2536,21 +1823,7 @@ $$\includegraphics{torn-edge-circle}$$ Here is the equilateral triangle point macro in action. $$\includegraphics{geometry-triangles-on-circle}$$ \vskip -12pt -\begin{code} -beginfig(1); -path c; c = fullcircle scaled 144; -pair a,b,p,q; -for i=0 upto 7: - a := point i of c; - b := point i+1 of c; - p := equilateral_triangle_point(a,b); - q := equilateral_triangle_point(b,a); - draw a -- p -- b withcolor .67 green; - draw a -- q -- b withcolor .67 red; -endfor -draw c withcolor .53 blue; -endfig; -\end{code} +\mpexternal[firstline=8,lastline=21,xleftmargin=0pt]{geometry-triangles-on-circle.mp} \vss}}% This section deals with drawing geometrical figures that involve lines, angles, polygons, and circles. Plain \MP\ provides very few tools that are @@ -2588,40 +1861,35 @@ vardef equilateral_triangle_point(expr a, b) = enddef; \end{code} And if you want to get right back to primitives you could even write that as: -\begin{code} -vardef equilateral_triangle_point(expr a, b) = - b shifted -a rotated 60 shifted a -enddef; -\end{code} +\mpexternal[firstline=5,lastline=7]{geometry-triangles-on-circle.mp} \newpage \subsection{Bisecting lines and paths} \moveright5.5in\vbox to 0pt{\hsize4in\noindent -$$\includegraphics{mediation-pitfall}$$ +$$\includegraphics{geometry-mediation-pitfall}$$ \vskip 50pt -$$\includegraphics[width=4in]{mediation-shapes}$$ +$$\includegraphics[width=4in]{geometry-mediation-shapes}$$ \bigskip -$$\includegraphics[width=4in]{mediation-sallows}$$ +$$\includegraphics[width=4in]{geometry-mediation-sallows}$$ \centerline{\textsl{Lee Sallows' theorem of median triangles}} \vss} \noindent -The best way to bisect a line depends on how you have defined it. -If you have two pairs $a$ and $b$, then the simplest way to find -the pair that bisects them is to write "1/2[a,b]". This mediation -mechanism is entirely general, so you can write \mpl{1/3[a,b]}, "1/4[a,b]", and +\textsc{The best way to bisect} a line depends on how you have defined it. +If you have two \<pair>s $a$ and $b$, then the simplest way to find +the \<pair> that bisects them is to write "1/2[a,b]". This mediation +mechanism is entirely general, so you can write "1/3[a,b]", "1/4[a,b]", and so on to define other pairs that are part of the way from $a$ to $b$. -The expression "0[a,b]" is equal to $a$, and "1[a,b]" is equal to $b$; -but the number before the left bracket does not have to +But the number before the left bracket does not have to be confined to the range $(0,1)$. If you write "3/2[a,b]" you will get a pair on the extension of the line from $a$ to $b$ beyond $b$. To get a pair going the other way you can either reverse $a$ and $b$, or use a negative number; but don't get caught out by the \MP\ precedence rules: "-1/2[a,b]" is interpreted as "-(1/2[a,b])" and not as "(-1/2)[a,b]", so either put in the parentheses or swap -the order of the pairs: "(3/2)[b,a]". See $\longrightarrow$. +the order of the pairs: "(3/2)[b,a]". See \rightarrowfill -If you want to work with a \kw{path} variable, rather than separate \kw{pair} +If you want to work with a \<path> variable, rather than separate \<pair> variables, you can use the \mpl{point t of p} notation to do mediation along the path. For a simple straight path $p$ of length 1 @@ -2632,33 +1900,32 @@ but for more complicated, curved paths you have to use this rather cumbersome no \begin{code} point arctime 1/2 arclength p of p of p \end{code} -If your path is closed, and makes a triangle or a regular polygon, -then you can bisect it with the line +If your path makes a regular polygon, then you can bisect the shape with the line \begin{code} point t of p -- point t + 1/2 length p of p \end{code} -\textbf{NB}: if the polygon has an odd number of sides, then $2t$ must be a whole -number. +\noindent +\hey If the polygon has an odd number of sides, then $2t$ must be a whole number. -\smallskip\noindent -In a triangle these bisecting lines are called medians. The three medians intersect +\vfill\noindent +\textsc{In a triangle} these bisecting lines are called medians. The three medians intersect at the centroid of the triangle. The centroid is a good place to put a label on a -triangle. You could find it \mpl{intersectionpoint} or with +triangle. You could find it using the macro from \ref{polygons}, or with a construction using \mpl{whatever} on any two medians, but since we know that the centroid divides each median in the ratio $2:1$ we can find the centroid of a triangle path $p$ most simply with: \begin{code} z0 = 2/3[point 0 of p, point 3/2 of p]; \end{code} -The median is the basis for several beautiful theorems about the geometry of the +The median lines are the basis for several beautiful theorems about the geometry of the triangle. The theorem shown here was first published in 2014. \newpage \subsection{Bisecting angles}\label{sec:bisect} \moveright5.5in\vbox to 0pt{\hsize4in\noindent -$$\includegraphics{bisection-euclidean}$$ +$$\includegraphics{geometry-bisection-euclidean}$$ \smallskip -$$\includegraphics{bisection-vector}$$ +$$\includegraphics{geometry-bisection-vector}$$ \vss} \noindent In an equilateral triangle the medians also bisect the angles at each vertex; this @@ -2677,7 +1944,7 @@ ABC$, then you could simplify this and make it more efficient by using $e = \frac12[p,q]$ instead of calling the triangle macro at all. However the macro is still making two calls to \mpl{intersectionpoint}. If you wanted to eliminate this you could use the -useful plain \MP\ macro "unitvector" to produce a solution based on adding two equal +useful plain \MP\ macro \mpl{unitvector} to produce a solution based on adding two equal length vectors from the corner to the two other points. Another approach is to exploit another geometric theorem that states that the bisector of an angle in a triangle divides the opposite side in the ratio of the two other sides. @@ -2685,7 +1952,7 @@ So if sides $AB$ and $BC$ have lengths $p$ and $q$ then the bisector will be ${p\over p+q}={1\over1+q/p}$ from $A$ to $C$, and you can express this simply using \MP's mediation syntax: \vbox to 0pt{ -$$\includegraphics{bisection-interior}$$ +$$\includegraphics{geometry-bisection-interior}$$ \vss} \newpage @@ -2693,23 +1960,12 @@ $$\includegraphics{bisection-interior}$$ There is no classical method to trisect an arbitrary angle, so you need to resort to measuring and arithmetic in \MP. If the angle is a given this is trivial: -\mpic{-12pt}{trisection-simple.pdf} -\begin{smallcode} -path ray; -numeric theta; -ray = origin -- 200 right; -theta = 42; -draw ray; -draw ray rotated 1/3 theta withcolor 2/3 red; -draw ray rotated 2/3 theta withcolor 2/3 red; -draw ray rotated theta; -dotlabel.llft("$0$", origin); -label("$\theta/3$", 72 right rotated 1/6 theta); -label("$\theta/3$", 72 right rotated 3/6 theta); -label("$\theta/3$", 72 right rotated 5/6 theta); -\end{smallcode} +\mpic{-12pt}{geometry-trisection-simple} +\smallmpexternal[firstline=6,lastline=17]{geometry-trisection-simple.mp} + +\noindent But if you have only the coordinates of some points then you need to use the -\mpl{angle} primitive to measure the angle first; \mpl{angle} takes a \kw{pair} +\mpl{angle} primitive to measure the angle first; \mpl{angle} takes a \<pair> argument and returns a numeric representing the angle in degrees measured clockwise from the $x$-axis to a line through the origin and the point represented by the pair. This definition means that if you have three points $A$, $B$, and $C$, then you can @@ -2722,13 +1978,13 @@ vardef measured_angle(expr P, Q, R) = (angle (P-Q) - angle (R-Q)) * turningnumber (P--Q--R--cycle) mod 360 enddef; \end{smallcode} -The primitive \mpl{turningnumber} is explained on p.\thinspace 111 of \textsl{The -METAFONTbook}. It takes a closed path and returns number of times that you would +The primitive \mpl{turningnumber} is explained on p.\thinspace 111 of \mfbook. +It takes a closed path and returns number of times that you would turn through 360${}^\circ$ if you traversed the path. We use this here to negate the measured angle if necessary, so that you always get the interior angle. The \mpl{mod 360} on the end ensures that the result is in the range $0 \le \theta < 360$. Armed with a measured angle, all you then need is arithmetic. -\mpic{-160pt}{trisection-classical.pdf} +\mpic{-160pt}{geometry-trisection-classical} It might be possible to use the \id{solve} macro to simulate the Neusis construction (that allows you to measure a length) illustrated on the right, but measuring the angles is rather easier. @@ -2738,27 +1994,15 @@ angles is rather easier. \moveright5.5in\vbox to 0pt{\hsize4in\noindent \centerline{A puzzle square featuring some intersections} -$$\includegraphics[width=3in]{magic-square-14}$$ +$$\includegraphics[width=3in]{geometry-magic-square-14}$$ The points were defined like this (the order was important). -\begin{code} -z1 = (10,10); -z4 = 144 right rotated 12; -z5 = z4 shifted (2, 78); -z7 = z4 reflectedabout(origin, (1,1)); - -z2 = 1/2 [z5, z7]; -z9 = whatever [z1, z4]; -z2-z9 = whatever * (z7-z1); -z8 = whatever [z1, z5] = whatever [z2, z4]; -z3 = whatever [z2, z9] = whatever [z4, z7]; -z6 = whatever [z1, z7] = whatever [z3, z5]; -\end{code} +\mpexternal[firstline=8,lastline=18]{geometry-magic-square-14.mp} \vss} \noindent If you have line segments defined by their endpoints, then the canonical way to find their intersection, is to use the mediation syntax with \id{whatever} twice: -$$\includegraphics[width=\textwidth]{whatever.pdf}$$ +$$\includegraphics{geometry-whatever}$$ The mediation syntax works even if the intersection point does not actually lie on either of the two line segments. The intersection will be the point where the two (infinite) lines through the pairs of points meet. If the two lines are parallel, @@ -2781,7 +2025,7 @@ than straight lines, you need to use the \mpl{intersectiontimes} primitive or th \subsubsection{The intersection algorithm} \MP\ inherits a fast algorithm for finding the intersection between two paths from -\MF. It is explained rather more gnomically than usual at the end of Chapter 14 of +\MF. It is explained rather more succinctly than usual at the end of Chapter 14 of \mfbook, with more detail given in the web source for \MF. The core algorithm works on paths of length 1. If you have longer paths, \MP\ works its way along the paths applying the core algorithm to successive pairs of unit subpaths. It does this is @@ -2798,14 +2042,12 @@ found will always be as early as possible on $A$. Note that after the call abov point $t$ of $A$ will be very close to point $u$ of $B$, as they both refer to the same intersection point. If you want the alternative point that is earlier on $B$, then use `$B \mathbin{\textrm{intersectiontimes}} A$' -instead.\mpic{-222pt}{intersection-AB-or-BA} +instead.\mpic{-222pt}{geometry-intersection-AB-or-BA} \vfill\noindent When we get down to paths of length 1, the algorithm works something like this: -$$ -\includegraphics{intersection-algorithm} -$$ +$$\includegraphics{geometry-intersection-algorithm}$$ \vadjust{\moveright 384pt\vbox to 0pt{\hsize 4.2in\vss \noindent The two paths are represented as rectangles that enclose the end points and the control points for each path. If these rectangles don't overlap then there is @@ -2817,7 +2059,7 @@ rectangles. The two times returned by \mpl{intersectiontimes} are the midpoints the subpaths enclosed by these two tiny rectangles, which is why they do not always refer to exactly the same point.}} -\subsubsection{Finding all intersection points} +\subsubsection{Finding all intersection points}\label{sec:allxp} As noted above, the \mpl{intersectiontimes} algorithm will stop at the first intersection of the two paths, but it is possible that the two paths will intersect @@ -2853,10 +2095,10 @@ intersectiontimes B}, but in a loop this causes an inconsistent equation error o the second iteration. If you need to avoid the repeated use of \mpl{xpart} and \mpl{ypart}, one alternative is to do this inside the loop: \begin{smallcode} - ... - numeric t, u; - (t, u) = A intersectiontimes B; - ... +... +numeric t, u; +(t, u) = A intersectiontimes B; +... \end{smallcode} Now the numerics are reset each time and the equation is not inconsistent. \vadjust{\moveright 384pt\vbox to 0pt{\hsize 4.2in\vss \noindent @@ -2865,7 +2107,7 @@ both of the paths are close together, so that the unit subpaths are short; But it is possible to create quite long paths of unit \mpl{length} and these may intersect each other more than once, like so: -$$\includegraphics{intersection-only-two}$$ +$$\includegraphics{geometry-intersection-only-two}$$ Here the two paths $A$ and $B$ are Bézier splines of with \mpl{length=1}, so the normal \MP\ algorithm is only ever going to give you one of the intersections. In the diagram above, the @@ -2875,18 +2117,10 @@ but what about the one in the middle? The most reliable approach is to take a copy of one of the paths, and snip it off at the intersection and try again until there is nothing left to snip. -$$\includegraphics{intersection-all-three}$$ +$$\includegraphics{geometry-intersection-all-three}$$ The three points marked here were captured like this: -\begin{code} -pair P[]; numeric n; n=0; -path R; R := A; % take a copy of A -forever: - R := R cutbefore B; % snip where we cross B - exitif length cuttings = 0; % stop if nothing was cut - P[incr n] = point 0 of R; % capture the point - R := subpath (epsilon, infinity) of R; % nudge along -endfor -\end{code} +\mpexternal[firstline=13,lastline=20]{geometry-intersection-all-three.mp} +\noindent This technique also works on paths with \mpl{length} greater than one, so you may prefer it as your general “get all the intersections†approach. Note that the \mpl{cutbefore} macro is defined using \mpl{intersectiontimes}. @@ -2899,7 +2133,7 @@ Note that the \mpl{cutbefore} macro is defined using \mpl{intersectiontimes}. Given five known points --- $A$, $B$, $C$, $D$, and $E$ --- \MP\ can find the point $F$ on the line $A \to B$, so that $E \to F$ is parallel to $C \to D$ like this: -\mpic{0pt}{parallel} +\mpic{0pt}{geometry-parallel} \begin{code} F = whatever[A, B]; % F is on the line A..B E-F = whatever * (C-D) % E..F || C..D @@ -2954,7 +2188,7 @@ find the other point by reversing the circle.\par} The canonical way to draw a circle in plain \MP\ is to use the pre-defined path \mpl{fullcircle} with a suitable transformation. -\mpic{-12pt}{drawing-circles.pdf} +\mpic{-12pt}{geometry-drawing-circles} The path is defined (in "plain.mp") using two \MP\ primitive commands: \begin{code} path fullcircle; fullcircle = makepath pencircle; @@ -2980,14 +2214,8 @@ points, but if the line between the two points is a diameter [\blue{II}], then y draw fullcircle scaled abs (B-A) shifted 1/2[A,B]; \end{code} Finally three points define a unique circle [\green{III}]: -\begin{code} -vardef circle_through(expr A, B, C) = - save o; pair o; - o = whatever * (A-B) rotated 90 shifted 1/2 [A,B] - = whatever * (B-C) rotated 90 shifted 1/2 [B,C]; - fullcircle scaled 2 abs (A-o) shifted o -enddef; -\end{code} +\mpexternal[firstline=27,lastline=32]{geometry-drawing-circles.mp} +\noindent Plain \MP\ also defines \id{halfcircle} and \id{quartercircle}, as the appropriate subpaths of \id{fullcircle}, both starting at point 0 (3 o'clock). Curiously, this differs from \MF\ where \id{quartercircle} is defined first, and the other two @@ -2997,45 +2225,26 @@ complete circle of which they would be part; so if you did “\kw{draw} $(34.5,21)$ to $(34,21.5)$. \newpage -\subsection{Incircle and excircle of a triangle} +\subsection{Incircle and excircles of a triangle} -The incircle of a triangle is the largest circle contained in the triangle. +\textsc{The incircle of a triangle} is the largest circle contained in the triangle. The centre of the incircle lies at the intersection of the internal angle bisectors. So we can use ideas from §\ref{sec:bisect} and §\ref{sec:intersect} to define a macro that returns the required path given points $A$, $B$, and $C$: -\mxpic{-1in}{5in}{incircle} -\begin{code} -vardef incircle(expr A,B,C) = - save a, b, m, t; pair a, b, m, t; - a = A + unitvector (C-A) + unitvector (B-A); - b = B + unitvector (A-B) + unitvector (C-B); - m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; - t-m = whatever * (B-A) rotated 90; - fullcircle scaled 2 abs (t-m) shifted m -enddef; -\end{code} +\mpic{-1in}{geometry-incircle} +\mpexternal[firstline=11,lastline=18]{geometry-incircle.mp} -\bigskip\noindent -The excircles of a triangle are the three circles lying outside the triangle and +\vfill\noindent +\textsc{The excircles of a triangle} are the three circles lying outside the triangle and tangent to one edge and the extensions of the other two. The centres of each excircle lie at the intersection of one internal angle bisector and the external angle bisector of one of the other corners. - To get the external angle bisector, -all you have to do is reverse the direction of one of the \mpl{unitvector} calls: -\mxpic{0pt}{5in}{excircle} -\begin{code} -vardef excircle(expr A,B,C) = - save a, b, m, t; pair a, b, m, t; - a = A + unitvector (C-A) - unitvector (B-A); - b = B + unitvector (A-B) + unitvector (C-B); - m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; - t-m = whatever * (B-A) rotated 90; - fullcircle scaled 2 abs (t-m) shifted m -enddef; -\end{code} - -\smallskip\noindent +all you have to do is reverse the direction of one of the \mpl{unitvector} calls +(can you see why?) +\mpic{-.5in}{geometry-excircle} +\mpexternal[firstline=11,lastline=18]{geometry-excircle.mp} +\noindent\hey To get the other excircles, call the macro with the points in a different order. \newpage @@ -3045,113 +2254,52 @@ The circumcircle of a triangle is the circle through the three corners, so if yo already have the corners of your triangle as separate \<pair> variables, you can use the \mpl{circle_through} macro from §\ref{sec:circles}. Or you can adapt the macro to take a single triangular path: -\begin{smallcode}[xleftmargin=0pt, xrightmargin=-60pt] -vardef circumcircle(expr T) = - save m; pair m; - m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T - = whatever * (point 1 of T - point 2 of T) rotated 90 shifted point 3/2 of T; - fullcircle scaled 2 abs (point 0 of T - m) shifted m -enddef; -\end{smallcode} -Note that as the diagram on the right shows,\mxpic{-2in}{4.6in}{circumcircle} +\smallmpexternal[firstline=11,lastline=16,xleftmargin=0pt, xrightmargin=-60pt]{geometry-circumcircle.mp} +\noindent +Note that as the diagram on the right shows,\mpic{-2in}{geometry-circumcircle} the centre of the circumcircle is the intersection of all three of the perpendicular bisectors of sides, but for the purposes of drawing in \MP\ you only need to find the -intersection of two of them. You could write +intersection of two of them. You could write \begin{smallcode}[xleftmargin=0pt, xrightmargin=-60pt] - m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T - = whatever * (point 1 of T - point 2 of T) rotated 90 shifted point 3/2 of T - = whatever * (point 2 of T - point 3 of T) rotated 90 shifted point 5/2 of T; + m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T + = whatever * (point 1 of T - point 2 of T) rotated 90 shifted point 3/2 of T + = whatever * (point 2 of T - point 3 of T) rotated 90 shifted point 5/2 of T; \end{smallcode} but this does not add any more information to the equation for $m$, and -\MP\ will sometimes give you an “inconsistent equation†error if your triangle +\MP\ will sometimes give you an “inconsistent equation†error if your triangle is long and thin. \vfill \noindent \hey The marks that show line segments are equal were created by this macro. -\begin{code} -vardef mark_equal(expr a, b, n) = - save m, s; numeric s; 2s = n - 1; - picture m; m = image(for t=-s upto s: - draw (down--up) scaled 2 rotated -13 shifted (t,0) - withpen pencircle scaled 1/4; - endfor); - draw m rotated angle (b-a) shifted 1/4[a,b]; - draw m rotated angle (b-a) shifted 3/4[a,b]; -enddef; -\end{code} -Given the triangular \<path> $T$, the macro was used like this: +\smallmpexternal[firstline=38,lastline=47]{geometry-circumcircle.mp} +Given the triangular \<path> $T$, the macro was used like this: $\longrightarrow$\vadjust{\moveright5.5in\vbox to 0pt{\vss -\begin{code} -mark_equal(point 0 of T, point 1 of T, 1); -mark_equal(point 1 of T, point 2 of T, 2); -mark_equal(point 2 of T, point 0 of T, 3); -\end{code}}} +\smallmpexternal[firstline=49,lastline=51]{geometry-circumcircle.mp} +}} \newpage \subsection{The nine-point circle of a triangle} -The orthocentre of a triangle is the point is the intersection of the three +The orthocentre of a triangle is the point at the intersection of the three altitudes, shown as point $D$ below. The point $N$, half-way from $D$ to the circumcentre $M$ is the centre of the remarkable nine-point circle which passes through the bases of the three altitudes and bisects the six line segments $AB$, $AC$, $AD$, -$BC$, $BD$, and $CD$.\vadjust{\moveright5.2in\vbox to 0pt{\hsize 4in\vskip-80pt\noindent -\begin{smallcode} -pair A, B, C, D, N, M, p, q, r; -A = origin; B = 377 dir 10; C = 233 dir 70; -% pedal points (not labelled) -p = whatever[B, C]; A - p = whatever * (B-C) rotated 90; -q = whatever[C, A]; B - q = whatever * (C-A) rotated 90; -r = whatever[A, B]; C - r = whatever * (A-B) rotated 90; - -D = whatever[A, p] = whatever[B, q]; -N = 1/4(A + B + C + D); % remarkably... -M = D rotatedabout(N, 180); % M is also the circumcentre - -path circumcircle, nine_point_circle; -nine_point_circle = fullcircle scaled 2 abs(N - 1/2[A, B]) shifted N; -circumcircle = fullcircle scaled 2 abs(M - A) shifted M; - -draw nine_point_circle withcolor 3/4 red; -draw circumcircle withcolor 1/2[3/4 blue, white]; - -drawoptions(dashed evenly scaled 1/4 withcolor 1/2); -draw 1/2[A,B] -- M -- 1/2[B, C]; -draw 1/2[C,A] -- M -- D; -draw A -- p; -draw B -- q; -draw C -- r; - -% show the nine points with small circle markers -drawoptions(withpen pencircle scaled 1/4); -draw fullcircle scaled 2 shifted 1/2[A, B]; -draw fullcircle scaled 2 shifted 1/2[A, C]; -draw fullcircle scaled 2 shifted 1/2[A, D]; -draw fullcircle scaled 2 shifted 1/2[B, C]; -draw fullcircle scaled 2 shifted 1/2[B, D]; -draw fullcircle scaled 2 shifted 1/2[C, D]; -draw fullcircle scaled 2 shifted p; -draw fullcircle scaled 2 shifted q; -draw fullcircle scaled 2 shifted r; - -drawoptions(); -draw A--B--C--cycle; -dotlabel.llft("$A$", A); -dotlabel.rt("$B$", B); -dotlabel.ulft("$C$", C); -dotlabel.urt("\ $D$", D); -dotlabel.llft("$M$", M); -dotlabel.llft("$N$", N); -\end{smallcode}\vss}} -$$\includegraphics[width=\textwidth]{nine-point-circle}$$ +$BC$, $BD$, and $CD$.\vadjust{\moveright5.25in\vbox to 0pt{\hsize 4in\vskip-88pt\noindent +\smallmpexternal[firstline=6,lastline=52,xleftmargin=0pt]{geometry-nine-point-circle.mp} +\vss}} + +\smallskip + +$$\includegraphics{geometry-nine-point-circle}$$ \newpage \subsection{Lines tangent to a point on a path} \MP\ represents paths internally as a sequence of nodes. Each node consists of three -pairs: the pre-control point, the point itself, and the post-control point. -\mpic{0pt}{tangents-on-path}% +pairs: the pre-control point, the point itself, and the post-control point. +\mpic{0pt}{geometry-tangents-on-path}% For a given path $p$ you can extract these points at time $t$ with these operators: \begin{code} precontrol t of p @@ -3159,7 +2307,7 @@ point t of p postcontrol t of p \end{code} Unless you explicitly set them differently, \MP’s curve fitting will make these -three points co-linear, so you can draw a tangent at point $t$ with +three points co-linear, so you can draw a tangent at point $t$ with \begin{code} draw precontrol t of p -- postcontrol t of p; \end{code} @@ -3167,7 +2315,7 @@ The length of the tangent line drawn like this depends on the size and shape of the curve, but it is somewhat arbitrary. So you may prefer to extract a \<pair> representing the tangent at point $t$ with \begin{code} -pair d; d = postcontrol t of p - precontrol t of p; +pair d; d = postcontrol t of p - precontrol t of p; \end{code} In fact, this is so useful that "plain.mp" provides \mpl{direction} as a shorthand: @@ -3176,7 +2324,7 @@ vardef direction expr t of p = postcontrol t of p - precontrol t of p enddef; \end{smallcode} which can save you some typing. But the clever bit is that $t$ does not have to be a whole number. If you set $t=\frac14$ (say), \MP\ works out the corresponding fractional -control points, so that you can use \mpl{direction t of p} to get a tangent at any point. +control points, so that you can use \mpl{direction t of p} to get a tangent at any point. The vector pairs returned have the right direction, but still have rather arbitrary magnitudes, so the usual idiom is something like this: @@ -3195,13 +2343,11 @@ outside a circle. To do this, you need to adapt the standard geometrical construction: for a given circle $C$ and a point $p$, find the midpoint of $p$ and the center of $C$; draw a semicircle through $p$, centred on this midpoint; the tangent point is where the semicircle intersects $C$. % -\mpic{-110pt}{tangents-point-to-circle.pdf} +\mpic{-110pt}{geometry-tangents-point-to-circle} Given a suitable \mpl{path C} and \mpl{pair p} you can do this: -\begin{code} -pair o, m, t, t'; o = center C; m = 1/2[o, p]; -t = C intersectionpoint halfcircle zscaled (p-o) shifted m; -t' = C intersectionpoint halfcircle zscaled (o-p) shifted m; -\end{code} +\mpexternal[firstline=11,lastline=13]{geometry-tangents-point-to-circle.mp} + +\noindent No parentheses are needed around the second path, because \mpl{intersectionpoint} is defined with \mpl{secondarydef}. @@ -3213,82 +2359,62 @@ that $b > a$ in all cases regardless of the relative rotation of $C$ and $p$. T means that \mpl{subpath (a, b) of C} is always the “long way round†C, on the opposite side from $p$, and \mpl{subpath (a, b-8) of C} is always the shorter segment. -\begin{code} -vardef tangent_times(expr C, p) = - % return the two times on C that correspond - % to the external tangents from p to C - save o, a, b, G, H; - pair o; numeric a, b; path G, H; - o = center C; - H = halfcircle zscaled (p-o) shifted 1/2[o, p]; - G = halfcircle zscaled (o-p) shifted 1/2[o, p]; - (a, whatever) = C intersectiontimes H; - (b, whatever) = C intersectiontimes G; - (a, b if b < a: + 8 fi) -enddef; -\end{code} -Note the elegant syntax here; -if \mpl{z} is a \<pair> then the operation \mpl{zscaled z} is equivalent -to \mpl{scaled abs z rotated angle z}. -\vpic{-200pt\noindent Here is the macro in action. +\mpexternal{geometry-tangent-times.mp} + +\noindent +Note the elegant syntax here; if \mpl{z} is a \<pair> then the operation +\mpl{zscaled z} is equivalent to \mpl{scaled abs z rotated angle z}. + +\moveright5.5in\vbox to 0pt{\hsize4in\vskip-200pt +\noindent Here is the macro in action. Having obtained the two times $a$ and $b$ from the macro, the dashed line -was drawn along a path that was composed with: -\vrule depth 20pt width 0pt height 2pt -\mpl{p -- subpath (a,b) of C -- cycle} -}{tangent-times-on-circle} +was drawn along a path that was composed with: \mpl{p -- subpath (a,b) of C -- cycle} +$$\includegraphics{geometry-tangent-times-on-circle}$$ +\vss} \newpage \subsection{Lines tangent to two circles (exterior)}\label{sec:adjust-times} The same \mpl{tangent_times} macro can be reused to find the tangents that touch two -circles, using an approach like this: \mwpic{-12pt}{tangents-two-circles-exterior} -\begin{code} -path A, B; -A = fullcircle scaled 144; -B = fullcircle scaled 60 shifted (200, 140); - -numeric R, r; -R = abs (point 0 of A - center A); -r = abs (point 0 of B - center B); +circles, using an approach like this: \mwpic{-36pt}{geometry-tangents-two-circles-exterior} -path C; numeric t, u; -C = fullcircle scaled (2R-2r) shifted center A; -(t, u) = tangent_times(C, center B); +\smallmpexternal[firstline=9,lastline=24]{geometry-tangents-two-circles-exterior.mp} -draw A withpen pencircle scaled 2 withcolor 3/4[blue, white]; -draw B withpen pencircle scaled 2 withcolor 3/4[blue, white]; - -draw subpath (t, u) of A -- subpath (u-8, t) of B -- cycle; -\end{code} Here $A$ and $B$ are the two circles you want to connect, and $A$ is larger than $B$. $R$ is the radius of the larger, $r$ of the smaller. $C$ is an auxiliary circle centred at the same point as $A$ and scaled so that its radius is $R-r$. If we then find the tangent points on $C$ from the center of $B$, the points we want are the corresponding points on $A$ and $B$. -\medskip\noindent -This works well, provided that none of three -circles $A$, $B$, or $C$ has been rotated (that is that point 0 is at 3 o'clock in -all of them). But -this may not always be the case. For example, you might have written +Notice how the times are used with \mpl{subpath}; if $a>b$, then the path returned +from \mpl{subpath (a, b) of P} is the same as \mpl{reverse subpath (b, a) of P}, +which means that \mpl{subpath (u,t) of B} would give you the wrong side. The remedy +is to subtract 8 from $u$ (or, more generally, to subtract the length of path $B$). +Because there are 8 points on a \mpl{fullcircle} path, point $u$ and point $u-8$ +refer to the same place, but since $u-8 < t$, the subpath will run clockwise as +required. + +\vfill +\noindent\hey +This all works provided that all three +circles $A$, $B$, or $C$ have the same rotation. +But this may not always be the case. +For example, you might have defined $B$ as \begin{code} -B = fullcircle scaled 60 shifted 240 right rotated 36; +B = fullcircle scaled 60 shifted 240 dir 36; \end{code} and then point $t$ of $B$ would \textit{not} correspond to point $t$ of the -auxiliary circle. So to make the code above more general you have to adjust the -tangent times to take account of the relative rotation of the circles. -\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vskip-24pt\noindent -\begin{code} -vardef adjust_time(expr tt, AA, BB) = - tt + 1/45 angle (point 0 of AA - center AA) - - 1/45 angle (point 0 of BB - center BB) -enddef; -\end{code} -\vss}} -The in the figure $t$ was adjusted to $t'$ for $A$ and $t''$ for $B$, using the -routine shown on the right. This routine shows the relationship between \mpl{angle} -and points around a circle: $360^\circ = 8\:\hbox{points}$. +auxiliary circle $C$. +\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent +To cope with circles that might not have the same rotation, you need to adjust the +tangent times to take account of the different relative rotation. +\mpexternal[firstline=7,lastline=10]{geometry-tangents-two-circles-interior.mp} +\noindent +This macro exploits the relationship between \mpl{angle} +and points around a \mpl{fullcircle} path: $360^\circ = 8\:\hbox{points}$. +You can see it in action on the following page. +}} \newpage \subsection{Lines tangent to two circles (interior)} @@ -3296,65 +2422,24 @@ and points around a circle: $360^\circ = 8\:\hbox{points}$. To find the interior tangents, you just need to add the smaller radius rather than subtract it, and add 4 to the times on the smaller circles, so that they are on the other side: -$$\includegraphics[width=\textwidth]{tangents-two-circles-interior}$$ +$$\includegraphics[width=\textwidth]{geometry-tangents-two-circles-interior}$$ \bigskip\noindent The complete code for this is shown on the right. It uses the same routines given above; \mpl{tangent_times} from section \ref{sec:tangent-times}, and \mpl{adjust_time} from section \ref{sec:adjust-times}. -\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent -\begin{smallcode} -path A, B; -A = fullcircle scaled 144 rotated uniformdeviate 360; -B = fullcircle scaled 60 shifted 240 right rotated 36; - -numeric R, r; -R = abs (point 0 of A - center A); -r = abs (point 0 of B - center B); - -path C; -C = fullcircle scaled (2R+2r) shifted center A; % NB +ve - -numeric t, t', t'', u, u', u''; -(t, u) = tangent_times(C, center B); -t' = adjust_time(t, C, A); -u' = adjust_time(u, C, A); -t'' = adjust_time(t + 4, C, B); % Note the plus fours -u'' = adjust_time(u + 4, C, B); - -draw A withpen pencircle scaled 2 withcolor 3/4[blue, white]; -draw B withpen pencircle scaled 2 withcolor 3/4[blue, white]; -draw C withpen pencircle scaled 1 withcolor 3/4[blue, white]; - -draw subpath (t', u') of A -- subpath (u'', t'') of B -- cycle; -draw center B -- subpath (t, u) of C -- cycle dashed evenly; - -draw center B -- point t'' of B dashed withdots scaled 1/2; -draw center B -- point u'' of B dashed withdots scaled 1/2; -draw point t of C -- point t' of A dashed withdots scaled 1/2; -draw point u of C -- point u' of A dashed withdots scaled 1/2; - -dotlabel.ulft(btex $t$ etex, point t of C); -dotlabel.lrt (btex $t'$ etex, point t' of A); -dotlabel.lrt (btex $t''$ etex, point t'' of B); -dotlabel.lrt (btex $u$ etex, point u of C); -dotlabel.ulft(btex $u'$ etex, point u' of A); -dotlabel.ulft(btex $u''$ etex, point u'' of B); -drawdot center B withpen pencircle scaled dotlabeldiam; - -drawoptions(withcolor 1/2[blue, white]); - label.urt(btex $A$ etex, point 1/2(t'+u'- 7.6) of A); - label.rt (btex $B$ etex, point 1/2(t''+u''- 2) of B); - label.urt(btex $C$ etex, point 1/2(t+u-8) of C); -drawoptions(); -\end{smallcode}\vskip -1in +\vadjust{\moveright5.25in\vbox to 0pt{\hsize 4in\vss\noindent +\smallmpexternal[firstline=12,lastline=54]{geometry-tangents-two-circles-interior.mp} +\vskip -72pt }} \subsection{Axis of similitude}\label{sec:axosim} -\bigskip -\noindent\hbox to \textwidth{\includegraphics[scale=0.92]{axis-of-similitude}\hss} -\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent +\vbox to 0pt{\vskip-\baselineskip\noindent\hbox to +\textwidth{\includegraphics[scale=0.92]{geometry-axis-of-similitude}\hss}\vss} + +\vfill +\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent Given three circles taken in pairs, you can use the techniques of the preceding sections to find the three points where the common external tangents intersect (shown here as $E_{12}$, $E_{31}$, and $E_{23}$) and the @@ -3364,58 +2449,53 @@ The line common to the three $E$ points is known as the \textit{Axis of Similitude}. The drawing is left as an exercise for the reader, except -to note that if $r_1$ and $r_2$ are \mpl{numeric} variables representing -the radius of the circles centred at the \mpl{pair} variables $C_1$ and $C_2$, -then we have: -$$\vbox{\openup3pt\halign{\hfil$#$&${}=#$\hfil\cr -E_{12}&({r_1\over r_1 - r_2})[C_1, C_2];\cr -I_{12}&({r_1\over r_1 + r_2})[C_1, C_2];\cr -}}$$ -which is a bit quicker than working out all the tangent points.}} +to note that if \mpl{r1} and \mpl{r2} are \<numeric> variables representing +the radius of the circles centred at the \<pair> variables \mpl{C1} and \mpl{C2}, +then: +\begin{smallcode} +E12 = (r1/(r1 - r2)[C1, C2]; I12 = (r1/(r1 + r2)[C1, C2]; +\end{smallcode} +which is a bit quicker than working out all the tangent points. +My version is in the file "geometry-axis-of-similitude.mp" +} \newpage \subsection{Inversion, pole, and polar}\label{sec:inversion} Inversion in a circle is a generalization of reflection in a line. -\mpic{-68pt}{pole-and-polar} -It is useful for certain constructions in geometry, and easy to -implement as a macro \MP. For given circle, and a -given point $P$ lying outside the circle, the inverted point $P'$ lies inside the -circle at the intersection of the line from $P$ to the centre of the circle, and the -line between the tangent points [§\ref{sec:tangent-times}] from $P$, shown here as -$Q$ and $R$.\rlap{\quad$\longrightarrow$} +\mpic{-48pt}{geometry-pole-and-polar} +It is useful for certain constructions in geometry, and easy to implement as a macro +\MP. For given circle, and a given point $P$ lying outside the circle, the inverted +point $P'$ lies inside the circle at the intersection of the line from $P$ to the +centre of the circle, and the line between the tangent points +[§\ref{sec:tangent-times}] from $P$, shown here as $Q$ and $R$.\rlap{\quad$\longrightarrow$} But $OPQ$ and $OQP'$ are similar triangles, so $r/OP=OP'/r$ and so $OP' = r^2/OP$, and since $P'$ must lie on the line through $O$ and $P$, this is enough to -define a macro directly to find $P'$ given $P$, $O$, and $r$: +to find $P'$ directly given $P$, $O$, and $r$: \begin{code} -P' = O + unitvector(P-O) scaled r * r / abs (P-O); +P' = O + unitvector(P-O) scaled (r * r / abs (P-O)); \end{code} -But examining \mpl{plain.mp} shows that \mpl{unitvector} is a macro defined like this: +But examining "plain.mp" shows that \mpl{unitvector} is a macro defined like this: \begin{code} vardef unitvector primary z = z/abs z enddef; \end{code} -which suggests this alternative (safer) approach: +which suggests this alternative formulation: \begin{code} -vardef invert(expr P, O, r) = - save s; numeric s; s = r / abs (P-O); - O + (P-O) * s * s -enddef; +P' = O + (P - O) scaled (r / abs (P - O) * r / abs (P - O)); \end{code} -This works well provided that $|P| > \frac1{180} r$, which is usually the case, but -you could also consider checking that $|t|>0$ and that $s$ was not too large. - -If it was more convenient to deal with the \<path> of the circle of inversion -instead of the centre and the radius, you get the macro to work out the centre and -the radius for you. +or as a macro, and dividing first to avoid overflow: \begin{code} -vardef invert(expr P, C) = - save o; pair o; o = 1/2[point 0 of C, point 4 of C]; - save r; numeric r; r = abs (point 0 of C - o); - save s; numeric s; s = r / abs (P - o); - o + (P - o) * s * s +vardef invert(expr P, O, r) = + save s; numeric s; s = abs(P - O); + O + (P - O) / s * r / s * r enddef; \end{code} +This works well in most cases, but you could consider checking that $s$ is not too small. +If it is more convenient to deal with the \<path> of the circle of inversion +instead of the centre and the radius, you can get the macro to calculate +them for you: +\mpexternal[firstline=6,lastline=11]{geometry-pole-and-polar.mp} \vfill @@ -3435,8 +2515,9 @@ perpendicular to the line through the point and the center of the circle of inversion. \smallskip -\noindent\llap{\nb}The small dotted circle through $O$ and $P'$ above is the inversion -of the whole polar line (infinitely extended).} +\noindent\llap{\nb}The inversion of points on the polar (shown as blue dots) +lie on a circle through $O$ and $P'$. The complete circle would be the inversion +of the infinitely extended polar.} \newpage \subsection{Radical axis and radical centre}\label{sec:radical} @@ -3447,64 +2528,27 @@ with respect to both circles; that is the points from which the tangents to each are of equal length. A circle centred at any point on the axis, and drawn with radius equal to the length of the tangent will cut both circles at right angles. -\medskip\noindent\centerline{\includegraphics{radical-axis}} +\medskip\noindent\centerline{\includegraphics{geometry-radical-axis}} \medskip\noindent -In a system of three circles as shown, the \textit{radical centre} is the +In a system of three circles as shown, the \textit{radical centre} ("radix") is the intersection of the three mutual radical axes. The tangents from this point to all three circles -have the same length, so a circle with this radius cuts all three circles at right -angles. - -\moveright5.5in\vbox to 0pt{\vss\hsize 4in\begin{smallcode} -vardef radical_axis(expr ca, cb) = - numeric t, d, ra, rb; - ra = abs(center ca - point 0 of ca); - rb = abs(center cb - point 0 of cb); - d = abs(center cb - center ca); - 2t = 1 + (ra+rb) / d * (ra-rb) / d; - (up -- down) scaled 89 - rotated angle (center cb - center ca) - shifted t[center ca, center cb] -enddef; -beginfig(1); - path c[], a[]; - z1 = origin; z2 = 233 right rotated 4; z3 = 209 right rotated -42; - c1 = fullcircle scaled 202 shifted z1; - c2 = fullcircle scaled 106 shifted z2; - c3 = fullcircle scaled 62 shifted z3; - a1 = radical_axis(c1, c2); - a2 = radical_axis(c2, c3); - a3 = radical_axis(c3, c1); - z0 = whatever [point 0 of a1, point 1 of a1] - = whatever [point 0 of a2, point 1 of a2]; - numeric t; (t, whatever) = tangent_times(c1, z0); - drawoptions(withpen pencircle scaled 1 withcolor 3/4[blue, white]); - draw c1; draw c2; draw c3; - drawoptions(withcolor 3/4[blue, white]); - draw z1 -- point t of c1 dashed evenly; - drawoptions(withpen pencircle scaled 1/4); - draw z1 -- z2 -- z3 -- cycle; - drawoptions(); - draw a1; draw a2; draw a3; - drawoptions(withcolor 2/3 red); - draw fullcircle scaled 2 abs (point t of c1 - z0) shifted z0; - draw z0 -- point t of c1 dashed evenly; - drawdot z0 withpen pencircle scaled dotlabeldiam; - drawoptions(withcolor 1/4[blue, white]); - drawdot z1 withpen pencircle scaled dotlabeldiam; - drawdot z2 withpen pencircle scaled dotlabeldiam; - drawdot z3 withpen pencircle scaled dotlabeldiam; - label.urt(btex $C_1$ etex, point 1 of c1); - label.urt(btex $C_2$ etex, point 1 of c2); - label.rt (btex $C_3$ etex, point 0 of c3); -endfig; -\end{smallcode}\vskip -1in} +have the same length, so a circle with this radius (shown above in \red{red}) +cuts all three circles at right angles. + +\moveright5.5in\vbox to 0pt{\vss\hsize 4in +\smallmpexternal[firstline=6,lastline=51]{geometry-radical-axis.mp} +\vskip -1in} \newpage \subsection{Circles tangent to other circles} -\bigskip -\noindent\hbox to \textwidth{\includegraphics[height=\textheight]{apollonius}\hss} -\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent + +\vbox to 0pt{\noindent +\hbox to \textwidth{\includegraphics[height=\textheight]{geometry-apollonius}\hss} +\vss} + +\vfill +\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent The classical Problem of Apollonius is to find a circle tangent to three others. All of the approaches are rather involved, but Gergonne's is probably the simplest to follow in \MP. @@ -3524,127 +2568,45 @@ technique [§\ref{sec:circles}]. \smallskip\noindent {\small -The drawing is also left as an exercise for the reader, although you can find my -version in the source code for this document. You might like to try to make a more -robust version or to find all the other tangent circles.} -}} +The drawing is left as an exercise for the reader, although you can find my +"geometry-apollonius.mp" in the source for this document. You might try to make a more +robust version or to find all the other tangent circles.}} \newpage \subsection{Coordinate geometry examples} \kern-\baselineskip -\vpic{-24pt}{desargues} -\kern-.5\baselineskip -\begin{code}[xleftmargin=0pt, xrightmargin=-72pt] -beginfig(1); - z.P = 200 up rotated 21; z.A = 100 left rotated -21; - z.B = origin; z.C = 90 right rotated 42; - - z.A' = 3/8[z.P, z.A]; - z.B' = 1/2[z.P, z.B]; - z.C' = 5/8[z.P, z.C]; - - z.R = whatever [z.A, z.B] = whatever [z.A', z.B']; - z.S = whatever [z.B, z.C] = whatever [z.B', z.C']; - z.T = whatever [z.C, z.A] = whatever [z.C', z.A']; - - path t[]; - t1 = z.A--z.B--z.C--cycle; - t2 = z.A'--z.B'--z.C'--cycle; - - fill t1 withcolor 7/8[red, white]; - fill t2 withcolor 7/8[blue, white]; - draw t1 withcolor 1/2 white; - draw t2 withcolor 1/2 white; - - drawoptions(dashed withdots scaled 1/2); - draw z.P--z.A; - draw z.P--z.B; - draw z.P--z.C; - - drawoptions(dashed evenly scaled 1/2); - draw z.B--z.R--z.B'; - draw z.C--z.S--z.C'; - undraw subpath (1/4, 3/4) of (z.C'--z.T) withpen - pencircle scaled 5; - draw z.C--z.T--z.C'; -\end{code} -\moveright 384pt \vbox to 0pt{\vss -\begin{code}[xleftmargin=0pt, xrightmargin=-72pt] - - drawoptions(withcolor 2/3 red); - draw 9/8[z.S,z.R] -- 9/8[z.R,z.S]; - picture pp; pp = thelabel("perspectrix", origin); - draw pp shifted 7 down rotated angle (z.S-z.R) - shifted 1/2[z.R, z.T]; - dotlabel.urt("perspector", z.P); - - drawoptions(); - dotlabel.lft (btex $A$ etex, z.A); - dotlabel.llft(btex $B$ etex, z.B); - dotlabel.lrt (btex $C$ etex, z.C); - dotlabel.lft (btex $A'$ etex, z.A'); - dotlabel.llft(btex $B'$ etex, z.B'); - dotlabel.bot (btex $C'$ etex, z.C'); - label.rt(btex Desargues' Theorem etex, (x.C', 1/2(y.P+y.C'))); -endfig; -\end{code} +\vpic{-24pt}{geometry-examples-desargues} + +\mpexternal[xleftmargin=0pt,firstline=6,lastline=37]{geometry-examples-desargues.mp} +\moveright 340pt \vbox to 0pt{\vss +\mpexternal[xleftmargin=0pt,xrightmargin=-80pt,firstline=38,lastline=53]{geometry-examples-desargues.mp} \vskip -42pt} \newpage -\moveright5.5in\vbox to 0pt{\vskip10pt\includegraphics[width=4.2in]{trisection-triangles}\vss} -\vskip-\baselineskip -\begin{code}[xleftmargin=0pt, xrightmargin=-80pt] -randomseed := 2485.81543; -vardef measured_angle(expr p, o, q) = - (angle (p-o) - angle (q-o)) mod 360 -enddef; -beginfig(1); -picture T; -for i=0 upto 1: - for j=0 upto 1: - clearxy; - T := image( - z1 = (120 + uniformdeviate 21, 0); - z2 = (120 + uniformdeviate 21, 0) rotated 120 rotated 21 normaldeviate; - z3 = (120 + uniformdeviate 21, 0) rotated 240 rotated 21 normaldeviate; - numeric a, b, c; - a = measured_angle(z3, z1, z2); - b = measured_angle(z1, z2, z3); - c = measured_angle(z2, z3, z1); - z4 = whatever [z1, z2 rotatedabout(z1, 1/3 a)] - = whatever [z2, z3 rotatedabout(z2, 2/3 b)]; - z5 = whatever [z2, z3 rotatedabout(z2, 1/3 b)] - = whatever [z3, z1 rotatedabout(z3, 2/3 c)]; - z6 = whatever [z3, z1 rotatedabout(z3, 1/3 c)] - = whatever [z1, z2 rotatedabout(z1, 2/3 a)]; - fill z4--z5--z6--cycle withcolor 3/4[red + 1/2 green, white]; - draw z4--z5--z6--cycle; - draw z1 -- z4 -- z2 -- z5 -- z3 -- z6 -- cycle - dashed withdots scaled 1/4; - draw z1 -- z2 -- z3 -- cycle; - ); - draw T shifted (200i, 240j); - endfor -endfor -label.rt(btex \vbox{\halign{#\hfil\cr The trisectors of each angle\cr -in any given triangle form a\cr central equilateral triangle.\cr}} etex, (24, 128)); -endfig; -\end{code} +\vpic{-36pt}{geometry-examples-trisections} +\vbox to 0pt{ + \mpexternal[xleftmargin=0pt,xrightmargin=-80pt,firstline=6,lastline=40]{geometry-examples-trisections.mp} +\vss} \newpage -\kern-\baselineskip -\vpic{1in}{projections} -\mpexternal[xleftmargin=0pt]{projections-code.mp} - +\kern-3\baselineskip +\vpic{0.25in}{geometry-examples-napoleon} +\vbox to 0pt{ + \mpexternal[xleftmargin=0pt,firstline=6,lastline=37]{geometry-examples-napoleon.mp} +\vss} \newpage -\moveright5.5in\vbox to 0pt{\hsize4in\noindent This needs an \mpl{invert} macro, such -as the one from [§\ref{sec:inversion}]. - -\smallskip\noindent -\includegraphics[width=288pt]{arbelos} +\kern-3\baselineskip +\vpic{1in}{geometry-examples-projections} +\vbox to 0pt{ + \mpexternal[xleftmargin=0pt,firstline=6,lastline=41]{geometry-examples-projections.mp} +\vss} -\vskip 1.414in\noindent +\newpage +\moveright5.25in\vbox to 0pt{\hsize4.25in\noindent +\smallmpexternal[firstline=7,lastline=14,xleftmargin=0pt]{geometry-arbelos.mp} +\centerline{\includegraphics{geometry-arbelos}} +\vfill\noindent \begingroup \raggedleft\fontsize{8}{10}\selectfont\textsf{% One must also recognize that any attempt to illustrate geometry\\ @@ -3654,48 +2616,113 @@ of finite length, of positive thickness, and rough edged.\\[2pt] — Benoit Mandelbrot, \textsl{The Fractal Geometry of Nature}} \par\endgroup \vss} -\begin{smallcode}[xleftmargin=0pt, xrightmargin=-72pt] -beginfig(1); -pair A,B,C; A = origin; C = 244 right; B = 7/8[A, C]; -path c[]; -c1 = fullcircle scaled 2 abs(A-C); % large circle for the inversions -c2 = fullcircle scaled abs(A-C) shifted 1/2[A,C]; -c3 = fullcircle scaled abs(A-B) shifted 1/2[A,B]; -c4 = fullcircle scaled abs(B-C) shifted 1/2[B,C]; -c5 = invert(c4,c1); -numeric d; d = abs(point 0 of c5 - point 4 of c5); % diameter of c5 - -drawoptions(withcolor 3/4 white); -draw c4; draw c5; -draw invert(subpath(0, 3/2) of c2, c1); -draw invert(subpath(0, 3/2) of c3, c1); -drawoptions(); -draw subpath(-1/4,1) of c1 withcolor 3/4[1/2 red,white]; -label.bot("\textit{circle of inversion}", point -1/4 of c1) - withcolor 1/4[1/2 red, white]; - -for i=1 upto 72: - path c, c'; - c = c5 shifted (0, i*d); c' = invert(c, c1); - if i < 5: - drawoptions(withcolor 3/4 white); - draw c; draw origin -- center c; - fill fullcircle scaled dotlabeldiam shifted center c; - fill fullcircle scaled dotlabeldiam shifted center c'; - drawoptions(); - fi - draw c' withpen pencircle scaled 1/4 withcolor 2/3 blue; -endfor -forsuffixes $=2,3,4: draw subpath (0,4) of c$ - withpen pencircle scaled 1/4 withcolor 2/3 blue; -endfor -draw A--C; -dotlabel.lft("$A$", A); dotlabel.llft("$B$", B); dotlabel.rt("$C$", C); -endfig; +\smallmpexternal[firstline=15,lastline=52,xleftmargin=0pt,xrightmargin=-72pt]{geometry-arbelos.mp} + +\newpage +\subsection{Drawing angle marks} + +\textsc{Observant readers} will have noticed that the occasional angle marks in the +preceding examples are generally drawn using plain \MP\ commands rather than a +macro. This is partly in order to make the examples self-contained and partly to +show what can be done with the default plain \MP\ format. + +\smallskip\noindent +To mark a right angle at point $a$ on the line $a\to b$ you can do something like +this: +\begin{code} +draw unitsquare scaled 5 rotated angle (b-a) shifted a; +\end{code} +with a suitable pen and a suitable colour. You \textit{could} write a macro to do +this, but it hardly seems worth the effort.% +\vadjust{\moveright 5.5in\vbox to 0pt{\hsize 4.2in\vskip -108pt\noindent +For example, this is one way to annotate a right-angle triangle: +\begin{code} +pair a, b, c; a = 10 dir 10; b = 160 dir 20; +c - a = whatever * (b - a rotated 90); ypart c = ypart b; +draw unitsquare scaled 5 rotated angle (b-a) shifted a + withcolor 3/4; +draw a--b--c--cycle; +\end{code} +which produces this: +$$\begin{mplibcode} +pair a, b, c; a = 10 dir 10; b = 160 dir 20; +c - a = whatever * (b - a) rotated 90; ypart c = ypart b; +draw unitsquare scaled 5 rotated angle (b-a) shifted a withcolor 3/4; +draw a--b--c--cycle; +dotlabel.llft("$a$", a); +dotlabel.rt ("$b$", b); +dotlabel.ulft("$c$", c); +\end{mplibcode}$$ + +\bigskip\noindent +Equipped with the macro shown on the left, you could add this: +\begin{code} + draw angle_mark(a, c, b, 16) withcolor 2/3 red; +\end{code} +to get this: +$$\begin{mplibcode} +pair a, b, c; a = 10 dir 10; b = 160 dir 20; +c - a = whatever * (b - a) rotated 90; ypart c = ypart b; +vardef angle_mark(expr P, O, Q, r) = + fullcircle scaled 2r rotated angle (P - O) + shifted O cutafter (O -- Q) +enddef; +draw unitsquare scaled 5 rotated angle (b-a) shifted a withcolor 3/4; +draw angle_mark(a, c, b, 16) withcolor 2/3 red; +draw a--b--c--cycle; + dotlabel.llft("$a$", a); + dotlabel.rt ("$b$", b); + dotlabel.ulft("$c$", c); +\end{mplibcode}$$ +Or, using the fancier macro: +$$\begin{mplibcode} +pair a, b, c; a = 10 dir 10; b = 160 dir 20; +c - a = whatever * (b - a) rotated 90; ypart c = ypart b; +vardef angle_label(expr P, O, Q, r) = image( + save a; path a; a = fullcircle scaled 2r rotated angle (P - O) shifted O cutafter (O -- Q); + fill O -- a -- cycle withcolor 7/8[red, white]; draw a withcolor 2/3 red; + save t; string t; t = decimal (round(angle (Q-O) - angle (P-O)) mod 360) & "°"; + label(t, O + r * (unitvector(P-O) + unitvector(Q-O))); +) enddef; +draw unitsquare scaled 5 rotated angle (b-a) shifted a withcolor 3/4; +draw angle_label(a, c, b, 16); +draw a--b--c--cycle; + dotlabel.llft("$a$", a); + dotlabel.rt ("$b$", b); + dotlabel.ulft("$c$", c); +\end{mplibcode}$$ +\vss}} + +\smallskip\noindent +On the other hand, you might want to make a macro for a curved angle mark since, it +is a bit more cumbersome. It is probably simplest make the macro create only the +required path, so you can use it with \mpl{draw} or \mpl{fill} as required. The +idea here is that $P$, $O$, and $Q$ are \<pair> variables and $r$ is a \<numeric> +representing the desired radius. +\begin{code} +vardef angle_mark(expr P, O, Q, r) = + fullcircle scaled 2r rotated angle (P - O) + shifted O cutafter (O -- Q) +enddef; +\end{code} +Note that \mpl{(P-O)} returns a \<pair>, but \mpl{(O--Q)} make a \<path>. Less is +usually more in coordinate geometry diagrams, but you could go on to make it much +fancier if you wanted: +\begin{smallcode}[xrightmargin=-40pt] +vardef fancier_angle_label(expr P, O, Q, r) = image( + save a, t; path a; string t; + a = fullcircle scaled 2r rotated angle (P - O) shifted O cutafter (O -- Q); + fill O -- a -- cycle withcolor 7/8[red, white]; draw a withcolor 2/3 red; + t = decimal (round(angle (Q-O) - angle (P-O)) mod 360) & "°"; + label(t, O + r * (unitvector(P-O) + unitvector(Q-O))); +) enddef; \end{smallcode} +Note that the angle label is calculated automatically. But +it is tediously time-consuming to make this sort of macro completely +general and fool-proof, so this example might not work for all angles. \newpage -\section{Trigonometry functions}\label{trig} +\section{The missing trigonometry functions}\label{trig} \MP\ provides only two basic trigonometry functions, "sind" and "cosd". This lack appears to be a deliberate design; in general it's much easier to use the "rotated" @@ -3708,45 +2735,7 @@ For this you need to know the value of $\pi$, but this is not built into plain \ If you are using the default number system then it's enough to define it to five decimal digits,% \vadjust{\moveright 384pt\vbox to 0pt{\kern-144pt -\begin{code} -numeric pi; -% approximate value -pi := 3.14159; -% measure round a circular arc... -pi := 1/4 arclength (quartercircle scaled 16); -% up to 32 digits of precision -pi := 3.1415926535897932384626433832795; -% as many digits as are needed... -vardef getpi = - numeric lasts, t, s, n, na, d, da; - lasts=0; s=t=3; n=1; na=0; d=0; da=24; - forever: - exitif lasts=s; - lasts := s; - n := n+na; na := na+8; - d := d+da; da := da+32; - t := t*n/d; - s := s+t; - endfor - s -enddef; -pi := getpi; - -% conversions -vardef degrees(expr theta) = 180 / pi * theta enddef; -vardef radians(expr theta) = pi / 180 * theta enddef; -% trig functions that expect radians -vardef sin(expr theta) = sind(degrees(theta)) enddef; -vardef cos(expr theta) = cosd(degrees(theta)) enddef; -% inverse trig functions -vardef acosd(expr a) = angle (a,1+-+a) enddef; -vardef asind(expr a) = angle (1+-+a,a) enddef; -vardef acos(expr a) = radians(acosd(a)) enddef; -vardef asin(expr a) = radians(asind(a)) enddef; -% tangents -vardef tand(expr theta) = save x,y; (x,y)=dir theta; y/x enddef; -vardef atand(expr a) = angle (1,a) enddef; -\end{code} +\mpexternal[firstline=1,lastline=37]{trigonometry-functions.mp} \vss}} but if you are using one of the new number systems you might want more digits of precision. In fact there's no harm in always defining these extra digits; even when @@ -3757,7 +2746,9 @@ multiple of $1\over65536$ (which turns out to be $3.14159$). The same applies to an error if you supply more digits that the default precision. So in general it's best to use no more than 32 digits. It's also possible, but not really worth the trouble, to define a routine to calculate $\pi$ to the current -precision.\rlap{\raise1ex\hbox{\ $\smash{\nearrow}$}} However you define it, once you are armed with a value for $\pi$ you can +precision.\rlap{\raise1ex\hbox{\ $\smash{\nearrow}$}} + +However you define it, once you are armed with a value for $\pi$ you can then define functions to convert between degrees and radians, and some more `normal' versions of sine and cosine. @@ -3770,12 +2761,11 @@ operator. $\kw{dir}\,30$ gives you the point $(x,y)$ on the unit circle such that $\tan 30^{\circ} = y/x$. You can use these ideas to define tangent and arctan functions if you really need them, but often "angle" and "dir" are more directly useful -for drawing. - -You should also be aware that the tangent function shown here does not -check whether $x=0$; if this is an issue, then add something like this +for drawing. +You should also be aware that the "tand" function shown here does not +check whether $x$ is close to zero; if this is an issue, then add something like this at the appropriate point: -$$\kw{if}\,x=0\!:\id{infinity}\: \kw{else}\!: y/x \kw{fi}$$ +$$\kw{if}\,\id{abs}(x)<\id{eps}\!:\id{infinity}\: \kw{else}\!: y/x \kw{fi}$$ \newpage \section{Traditional labels and annotations}\label{sec:trad-labels} @@ -3788,14 +2778,14 @@ annotations in the newfangled (but better) world of "lualatex" and the \noindent \MP\ does not draw text directly; but it provides two different mechanisms to -turn some text into a \<picture>, which can then be treated like any other; +turn some text into a \<picture>, which can then be treated like any other; saved as a variable, drawn directly, or transformed in some way with a scaling, a reflection, or a rotation. The first mechanism is described below, -the other in §\ref{btex}. +the second in §\ref{btex}. \subsection{Simple strings in PostScript fonts with \texttt{infont}}\label{infont} -The first mechanism is the primitive binary operation "infont". As explained in +The first mechanism is the primitive binary operation \mpl{infont}. As explained in section~8.3 of the \MP\ manual, it takes two strings as arguments: the left hand argument is the string of text to be printed; the right hand argument is the name of the font to use; and the result is a "picture" primary.\vadjust{ @@ -3804,7 +2794,7 @@ the font to use; and the result is a "picture" primary.\vadjust{ To find the name of a suitable font, you have to consult your local "psfonts.map" file, and probably the PSNFSS documentation. Here are a few of the many fonts available on my local \TeX\ installation; the name -to use with "infont" is in the first column. +to use with \mpl{infont} is in the first column. $$\includegraphics{trad-font-samples}$$ The text example in the first line of this table was produced with @@ -3840,7 +2830,7 @@ one of these: the numeric expression is rounded to the nearest integer modulo 256. - \item Use \mpl{decimal} to get a string representing + \item Use \mpl{decimal} to get a string representing the value of a numeric expression. \item Apply \mpl{str} to any suffix (and hence to any variable). You get back a @@ -3858,22 +2848,20 @@ one of these: \end{itemize} \newpage -\subsubsection{Character sets used by \texttt{infont} to set -text}\label{sec:charsets} +\subsubsection{Character sets used by \texttt{infont} to set text}\label{sec:charsets} Standard \MP\ is configured to accept as input only space and the usual 94 visible ASCII characters (that is the characters numbered 32 to 126 in the tables at the -right), but you can use any 8-bit characters as the payload of a string. -However, plain \MP\ is set by default to use "cmr10", the familiar Computer Modern typeface +right), but you can use any 8-bit characters as the payload of a string. However, +plain \MP\ is set by default to use "cmr10", the familiar Computer Modern typeface developed by Knuth for \TeX, and unfortunately, this is encoded using the \TeX\ text -font encoding (also known as `OT1', and as shown in the first table in Appendix~F of the {\sl \TeX book}). -\mpic{-108pt}{trad-font-tables} -From the point of -view of using "infont" to make simple labels, this means that the characters for -space and seven other characters ("< > \ _ { | }") are in the wrong place. -You are likely to notice this first if you try to set a label with two words; the -space will come out as a small diagonal stroke accent that is used in plain \TeX\ -to make the characters Å and Å‚, used in Polish and other Slavic languages. +font encoding (also known as `OT1', and as shown in the first table in Appendix~F of +the {\sl \TeX book}). \mpic{-108pt}{trad-font-tables} From the point of view of +using \mpl{infont} to make simple labels, this means that the characters for space +and seven other characters ("< > \ _ { | }") are in the wrong place. You are likely +to notice this first if you try to set a label with two words; the space will come +out as a small diagonal stroke accent that is used in plain \TeX\ to make the +characters Å and Å‚, used in Polish and other Slavic languages. To fix this you should change the default font at the start of your program: \begin{code} @@ -3887,16 +2875,16 @@ arrangement or "8r" to get the arrangement shown in the lower table. Choosing a font with one of these encodings means that if you use Windows code page 1252 or ISO Latin 1 as the encoding for your text editor, you can create labels with -accented characters using "infont" and without resorting to "btex" \dots\ "etex". +accented characters using \mpl{infont} and without resorting to \mpl{btex ... etex}. But if you are using UTF-8 characters (as many of us are now), then you have to do -some extra work to get them printed correctly with "infont". A solution is shown on +some extra work to get them printed correctly with \mpl{infont}. A solution is shown on the next page. -In the normal course of labelling a drawing, it is always possible to -use "btex" \dots\ "etex" to produce your accented characters as discussed in section -\ref{btex} below; but it may be that you are using \MP\ to represent data and labels -supplied from some other program or a website. In this case it can be useful to be -able to work with at least a subset of UTF-8 input. +When labelling a drawing, it is always possible to use \mpl{btex ... etex} to +produce your accented characters as discussed in section \ref{btex} below; but it +may be that you are using \MP\ to represent data and labels supplied from some other +program or a website. In this case it can be useful to be able to work with at +least a subset of UTF-8 input. This is discussed in the next section. \newpage \subsubsection{Mapping a subset of UTF-8 for \texttt{infont}} @@ -3914,7 +2902,7 @@ UTF-8.\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip -9.5pt\parindent 0pt then pick the appropriate character in your encoding with "char". But your output is still, of course, limited to the 256 characters in your encoded font. -\item If you get tired of writing "decode", you could define a short cut with a +\item If you get tired of typing "decode", you could define a short cut with a shorter name. You could even write it as a primary without parentheses like this: \begin{code} @@ -3922,53 +2910,30 @@ def U primary s = if string s: decode(s) fi enddef; \end{code} which would let you write: \begin{code} -label.rt(U"café à la möde", (x,y)); +label.rt(U"café à la crème", (x,y)); \end{code} -\item However, there's no point in making any of this too elaborate. If you - really want proper Unicode support you should use \MP\ with Lua\TeX. (See +\item \red{However, there's no point in making any of this too elaborate}. If you + really want proper Unicode support you should use \MP\ with Lua\TeX. (See below in §\ref{sec:neo-labels}). \vss}} -\begin{code}[xrightmargin=-10pt] -vardef decode(expr given) = - save a,i,s,out; string s, out; numeric a, i; - out = ""; i=0; - forever: - i := i+1; s := substring (i-1,i) of given; a := ASCII s; - if a < 128: - elseif a = 194: - i := i+1; s := substring (i-1,i) of given; - elseif a = 195: - i := i+1; s := char (64 + ASCII substring (i-1,i) of given); - else: - s := "?"; - fi - out := out & s; - exitif i >= length given; - endfor - out -enddef; -\end{code} -Use it with "infont" like this: \verb|decode("café") infont "ptmr8r"| to produce a -normal "picture" that can be passed to \mpl{draw} or saved as -usual.\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip -9.5pt -\noindent The fragment on the left produces: -$$\includegraphics{utf8}$$ +\mpexternal[firstline=6,lastline=23,xrightmargin=-10pt]{trad-utf8.mp} +\noindent +Use it with \mpl{infont} like this: ‘\mpl{decode("café") infont "ptmr8r"}’ +to produce a normal \<picture> that can be passed to \mpl{draw} or saved as +usual.\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip -9.5pt\noindent +The fragment on the left produces: +$$\includegraphics{trad-utf8}$$ The \texttt{label} macro automatically calls \texttt{infont} with the current value -of \texttt{defaultfont}; notice how it also adds some extra space. +of \texttt{defaultfont}; notice how it also adds \mpl{labeloffset} space. \vss}} -\begin{code} -draw "café noir £2.50" infont "pncr8r"; -draw decode("café noir £2.50") infont "pncr8r" shifted 12 down; -defaultfont := "pncr8r"; -label.rt("café noir £2.50", 24 down); -label.rt(decode("café noir £2.50"), 36 down); -\end{code} +\mpexternal[firstline=25,lastline=29]{trad-utf8.mp} + +\noindent Note that you can't just use \mpl{draw} with a string variable; you have to use -"infont" to turn the string into a picture. -On the other hand, "label" calls "infont" automatically, but you must explicitly set -the default font, preferably to one with an encoding that -is compatible with ISO Latin~1. +\mpl{infont} to turn the string into a picture. On the other hand, \mpl{label} calls +\mpl{infont} automatically, but you must explicitly set the default font, preferably +to one with an encoding that is compatible with ISO Latin~1. \newpage @@ -3985,18 +2950,18 @@ because the first character of the string produced by \mpl{decimal -1} is an which is the hyphen character. What we need is the mathematical minus sign instead; this is what you get with \mpl{btex $-1$ etex} of course, but that's harder to put in a loop with traditional \MP. Instead you can do this:\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize4in -$$\includegraphics{minus}$$ +$$\includegraphics{trad-minus}$$ \vss}} \begin{code} string minus_sign; minus_sign := char 143; % if you are using the texnansi encoding minus_sign := char 12; % if you are using the 8r encoding for x = -3 upto 3: - label.bot(if x<0: minus_sign & fi decimal abs(x), (x*cm, 0)); + label.bot(if x<0: minus_sign & fi decimal abs(x), (x*cm, 0)); endfor \end{code} Note that this does not work with the default encoding used in "cmr10" because -there is no minus sign available in that font. Plain TeX uses "char 0" from +there is no minus sign available in that font. Plain TeX uses \mpl{char 0} from "cmsy10". \subsubsection{Bounding boxes and clipping with \texttt{infont}} @@ -4005,28 +2970,27 @@ Once the encoding is fixed, the other two parts of a PostScript font are the fon metrics and the programs that draw the actual glyphs. The font metrics define the width of each character and provide a kerning table to adjust the space between particular pairs.\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize4in -$$\includegraphics{infont-example}$$ -}} This means that certain characters will overlap each other or stick out -beyond the bounding box of the picture produced by "infont". This is not normally a +$$\includegraphics{trad-infont-example}$$ +}} This means that certain characters will overlap each other or stick out beyond +the bounding box of the picture produced by \mpl{infont}. This is not normally a problem unless the picture happens to be at the edge of your figure. In the first -example observe how the last letter sticks out to the right; in the second a -wider baseline has been added to prevent this. -If you want this effect, but you -don't want to see the baseline, then draw it -using the colour \mpl{background}. +example observe how the last letter sticks out to the right; in the second a wider +baseline has been added to prevent this. If you want this effect, but you don't +want to see the baseline, then draw it using the colour \mpl{background}. \subsubsection{But what about the \texttt{label} command?} -As a convenience, the plain \MP\ format provides a "label" macro that automatically -turns strings into pictures for you using whatever font name is the current value of -"defaultfont" and scaled to the current value of "defaultscale".\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize4in +As a convenience, the plain \MP\ format provides a \mpl{label} macro that +automatically turns strings into pictures for you using whatever font name is the +current value of \mpl{defaultfont} and scaled to the current value of +\mpl{defaultscale}.\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize4in \noindent -The "label" macro is defined (essentially) to do this: +Plain \MP\ defines a \mpl{label} macro (approximately) like this: \begin{code} - def *label(expr s, z) = - draw s if string s: infont defaultfont - scaled defaultscale fi shifted z - enddef; +def label(expr s, z) = + draw s if string s: infont defaultfont + scaled defaultscale fi shifted z +enddef; \end{code} plus some clever code to align the label for you. }} @@ -4036,25 +3000,24 @@ plus some clever code to align the label for you. \label{infontbbox} To allow you to align a text label on a specific point, \MP\ provides five unary -operators to measure the bounding box of a picture; they are shown in -\textcolor{red!67!black}{red} in the diagram, and you can use them to measure the -width, depth, and height of a textual picture. You can also work out the location -of the baseline of the text or the x-height, provided you know how much your picture -has been shifted. -The easiest way to do this is to -measure the picture \textit{before} you shift it.\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize4in -$$\includegraphics[width=4in]{infont-annotated}$$ +operators to measure the bounding box of a picture; they are shown in \red{red} in +the diagram, and you can use them to measure the width, depth, and height of a +textual picture. You can also work out the location of the baseline of the text or +the x-height, provided you know how much your picture has been shifted. +The easiest way to do this is to measure the picture \textit{before} +you shift it.\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize4in +$$\includegraphics[width=4in]{trad-infont-annotated}$$ \vss}} \begin{code} - picture pp; pp = "proof" infont "pplri8r"; +picture pp; pp = "proof" infont "pplri8r"; \end{code} Here the picture \id{pp} is created with the origin of the text sitting at coordinates $(0,0)$; then you can get the dimensions like this \begin{code} - wd = xpart urcorner pp; - ht = ypart urcorner pp; - dp = ypart lrcorner pp; +wd = xpart urcorner pp; +ht = ypart urcorner pp; +dp = ypart lrcorner pp; \end{code} In this particular case you will find that you have $wd=20.47292$, $ht=7.19798$, and $dp=-2.60017$. The depth is negative because the descenders on the @@ -4070,7 +3033,7 @@ regardless of any ascenders or descenders. To draw your label left-aligned with origin at position $(x,y)$ you just need to use: \kw{draw} \id{pp} \kw{shifted} $(x,y)$. To draw it right-aligned, you subtract \id{wd} from the $x$-coordinate: \kw{draw} \id{pp} \kw{shifted} $(x-wd,y)$. Or to -centre it, subtract $1/2wd$. To center it vertically on the lowercase letters, +centre it, subtract $1/2\id{wd}$. To center it vertically on the lowercase letters, subtract $1/2\id{xheight}$ from the $y$-coordinate. You might of course like to wrap these adjustments up in your own convenient macro to help you maintain consistency in a diagram with many labels. @@ -4079,20 +3042,20 @@ Alternatively you can adjust the bounding box of your textual picture and then u it with "label" as normal. Assuming \id{wd} is set to the width of your picture and \id{xheight} is set correctly for the current font, then \begin{code} - setbounds pp to unitsquare xscaled wd yscaled xheight; +setbounds pp to unitsquare xscaled wd yscaled xheight; \end{code} will make the "label" alignment routines ignore any ascenders or descenders. \vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in \vss \small \noindent\llap{\nb}Beware that if the resulting label is right at the edge of your drawing then any parts of the text that stick out of the adjusted bounding box will -be clipped. See also §\ref{sec:rotated-boxes} for more on what happens if you -rotate the text.}} +be clipped.\\ +See also §\ref{sec:rotated-boxes} for more on what happens if you rotate the text.}} \newpage \subsubsection{Setting Greek letters with \texttt{infont}} \leavevmode\hbox{} -$$\includegraphics[width=0.5\textwidth]{greek-homer}$$ +$$\includegraphics[width=0.5\textwidth]{trad-greek-homer}$$ While it's technically possible to set the whole of Homer's \textsl{Iliad} using the Greek fonts available to \mpl{infont}, it's probably not a great use of time; on the other hand you might want to label parts of a diagram with Greek letters, and for single Greek @@ -4109,30 +3072,11 @@ the right, or check the table in §\ref{euler} that shows Herman Zapf's elegant Euler font, available as "eurm10". This makes a refreshing change for some diagrams.\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\kern-164pt -\begin{code} -beginfig(1); -string ab, AB; -ab = ("" for i=11 upto 23: & char i endfor - & "o" for i=24 upto 33: & char i endfor); -AB = ("AB" & char 0 & char 1 & "EZH" & char 2 & "IK" - & char 3 & "MNO" & char 4 & char 5 & "P" - & char 6 & "T" & char 7 & char 8 & "X" - & char 9 & char 10); - -draw ab infont "cmmi10"; -draw AB infont "cmmi10" shifted 12 down; -draw ab infont "eurm10" shifted 32 down; -draw AB infont "eurm10" shifted 44 down; -endfig; -\end{code} -\centerline{\includegraphics{greek-default-encoding}} +\mpexternal[firstline=5,lastline=18]{trad-greek-default-encoding.mp} +\centerline{\includegraphics{trad-greek-default-encoding}} -\begin{code} -string ab, AB; -ab = "abgdezhjiklmnoxprstufqyw"; -AB = "ABGDEZHJIKLMNOXPRSTUFQYW"; -\end{code} -\centerline{\includegraphics{greek-gfs-encoding}} +\mpexternal[firstline=6,lastline=8]{trad-greek-gfs-encoding.mp} +\centerline{\includegraphics{trad-greek-gfs-encoding}} \vss}} \medskip\noindent @@ -4143,7 +3087,7 @@ so much. However in recent versions there is no character you can use as a word space, so if you want to set Greek text rather than individual letters, see §\ref{sec:neo-otf}. -\vbox to 0pt{\centerline{\includegraphics{porson}}\vss} +\vbox to 0pt{\centerline{\includegraphics{trad-porson}}\vss} @@ -4151,14 +3095,14 @@ letters, see §\ref{sec:neo-otf}. \subsection{Setting text with \texttt{btex ... etex}}\label{btex} As soon as you need anything complicated in a label, like multiple fonts, multiple -lines, or mathematics, you will find it easier to switch from "infont" to the -"btex ... etex" mechanism that calls \TeX\ to create your textual picture. In fact +lines, or mathematics, you will find it easier to switch from \mpl{infont} to the +\mpl{btex ... etex} mechanism that calls \TeX\ to create your textual picture. In fact you might prefer to use \TeX\ for all your labels, even simple strings, for the sake of consistency. The only downside is that this mechanism is a little bit slower. -The "btex" mechanism produces a textual picture just as "infont" does with a height, +The "btex" mechanism produces a textual picture just as \mpl{infont} does with a height, width, and depth that you can measure, and adjust, as discussed in -section~\ref{infontbbox}. And again, just like "infont" you can either use \mpl{draw} +section~\ref{infontbbox}. And again, just like \mpl{infont} you can either use \mpl{draw} to place the resulting picture directly, or pass it to the "label" macro. What you need to be aware of is that \MP\ places everything you put between the @@ -4200,11 +3144,12 @@ neatly:\quad\mpl{label(btex \\strut a etex, origin);} \subsubsection{Multi-line text labels} -Another consequence of the "hbox" feature is that there is no automatic text +Another consequence of the "\hbox" feature is that there is no automatic text wrapping done for you, but again you can work round this easily because \TeX\ lets you nest a "\vbox" inside an "\hbox". This gives you proper paragraph-like wrapping but you will almost certainly need to adjust the line length, justification, and -indentation in order to get a satisfactory result \rightarrow \vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vskip -42pt\noindent +indentation in order to get a satisfactory result \rightarrow +\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vskip -64pt\noindent \begin{code} ... label(btex \vbox{\hsize 2in\parindent 0pt\raggedright @@ -4239,27 +3184,65 @@ Notice how you can still use the macro with single lines, you just get a one-lin table as it were. Note also that the definition of "\s" as given will centre each line of the text under the one above. If you want them left aligned or right aligned, omit one of the -"\hfil" commands. \mpic{-160pt}{split-labels} -The three examples from this page are typeset over here \rightarrow\break +"\hfil" commands. \mpic{-212pt}{trad-split-labels} +The three examples given above are typeset over here $\longrightarrow$\break The small red circle show the reference points and the pale blue lines the bounding boxes of the pictures that \MP\ gets back from \TeX. You can of course achieve the same effects using \LaTeX\ tabular structures, but -then you have to use the "-tex=latex" option to run -\MP. +then you have to use the "-tex=latex" option to run \MP. \smallskip\noindent \textbf{Note}: In case it's not obvious, if you want text wrapping or tabular -arrangements as discussed here, you need to use \texttt{btex ... etex} to set your -labels. There's no text wrapping with "infont". On the other hand if all of your -labels are in "infont" but you just want one extra that has two lines, you can split +arrangements as discussed here, you need to use \mpl{btex ... etex} to set your +labels. There's no text wrapping with \mpl{infont}. On the other hand if all of your +labels are done with \mpl{infont}, but you just want one extra that has two lines, you can split the text into two separate labels and position them independently. \newpage +\subsubsection{Pins and braces}\label{sec:braces} + +\textsc{In some awkward corners}, you may find that you just can't get your label in +the right place with \mpl{dotlabel} even if you adjust \mpl{labeloffset}. In these +cases there are two simple techniques you can use. First, you could separate +drawing the dot from placing the label; given a point $P$ you can try:\mpic{0pt}{trad-callout} +\mpexternal[firstline=9,lastline=10]{trad-callout.mp} +\noindent +Using \mpl{dotlabeldiam} ensures that your dots match any others done with +\mpl{dotlabel}. +Secondly, if that's not enough, use a temporary pair to create a call out line: +\mpexternal[firstline=11,lastline=15]{trad-callout.mp} +\noindent +If you want to do this sort of thing often, then it might be worth making a macro; +it is hard to write anything completely general, but see §\ref{sec:extimage} for an +example. + +\enlargethispage{24pt} + +\vfill\noindent +\textsc{You might also want} to mark a straight line between two points. +\vadjust{\moveright5.3in\vbox to 0pt{\hsize 4.2in\vspace{-2\baselineskip} +\smallmpexternal[firstline=6,lastline=19]{trad-braces.mp} +\smallmpexternal[firstline=28,lastline=28]{trad-braces.mp} +\noindent +Note that, as well as drawing the braces, the macro uses the grouping provided by \mpl{vardef} to return the +mid point so that you can put a label next to it. +\vss}} +The simplest way to do this is just to use \mpl{drawdblarrow} on a copy of your straight +path shifted to one side, like so: +\begin{code} +drawdblarrow (z1--z2) shifted (12 up rotated angle (z2-z1)); +\end{code} +If you combine this with temporarily setting \mpl{ahangle:=180}, you get the simple +dimension line shown in blue. +$$\includegraphics{trad-braces}$$ +The red braces are a more complex variation on this theme $\longrightarrow$ + +\newpage \subsubsection{Dynamic labels}\label{sec:old-and-dynamic} If you are a maven of programming language syntax you may have noticed that -"btex ... etex" fits into the type system that \MP\ inherits from \MF\ as a "picture" and +\mpl{btex ... etex} fits into the type system that \MP\ inherits from \MF\ as a "picture" and not as a "string". Effectively, "btex" and "etex" act as a special pair of quotation marks that create a picture; however the contents are used verbatim, so that the whole construction is a syntactical atom. This means that you \textbf{cannot} write @@ -4271,9 +3254,9 @@ endfor \end{code} Given this input \MP\ would attempt to get \TeX\ to typeset -\begin{code} +\begin{texcode} \hbox{"$p_" & decimal i & "$"} -\end{code} +\end{texcode} which would probably result in a `Misplaced alignment tab character' error. To get round this problem, \MP\ provides a general mechanism to write out a @@ -4298,22 +3281,11 @@ The example on the right shows how to speed things up, by using the same file fo all the labels and only writing it once. The "write" command is a \MP\ primitive, and "EOF" is defined in "plain.mp".% \vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize4in\noindent -\begin{code} -path c; c = fullcircle scaled 100; draw c withcolor .67 red; -for i=0 upto 7: - fill fullcircle scaled 3 shifted point i of c; - z[i] = point i of c scaled 1.15; - write "label(btex $p_" & decimal i & "$ etex,(" - & decimal x[i] & "," & decimal y[i] - & "));" to ".mplabels"; -endfor -write EOF to ".mplabels"; -input ".mplabels"; -\end{code} +\mpexternal[firstline=7,lastline=16]{trad-dynamic-labels.mp} $$ -\includegraphics{dynamic-labels} +\includegraphics{trad-dynamic-labels} $$ -Note that you can't use "decimal" on a "pair" variable, but you can save the pair +Note that you can't use \mpl{decimal} on a \<pair> variable, but you can save the pair as a "z"-variable and then use the "x" and "y" syntax. The scaling trick used here only works because "c" is centred on the origin. If "c" were drawn elsewhere, you would have to write: @@ -4322,10 +3294,11 @@ would have to write: scaled 1.15 shifted center c ... \end{code} +\vskip -12pt }} \newpage -\subsection{Matching fonts}\label{sec:fonts} +\subsubsection{Matching fonts}\label{sec:fonts} Despite the apparent restriction of using plain \TeX\ it is almost always possible to match the font and format of an enclosing \LaTeX\ document. @@ -4386,22 +3359,17 @@ are limited to whatever font packages you have that work with the traditional \ref{sec:neo-labels}. \newpage -\subsection{Setting verbatim listings}\label{sec:verbatim} +\subsubsection{Setting verbatim listings}\label{sec:verbatim} -\textsc{There is a good chance} that you will never need to set a verbatim +\textsc{There is a good chance} that you will never need to set a verbatim listing in a \MP\ drawing, but if you do there are a couple of things to think about. The issue about setting text verbatim with \TeX\ is that turning off the control characters can be tricky, so if you have text for a label with characters that are special in \TeX\ like the backslash or the underscore, then the simplest thing to do is to avoid \TeX\ completely and use \mpl{infont} instead. -\mpic{-36pt}{verbatim-with-infont} -\begin{code} -string s; s = "\TeX\ sets maths like this $e=mc^2$"; -draw ("1. " & s) infont defaultfont; -draw ("2. " & s) infont "texnansi-lmr10" shifted 20 down; -draw ("3. " & s) infont "cmtt10" shifted 40 down; -draw ("4. " & s) infont "texnansi-lmtt10" shifted 60 down; -\end{code} +\mpic{-48pt}{trad-verbatim-with-infont} +\mpexternal[firstline=6,lastline=10]{trad-verbatim-with-infont.mp} +\noindent But as you can see, (1) this is a bit of a disaster with the default font "cmr10" because it does not have all the glyphs in the usual ASCII positions (as noted above §\ref{sec:charsets}). The solution is to use the version of the font @@ -4409,89 +3377,20 @@ with the "texnansi" encoding (2), but you probably want it in the monofont (3) a as you can see "cmtt10" has the “visible space†character instead of a regular space. If this is not what you want then use the alternative encoding (4). +\vfill If you want more than this, then you really need to use \LaTeX\ to process the label, as discussed in §\ref{sec:fonts}, and load the appropriate preamble. \rightarrowfill\break -\vadjust{\moveright5.5in\vbox to 0pt{\vskip -72pt\begin{smallcode} -prologues := 3; outputtemplate := "%j.eps"; -verbatimtex -\documentclass{article} -\usepackage{listings} -\newcommand\mpstyle{\lstset{language=Metapost, basicstyle=\ttfamily, -columns=fullflexible, keepspaces=true, showstringspaces=false}} -\lstnewenvironment{code}[1][]{\mpstyle\lstset{#1}}{} -\begin{document} -etex -beginfig(1); -picture P; -P = thelabel(btex \vbox{\begin{code} - % special operators - vardef incr suffix $ = $:=$+1; $ enddef; - vardef decr suffix $ = $:=$-1; $ enddef; - - def reflectedabout(expr w,z) = % reflects about the line w..z - transformed begingroup transform T_; - w transformed T_ = w; - z transformed T_ = z; - xxpart T_ = -yypart T_; - xypart T_ = yxpart T_; % T_ is a reflection - T_ endgroup enddef; -\end{code}} etex, origin); -fill bbox P withcolor (1,1,31/32); draw P; draw bbox P; -endfig; end. -\end{smallcode}\vss}} +\vadjust{\moveright5.5in\vbox to 0pt{\vskip -10\baselineskip +\smallmpexternal{trad-verbatim-listing.mp} +\noindent\hey Compile this with "mpost -tex=latex" and use "epstopdf" to make a PDF. +\vss}} +$$\includegraphics[width=0.9\textwidth]{trad-verbatim-listing}$$ -\bigskip -$$\includegraphics[width=0.9\textwidth]{verbatim-listing}$$ - - - -%% \subsubsection{Getting full access to your system fonts} -%% -%% If you want full access to all of your system fonts you can -%% approach the problem the other way round and use one of the various means to include -%% \MP\ graphics as part of your \LaTeX\ source code. These include "gmp" for -%% pdf\LaTeX, "luamplib" for lua\LaTeX, and the whole Context system. The great -%% advantage of these systems is that all of your \MP\ labels directly inherit the -%% environment of the parent document, and give you access to all your system fonts and -%% full Unicode support -- the only disadvantages are that it's not so fast or simple as plain \MP\ -%% and you have to compile every graphic everytime you compile the document. It is of course always possible to -%% use these systems to produce standalone PDF graphics that you can then include in a -%% more conventional \TeX\ document. The example on the right shows how; in this case -%% the text uses the fonts set in the \LaTeX\ preamble.\vadjust{\moveright5.5in\vbox to -%% 0pt{\hsize 4in\vss\noindent -%% Here is a version of the Lua logo, with a Unicode accent for show. -%% $$\includegraphics[scale=0.7]{lulu.pdf}$$ -%% produced with "luamplib": -%% \begin{smallcode} -%% \documentclass[margin=5mm]{standalone} -%% \usepackage{fontspec} -%% \setmainfont{TeX Gyre Heros} -%% \usepackage{luamplib} -%% \begin{document} -%% \begin{mplibcode} -%% beginfig(1); -%% color lemon, midnight; lemon = (1,1,1/2); midnight = (0,0,1/2); -%% -%% fill unitsquare shifted -(1/2,1/2) scaled 4cm withcolor lemon; -%% fill fullcircle scaled 3cm withcolor midnight; -%% draw fullcircle scaled 3.7cm dashed evenly scaled 2 withcolor .5 white; -%% -%% fill fullcircle scaled 8mm shifted (0.7cm,0.7cm) withcolor white; -%% fill fullcircle scaled 8mm shifted (1.4cm,1.4cm) withcolor midnight; -%% -%% label.bot(btex Luã etex scaled 2.8,origin) withcolor white; -%% endfig; -%% \end{mplibcode} -%% \end{document} -%% \end{smallcode} -%% }} - - -\newpage -\section{Modern labels and annotations}\label{sec:neo-labels} +\newpage +\section{Modern labels, annotations, and other goodies}\label{sec:neo-labels} This section is a re-working of the previous section, that attempts to show how much -nicer it is to handle labels in the new world of "luamplib". If this is all new +nicer it is to work in the new-fangled world of "luamplib". If this is all new to you, you probably should start by doing "texdoc luamplib" on your system and reading the documentation provided with the package. In order to use these newfangled facilities you need to create your \MP\ diagrams inside a \TeX-wrapper @@ -4500,8 +3399,8 @@ as explained above in §\ref{sec:sa-lua-flow}. \medskip\noindent The first thing to say is that everything in the preceding section will continue to work more or less the same when you use "luamplib" with Lua\LaTeX. -It is designed to be backwards-compatible, so that existing \MP\ programs using "infont" and -"btex" \dots\ "etex" will continue to work without change. The only differences are: +It is designed to be backwards-compatible, so that existing \MP\ programs using \mpl{infont} and +\mpl{btex ... etex} will continue to work without change. The only differences are: that the "TEX()" macro is re-implemented with internal library functions so that it no longer uses temporary files, and is therefore very much faster; and it is easier to integrate your drawings into \LaTeX\ because you no longer need to muck @@ -4516,27 +3415,7 @@ So the example code shown on the right,\vadjust{\moveright5.5in\vbox to 0pt{\hsi \begin{mplibcode} \end{texcode} \vskip-\baselineskip -\begin{smallcode} - beginfig(1); - for x = 0 upto 1: - draw (80x,16) -- (80x, -68) withcolor 3/4[red, white]; - endfor - for y = 0 upto 3: - draw (0, -20y) -- (160, -20y) withcolor 3/4[red, white]; - endfor - - string s; s = "Hand gloves"; - draw s infont defaultfont shifted (0, 0); - draw s infont "phvr8r" shifted (0, -20); - draw TEX(s) shifted (0, -40); - draw btex Hand gloves etex shifted (0, -60); - - dotlabel.urt(s, (80, 0)); - dotlabel.urt(s infont "phvr8r", (80, -20)); - dotlabel.urt(TEX(s), (80, -40)); - dotlabel.urt(btex Hand gloves etex, (80, -60)); - endfig; -\end{smallcode} +\smallmpexternal[firstline=7,lastline=25]{neo-labels.mp} \vskip-\baselineskip \begin{texcode} \end{mplibcode} @@ -4547,13 +3426,12 @@ $$\includegraphics{neo-labels.pdf}$$ Note that "defaultfont" is still "cmr10" with the encoding that has the small stroke (that plain \TeX\ uses for the \L\ character) instead of a space, and that you can still use PostScript fonts like "phvr8r". But also notice that the "TEX()" macro -and the "btex" \dots\ "etex" construction have picked up the font set by the \LaTeX\ +and the \mpl{btex ... etex} construction have picked up the font set by the \LaTeX\ wrapper. As you can see they produce exactly the same output; "TEX()" is generally more useful because you can pass a primary string variable as an argument, which makes it easier to construct dynamic labels. "TEX()" also has the synonym -"textext()" for compatibility with ConTexT. You can use either name, as you prefer. - -\smallskip\noindent +"textext()" for compatibility with ConTexT. You can use either name, as you +prefer.\\ But this isn't the clever bit\dots \clearpage @@ -4567,7 +3445,7 @@ to the preamble: \mplibtextextlabel{enable} \end{texcode} If you add this line to the example from the previous -page,\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip-80pt +page,\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip-78pt \begin{texcode} \documentclass[border=5mm]{standalone} \usepackage{fontspec} @@ -4578,27 +3456,7 @@ page,\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip-80pt \begin{mplibcode} \end{texcode} \vskip-\baselineskip -\begin{smallcode} - beginfig(1); - for x = 0 upto 1: - draw (80x,16) -- (80x, -68) withcolor 3/4[red, white]; - endfor - for y = 0 upto 3: - draw (0, -20y) -- (160, -20y) withcolor 3/4[red, white]; - endfor - - string s; s = "Hand gloves"; - draw s infont defaultfont shifted (0, 0)0 - draw s infont "phvr8r" shifted (0, -20); - draw TEX(s) shifted (0, -40); - draw btex Hand gloves etex shifted (0, -60); - - dotlabel.urt(s, (80, 0)); - dotlabel.urt(s infont "phvr8r", (80, -20)); - dotlabel.urt(TEX(s), (80, -40)); - dotlabel.urt(btex Hand gloves etex, (80, -60)); - endfig; -\end{smallcode} +\smallmpexternal[firstline=8,lastline=26]{neo-labels-tte.mp} \vskip-\baselineskip \begin{texcode} \end{mplibcode} @@ -4643,23 +3501,15 @@ these new facilities with plain Lua\TeX, but this chapter is about using them wi Lua\LaTeX, and in particular it assumes some familiarity with the packages "fontspec" and "unicode-math" that provide complete support for Unicode and OTF fonts; you need this familiarity in order to use "luamplib" properly. -\mpic{1cm}{unicode} +\mpic{1cm}{neo-unicode} You also need an editor that will handle Unicode. \MP\ still restricts you to using -printable ASCII in your source code, except within a string literal or a "btex" -\dots\ "etex" picture literal. So it becomes very easy to write this sort of label: -\begin{smallcode} -label("café noir £2.50", origin); -\end{smallcode} +printable ASCII in your source code, but you can put whatever you want inside a string literal or a "btex" +\dots\ "etex" picture literal. So it becomes very easy to produce this sort of label: +\smallmpexternal[firstline=8,lastline=8]{neo-unicode.mp} +\noindent or even whole paragraphs that use Unicode: -\begin{smallcode} -label(btex \vbox{\hsize 4in - Nous étions à l'Étude, quand le Proviseur entra, suivi d'un - \textit{nouveau} habillé en bourgeois et d'un garçon de classe - qui portait un grand pupitre. Ceux qui dormaient se réveillèrent, - et chacun se leva comme surpris dans son travail. -\par} etex, 40 down); -\end{smallcode} +\smallmpexternal[firstline=9,lastline=14]{neo-unicode.mp} But you also need a font that actually supports the Unicode characters you use. The default Latin Modern font used by Lua\LaTeX\ has a good range for English and most European languages, but is a bit lacking in (say) polytonic Greek. So you will @@ -4679,7 +3529,7 @@ label(btex \vbox{\polytonic\halign{#\hfil\cr \end{smallcode} will produce the first few lines of the Iliad (just in case you wanted them). Essentially if you can produce something in \LaTeX, you can produce exactly the same -in \MP\ using "luamplib" (but see also §\ref{sec:verbatim}). +in \MP\ using "luamplib". \newpage @@ -4688,39 +3538,28 @@ in \MP\ using "luamplib" (but see also §\ref{sec:verbatim}). It is a rule of syntax in \MP\ that a string token has to be given all on one line. So if you have very long labels, or paragraphs of text, then you have to split them up into separate shorter string tokens: -\begin{code} -label("\vbox{\hsize 4in It is a truth universally acknowledged," - & " that a single man in possession of a good fortune," - & " must be in want of a wife.\par}", origin); -\end{code} +\mpexternal[firstline=7,lastline=9]{neo-multi-line-labels.mp} +\noindent taking care to include the necessary spaces, which can get fiddly. -\mpic{-15mm}{multi-line-labels} +\mpic{-15mm}{neo-multi-line-labels} -But this is where the "btex" \dots\ "etex" construction comes into play, even with +But this is where the \mpl{btex ... etex} construction comes into play, even with "luamplib". As we saw in the preceding section the construction fits into the \MP\ syntax scheme as a special pair of quotation marks that produces a \<picture>. -Unlike regular string token, a "btex" \dots\ "etex" picture token can span several +Unlike regular string token, a \mpl{btex ... etex} picture token can span several lines of source code, so you can (more easily) write long \TeX\ labels like this: -\begin{code} -label(btex \vbox{\hsize 4in - It is a truth universally acknowledged, - that a single man in possession of a good fortune, - must be in want of a wife. - \par} etex, 128 down); -\end{code} +\mpexternal[firstline=10,lastline=13]{neo-multi-line-labels.mp} +\noindent Thanks to the backward compatibility of the implementation, this works very well even when you have "mplibtextextlabel" enabled. -You also have full access to your \LaTeX\ environment, so you can get tables in the -same way in \MP\ using environments like "tabular": -\begin{code} -label(btex - \begin{tabular}{c} - A way to get simple\\ - two line labels - \end{tabular} etex, 256 down); -\end{code} -But recall that whatever you ask the \mpl{TEX()} macro to typeset like this is going into +\vfill +\noindent +You also have comprehensive access to your \LaTeX\ environment, so with "luamplib" +you can get tables in in \MP\ using environments like "tabular": +\mpexternal[firstline=14,lastline=17]{neo-multi-line-labels.mp} + +But keep in mind that whatever you ask the \mpl{TEX()} macro to typeset is going into a restricted horizontal mode box; so don't try to use floating environments like "table" or "figure". And if you want automatic paragraph wrapping, you will have to wrap your text in a suitable "\vbox", as shown above. @@ -4731,11 +3570,10 @@ Because the \mpl{TEX()} macro typesets everything in restricted horizontal mode, cannot use "$$ .. $$" to create display maths directly. This is not a \TeX\ \textit{v} \LaTeX\ issue, it is just that for compatibility with plain \MP\ (and common sense), the designers of "luamplib" chose to typeset labels into -horizontal-mode boxes This is usually what you want. If you prefer -large integral -operators (etc) in your labels, -then you should either add -"\displaystyle" at the beginning of your formula $\longrightarrow$\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent +horizontal-mode boxes This is usually what you want. If you prefer large integral +operators (etc) in your labels, then you should either add "\displaystyle" at the +beginning of your formula \rightarrowfill\break +\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4in\vss\noindent \begin{code} ... label("$\displaystyle \int_0^t 3x^2\, dx$", z0); @@ -4743,22 +3581,17 @@ label("$\displaystyle \int_0^t 3x^2\, dx$", z0); label("\vbox{\hsize 2in $$\int_0^t 3x^2\, dx$$}", z1); ... \end{code} -}} -\\ +\vskip-1.5\baselineskip}}% or wrap the formula in a "\vbox" with a suitable "\hsize". Using "\displaystyle" is probably simpler. -\subsection{Typographical minus signs and other dynamic labels} +\subsection{Typographical minus signs and other dynamic labels}\label{sec:new-dynamic} This is really easy with "mplibtextextlabel" enabled, because we can assemble a string -on the fly using standard \MP\ syntax:\mpic{0pt}{simple-number-line} -\begin{code} -draw (left--right) scaled 2in withcolor 2/3 red; -for i=-4 upto 4: - dotlabel.top("$" & decimal i & "$", (32i, 0)); -endfor -\end{code} +on the fly using standard \MP\ syntax:\mpic{0pt}{neo-simple-number-line} +\mpexternal[firstline=8,lastline=11]{neo-simple-number-line.mp} +\noindent The normal operator precedence rules ensure that the string argument to \mpl{dotlabel} is assembled before it is passed to the \mpl{TEX()} macro. The individual parts of the string you assemble do not have to be @@ -4766,31 +3599,24 @@ valid bits of \TeX\ in themselves; they only have to make sense once they are actually passed to the macro. With "luamplib" there are no slow external files being used, so the complexities used above [§\ref{sec:old-and-dynamic}] to label points around a -circle can be simplified without sacrificing speed:\mpic{-80pt}{simple-circle-labels} -\begin{code} -path C; C = fullcircle scaled 100; draw C withcolor 2/3 red; -for i=0 upto 11: - drawdot point 2/3 i of C withpen pencircle scaled dotlabeldiam; - label("$p_{" & decimal i & "}$", point 2/3 i of C scaled 1.17); -endfor -\end{code} +circle can be simplified without sacrificing speed:\mpic{-80pt}{neo-simple-circle-labels} +\mpexternal[firstline=7,lastline=12]{neo-simple-circle-labels.mp} + +\smallskip\noindent\nb Note that you can't do this string concatenation with \mpl{btex ... etex}; +although these operators might appear to be special quotation marks, they produce +\<picture> values, and in this context \mpl{&} only works with \<string> values. -\smallskip\noindent\nb But note that you can't do this string concatenation with "btex" \dots\ "etex"; -although they might appear to be special quotation marks, they produce a -\<picture>, and \mpl{&} only works with strings or paths. \newpage \subsection{Drawing on an external image}\label{sec:extimage} -One of the limitations of the way that plain "mpost" uses \TeX\ is that -any "\special" commands are removed from the intermediate file that \MP\ translates -into a \<picture> variable. Hence, in particular, you cannot use -"\includegraphics" in a \TeX\ label. Fortunately, "luamplib" removes this -limitation, so it is now possible to annotate images using the full array of \MP\ -tools. -$$\includegraphics[width=360pt]{marked-up-photo}$$ -The source is shown on the right. -\vadjust{\moveright5.5in\vbox to 0pt{\vskip-3.75in\hsize 4in\raggedright\noindent +A limitation of plain "mpost"'s use of \TeX\ is that +"\special" commands are removed from the ".dvi" file that is made +into a \<picture> variable. So, in particular, you can’t use +"\includegraphics" in a \TeX\ label. But "luamplib" removes this +limitation, so you can annotate images using the full array of \MP\ +tools, as shown here \rlap{$\longrightarrow$}% +\vadjust{\moveright5.25in\vbox to 0pt{\vskip-60pt\hsize 4.5in\raggedright\noindent \begin{texcode} \documentclass[border=1mm]{standalone} \usepackage{luamplib} @@ -4800,43 +3626,69 @@ The source is shown on the right. \begin{document} \begin{mplibcode} \end{texcode} -\begin{smallcode} -beginfig(1); -draw btex \includegraphics[width=5in]{glenshiel.jpg} etex; -if false: -for i=1 upto 36: - draw (origin -- 180 up) shifted (10i, 0) - withcolor if i mod 10 = 0: red else: 1/2 fi; -endfor -for i=1 upto 18: - draw (origin -- 360 right) shifted (0, 10i) - withcolor if i mod 10 = 0: red else: 1/2 fi; -endfor -fi -vardef callout@#(expr t, p, o) = - save T; picture T; T = thelabel.@#(t, p+o); - draw T; drawarrow p+o -- p cutbefore bbox T; -enddef; -ahangle := 20; ahlength := 2; -drawoptions(withpen pencircle scaled 1/4 withcolor 1/2 blue); -callout.top("Sgurr na Ciste Dubhe", (80, 96), (-10, 20)); -callout.top("Sgurr nan Spainteach", (100, 91), (6, 12)); -label.top("\tiny Cuillin Ridge, Isle of Skye", (140, 81)); -label.top("Sgurr na Carnach", (190, 90)); -label.top("Sgurr Fhuaran", (282, 94)); -label.bot("\itshape View looking west ...", - point 5/2 of bbox currentpicture shifted 4 down); -endfig; -\end{smallcode} -\begin{texcode} -\end{mplibcode} -\end{document} -\end{texcode} +\vskip -\baselineskip +\smallmpexternal[firstline=8,lastline=24,xleftmargin=0pt,xrightmargin=-10pt]{neo-marked-up-photo.mp} +\small +If you uncomment the \mpl{\% input neo-reference-grid} line, so that the +code on \llap{$\leftarrow$\;}the left is included, you get this automatically-sized grid superimposed: +$$\includegraphics[width=3in]{neo-marked-up-photo-grid}$$ +The grid makes it easier to find the coordinates for your annotations. \vss}} -The two loops commented out with \mpl{if false:} will add a grid -on top of the photo like this: -$$\includegraphics[width=200pt]{marked-up-photo-with-grid}$$ -This makes it easier to find the appropriate coordinates for your annotations. + +\medskip\noindent +\includegraphics[width=\textwidth]{neo-marked-up-photo} + +\vfill\noindent +Here is a general purpose reference grid routine: +\smallmpexternal[firstline=3,lastline=16,xleftmargin=0pt,xrightmargin=-36pt]{neo-reference-grid.mp} + +\newpage +\subsection{Using PDF transparency}\label{sec:transparent} + +\textsc{Another limitation} of the plain "mpost" compiler is that it does not +support any transparent colours. However, if you use the "luamplib" package with +"lualatex" you get access to the PDF 1.4 transparency functions. Currently (2024) there +is little documentation for this support and no ‘official’ macro for it, but you can +add your own like this: +\begin{code} +def withalpha expr a = + withprescript "tr_alternative=2" + withprescript "tr_transparency=" & decimal a +enddef; +\end{code} +and then use it like this, adding \mpl{withalpha} after the +colour specification:\mpic{-144pt}{new-fangled-transparency} +\begin{code} +path r, g, b; +r = fullcircle scaled 40 shifted 10 up; +g = r rotated 120; b = g rotated 120; + +numeric a; a = 0.5; +fill r withcolor 1/2[white, red] withalpha a; +fill g withcolor 1/2[white, green] withalpha a; +fill b withcolor 1/2[white, blue] withalpha a; +draw r withcolor 1/2; +draw g withcolor 1/2; +draw b withcolor 1/2; +\end{code} + +\smallskip\noindent +The effect of changing the alpha value is shown on the right. The magic variable +names "tr_transparency" and "tr_alternative" are only understood by the "luamplib" code, +plain "mpost" simply ignores them. \textit{Note that since these are not documented anywhere +except in the source code, they might change in future}. +You can see from the figure that "tr_transparency" +controls the alpha value, but the other variable is slightly more mysterious --- +"tr_alternative" appears to control the PDF blending mode. A value of 1 seems to apply PDF +‘normal’ mode, which makes colours completely opaque with when alpha is 1; a value +of 2, as used here, seems to apply PDF ‘multiply’ mode which blends all colours +evenly, so that the order that you fill overlaps does not matter. This mode works +well with slightly lighter colours. + +\newpage\noindent +Here is a slightly more ambitious example, using the same \mpl{withalpha} +macro.\mpic{-12pt}{new-fangled-trilobe} +\smallmpexternal[firstline=6,lastline=43,xleftmargin=0pt,xrightmargin=-44pt]{new-fangled-trilobe.mp} \newpage \section{Working with pictures} @@ -4849,7 +3701,7 @@ of the variable is a pattern of pixels for a font, in \MP\ the contents are vect graphics commands. This section reviews some of the things you can do with a \<picture> variable — including putting one in a frame (see §\ref{sec:pictureframe}) like so\rlap{\ $\longrightarrow$} -\mpic{-96pt}{youth} +\mpic{-96pt}{pics-youth} \bigskip\noindent Plain \MP\ provides two built-in \<picture> variables: \mpl{nullpicture}, which is @@ -4915,8 +3767,8 @@ picture, you could do: \end{code} and \MP\ will add copies of $P$ with the reference points shifted to $(20,0)$, $(40,0)$, and $(60,0)$. A selection of other transformations is shown on the right $\longrightarrow$ -\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip-240pt\centerline{\includegraphics[width=4in]{twister}}\par -\centerline{\textsl{\small The reference point for each compass is the small dot in the middle.}} +\vadjust{\moveright5.5in\vbox to 0pt{\hsize4in\vskip-240pt\centerline{\includegraphics[width=4in]{pics-twister}}\par +\centerline{\textit{\small The reference point for each compass is the small dot in the middle.}} \vss}} \smallskip\noindent @@ -4960,30 +3812,11 @@ You can apply \mpl{clip} to any picture, so you might prefer to capture your pattern in \<picture> variable with \mpl{image}, apply \mpl{clip} to that, and then \mpl{draw}. This works nicely if you want to repeat the clipped image. \vadjust{\moveright 5.5in\vbox to 0pt{\hsize 4.2in \vss -\noindent\includegraphics[width=4in]{shady-circles} +\noindent +\centerline{\includegraphics{pics-shady-circles}} \medskip -\begin{smallcode} -path c, C; numeric r; r = 60; -c = fullcircle scaled 2r shifted (-r, 0); -C = fullcircle scaled 4r shifted (2r, 0); - -numeric t, u; -(t, whatever) = C intersectiontimes - C shifted (center c - center C); -(u, whatever) = c intersectiontimes (point t of C -- center c); - -path s; -s = subpath (0, u) of c -- subpath (t, 4) of C -- cycle; -for i=0 upto r: - draw (left--right) scaled 2r rotated -42 shifted (3i, 0) - withpen pencircle scaled 1/4 withcolor 2/3 blue; -endfor -clip currentpicture to s; - -draw c; draw C; -draw center c -- center C -- point t of C -- cycle; -\end{smallcode} +\mpexternal[firstline=6,lastline=27,xleftmargin=0pt]{pics-shady-circles.mp} \vskip -126pt}} You can also use this technique to fill with a gradient: just reduce the gap @@ -5009,7 +3842,7 @@ also change, but not quite in the way you might think. It turns out that the \mpl{bbox} is always a rectangle aligned to the edges of your page. Effectively, the corners are determined \textit{after} any transformation, and the \mpl{center} is strictly the intersection of the lines between opposite -corners.\mpic{-68pt}{corners} +corners.\mpic{-68pt}{pics-corners} You will notice this if you use the technique given on p.\thinspace29 of the \MP\ manual to draw a label on a coloured (or erased) background; if you have rotated the label, the @@ -5049,8 +3882,8 @@ draw P1 shifted 100 up; draw P2 shifted 100 down; Sometimes it is more convenient to use \mpl{label} to place the pictures, taking advantage of the automatic alignment provided. Note also that, unless you have -explicitly filled them with \mpl{white} colour, the blank parts of each picture are -really transparent so you can overlap them when appropriate. +explicitly or implicitly filled them with the \mpl{background} colour, the blank +parts of each picture are really transparent so you can overlap them when appropriate. \newpage \subsection{Adding a caption to the current picture} @@ -5101,7 +3934,7 @@ centered on the origin and scaled to $2 \id{bboxmargin}$. \moveright5.5in\vbox to 0pt{\hsize 4in \vss \noindent Here is an example. -$$\includegraphics[width=4in]{double-angle}$$ +$$\includegraphics[width=4in]{pics-double-angle}$$ The labels at the bottom were added like this: \begin{smallcode} label.bot("$\triangle ACD \sim \triangle ABC$", @@ -5122,30 +3955,7 @@ Consider the \<picture> with different colours and pens in the example here $\longrightarrow$ \vadjust{\moveright5.5in\vbox to 0pt{\vskip -1.5\baselineskip -\begin{smallcode} -numeric s; s = 21; -path alpha; -alpha = ((-2s, s) {right} - .. halfcircle rotated -90 scaled 2s shifted (2s, 0) - .. {left} (-2s, -s)) shifted (s*left); - -vardef overdraw(expr a, b, r, P, shade) = - linecap := butt; - undraw subpath (a+r, b-r) of P withpen pencircle scaled 2; - draw subpath (a, b) of P withcolor shade; -enddef; - -picture cb; cb = image( - draw alpha withcolor 2/3 red; - undraw alpha rotated 180 withpen pencircle scaled 2; - draw alpha rotated 180 withcolor 2/3 blue; - overdraw(0.21, 0.36, 0.02, alpha, 2/3 red); - overdraw(0.67, 0.86, 0.02, alpha, 2/3 red); - overdraw(3.4, 4.3, 0.1, alpha, 2/3 red); - overdraw(5.4, 5.6, 0.02, alpha, 2/3 red); - overdraw(5.4, 5.6, 0.02, alpha rotated 180, 2/3 blue); -); -\end{smallcode} +\smallmpexternal[firstline=8,lastline=29]{pics-draw-picture.mp} \vskip 48pt\noindent \begin{minipage}{4in} @@ -5156,7 +3966,7 @@ picture cb; cb = image( \item Examples 2, 3, and 4 show what happens if you change the pen, or the colour, or both. - \item Example 5 shows you how to make a bagel in \MP. + \item Example 5 shows you how to make a pretzel in \MP. \item Example 6 shows you the slightly tricky syntax to extract the paths, pens, and colours from the \<picture> and adjust them as needed. @@ -5165,50 +3975,31 @@ picture cb; cb = image( \vss}} With this captured in a \<picture> variable, you can \mpl{draw} it with different colours and pens to obtain a variety of effects: -$$\includegraphics[width=\textwidth]{draw-picture.pdf}$$ +$$\includegraphics[width=\textwidth]{pics-draw-picture}$$ The picture is supposed to represent a fancy knot (a “Carrick bendâ€), and to show the red and blue strands crossing each other. The \mpl{overdraw} macro tries to do -this by undrawing with a thick pen, then redrawing the upper strand on top. +this by using \mpl{undraw} with a thick pen, then drawing the upper strand on top. \newpage -\subsection{Simulating transparency} +\subsection{Simulating transparency with pictures}\label{sec:simulated_alpha} -Filling with transparent colour can sometimes be a very effective graphic technique, but the -underlying technical implementation is often dauntingly complex. Plain \MP\ -provides no colour model that directly supports transparency for any output format, -so if you need it you will have to resort to layering and managing the colour -blending yourself. This page presents an example of the basic technique, that can -be adapted to more general purpose macros as required. The technique is included in -this section, because it involves more manipulation of \<picture> variables. +Filling with transparent colour can sometimes be a very effective graphic technique, +but plain \MP\ provides no colour model that directly supports transparency for any +output format. If you are using "mpost", you will have to resort to layering and +managing the colour blending yourself. This section presents an example of the +basic technique, that could be adapted to more general purpose macros as +required.\\ +\hey \red{But, the technique is quite laborious so you might prefer to switch to "luamplib" +which provides support for the PDF transparency model, as discussed in +§\ref{sec:transparent}}. \vadjust{\moveright5.5in\vbox to 0pt{\vskip -128pt -$$\includegraphics[width=3in]{fake-transparency}$$ +$$\includegraphics[width=3in]{pics-fake-transparency}$$ + Omitting the simple grid, this drawing was produced like this: -\begin{smallcode} -% Large A -label.urt("A" infont defaultfont scaled 8, origin) withcolor 1/4 green; -% An arbitrary shape -path shape; shape = (superellipse(right, up, left, down, 0.81)) - shifted 1/2 right scaled 30 rotated 30; -% Parameters -alpha = 5/8; % alpha: 0=invisible, 1=opaque -color filler; filler = .95[red,white]; -picture fg, bg; -bg = currentpicture; % capture the current drawing -fg = image( - for e within bg: % redraw everything in blended color - draw e withcolor alpha[colorpart e, filler]; - endfor % and add some decorations - draw shape withpen pencircle scaled 2 withcolor 3/4; - draw subpath (2.718, 3.1415) of shape - shifted - center shape scaled 7/8 shifted + center shape - withpen pencircle scaled 2 withcolor white; -); -clip fg to shape; % now clip the fg drawing to the shape -fill shape withcolor filler; % fill the shape -draw fg; % and put the fg drawing on top -draw shape withcolor 3/4 blue; % make a nice edge -\end{smallcode} +\smallmpexternal[firstline=28,lastline=48]{pics-fake-transparency.mp} \vss}}% + +\smallskip\noindent The two useful tools in the plain \MP\ kit bag are: \begin{itemize} \item The ability to loop through all the elements of a picture @@ -5239,36 +4030,17 @@ The \<picture> capture technique provides a simple way to add a background or do other post-processing on your drawing. The advantage is that you do not have to work out the size of your drawing before you start. -\moveright5.5in\vbox to 0pt{\vskip -43pt -Here is an example that adds graph paper behind -a drawing. -$$\includegraphics{graph-paper}$$ -\begin{smallcode} -input colorbrewer-rgb -path C; C = fullcircle scaled 120 shifted 12 up rotated 6; -for t=0,1.2,4: draw center C -- point t of C withcolor Blues 8 8; endfor -draw C withcolor Reds 8 8; dotlabel.urt("Start", point 0 of C); - -vardef grid(expr ll, ur, grid_unit) = - save llx, lly, urx, ury, G; numeric llx, lly, urx, ury; - (llx, lly) = ll; (urx, ury) = ur; - picture G; G = image( - for x = floor(llx / grid_unit) + 1 upto floor(urx / grid_unit): - draw (x * grid_unit, lly) -- (x * grid_unit, ury); - endfor - for y = floor(lly / grid_unit) + 1 upto floor(ury / grid_unit): - draw (llx, y * grid_unit) -- (urx, y * grid_unit); - endfor - fill fullcircle; % <-- show the origin - ); G enddef; - -picture P; P = currentpicture; currentpicture := nullpicture; -drawoptions(withpen pencircle scaled 1/4); -draw grid(llcorner P, urcorner P, 1mm) withcolor Blues 8 1; -draw grid(llcorner P, urcorner P, 10mm) withcolor Blues 8 2; -drawoptions(); -draw P; -\end{smallcode} +\moveright5.5in\vbox to 0pt{\vskip -96pt\hsize 4.2in +\noindent\includegraphics{pics-graph-paper-example} + +\smallmpexternal[firstline=8,lastline=11, xleftmargin=0pt]{pics-graph-paper-example.mp} +\noindent +This is "pics-graph-paper-inch.mp": +\smallmpexternal[xleftmargin=0pt]{pics-graph-paper-inch.mp} + +\noindent +And this is "automatic-grid.mp" +\smallmpexternal[xleftmargin=0pt]{automatic-grid.mp} \vss} \smallskip\noindent @@ -5280,7 +4052,7 @@ Or you can be more ambitious, as shown in the example on the right \rightarrowfill\break In general, you draw any background you want, like this: \begin{smallcode} -picture P; P = currentpicture; currentpicture := nullpicture; +picture P; P = currentpicture; clearit; % do complex background drawing... clip currentpicture to bbox P; draw P; \end{smallcode} @@ -5297,7 +4069,7 @@ if wd > 360: currentpicture := currentpicture scaled (360/wd); fi If you wanted to apply one of these changes to all the figures in your "mpost" input file then you can use the hook provided by plain \MP: \begin{smallcode} -extra_endfig := "picture P; P = currentpicture;" & +extra_endfig := "picture P; P = currentpicture; clearit;" & "fill bbox P withcolor (1,1,31/32); draw P;"; \end{smallcode} The definition of \mpl{endfig}, includes the line \mpl{scantokens extra_endfig;} so @@ -5315,51 +4087,29 @@ fill bbox P withcolor (1,1,31/32); draw P; endfig;} \textsc{If you wish} to check the dimensions of your drawing, it can be useful to add a temporary ruler that shows you the dimensions of the bounding box like this: -$$\includegraphics{icosahedron}$$ +$$\includegraphics{pics-icosahedron}$$ The red rulers were added by putting \mpl{input ruler-cm} at the end of the figure. -\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize 4in\raggedright\noindent +\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize 4in\noindent Here is the implementation of "ruler.mp": -\begin{code} -% add a ruler along the left hand and lower edges -% of the bounding box of the currentpicture -path B; B = bbox currentpicture; -for s=0, 1: - path p; numeric a; pair o; - p = subpath (0, 1) of if s=0: reverse fi B; - a = arclength p; - o = if s=0: left else: down fi; - for i=0 upto 3: - exitif not known u[i]; - for j=0 upto floor(a/u[i]): - pair t; t = point arctime j*u[i] of p of p; - draw (origin -- (6 - 2i) * o) shifted t; - if i=0: label(decimal j, t shifted 12 o); fi - endfor - endfor - draw p; -endfor -\end{code} +\mpexternal{ruler.mp} +\noindent The inner loop draws successively shorter lines at each of the minor units, and numbers at the major units. + +Note that this macro designed to be used a temporary input added at the +bottom of a drawing to see how big it is. You would not usually leave it in place +in a final drawing. This is why none of the variable names is protected. +To make the macros more robust you could enclose them with \mpl{begingroup} and +\mpl{endgroup}, and \mpl{save} the names, and clear \mpl{drawoptions}. \vss}} They are drawn round the bounding box, set here with the default margin of 2\unit{bp}. The "ruler-cm.mp" file looks like this: -\begin{code} -numeric u[]; u0 = 1 cm; u1 = 1 mm; -drawoptions(withcolor 0.54 red); -input ruler -drawoptions(); -\end{code} -and there is a companion "ruler-inch.mp" file that looks like this: -\begin{code} -numeric u[]; u0 = 1 in; u1 = 1/4 in; u2 = 1/12 in; -drawoptions(withcolor 3/4 blue); -input ruler -drawoptions(); -\end{code} -The idea is that you set a subscripted variable \mpl{u[]} to a number of unit sizes -where you want markers and then call \mpl{input ruler}. +\mpexternal{ruler-cm.mp} +\noindent and there is a companion "ruler-inch.mp" file that looks like this: +\mpexternal{ruler-inch.mp} +\noindent The idea is that you set a subscripted variable \mpl{u[]} to a number of unit sizes +where you want markers and then call \mpl{input ruler}. \newpage @@ -5369,257 +4119,550 @@ where you want markers and then call \mpl{input ruler}. you might want to add emphasis or pick out part of a drawing. The examples here can be applied to \mpl{currentpicture} or any other \<picture> variable.\vadjust{\moveright 396pt\vbox to 0pt{\hsize 4in\vskip -42pt -$$\includegraphics{border.pdf}$$ -\begin{smallcode} -% don't take this one too seriously... -vardef rope expr c = -save hemp, s, w, n, A, a, b; -color hemp; hemp = 1/256 (224, 202, 169); -numeric s, w, n, A; -A = arclength c; s = A/floor(A/2); w = -1; n = -1; -path a[]; for t=0 step s until A + 1: a[incr n] = - (0,+w) rotated angle direction arctime t-3/2s of c of c - shifted point arctime t-3/2s of c of c -.. (0,+w) rotated angle direction arctime t-1/2s of c of c - shifted point arctime t-1/2s of c of c -.. (0,-w) rotated angle direction arctime t+1/2s of c of c - shifted point arctime t+1/2s of c of c -.. (0,-w) rotated angle direction arctime t+3/2s of c of c - shifted point arctime t+3/2s of c of c; -endfor -image(for i=1 upto n: - path b; b = buildcycle(a[i-1], reverse a[i]); - fill b withcolor hemp; - draw b withpen pencircle scaled 1/8; -endfor) enddef; -interim bboxmargin := 16; -draw rope rounded_corners bbox currentpicture; -\end{smallcode}\vss}} +$$\includegraphics{pics-border-rope}$$ +Don't take this one too seriously\dots +\smallmpexternal[xleftmargin=0pt]{rope.mp} +\smallmpexternal[xleftmargin=0pt,firstline=9,lastline=10]{pics-border-rope.mp} +\vss}} -$$\vbox{\halign{$\vcenter{\hbox{\includegraphics[width=150bp]{#}}}$&\quad$\vcenter{\hbox{#}}$\cr -border-shadow& -\begin{smallcode} -picture P; P = currentpicture; -fill bbox P shifted (3,-3) withcolor 3/4; -unfill bbox P; draw bbox P; -draw P; -\end{smallcode}\cr -border-dashed& -\begin{smallcode} -vardef rounded_corners expr p = - for i=1 upto length p: - subpath (i-15/16, i-1/16) of p .. - endfor cycle -enddef; +\bigskip -interim bboxmargin := 16; -draw rounded_corners bbox currentpicture - dashed evenly scaled 3/4; -\end{smallcode}\cr -}}$$ +\noindent\includegraphics[width=.95\textwidth]{pics-border-shadow} + +\bigskip + +\noindent\includegraphics[width=\textwidth]{pics-border-dashed} \newpage \subsection{Adding a frame}\label{sec:pictureframe} As promised at the start of this section, here is the code for the picture frame drawn round Raphael's young man. -\begin{code} -input picture_frame -beginfig(1); - picture F; - F = thelabel(TEX("\includegraphics{youth.jpg}"), origin); - draw F; draw frame bbox F; -endfig; -\end{code} +\smallmpexternal[firstline=6,lastline=11]{pics-youth.mp} +\noindent All the heavy lifting is done by "frame" macro defined in "picture_frame.mp" $\longrightarrow$ -\vadjust{\moveright5.2in\vbox to 0pt{\hsize 4in\vskip-184pt -\begin{smallcode} -vardef frame expr P = - save base, side, f, t, u, xx; - picture base, side; path f; numeric t, u, xx; - % work out some measurements - t = arclength subpath (0,1) of P; - u = arclength subpath (1,2) of P; - xx = max(t, u) + 2 pf_wd; - f = unitsquare xscaled xx yscaled pf_wd; - % convenience / nonce function - vardef paint_strip(expr y, wd, shade) = - draw subpath (0, 1) of f - shifted (0, if y < 0: pf_wd + fi y) - withpen pencircle scaled wd - withcolor shade - enddef; - base = image( - % background colour - fill f withcolor gold; - % grey strips - paint_strip(2, 3, 5/4 grey); - paint_strip(3.5, 1/4, grey); - paint_strip(5, 1/4, 1/2[gold, dark]); - paint_strip(-6.5, 1/4, 1/2[gold, dark]); - paint_strip(-6, 1/4, 1/2[gold, dark]); - paint_strip(-2, 2, 5/4 grey); - % spatter with random spots - for i=0 upto 4 * arclength(subpath (0,1) of f): - fill fullcircle scaled uniformdeviate 3/4 - shifted (uniformdeviate xx, uniformdeviate pf_wd) - withcolor dark; - endfor - % decorative balls - for x = 2 step 3 until xx: - draw ball shifted (x, 2); - endfor - ); - % make two trapezium shapes - side = base; - clip side to (pf_wd, 0) -- (pf_wd + u, 0) - -- (2 pf_wd + u, pf_wd) -- (0, pf_wd) -- cycle; - clip base to (pf_wd, 0) -- (pf_wd + t, 0) - -- (2 pf_wd + t, pf_wd) -- (0, pf_wd) -- cycle; - % arrange the pieces around path P - image( - draw base rotated 180 shifted point 1 of P shifted (+pf_wd, 0); - draw base rotated 0 shifted point 3 of P shifted (-pf_wd, 0); - draw side rotated 90 shifted point 0 of P shifted (0, -pf_wd); - draw side rotated 270 shifted point 2 of P shifted (0, +pf_wd); - ) -enddef; -\end{smallcode} +\vadjust{\moveright5in\vbox to 0pt{\hsize 4.2in\vskip-164pt +\smallmpexternal[firstline=18,lastline=64,xrightmargin=-40pt]{picture_frame.mp} \vss}} \noindent This macro also needs some colours: +\smallmpexternal[firstline=4,lastline=7]{picture_frame.mp} +\noindent a picture of a small silvery-gold ball: +\smallmpexternal[firstline=9,lastline=14]{picture_frame.mp} +\noindent and an internal variable that defines the width of the frame: +\smallmpexternal[firstline=16,lastline=16]{picture_frame.mp} +\noindent The macro takes a path or picture $P$ as an argument, and makes a thin rectangle $f$ +that is scaled to the desired width and the longer of the two sides of the bounding +box. This thin rectangle is then decorated with background colour, strips of colour +to suggest depth, a random spatter-pattern, and a row of little balls. The macro +then makes two trapezium shaped copies of the decorated rectangle, pieces them +together around $P$, and returns the result as a \<picture>. + +\newpage +\section{Drawing and decorating lines} + +\textsc{This section} is all about making marks along a \<path> using +\mpl{draw} and a number of other more sophisticated techniques. + +\subsection{Choosing a pen} + +\MP\ inherits a rather complicated system of pens from \MF. As explained in \mfbook, +the original intention of this system was to improve the digitisation of font +characters so that low-resolution raster versions would look aesthetically pleasing. +This is not really a problem for graphics that you might produce with \MP, and so +for most purposes you can stick to the default circular pen, and not worry about +using \mpl{pensquare}, \mpl{penrazor}, and \mpl{penspeck}, nor creating your own +\<pen> variables. On the other hand, you probably will need to change the size and +shape of the pen occasionally, and it is good to understand the mechanisms +available. + +The default, built-in, pen is \mpl{pencircle} -- at the start of every job +this pen is scaled to $0.5\unit{bp}$ and saved as \mpl{currentpen} and +\mpl{defaultpen}. Every time you use \mpl{draw}, \MP\ automatically adds +\mpl{withpen currentpen} unless you have added your own \mpl{withpen}. +\begin{code}[xrightmargin=-42pt] +draw origin -- 20 right; % uses "currentpen" +draw (0,10) -- (20,10) withpen pencircle scaled 2; % thick pen +\end{code} +If you get tired of typing \mpl{withpen}, +you can change pens with the \mpl{pickup} macro; essentially this just updates the value of +\mpl{currentpen}.\vadjust{\moveright 4in\vbox to 0pt{\bigskip +\begin{mplibcode} +draw origin -- 42 right; % uses "currentpen" +pickup pencircle scaled 2; % use a thick pen +draw (0,-24) -- (42,-24); +draw (0,-36) -- (42,-36); +pickup defaultpen; % change back to default +\end{mplibcode}\vss}} +\begin{code} +draw origin -- 42 right; % uses "currentpen" +pickup pencircle scaled 2; % use a thick pen +draw (0,-24) -- (42,-24); +draw (0,-36) -- (42,-36); +pickup defaultpen; % change back to default +\end{code} +If you are using a fat pen and you don't like the big rounded ends, then +you can use \mpl{cutdraw} or set \mpl{linecap := butt;} — see +§\ref{sec:linecaps} for more. +\vadjust{\moveright5.5in\vbox to 0pt{\vss\hsize 4.4in\noindent +Here is an example that makes use of a circular pen transformed to a thin ellipse. +\begin{texcode} +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\newcommand\fleuron{\begin{mplibcode} +\end{texcode} +\vskip-\baselineskip +\begin{smallcode} +beginfig(1); + -z1 = z4 = 7 dir 8; + y2 - y1 = y4 - y3 = 3(y4 - y1); + z2 - z1 = z4 - z3 = whatever * dir 50; + draw z1 .. controls z2 and z3 .. z4 + withpen pencircle xscaled 1.2 yscaled 0.2 rotated 50; + currentpicture := currentpicture rotated - angle z4; +endfig; +\end{smallcode} +\vskip-\baselineskip +\begin{texcode} +\end{mplibcode}} +\begin{document} +Here is a \fleuron\ mark. +\end{document} +\end{texcode} +This example shows how to use an elliptical pen to draw a little twiddle mark +— and incidentally how to define a La\TeX\ command that draws a \MP\ +figure — that comes out looking like this: \fleuron. The idea is that you could use +it as a decoration. + +\medskip +\centerline{\fleuron\quad \textit{A typographical ornament} \quad\fleuron} +\medskip + +\noindent +With a little work, you could also use it as a fancy rule between +sections. +$$\includegraphics{pens-fleuron}$$ +The important parts are that \mpl{pencircle} is scaled to be wider than it is tall, +and then rotated so that it is at the correct angle at the start and at the end of +the path. Think of it as a calligraphic nib. For another example, look at +§\ref{sec:braces}, which uses a similar pen to draw the braces for the dimension +label.}} + + +\newpage +\subsection{Multiple lines} + +\textsc{The pens available} in \MP\ are all simple convex polygons without holes, so +if you want to draw double or triple lines, you have to draw the individual parts of +the marks you want along the path. + +The simplest approach is to draw the path with a thicker pen, then draw over it with +a thinner pen using the background colour, like this: +\begin{code} +path a; a = origin -- (48, 3) -- (96, -3) -- 144 right; +draw a withpen pencircle scaled 3/2; +draw a withpen pencircle scaled 1/2 withcolor background; +\end{code} +which produces this: +\begin{mplibcode} +path a; a = origin -- (48, 3) -- (96, -3) -- 144 right; +draw a withpen pencircle scaled 3/2; +draw a withpen pencircle scaled 1/2 withcolor background; +\end{mplibcode}\enspace +Notice that the lines have been drawn with the default rounded ends. If you don't +want this then use \mpl{cutdraw} for the background lines (or set \mpl{linecap := +butt}), so that you get ends that look open, like this: +\begin{mplibcode} +path a; a = origin -- (48, 3) -- (96, -3) -- 144 right; +cutdraw a withpen pencircle scaled 3/2; +draw a withpen pencircle scaled 1/2 withcolor background; +\end{mplibcode}\enspace +For triple lines, you will need to draw three times: first broad, then medium with +the background colour, then thin in the middle; and so on. + +Beware that you will need to be careful if the line needs to have an arrowhead or to +touch another object. Beware also that drawing with the background colour does not +erase anything, it just draws over the path with an opaque line that happens to be +the same colour as the background, so you will not see +anything that happens to lie under the line even if you want to. + +If you want to draw real separate parallel lines, then the simplest approach is just to shift +the path sideways using something like this: \begin{smallcode} -color gold, dark, grey; -gold = 1/256(243, 197, 127); -dark = 1/256(144, 87, 50); -grey = 1/256(156, 147, 138); +path p; p = origin -- 100 dir 30; draw p; +draw p shifted 4 unitvector(direction 1/2 of p rotated 90); +\end{smallcode} +If your path is a regular cycle, like a circle or a polygon, then another approach +is to draw a scaled copy. +\begin{smallcode}[xrightmargin=-20pt] +path p; p = fullcircle scaled 100 shifted 42(normaldeviate, normaldeviate); +draw p; draw p shifted -center p scaled 0.98 shifted center p; \end{smallcode} -a picture of a small silvery-gold ball: +but if your path is more complex, then you need something like the macro +shown at the right. The piano-shaped path $p$ is drawn in black; the outer blue path +was drawn with \mpl{draw beside(p, 2)} and the red one with +\mpl{draw beside(p, -2)}. + +\moveright5.5in\vbox to 0pt{\vss\hsize 4.4in\noindent +\smallmpexternal[firstline=8,lastline=32,xleftmargin=0pt]{pens-besides.mp} +\noindent\includegraphics[width=4in]{pens-besides} +\vskip -60pt +} + +\newpage +\subsubsection*{Making tubes} + +Drawing with multiple lines can also produce a three-dimensional effect for +knot diagrams (provided that you don't think of toothpaste). +$$ +\begin{mplibcode} +path a; a = origin .. (72, 10) .. (144, -10) .. (216, 0); +for i=4 step -1/8 until 1/2: + draw a withpen pencircle scaled i withcolor (i*i/16)[white, 1/2 blue]; +endfor +\end{mplibcode} +$$ +This tube-like effect can be created with a loop like this: \begin{smallcode} -picture ball; ball = image(for i=0 upto 16: - fill interpath(i/16, - fullcircle scaled 10, - fullcircle scaled 3 shifted (-2, 2) - ) withcolor (i/16)[gold, 15/16 white]; -endfor) scaled 1/4; +path a; a = origin .. (72, 10) .. (144, -10) .. (216, 0); +for i=4 step -1/8 until 1/2: + draw a withpen pencircle scaled i withcolor (i*i/16)[white, 1/2 blue]; +endfor \end{smallcode} -and an internal variable that defines the width of the frame: +The idea is to +draw a path repeatedly with lines that get thinner and use a lighter shade +Notice the colour fades from white to dark blue using the mediation syntax. +You might like to experiment with linear or quadratic transitions until you get a +gradient that you like. In the loop above as $i$ varies from 4 down to $\frac12$, +the mediation fraction varies from 1 down to $\frac1{64}$, like this: +$$\vbox{\halign{\hss #:\quad&&\hss #\hss\cr +$i$ & 4.00 & 3.75 & 3.50 & 3.25 & 3.00 & 2.75 & 2.50 & 2.25 & 2.00 & 1.75 & 1.50 & 1.25 & 1.00 & 0.75 & 0.50 \cr +$i^2/16$ & 1.00 & 0.88 & 0.77 & 0.66 & 0.56 & 0.47 & 0.39 & 0.32 & 0.25 & 0.19 & 0.14 & 0.10 & 0.06 & 0.04 & 0.02 \cr +}}$$ +which makes the gradient steeper nearer the edges. +If you don't want the rounded ends, then you should use \mpl{cutdraw} instead of +\mpl{draw}. + +\subsection{Showing crossings} + +In general it is a good idea to avoid line crossings completely, but +occasionally you may end up with a diagram where at least one line +has to cross another. The simple way to deal with this is to use the technique +shown in §\ref{sec:cd}; capture the line to be drawn in a \<path> +variable, and then do \begin{smallcode} -newinternal pf_wd; pf_wd := 21; +cutdraw line withpen pencircle scaled 4 withcolor background; draw line; \end{smallcode} -The macro takes a rectangular path $P$ as an argument, and -makes a thin rectangle $f$ that is scaled to the desired width and -the longer of the two sides of the path. This thin rectangle is then -decorated with background colour, strips of colour to suggest depth, a random -spatter-pattern, and a row of little balls. The macro then makes two trapezium -shaped copies of the decorated rectangle, pieces them together around $P$, and returns the result as a -\<picture>. +so that you erase behind the line before you draw it. Alternatively you could use +the ideas in §\ref{sec:allxp} to find all the intersections between two paths +and mark them appropriately. But the marks might not improve legibility; compare +these two \rlap{$\longrightarrow$}\mpic{-6in}{pens-crossings} + \newpage -\section{Annotations} +\subsection{Using dash patterns with extra precision} -\textsc{In some awkward corners}, you may find that you just can't get your label in -the right place with \mpl{dotlabel} even if you adjust \mpl{labeloffset}. In these -cases there are two simple techniques you can use. First, you could separate -drawing the dot from placing the label; given a point $P$ you can try:\mpic{0pt}{callout} +\textsc{As you may know}, plain \MP\ provides two +built-in dash patterns, so that you can draw a path \mpl{dashed withdots} or +\mpl{dashed evenly}. +\vadjust{% +\moveright384pt\vbox to 0pt{\vskip-46pt\hsize 4.2in\small +$$ +\begin{mplibcode} +vardef exactly(expr a) = + save m; numeric m; 2m = (a-6) / round(a/6); + dashpattern(on m off m) +enddef; +vardef gooddots(expr a) = + save m; numeric m; 2m = (a-5) / round(a/5); + dashpattern(off m on 0 off m) +enddef; + for i=2 upto 8: + path c[]; + c1 = fullcircle scaled 16i shifted 80 left; + c2 = fullcircle scaled 16i shifted 80 right; + draw c1 dashed evenly withcolor 2/3 blue; + draw c2 dashed exactly(arclength c2) withcolor 1/2 red; + %draw c1 shifted 160 down dashed withdots withcolor 2/3 blue; + %draw c2 shifted 160 down dashed gooddots(arclength c2) withcolor 1/2 red; + endfor +\end{mplibcode} +$$ + +\noindent +The blue circles on the left were drawn with \mpl{dashed evenly}, and the uneven +gaps are noticeable at the “three o’clock†positions where the paths begin and end. +As you can see the default dash spacing looks fine at some sizes but bad on others. +On the right you can see the same circular paths coloured red, and drawn with +\mpl{dashed exactly(arclength c, 6)}. + +$$ +\begin{mplibcode} +vardef exactly(expr a, u) = + save m; numeric m; 2m = a / round(a/u); + dashpattern(on m off m) +enddef; + for i=2 upto 8: + path c[]; + c1 = unitsquare shifted -(1/2, 1/2) scaled 16i shifted 80 left; + c2 = unitsquare shifted -(1/2, 1/2) scaled 16i shifted 80 right; + draw c1 dashed evenly withcolor 2/3 blue; + draw c2 dashed (exactly(arclength c2, 8) shifted 6 right) withcolor 1/2 red; + endfor +\end{mplibcode} +$$ +Other paths may require a bit more ingenuity and thought. Because the square paths +have four equal sides, they work better with a target dash length that is a multiple +of 4. Here the blue squares on the left use the default \mpl{dashed evenly}, and the +red squares on the right were done with: \begin{code} -drawdot P withpen pencircle scaled dotlabeldiam; -label("$P$", P shifted 10 dir 68); +dashed (exactly(arclength s, 8) shifted 6 right) \end{code} -Using \mpl{dotlabeldiam} ensures that your dots match any others done with -\mpl{dotlabel}. -Secondly, if that's not enough, use a temporary pair to create a call out line: +The right shift made the corners look better. +\vss}} + +The keyword \mpl{dashed} gives you access to the PostScript "setdash" command, whose +argument is a special \<picture> defined with the \MP\ \mpl{dashpattern} function. +If you look in "plain.mp" you will find these declarations: \begin{code} -z0 = P + 20 dir -20; -draw z0 -- P - cutafter fullcircle scaled 8 shifted P - withpen pencircle scaled 1/4; -label.rt("\textit{pole}", z0); +picture evenly,withdots; +evenly = dashpattern(on 3 off 3); % dashed evenly +withdots = dashpattern(off 2.5 on 0 off 2.5); % dashed withdots \end{code} -If you want to do this sort of thing often, then it might be worth making a macro. -It is hard to write anything completely general, but see §\ref{sec:extimage} for an -example. +The detailed syntax is explained in §9.4 of the \MP\ manual, but essentially +\mpl{withdots} creates a unit 5 points long with a dot in the middle, and +\mpl{evenly} creates a unit 6 points long with the dashes 3pt long (plus the round +bit at the end of each dash, unless you have changed \mpl{linecap}) and gaps 3pt +long (minus any round bits). -\medskip\noindent -\textsc{You might also want} to mark a straight line between two points. -\vadjust{\moveright5.3in\vbox to 0pt{\hsize 4.2in -\begin{smallcode} -vardef do_brace(expr a,b,m,r) = - save d, e, n, bb; numeric d, n; pair e; path bb; - n = 1/2 m; d = angle (b-a); - e = up scaled m rotated d shifted r[a,b]; - bb = ((origin {0,n} .. {right} (abs n,n)) - rotated d shifted a -- - ((-abs n,-n){right} .. {0,n} origin {0,-n} .. {right}(abs n,-n)) - rotated d shifted e -- - ((-abs n,n){right} .. {0,-n} origin) - rotated d shifted b - ) shifted (up scaled n rotated d); - draw bb withpen pencircle yscaled .6 xscaled .1666 rotated d; - point 3 of bb -enddef; +You might be tempted to get creative with this and make complex dot-dot-dash patterns, +but they rarely look very good and they may puzzle your readers. Scaling the two +default patterns is probably all you ever need; so if you want a denser dotted line +try \mpl{dashed withdots scaled 1/2}, +or to get very long dashes you could use +\mpl{dashed evenly scaled 4}. -label.lrt("Here",do_brace(z1, z2, -12, 3/4)); -\end{smallcode} -Note that, as well as drawing the braces, the macro uses the grouping provided by \mpl{vardef} to return the -mid point so that you can put a label next to it. -\vss}} -The simplest way to do this is just to use \mpl{drawdblarrow} on a copy of your straight -path shifted to one side, like so: +But you may also notice that the dash patterns (particularly the longer ones) do not +always fit your paths exactly -- this is especially noticeable with closed paths, +where you may end up with one unsightly long dash or a very short gap at the point +where the path begins and ends. + +There is a simple solution: adjust the length of the dash pattern +so that an integer number of dash units exactly fit your path. \begin{code} -drawdblarrow (z1--z2) shifted (12 up rotated angle (z2-z1)); +vardef exactly(expr a, u) = + save m; numeric m; 2m = (a-u) / round(a/u); + dashpattern(on m off m) +enddef; \end{code} -If you combine this with temporarily setting \mpl{ahangle:=180}, you get the simple -dimension line shown in blue. -$$\includegraphics{braces}$$ -The red braces are a more complex variation on this theme $\longrightarrow$ +Here $a$ is supposed to be the \mpl{arclength} of your path, and $u$ the desired +unit size, so you can use it like this: +\begin{code} +path c; c = fullcircle scaled 200; +draw c dashed exactly(arclength c, 6); +\end{code} +to get a close approximation to \mpl{dashed evenly} that exactly fits the path. \newpage -\section{Line caps and line joins} +\subsection{Decorating a path} + +\textsc{A little decoration} generally goes a long way, so you may want to restrain +your creativity before you apply too many of the ideas from this page. There are +two basic techniques shown here: creative use of dash patterns; and drawing shapes +along the path.\mpic{-48pt}{pens-strokes} + +\smallskip\noindent +With a curved path $S$, the first “with a dash pattern†was drawn like this: +\smallmpexternal[firstline=21,lastline=21,xleftmargin=0pt]{pens-strokes.mp} +\noindent +Notice that the default rounded pen makes dots and dashes with rounded ends. +The second line “with a sharp dash pattern†uses \mpl{cutdraw} to change the line +ends. +\smallmpexternal[firstline=26,lastline=26,xleftmargin=0pt]{pens-strokes.mp} +\noindent +The “railway line†uses a combination of three drawing operations: +\smallmpexternal[firstline=31,lastline=33,xleftmargin=0pt,xrightmargin=-30pt]{pens-strokes.mp} + +\smallskip\noindent +The “plainer railway line†was done like this: +\smallmpexternal[firstline=40,lastline=44,xleftmargin=0pt]{pens-strokes.mp} +\noindent +Note that it's essential to use \mpl{arctime} and \mpl{arclength} in order to get +the markers evenly spaced. But you don't need to worry about the rotation in order +to get the “fading away†effect: +\smallmpexternal[firstline=49,lastline=52,xleftmargin=0pt]{pens-strokes.mp} +\noindent +The remaining three are just fancy variations on the same theme. You might +like to try to re-create them as an exercise, or you can look in the source file. + +\newpage +\subsection{Morphing a path} + +A more flexible, but more complicated, decoration technique is to use a macro +to morph your path before you actually draw it. This is how the venerable "feynmp" +package marks photons and gluons etc in Feynman diagrams. Since "feynmp" is a +standard part of the base \MP\ distribution you can use these macros in normal +drawings; so to draw a zigzag line you can do: +\begin{code} +input feynmp +path S; S = (left {dir 30} .. right {dir 30}) scaled 100; +draw zigzag S; +\end{code} +The package also provides "curly", and "wiggly", as shown at the +right\mwpic{-100pt}{pens-feynmp-styles}, and defines a number of parameters +to control the sizes of the shapes: +\begin{itemize}[itemsep=0pt] + \item "curly_len" sets the wave length of the loops, default 8.5 + \item "wiggly_len" ditto for waves, default 11.34 + \item "zigzag_len" ditto for zigs, default 5.67 + \item "wiggly_slope" steepness of waves, default 60° + \item "zigzag_width", amplitude of zigs, default 4 +\end{itemize} + +\noindent +You might like to try your hand at defining your own. Here is one that does +a vaguely hellenic meander pattern, adapted to cope with curved +paths.\mwpic{80pt}{pens-greek-meander} +\smallmpexternal[firstline=6,lastline=21,xrightmargin=-42pt]{pens-greek-meander.mp} + +\newpage +\subsection{Arrow styles} + +Plain \MP\ provides just two commands for drawing arrows: \mpl{drawarrow} and +\mpl{drawdblarrow}. The default arrows are shown at +\sep{"1"}\mwpic{-48pt}{pens-arrow-styles} in the drawing on the +right.\rlap{$\rightarrow$} + +There are two parameters that you can set to control the shape. The length of the +arrow head is defined by \mpl{ahlength} which is set to 4pt, and the angle is +defined by \mpl{ahangle} which starts at 45°. In some diagrams your arrows may look +more elegant if they are a bit longer and slightly sharper. The arrows shown at +\sep{"2"} were created by setting \mpl{ahangle := 20;} and \mpl{ahlength := 6;} +(note that you need to use the assignment operator to update them). + +\bigskip + +If your diagram needs a wider range of arrow head styles, perhaps because you are +drawing UML, then you can use the "mparrows" package from CTAN. If +you have a complete \TeX\ distribution installed, you can just put \mpl{input +mparrows} near the top of your program, and then use the "setarrows" macro +to change the arrow style. +In the drawing on the right +\begin{itemize} + \item \sep{"mp1"} shows the result of \mpl{setarrows(open)}, + \item \sep{"mp2"} shows \mpl{setarrows(defaultunfilled)}, and + \item \sep{"mp3"} shows \mpl{setarrows(barbed)}. +\end{itemize} + +\noindent +The package uses the same length and angle parameters as the default arrows. It also +provides an extra parameter called "barbedarrowindent" to control the shape of the +barbed arrows. For full details try: "texdoc mparrows" + +\bigskip + +If you would rather have arrows in your drawings that match the various arrows +provided by the Computer Modern font, then you can use the "cmarrows" package from CTAN. You can +include this package by adding \mpl{input cmarrows} near the top of your program. +It is slightly more complicated to control, but the details are explained in the +manual. At \sep{"cm1"} you can see the result of +\begin{smallcode}[xrightmargin=-40pt] +setup_cmarrows(macro_name="drawarrow"; arrow_name="texarrow"; ... ); +setup_cmarrows(macro_name="drawdblarrow"; arrow_name="twowayarrow"; ...); +\end{smallcode} +Here I have chosen to override the built-in command, but you can assign a +different macro name if you prefer. The arrow names used at \sep{"cm2"} were +"lefthalfarrow" and "paralleloppositelefthalfarrows". + +\newpage +\subsection{Line caps and line joins}\label{sec:linecaps} The PostScript language defines parameters that affect how the ends of each line are drawn and how lines are joined together. Plain \MP\ provides access to these -parameters through internal variables called "linecap" and "linejoin"; it sets both -of them to the value "rounded" at the start of each job. -\mpic{0pt}{line-caps-and-joins} +parameters through internal variables called \mpl{linecap} and \mpl{linejoin}; it +sets both of them to the value \mpl{rounded} at the start of each job. +\mwpic{-20pt}{pens-line-caps-and-joins} -The figure on the right shows the affect of the different settings, using an +The figure on the right shows the effect of the different settings, using an exaggerated line width of 2 points (instead of the usual 0.5 points). Some observations to note: \begin{itemize} - \item When $\id{linecap}=\id{squared}$ then \kw{drawdot} produces diamond-shaped + \item When \mpl{linecap = squared} then \mpl{drawdot} makes diamond-shaped dots, even when you are drawing with the default circular pen. - \item When $\id{linecap}=\id{butt}$ then \kw{drawdot} produces invisible dots. + \item When \mpl{linecap = butt} then \mpl{drawdot} produces invisible dots. They still count towards the bounding box of the picture but there's no mark on the page. - \item When $\id{linecap}=\id{squared}$ then \kw{drawarrow} produces some - unpleasant results; even when $\id{linejoin}=\id{mitered}$, you can still + \item When \mpl{linecap = squared} then \mpl{drawarrow} produces some + unpleasant results; even when \mpl{linejoin = mitered}, you can still see small jaggies on the slopes of the arrows. \item The arrows are nice and sharp when - $\id{linejoin}=\id{mitered}$, but they over shoot the mark slightly. + \mpl{linejoin = mitered}, but they over shoot the mark slightly. - \item If you zoom in, you can see the effect of $\id{linejoin}$ on the corners of the grey box - as well as on the arrow heads, but you might not notice the difference when - the picture is printed unless you have a very high resolution printer. + \item If you zoom in, you can see the effect of \mpl{linejoin} on the corners in + the centre as well as on the arrow heads, but you might not notice the + difference when the picture is printed unless you have a very high + resolution printer. \item This drawing was done with \mpl{pencircle scaled 2}, so that the dots would be easy to see. This does make the arrows drawn with the default line modes (rounded caps and rounded joins) looks a bit fat; - they look better with the usual \mpl{pencircle scaled .5}. + they look better with the usual \mpl{pencircle scaled .5}, Like this: + \begin{mplibcode}drawdblarrow (left--right) scaled 20;\end{mplibcode} \end{itemize} -There is one more PostScript parameter affecting line joins. \MP\ makes it available as "miterlimit" -and it affects how much a mitered join is allowed to stick out at each corner. Plain \MP\ sets -"miterlimit=10;" which is correct for nearly all drawings. If you set -"miterlimit:=0;" then the mitered line join mode becomes more or less the same as the -beveled mode. +There is one more PostScript parameter affecting line joins. \MP\ makes it available +as \mpl{miterlimit} and it affects how much a mitered join is allowed to stick out +at each corner. Plain \MP\ sets \mpl{miterlimit = 10;} which works well for most +drawings. If you set \mpl{miterlimit := 0;} then the mitered line join mode becomes +more or less the same as the beveled mode. + +\newpage +\subsection{Line caps and line joins with square pens} + +\textsc{The parameters explained} in the previous section were designed (or at least +named) for use with the default pen \mpl{pencircle}.\mwpic{-60pt}{pens-pen-oddity} +You will get some rather odd shapes if you use them with any other pen, such as +\mpl{pensquare}, especially if you use a large pen. In the drawings on the right, +the thin red lines are drawn with each pen scaled to $0.5\unit{bp}$ (the default +size), and +the large grey and blue areas show what would be draw with the same pens scaled to +16\unit{bp}, so that you can see the artefacts more clearly. +From these drawings you can see: +\begin{itemize} + \item The default setting \mpl{linecap := rounded} actually seems to mean “draw + a dot with the current pen at each end of the pathâ€, so with + \mpl{pensquare} you get a square dot on the end and it's not rounded at all. + + \item With \mpl{linecap := butt}, \MP\ appears to draw the terminal dots using + half of the current pen. With the square pen, this has the unfortunate + effect of cutting the pen at 45°, so that the end of the lines appear + bevelled rather than squared off. Notice also that the cut is correctly + rotated with the circular pen, but remains at 45° with the square pen. + + \item You get a similar effect with \mpl{linecap := squared}. \MP\ uses the + same cut “across†the pen, but pushes it out so that it just touches the + far edge of the pen-sized dot that would be drawn with \mpl{linecap := rounded}. + +\end{itemize} + +You can also see from the drawings that the effect of the \mpl{linejoin} setting, which is +admittedly pretty subtle with a circular pen, is null with the square pen. And +that the single point dots disappear unless you have \mpl{linecap := rounded}. + +\bigskip +\noindent +If you need to use a large square pen, then you can mitigate some of the artefacts +if you rotate the pen by 45°. Using \mpl{pensquare rotated 45} corrects most of the +faults, except that \mpl{linecap := rounded} will give you lines with pointed ends, +and that the squared off ends of the lines with the other settings may not be +exactly orthogonal to the direction of the path at each end. \newpage \section{Plotting functions}\label{func} @@ -5634,162 +4677,47 @@ hours scratching your head wondering how to adjust the axis labels. \subsection{Making axes} -You can start by drawing a simple set of axes.\mpic{-124pt}{plain-axes} -\begin{smallcode} -path xx, yy; -xx = (left -- right) scaled 130; -yy = (down -- up) scaled 80; -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); -\end{smallcode} +You can start by drawing a simple set of axes.\mpic{-124pt}{func-plain-axes} +\smallmpexternal[firstline=6,lastline=10]{func-plain-axes.mp} +\noindent Here the axes are scaled arbitrarily to 130\,pt and 80\,pt, but you will probably find it useful to set consistent units, and express sizes in terms of them. Purely from habit, I use $u$ for the horizontal unit and $v$ for the vertical unit. This makes it more convenient when you want to add a grid and/or a number -scale.\mpic{-16pt}{numbered-axes} +scale.\mpic{-16pt}{func-numbered-axes} \vskip -12pt \vbox to 0pt{ -\begin{smallcode} -numeric u, v; u = 40; v = 29; -path xx, yy; -xx = (3/2 left -- 5 right) scaled u; -yy = (3/2 down -- 4 up) scaled v; -for x=-1, 1, 2, 3, 4: - draw yy shifted (x * u, 0) withcolor 7/8; % grid - draw (down--up) shifted (x * u, 0); % ticks - label("$" & decimal x & "$", (x * u, -8)); -endfor -for y=-1, 1, 2, 3: - draw xx shifted (0, y * v) withcolor 7/8; % grid - draw (left--right) shifted (0, y * v); % ticks - label("$" & decimal y & "$", (-10, y * v)); -endfor -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); -\end{smallcode}\vss} +\smallmpexternal[firstline=7,lastline=21]{func-numbered-axes.mp} +\vss} \newpage \subsection{Drawing linear functions} -\textsc{For simple} linear graphs, you just need to define two points and draw a +\textsc{For simple} linear graphs, you just need to define two points and draw a line between them; it is tempting to try to make some generalized macro to do this, but it is hard to make something completely general, so for most graphs it is easier just to specify two points and use \mpl{draw}; often it is handy to making your line longer than you need, then trim it using \mpl{cutbefore} and/or \mpl{cutafter} so that it fits neatly. -\vadjust{\moveright 384pt\vbox to 0pt{\hsize 4in\vskip -100pt\begin{smallcode} -numeric u, m, m', b, b'; -u = 1.44cm; -b = 3.6u; b' = b + 1/2 u; -m = -1; m' = 3/4 m; - -path xx, yy; -xx = (left -- 5 right) scaled u; -yy = xx rotated 90; - -numeric minx, maxx; path ff, gg; -minx = xpart point 1/16 of xx; -maxx = xpart point 15/16 of xx; -ff = (minx, minx * m + b) -- (maxx, maxx * m + b); -gg = (minx, minx * m' + b') -- (maxx, maxx * m' + b'); - -z0 = point 0.4 of ff; -z1 = point 0.54 of ff; -z1 0 = whatever [point 0 of gg, point 1 of gg]; x1 0 = x0; -z1 1 = whatever [point 0 of gg, point 1 of gg]; x1 1 = x1; - -forsuffixes @=0, 1: - draw (x@, 0) -- z@ -- (0, y@) dashed evenly scaled 3/4; - draw z@ -- z1 @ -- (0, y1 @) dashed withdots scaled 1/2; - label.bot("$x_{" & decimal @ & "}$", (x@, 0)); - label.lft("$y_{" & decimal @ & "}$", (0, y@)); - label.lft("$y'_{" & decimal @ & "}$", (0, y1 @)); -endfor -draw ff withcolor 2/3 red; -draw gg withcolor 3/4 blue; -drawarrow xx; drawarrow yy; - -label.rt("$x$", point 1 of xx); -label.top("$y$", point 1 of yy); - -dotlabel.urt("$b$", (0, b)); -dotlabel.urt("$b'$", (0, b')); - -draw thelabel("slope: $m=" & decimal m & "$", 7 up) - rotated angle (1, m) shifted point 2/3 of ff; -draw thelabel("slope: $m'=" & decimal m' & "$", 7 up) - rotated angle (1, m') shifted point 2/3 of gg; -\end{smallcode}\vss}} -$$\includegraphics[width=0.84\textwidth]{linear-graph.pdf}$$ +\vadjust{\moveright 384pt\vbox to 0pt{\hsize 4in\vskip -100pt +\smallmpexternal[firstline=6,lastline=49]{func-linear-graph.mp} +\vss}} +$$\includegraphics[width=0.84\textwidth]{func-linear-graph}$$ But in this example it was easier to calculate them using $y=mx+b$. Note also that spaces are allowed in suffixes, which makes the loop a bit simpler. -\newpage -In this second example of a linear function, the emphasis of the diagram was on +\newpage\noindent +In this second example of a drawing with linear functions, the emphasis of the diagram was on the angles at the $x$-axis made by the two lines, so the lines were defined using \mpl{rotated}, \mpl{shifted}, and \mpl{cutbefore} instead. -\vadjust{\moveright 384pt\vbox to 0pt{\hsize 4in\vskip -24pt\begin{smallcode} -path ell, tee, arc; -ell = (left--right) scaled 10u rotated theta shifted P cutbefore xx; -tee = (left--right) scaled 10u rotated psi shifted P cutbefore xx; -arc = subpath (1.6, 3.2) of halfcircle rotated -180 shifted 1/2 up - scaled 10u shifted P rotatedabout(P, psi); -% the rest of the points then follow... -Q = ell intersectionpoint subpath (1.5, 3) of arc; -H = P + whatever * dir psi; -xpart H = xpart Q = xpart M; ypart M = ypart N = 0; -xpart N = xpart P; -L = point 0 of ell; -T = point 0 of tee; -% now get on with the drawing -draw arc dashed withdots scaled 1/4 withcolor 1/2 red; -draw P--N dashed withdots scaled 1/2; -draw Q--M dashed withdots scaled 1/2; -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); -drawoptions(withcolor 2/3 blue); -draw fullcircle scaled 32 shifted T cutafter tee; -draw fullcircle scaled 28 shifted L cutafter ell; -label("$\psi$", 24 right rotated 1/2 psi shifted T); -label("$\theta$", 20 right rotated 1/2 theta shifted L); -drawoptions(); -% trim the function lines neatly -path boundary; -z1 = point .95 of xx; -z2 = point .95 of yy; -boundary = z1--(x1,y2)--z2; -draw ell cutafter boundary; -draw tee cutafter boundary; -% and finally label the points. -label.bot("$T$", T); -label.bot("$L$", L); -label.bot("$N$", N); -label.bot("$M$", M); -dotlabel.ulft("$P$", P); -dotlabel.lrt("$Q$", Q); -dotlabel.lrt("$H$", H); -\end{smallcode}\vss}} -$$\includegraphics[width=\textwidth]{angles-lines.pdf}$$ -The lines are both trimmed to a convenient path (\id{boundary}) when they are -drawn.\vadjust{\moveright296pt\vbox to 0pt{\vskip 80pt\begin{mplibcode}beginfig(0);drawarrow -origin {right} .. {dir 70} 42 dir 60; - label.lft("\small \dots continues", origin); -endfig;\end{mplibcode}\vss}} - -\begin{smallcode} -numeric u; u = 1cm; - -path xx, yy; -xx = (2 left -- 10 right) scaled u; -yy = (down -- 7 up) scaled u; - -numeric theta, psi; psi = 28; theta = 50; - -pair P, Q, H, N, M, T, L; -P = (4u, 3u); -\end{smallcode} - +$$\includegraphics[width=\textwidth]{func-angles-lines}$$ +The lines are both trimmed to a convenient path (\id{boundary}) when they are drawn. +\smallmpexternal[firstline=6,lastline=12]{func-angles-lines.mp} +\vskip-12pt\continued +\moveright 384pt\vbox to 0pt{\hsize 4in\vss +\smallmpexternal[firstline=14,lastline=51]{func-angles-lines.mp} +\vskip -12pt} \newpage \subsection{Making curves for functions with a loop} @@ -5800,15 +4728,15 @@ loop like this: \begin{code} vardef f(expr x) = x ** 2 enddef; path ff; -ff = (for x = minx step s until maxx - s: - (x, f(x)) .. - endfor (maxx, f(maxx))) xscaled u yscaled v; +ff = (for x = minx step s until maxx - s: + (x, f(x)) .. + endfor (maxx, f(maxx))) xscaled u yscaled v; \end{code} provided you have first defined variables \id{minx} and \id{maxx} to represent the domain of $x$, and worked out appropriate values for horizontal and vertical -units, $u$, and $v$ so that the range of $f(x)$ fits neatly on your graph. +units, $u$, and $v$ so that the range of $f(x)$ fits neatly on your graph. -The loop +The loop above also uses a variable $s$ to control the number of points used to define the path.\mwpic{-180pt}{func-powers} The figures on the right show that over the domain $-3$ to $3$ a step of $\frac12$ @@ -5829,9 +4757,9 @@ step using the $\{\<pair>\}$ syntax: vardef f(expr x) = x ** 2 enddef; vardef fp(expr x) = 2x enddef; % NB "fp" because "f'" is illegal path ff; -ff = (for x = minx step s until maxx - s: - (x, f(x)){1, fp(x)} .. - endfor (maxx, f(maxx))) xscaled u yscaled v; +ff = (for x = minx step s until maxx - s: + (x, f(x)){1, fp(x)} .. + endfor (maxx, f(maxx))) xscaled u yscaled v; \end{code} \vfill @@ -5842,22 +4770,12 @@ smaller step size. \newpage \subsection{Making curves for functions from path pieces}\label{sec:pathpieces} -\textsc{In some situations}, you might find it easier to stich together various +\textsc{In some situations}, you might find it easier to stitch together various \<path> pieces to make your curve. This can be especially elegant if there is a symmetry in the path. For example:\mwpic{-48pt}{func-reflection} -\begin{code} -path ff, negative_ff; - -ff = (1,1) for x = 3/2 step 1/2 until 6: ... (x, 1/x) endfor; -ff := reverse ff reflectedabout(origin, dir 45) & ff; -ff := ff scaled 24; -negative_ff = ff reflectedabout(origin, dir -45); - -draw ff withcolor 2/3 red; -draw negative_ff withcolor 2/3 red; -\end{code} +\mpexternal[firstline=15,lastline=23]{func-reflection.mp} -\smallskip\centerline{\small (Omitting code for the axes, the grid, and the dots at +\centerline{\small (Omitting code for the axes, the grid, and the dots at each \mpl{point} of the paths).} \smallskip @@ -5865,7 +4783,7 @@ each \mpl{point} of the paths).} \begin{itemize} \item Notice that you can update the path using the assignment operator “\mpl{:=}â€. - \item You need to \mpl{reverse} the reflected portion so that the two ends coincide. + \item You need to \mpl{reverse} the reflected portion so that the two ends coincide. \item The two path segments are spliced together with \mpl{&}. You could use a path join like \mpl{..} instead, but then the joined path would have an extra \mpl{point} at \mpl{(1,1)}. @@ -5873,12 +4791,13 @@ each \mpl{point} of the paths).} the more horizontal part. \end{itemize} +\vfill\noindent Reflection of a function in the line at 45° gives the inverse of the function, which is especially useful for $y=1/x$, but it applies to functions generally. So if you want to plot $y=\sqrt x$ it may be easier to define a path for $y=x^2$ and then reflect it. This is particularly useful if you want to plot, say, $y=\sqrt[3]x$, over a domain that includes negative numbers, because \MP\ will not calculate reciprocal powers of -negative numbers.\mwpic{-60pt}{func-cuberoot} +negative numbers.\mwpic{-90pt}{func-cuberoot} The curve in this chart was created by reflecting the line $y=x^3$. \newpage @@ -5886,89 +4805,23 @@ The curve in this chart was created by reflecting the line $y=x^3$. \textsc{A further example} of creating paths by transformation.\mpic{-36pt}{func-exponential} -\begin{smallcode} -numeric u; u = 42; -path xx, yy; -xx = (-3u, 0) -- (5u, 0); -yy = xx rotated 90; -path ee, ll, nn; -numeric minx, maxx, s; -minx = -3; maxx = 1/256 mlog(4.5); s = 1/4; -ee = (for x = minx step s until maxx - s: - (x, mexp(256x)){1, mexp(256x)} ... -endfor (maxx, mexp(256 maxx)){1, mexp(256 maxx)}) scaled u; -ll = ee reflectedabout(origin, dir 45); -nn = (for x=1 step s until 4-s: (x, 1/x) ... endfor (4, 1/4)) scaled u; -nn := reverse nn reflectedabout(origin, dir 45) & nn; - -draw unitsquare xscaled mexp(256) scaled u withcolor 7/8; -draw unitsquare yscaled mexp(256) scaled u withcolor 7/8; -path T[]; -numeric p; p = directiontime dir 45 of ee; -T1 = (precontrol p of ee -- postcontrol p of ee) - shifted - point p of ee scaled 1/2 u shifted point p of ee; -T2 = (precontrol p of ll -- postcontrol p of ll) - shifted - point p of ll scaled 1/2 u shifted point p of ll; -drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); -draw T1; draw T2; draw interpath(1/2, T1, T2) dashed evenly; -drawoptions(); - -draw nn; label.urt("$1/x$", point 0 of nn); -draw ee withcolor 2/3 blue; label.top("$e^x$", point infinity of ee); -draw ll withcolor 3/4 red; label.top("$\ln(x)$", point infinity of ll); -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); -dotlabel.lft("$e$", (0, mexp(256) * u)); -dotlabel.bot("$e$", (mexp(256) * u, 0)); -dotlabel.ulft("$1$", (0, u)); -dotlabel.lrt("$1$", (u, 0)); -\end{smallcode} -\moveright6in\vbox to 0pt{\vss\noindent +\vadjust{\moveright5.5in\vbox to 0pt{\vskip5in\noindent If you prefer more ‘normal’ functions, you can define: \begin{smallcode} vardef exp(expr x) = mexp(256x) enddef; vardef log(expr x) = 1/256 mlog(x) enddef; -\end{smallcode}} +\end{smallcode}\vss}} + +\smallmpexternal[firstline=6,lastline=40,xleftmargin=0pt]{func-exponential.mp} \newpage \subsection{Functions using trigonometric functions} \textsc{As noted} in §\ref{trig}, \MP’s built-in trigonometric functions work in degrees, this example shows how you might use them in a graph.% -\vadjust{\moveright5in\vbox to 0pt{\vskip-24pt\begin{code} - numeric u, pi; u = 50; pi = 3.141592653589793; - - path xx, yy; - xx = (3.5 left -- 3.6 right) scaled u; - yy = (1.1 down -- 1.2 up) scaled u; - - path ss; - ss = origin for t=1 upto 360: -- (t, sind(t)) endfor; - ss := ss shifted 360 left & ss; - ss := ss xscaled (pi/180) scaled u; - - draw ss cutbefore yy shifted point 0 of xx - cutafter yy shifted point 1 of xx - withcolor 3/4 blue; - draw ss shifted (-1/2 pi * u ,0) - cutbefore yy shifted point 0 of xx - cutafter yy shifted point 1 of xx - withcolor 2/3 red; - - drawoptions(dashed withdots scaled 1/4); - draw ((1/4 pi, 0) .. (1/4 pi, sind(45))) scaled u; - draw ((1/2 pi, 0) .. (1/2 pi, sind(90))) scaled u; - draw ((3/4 pi, 0) .. (3/4 pi, sind(135))) scaled u; - drawoptions(); - - drawarrow xx; label.rt("$t$", point 1 of xx); - drawarrow yy; label.top("$u(t)$", point 1 of yy); - - for i=-4, -3, -2, -1, 1, 2, 3, 4: - draw (down--up) scaled 2 shifted (pi * i/4 * u, 0); - label.bot(pi_quarters(i), (pi * i/4 * u, -2)); - endfor -\end{code}\vss}} +\vadjust{\moveright5.25in\vbox to 0pt{\vskip-30pt +\mpexternal[firstline=15,lastline=50]{func-sines.mp} +\vss}} $$\includegraphics[width=\textwidth]{func-sines}$$ For this diagram, the sine wave path ("ss", shown in \blue{blue}) @@ -5977,194 +4830,66 @@ section from the origin to $2\pi$ is created in a loop; with 360 steps, you can \mpl{--} and still get a smooth path. Secondly the cycle is duplicated by splicing itself to a shifted copy. Thirdly it is $x$-scaled to radians, and then scaled in both directions to the chosen unit size, and drawn chopped off to the width of -the $x$-axis. The cosine path is the same path, shifted $\frac12\pi$ left, +the $x$-axis. The cosine path is the same path, shifted $\frac12\pi$ left, drawn in \red{red}, and chopped off to fit the same width. - The fancy fraction labels were produced with this subroutine: -\begin{smallcode} -vardef pi_quarters(expr n) = - save s, f, q; string s, f; numeric q; - s = if n < 0: "-" else: "" fi; q = abs(n); - if q mod 4 = 0: - f = if q > 4: decimal 1/4 q else: "" fi; - elseif q mod 2 = 0: - f = "\frac{" & decimal 1/2 q & "}{2}"; - else: - f = "\frac{" & decimal q & "}{4}"; - fi - "$\scriptstyle" & s & f & "\pi$" -enddef; -\end{smallcode} +\smallmpexternal[firstline=6,lastline=13]{func-sines.mp} \newpage \subsection{Manipulating functions} \textsc{This second example} with trigonometric functions shows one way to add two functions, by combining the \MP\ paths themselves.% -\vadjust{\moveright5in\vbox to 0pt{\vskip-24pt\begin{code} - numeric u, pi; u = 50; pi = 3.141592653589793; - - path xx, yy; - xx = (3.5 left -- 4 right) scaled u; - yy = (1.2 down -- 1.3 up) scaled u; - - path ss, tt, uu; - ss = origin for x=1 upto 360: -- (x, sind(x)) endfor; - tt = origin for x=1 upto 360: -- (x, 1/2 sind(3x)) endfor; - uu = origin for x=1 upto 360: -- - (x, ypart point x of ss + ypart point x of tt) endfor; - - forsuffixes $=ss, tt, uu: - $ := $ shifted 360 left & $; - $ := $ xscaled (pi/180) scaled u; - $ := $ cutbefore yy shifted point 0 of xx - cutafter yy shifted point 1 of xx; - endfor - - draw ss withcolor 1/2[blue, white]; - draw tt withcolor 1/2[red, white]; - draw uu withcolor 1/4 green; - - label.top("$f(x)=sin(x)$", point 290 of ss); - label.bot("$g(x)=\frac12 sin(3x)$", point 295 of tt); - label.urt("$f(x) + g(x)$", point 350 of uu); - - drawarrow xx; label.rt("$x$", point 1 of xx); - drawarrow yy; label.top("$y$", point 1 of yy); - - for i=-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7: - draw (down--up) scaled 2 shifted (pi * i/6 * u, 0); - label.bot(pi_sixths(i), (pi * i/6 * u, -2)); - endfor -\end{code}\vss}} +\vadjust{\moveright5.25in\vbox to 0pt{\vskip-28pt +\mpexternal[firstline=22, lastline=56, xrightmargin=-20pt]{func-addition-of-sines.mp} +\vss}} $$\includegraphics[width=\textwidth]{func-addition-of-sines}$$ Notice how the same extension, scaling, and trimming operations -can be applied to all three paths using a \mpl{forsuffixes} loop. -Note that you can use any regular variable name for the loop index; -you don't have to use \mpl{$}, but like \mpl{@} it is a +can be applied to all three paths using a \mpl{forsuffixes} loop. +Note that you can use any regular variable name for the loop index; +you don't have to use \mpl{$}, but like \mpl{@} it is a valid variable name in \MP, and it looks a bit like a placeholder marker in other languages. Note that you need to start with the first point of the path outside the loop -so that you don't end up with a dangling \mpl{--} path connector. Using +so that you don't end up with a dangling \mpl{--} path connector. Using \mpl{origin} is just a short cut for writing \mpl{(0, sind(0))}. If you were plotting a different function this would not work. For example, \mpl{(0, cosd(0))} is \mpl{(0,1)}. -\bigskip\noindent -\hey The missing \mpl{pi_sixths} macro is left as an exercise for the reader. +\vfill\noindent +\hey The missing \mpl{pi_sixths} macro is left as an exercise for the reader. Hint: you can adapt the \mpl{pi_quarters} on the previous page, allowing for halves, thirds, and sixths instead of halves and quarters. \newpage \subsection{Focus on a specific region of a function} -\textsc{This visual proof} required a large $y$-axis scale.\mwpic{-24pt}{func-epi-v-pie} -The axes are separated to show the +\textsc{This visual proof} required a large $y$-axis scale.\mwpic{-36pt}{func-epi-v-pie} +The axes are separated to show the discontinuity in scales, and that the origin is not on the chart.\enlargethispage\baselineskip -\begin{smallcode}[xleftmargin=0pt] -numeric minx, maxx, s, u, v; -minx = 13/8; s = 1/16; maxx = 19/4; u = 89; v = 3072; - -def f(expr x) = 1/256 mlog(x) / x enddef; -path ff, xx, yy; -ff = for x=minx step s until maxx-s: (x, f(x)) .. endfor (maxx, f(maxx)); -ff := ff xscaled u yscaled v; -xx = origin -- right scaled (maxx-minx) scaled u; -yy = origin -- up scaled 0.09v; -xx := xx shifted point 0 of ff shifted 20 down; -yy := yy shifted point 0 of ff shifted 20 left; - -numeric pi, e, fpi, fe; -pi = 3.141592653589793 u; fpi = f(3.141592653589793) * v; -e = 2.718281828459045 u; fe = f(2.718281828459045) * v; -path ee, pp; -ee = (e, ypart point 0 of xx) -- (e, fe) -- (xpart point 0 of yy, fe); -pp = (pi, ypart point 0 of xx) -- (pi, fpi) -- (xpart point 0 of yy, fpi); - -draw ee dashed withdots scaled 1/4 withcolor 2/3 red; -draw pp dashed withdots scaled 1/2 withcolor 2/3 red; -draw ff withcolor 3/4 blue; - -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); -for x=2 upto 4: - draw (down--up) scaled 2 shifted (x * u, ypart point 0 of xx); - label.bot("$" & decimal x & "$", (x * u, ypart point 0 of xx - 2)); -endfor -for y=31 upto 38: - draw (left--right) scaled 2 shifted (xpart point 0 of yy, y/100*v); -endfor -for y=32, 35, 38: - label.lft("$" & decimal (y/100) & "$", (xpart point 0 of yy-2, y/100*v)); -endfor -\end{smallcode} - -\moveright384pt\vbox to 0pt{\vss\hsize 4in\begin{smallcode} -drawoptions(withcolor 1/2 red); -label.bot("$e$", point 0 of ee shifted 4 down); -label.lft("$1/e$", point 2 of ee shifted 2 left); - -label.bot("$\pi$", point 0 of pp shifted 4 down); -label.lft("$\ln\pi/\pi$", point 2 of pp shifted 2 left); - -drawoptions(withcolor 2/3 blue); -label.urt("$\displaystyle y={\ln x\over x}$", point 42 of ff); - -drawoptions(); -label("\dots\ hence\enspace $e^\pi > \pi^e$.", (4u, 0.38v)); -\end{smallcode}} +\smallmpexternal[xleftmargin=0pt, firstline=8, lastline=42]{func-epi-v-pie.mp} +\vskip-12pt\continued +\moveright384pt\vbox to 0pt{\vss\hsize 4in\null\bigskip +\smallmpexternal[firstline=44, lastline=57]{func-epi-v-pie.mp} +} \newpage \subsection{Approximate function diagrams} \textsc{Sometimes} you may need to plot a function that does not have a simple -mathematical definition. You can use \MP’s normal path definitions to make a likely -looking approximation.\mwpic{-48pt}{func-stress} -\begin{smallcode}[xleftmargin=0pt, xrightmargin=-140pt] -z1 = 377 right; z2 = 233 up; -path ff; ff = origin .. (72, 144){1,2} .. (84, 144) .. (96, 144){1,1} - .. (220, 220){right} .. (370, 160){2,-1.3}; - -for t=2, 4, 4.9: - draw point t of ff -- (xpart point t of ff, y2 + 6) - dashed evenly scaled 1/2; -endfor -label.top("Strain hardening", - (1/2 (xpart point 2 of ff + xpart point 4 of ff), y2)); -label.top("Necking", - (1/2 (xpart point 4 of ff + xpart point 4.9 of ff), y2)); - -path rr; -rr = point 0.4 of ff -- (xpart point 0.8 of ff, ypart point 0.4 of ff) -- point 0.8 of ff; -draw rr; label.bot("Run", point 1/2 of rr); label.rt("Rise", point 3/2 of rr); - -vardef pin_label@#(expr p, a, b)= - draw a -- b cutbefore fullcircle scaled 8 shifted a withpen pencircle scaled 1/4 withcolor 1/2 white; - label@#(p, b); -enddef; -pin_label.lrt("Yield strength", point 1.2 of ff, point 2 of ff + (8, -18)); -pin_label.bot("Ultimate strength", point 4 of ff, point 4 of ff + (4, -24)); -pin_label.bot("Fracture", point 5 of ff, point 5 of ff + (-8, -18)); - -draw ff withpen pencircle scaled 1 withcolor 2/3 blue; -clip currentpicture to unitsquare scaled 400; % clip thick pen at origin - -drawdblarrow z1 -- origin -- z2; -label.ulft("Strain, $\epsilon$", z1); -label.urt("Stress, $\sigma$", z2); - -label("$\displaystyle\hbox{Young's modulus} = \hbox{Slope} = {\hbox{Rise}\over\hbox{Run}}$", - 1/2 z1 shifted 36 up) withcolor 2/3 blue; -\end{smallcode} +mathematical definition. You can a \MP \<path> to make a likely looking approximation. +\mwpic{-48pt}{func-stress} +\vskip-12pt +\smallmpexternal[firstline=6,lastline=40,xleftmargin=0pt, xrightmargin=-300pt]{func-stress.mp} \newpage \subsubsection{Taming Bezier paths with controls} -\textsc{It takes some} practice to translate a sketch of a curve into a smooth +\textsc{It takes some} practice to translate a sketch of a curve into a smooth path. Plain \MP\ inherits from \MF\ a useful \id{flex} macro, that takes a list of \<pair>s (any number of them) and produces a pleasing path through them. As Knuth says in the -\mfbook: +\mfbook: “The idea is to specify two endpoints, $z_1$ and $z_n$, together with one or more intermediate points where the path is traveling in the same direction as the straight line from $z_1$ to~$z_n$; these @@ -6176,7 +4901,6 @@ flex(z5,z6,z7) & flex(z7,z8,z9,z1) & cycle; \end{code} (with appropriate definitions of the points), produces this: \lower 12pt\hbox{\smash{\begin{mplibcode} -beginfig(0); z1=(0,509); z2=(-14,492); z3=(-32,481); @@ -6190,27 +4914,14 @@ z9=(4,493); flex(z5,z6,z7) & flex(z7,z8,z9,z1) & cycle; for i=1 upto 9: draw z[i] withpen pencircle scaled 2 withcolor red; endfor currentpicture := currentpicture scaled 0.7071 rotatedabout(z3, -20); -endfig; \end{mplibcode}}} \bigskip\noindent \textsc{Another approach} is just to define the end-points and some control points, and then define a path that is shaped by the control points but does not actually go -through them. Consider this program:\mwpic{-20pt}{func-pulse} -\begin{code} -vardef pulse(expr w, h, d) = -for i=0 upto 4: x[i] = w/4 * i; endfor - y0 = y1 = 0; - y3 = y4 = d; - y2 = h; - z0 .. 1/2[z0, z1] .. controls z1 - .. 1/2[z1, z2] .. controls z2 - .. 1/2[z2, z3] .. controls z3 - .. 1/2[z3, z4] .. z4 -enddef; -draw pulse(300, 100, -40); -\end{code} -This produces the smooth blue line shown on the right. A second copy of the line is +through them. Consider this program:\mwpic{-36pt}{func-pulse} +\mpexternal[firstline=7,lastline=16]{func-pulse.mp} +\noindent This produces the smooth blue line shown on the right. A second copy of the line is shown below, decorated with the three control points $z_1$, $z_2$, and $z_3$ in red, and showing the six points of the path as small black circles. You can tweak this curve by adjusting the controls left or right, or changing the mediation parameters @@ -6219,50 +4930,32 @@ so that the points on the path are closer to one control point than the other. \newpage \subsection{Parametric plots} -\textsc{If you want to plot} one function against another, then you can make each +\textsc{If you want to plot} one function against another, then you can make each coordinate a function of an independent variable. All functions can be converted, trivially, to this form: \begin{code} vardef f(expr x) = x enddef; vardef g(expr x) = sind(x) enddef; % or whatever function ... -path ff; ff = for t = mint step s until maxt - s: - (f(t), g(t)) .. +path ff; ff = for t = mint step s until maxt - s: + (f(t), g(t)) .. endfor (f(maxt), g(maxt)); \end{code} -But you can make more complicated curves, for example curves +But you can make more complicated curves, for example curves that can have more than one value for $y$ for a given $x$, if you change $f(x)$ and $g(x)$ appropriately. The first example\mwpic{-24pt}{func-lemniscate} shows the lemniscate of Bernoulli and was drawn like this: -\begin{smallcode} -numeric a, c; c = 128; a = sqrt(2) * c; -vardef f(expr x) = a * cosd(x) / (1 + sind(x) ** 2) enddef; -vardef g(expr x) = f(x) * sind(x) enddef; -numeric mint, maxt, s; mint = 0; s = 30; maxt = 360; -path p; -p = for t = mint step s until maxt - s: - (f(t), g(t)) ... -endfor cycle; -draw p withcolor 3/4 blue; -path xx, yy; -xx = (left -- right) scaled 200; -yy = (down -- up) scaled 64; -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); -dotlabel.bot("$F_1$", c * left); -dotlabel.bot("$F_2$", c * right); -\end{smallcode} +\smallmpexternal[firstline=6,lastline=21]{func-lemniscate.mp} +\noindent Although sometimes, especially when you know the domain is 0° to 360° and that the path is cyclic, it is simpler to write the two expressions directly in the loop:\mwpic{-108pt}{func-parametric} -\begin{smallcode} -path p; -p = for t = 0 upto 360: (144 cosd(3t), 89 sind(2t)) ... endfor cycle; -draw p withcolor 2/3 red; -\end{smallcode} +\smallmpexternal[firstline=12,lastline=14]{func-parametric.mp} +\noindent which produces this Lissajous curve $\longrightarrow$ \newpage -\subsubsection{Parametric plots with polar coordinates: Maurer roses} + +\subsection*{Parametric plots with polar coordinates: Maurer roses} \textsc{Instead of} defining separate functions for the $x$ and $y$ coordinates in a parametric plot, it is sometimes convenient to use \MP’s polar coordinate notation (discussed in @@ -6270,41 +4963,25 @@ parametric plot, it is sometimes convenient to use \MP’s polar coordinate nota do in this way. Here is a Maurer rose, based on $r=\cos(2\theta)$ and connecting every 29th point on the curve.\mpic{-24pt}{func-maurer-rose} -\begin{code} - numeric n; n = 2; - path r; r = (for t=0 upto 360: - cosd(n * t) * dir t ... - endfor cycle) scaled 150; - - numeric d; d = 29; - path k; k = for t = 0 upto 360: - point d * t mod 360 of r -- - endfor cycle; - - draw k dashed withdots scaled 1/8 - withpen pencircle scaled 1/4 - withcolor 1/2[blue, white]; - - draw r withcolor 2/3 red; - - path xx, yy; % you might not need the axes... - xx = (left -- right) scaled 160; - yy = (down -- up) scaled 160; - drawarrow xx; label.rt("$x$", point 1 of xx); - drawarrow yy; label.top("$y$", point 1 of yy); -\end{code} -Different values of $n$ and $d$ give an endless variety of patterns. But note that if -your choice of $d$ exceeds $2^{15}/360 \simeq 91$ you will need to use -"-numbersystem=double" to avoid arithmetic overflow. +\mpexternal[firstline=6,lastline=23]{func-maurer-rose.mp} + +\noindent +Different values of the parameters in $r$ and $k$ give an endless variety of patterns. But note that if +you put anything higher than \mpl{point 91t of r} in $k$, you will need to use +"-numbersystem=double" to avoid arithmetic overflow (because $360\times92 > 32768$). +You get prettier curves if the parameter in $k$ is a prime number. \newpage \section{Drawing plane curves} -{\textsc{“Plane curves offer} a rich \dots\ field of study which may be approached +\moveright72pt\vbox{\begingroup\hsize4in +\raggedleft\fontsize{8}{10}\selectfont\textsf{% +Plane curves offer a rich \dots\ field of study which may be approached from a quite elementary level. Anyone who can draw a circle with a given centre and a given radius can draw a cardioid or a limaçon. Anyone who can use a set square -can draw a parabola or a strophoid†\hfill — \textsl{A Book of Curves}, E.\@ H.\@ -Lockwood\parfillskip0pt\par} +can draw a parabola or a strophoid \hfill — \textsl{A Book of Curves}, E.\@ H.\@ +Lockwood\parfillskip0pt +}\par\endgroup} \subsection{Parabola} @@ -6312,71 +4989,28 @@ Lockwood\parfillskip0pt\par} \le 1$ and then transform as required (see next page), but it can be illuminating to follow more traditional constructions, such as that shown on the right.\mwpic{-180pt}{curves-parabola} -\vadjust{\moveright7.2in\vbox to 0pt{\hsize 200pt\noindent +\vadjust{\moveright7.2in\vbox to 0pt{\vskip48pt\hsize 200pt\noindent The idea here is that you put the right angle of your set square on the vertical -axis with the short side touching $S$, and then draw the long side. If you do this +axis with the short side touching $S$, and then draw the long side. If you do this in enough places, the edges form a parabola. In the \MP\ code here, the intersection of each ray with the one before is captured as variable $t$ and then added one at a time to the \<path> \id{parabola}, (using a neat trick at the beginning). \vss}} -\begin{smallcode}[xleftmargin=0pt] -pair A, S; A = origin; S = 66 right; -path parabola, last; -for q = -144 step 8 until 144: - pair Q; Q = (0, q); - path ray; - ray = (origin -- unitvector(S - Q)) scaled 300 - rotated if q < 0: - fi 90 shifted Q; - draw S -- ray withcolor 7/8; - if known last: - pair t; - t = whatever[point 0 of ray, point 1 of ray] - = whatever[point 0 of last, point 1 of last]; - parabola := if known parabola: parabola .. fi t; - fi - last := ray; -endfor - -draw parabola withcolor 3/4[red, white]; -for t=0 upto length parabola: - draw point t of parabola withpen pencircle scaled 3/2 withcolor red; -endfor -draw (up--down) scaled 300; - -dotlabel.lft("$A$", A); -dotlabel.rt("$S$", S); -\end{smallcode} +\mpexternal[firstline=6,lastline=26,xleftmargin=0pt,xrightmargin=-36pt]{curves-parabola.mp} \newpage -\subsubsection{Parabola from directrix and focus} +\subsubsection*{Parabola from directrix and focus} -\textsc{The classical definition} of the parabola is the locus of points that are +\textsc{The classical definition} of the parabola is the locus of points that are equidistant from a given line (the \textit{directrix}, shown as $A\to B$ on the right) to a given focus point (shown as $S$).\mpic{-24pt}{curves-parabola-directrix} -Each point on the parabola path is related to each point, and you can construct an +Each point on the parabola path is related to each point on the directrix, and you can construct an equilateral parallelogram at each point as shown. This leads to a macro that generates a parabola given two \<pair> variables to define the directrix and another to define the focus: -\begin{code} -vardef parabola(expr A, B, S) = - save m, q, n, parabola; - pair n; % n = nearest point to S on A--B - n = whatever[A, B]; n - S = whatever * (A-B) rotated 90; - path parabola; - for t=0 step 1/64 until 1: - pair m, q; - m = 1/2[S, t[A, B]]; - q = whatever[S, n]; - q - m = whatever * (S - m) rotated 90; - parabola := if known parabola: parabola -- fi - q reflectedabout(S, m); - endfor - parabola -enddef; - -\end{code} +\mpexternal[firstline=17,lastline=31]{curves-parabola-directrix.mp} -\subsubsection{Parabola from $y=x^2$ and $dy/dx=2x$} +\subsubsection*{Parabola from $y=x^2$ and $dy/dx=2x$} Alternatively you could define a “unit parabola†like this: \begin{code} @@ -6400,8 +5034,8 @@ the lines from the centre of the circle $O$ through the tangent points from the $S$. When the ratio of $OS/OA = \sqrt2$, the asymptotes are at right angles. You can also draw the hyperbola as the function $y=1/x$ (as shown in -§\ref{sec:pathpieces}), which can be transformed to any desired shape. -The untransformed function is shown on the bottom left, with the focus $S$ +§\ref{sec:pathpieces}), which can be transformed to any desired shape. +The untransformed function is shown on the bottom left, with the focus $S$ at the point $(\sqrt2, \sqrt2)$. If the desired angle between the asymptotes is $2\alpha$, the transformation can be created like this: \begin{code} @@ -6421,52 +5055,45 @@ $$\includegraphics[width=0.9\textwidth]{curves-hyperbola-function}$$ path by a different amount in each direction. By convention, the $y$-axis is the minor axis of an ellipse.\mwpic{-24pt}{curves-ellipse} The ellipse shown on the right, was defined like this: -\begin{code} -path ellipse; -ellipse = fullcircle scaled 320 yscaled 5/8 rotated 13; -\end{code} +\mpexternal[firstline=10,lastline=11]{curves-ellipse.mp} +\noindent Then the lengths of the semi-major axes, $a$ and $b$, were extracted like this: -\begin{code} -numeric a, b; -2a = abs (point 4 of ellipse - point 0 of ellipse); -2b = abs (point 6 of ellipse - point 2 of ellipse); -\end{code} +\mpexternal[firstline=13,lastline=15]{curves-ellipse.mp} +\noindent If you already had $a$ and $b$, then you could use them directly to scale your ellipse; the following snippet would produce the same elliptical path: \begin{code} -numeric a, b; a = 160; b = 100; path ellipse; -ellipse = fullcircle xscaled 2a yscaled 2b rotated 13; +numeric a, b; a = 160; b = 100; path ellipse; +ellipse = fullcircle xscaled 2a yscaled 2b rotated 13; \end{code} - -\bigskip\noindent The “eccentricityâ€, $e$, of the ellipse is the ratio between the distance from the centre to each focus and the semi-major axis, $a$. By definition, the distance from $F_1$ to $T$ to $F_2$ is constant as $T$ moves round the ellipse and is equal to $2a$. Hence when $T$ lies on the minor axis, you have $TF_1=a$, and so $a^2 = b^2 + a^2e^2$, and $e^2=1-b^2/a^2$: -\begin{code} -numeric e; e = 1 +-+ b/a; % the Pythagorean difference operator -\end{code} +\mpexternal[firstline=17,lastline=17]{curves-ellipse.mp} +\noindent The focus points can then be found like this: -\begin{code} -z0 = 1/2[point 0 of ellipse, point 4 of ellipse]; -z1 = e[z0, point 0 of ellipse]; -z2 = e[z0, point 4 of ellipse]; -\end{code} +\mpexternal[firstline=19,lastline=21]{curves-ellipse.mp} +\noindent +Note that in the example above the ellipse is centred at the origin, because +the \mpl{fullcircle} path was only scaled and rotated, not shifted. But the method +shown will find the centre of any ellipse no matter where you have placed it. + \vfill -\moveright 384pt\vbox to 0pt{\vss -The tangent and the normal at $T$ were added like this: -\begin{code} -numeric t; t = 1.732; -draw (left--right) scaled 21 - rotated angle direction t of ellipse - shifted point t of ellipse; -draw (1/2 down--up) scaled 21 - rotated angle direction t of ellipse - shifted point t of ellipse; -\end{code}} + +\noindent +\hey If you already have the two focus points, then the distance between them will be +$2ae$, so if you also have $a$ or $e$ you can calculate $b$ and hence draw your +ellipse appropriately scaled, rotated, and shifted. + +\moveright 5.5in\vbox to 0pt{\vss\noindent +The tangent and the normal at $T$ above were added like this: +\mpexternal[firstline=39,lastline=46]{curves-ellipse.mp} +} + \newpage -\subsubsection{Tangent from external point to ellipse} +\subsection*{Tangent from external point to ellipse} $$\includegraphics[width=\textwidth]{curves-ellipse-tangents}$$ To find the tangent points from an external point $A$ to an ellipse, the classical @@ -6475,78 +5102,30 @@ second arc centred at the other focus with radius $2a$. The intersection points $P$ and $Q$, of these two arcs are the images of the first focus point in the required tangents (because $F_2TF_1=2a$ by definition, and $F_2P=2a$ by construction), and so the tangent points $T$ and $T'$ are the intersections of -$F_2P$ and $F_2Q$ with the ellipse. +$F_2P$ and $F_2Q$ with the ellipse. -\vfill\noindent There is no such direct construction for the nearest point on an ellipse to a given point, but you can use the macro \id{solve} to find it numerically. The blue arrow shows the shortest distance from $A$ to the ellipse. -\vadjust{\moveright 384pt\vbox to 0pt{\vss -\begin{smallcode} -secondarydef a through b = - begingroup; save d; numeric d; d = abs(a-b); - (1+12/d)[b,a]--(1+12/d)[a,b] endgroup -enddef; -path ellipse; ellipse = fullcircle scaled 300 yscaled 5/8 rotated 13; -z0 = 1/2[point 4 of ellipse, point 0 of ellipse]; -numeric a, b, e; -2a = abs (point 4 of ellipse - point 0 of ellipse); -2b = abs (point 6 of ellipse - point 2 of ellipse); -e = 1 +-+ b/a; -z1 = e[z0, point 0 of ellipse]; -z2 = e[z0, point 4 of ellipse]; -z3 = 240 dir 25; -path pp, qq; -pp = fullcircle scaled 2 abs (z1 - z3) shifted z3; -qq = fullcircle scaled 4a shifted z2; -z4 = pp intersectionpoint qq; -z5 = reverse pp intersectionpoint qq; -numeric t, u; -(t, whatever) = ellipse intersectiontimes (z2 -- z4); -(u, whatever) = ellipse intersectiontimes (z2 -- z5); -vardef f(expr x) = - angle (z3 - point x of ellipse) + 90 > angle direction x of ellipse -enddef; -drawarrow z3 -- point solve f(0, t) of ellipse withcolor 2/3 blue; -drawoptions(dashed evenly withcolor 7/8); -draw point 0 of ellipse through point 4 of ellipse; -draw point 2 of ellipse through point 6 of ellipse; -drawoptions(withcolor 3/4); -draw z4 -- z1 -- z5; -draw z2 -- z4 -- z3 -- z5 -- cycle; -draw point t of ellipse -- z1 -- point u of ellipse; -drawoptions(); -draw point t of ellipse -- z3 -- point u of ellipse withcolor 2/3 red; -dotlabel.llft("$F_1$", z1); dotlabel.llft("$F_2$", z2); -dotlabel.urt("$A$", z3); -dotlabel.ulft("$P$", z4); dotlabel.lrt ("$Q$", z5); -dotlabel.ulft("$T$", point t of ellipse); -dotlabel.lrt("$T'$", point u of ellipse); -draw ellipse; -picture P; P = currentpicture; currentpicture := nullpicture; -draw pp dashed withdots scaled 1/2; -draw qq dashed withdots scaled 1/2; -bboxmargin := 24; clip currentpicture to bbox P; draw P; -\end{smallcode} -\vskip -48pt}} +\vadjust{\moveright 382pt\vbox to 0pt{\vss +\mpexternal[firstline=7,lastline=44,xleftmargin=0pt,xrightmargin=-36pt]{curves-ellipse-tangents.mp} +\vskip -36pt}} \newpage \subsection{Cardioid} -\textsc{To draw a cardioid by hand}, you can draw a base circle, mark a fixed point $A$ on it, and -then draw a circle centred at any point $Q$ on the circle that passes through point -$A$. If you then repeat this for many different positions of Q, the cardioid is the -curve that encloses all the circles.\mpic{-24pt}{curves-cardioid-simple} +\textsc{To draw a cardioid by hand}, you can draw a base circle, mark a fixed point +$A$ on it, and then draw a circle centred at any point $Q$ on the circle that passes +through point $A$. If you then repeat this for many different positions of Q, the +cardioid is the curve that encloses all the circles.\mpic{-24pt}{curves-cardioid-simple} But for \MP, you want only a single point $P$ from the circumference of each circle; -this turns out to be the image of $A$ reflected in the tangent at each point $Q$, like so: +this turns out to be the image of $A$ reflected in the tangent at each point $Q$, +like so: $$\includegraphics[width=0.7\textwidth]{curves-cardioid-construction}$$ \vskip -84pt\noindent -With a small step size $s$ and a base circle \id{base}, this suggests: \begin{smallcode} -pair A; A = point 0 of base; -path cardioid; cardioid = for t = 0 step s until length base: - A reflectedabout(precontrol t of base, postcontrol t of base) .. -endfor cycle; -\end{smallcode} +With a small step size $s$ and a rotated circle \id{base}, this suggests: +\smallmpexternal[firstline=13,lastline=16]{curves-cardioid-construction.mp} +\noindent You can also show that $AP=2a(1+\cos\theta)$, where $a$ is the radius of the base circle and $\theta$ is the angle that $AP$ makes with the diameter through $A$, so you might use: @@ -6557,7 +5136,7 @@ cardioid = for t=0 upto 360: 2a * (1+cosd(t)) * dir t .. endfor cycle; \newpage \subsection{Limaçon} -\textsc{The limaçon can be seen} as a generalization of the cardioid, obtained by +\textsc{The limaçon can be seen} as a generalization of the cardioid, obtained by moving point $A$ off the base circle. \vadjust{\moveright356pt\vbox to 0pt{\vskip -20pt\noindent \rlap{\includegraphics[scale=0.833]{curves-limacon-simple}}\vss}} @@ -6565,15 +5144,10 @@ Here $A$ has been moved to the left, but each $P$ on the curve is still $A$ reflected in the tangent at each $Q$. The “hole†gets larger as $A$ moves away from the \id{base} circle; when $A$ touches the \id{base} the hole disappears and the curve becomes the cardioid, as before. - Following this ruler-and-compasses approach, the red limaçon path in the figure here was generated from the \id{base} circle shown in blue. -\begin{smallcode} -pair A; A = 2[center base, point 0 of base]; -path limacon; limacon = for t = 0 step s until length base: - A reflectedabout(precontrol t of base, postcontrol t of base) .. -endfor cycle; -\end{smallcode} +\smallmpexternal[firstline=12,lastline=15]{curves-limacon-simple.mp} +\noindent Or if you prefer a more trigonometrical approach: \begin{smallcode} limacon = for t=0 upto 359: 2a*(1+2cosd(t))*dir t .. endfor cycle; @@ -6583,12 +5157,12 @@ Here $2a$ is the diameter of the blue \id{base} circle. Note that if you use \vfill \noindent -An alternative approach (due to Albrecht Dürer) is shown below. In this dia- +\textsc{An alternative approach} (due to Albrecht Dürer) is shown below. In this \par\kern 2pt -\vbox{\halign{#&\quad\vbox{\hsize=2.4in\noindent #}\cr +\vbox{\halign{#&\kern 1em\vbox{\hsize=18em\noindent #}\cr $$\includegraphics{curves-limacon-durer}$$ -&gram the base circle is divided into 12 parts like a -clock face. At 1 o’clock, you draw a line segment of a given +&diagram, the base circle is divided into 12 parts like a +clock face. At 1 o’clock, you draw a line segment of a given length parallel to the radius to 2 o’clock; at 2 you draw the same length segment parallel to 4 o’clock, and so on. The limaçon is the curve through the far ends of each segment (plus any intermediate points required). @@ -6613,46 +5187,33 @@ part and $y$ part of each point $T$ round the base circle. $$\includegraphics[scale=0.8]{curves-astroid-construction}$$ Then the point $P$ on $A \to B$ that is closest to $T$ will lie on the astroid, so you can make the path with: -\begin{smallcode} -path astroid; astroid = for t=0 step 1/16 until 8: - hide(pair a, b, p; - a = (xpart point t of base, 0); b = (0, ypart point t of base); - p = whatever[a, b]; p-point t of base = whatever * (a-b) rotated 90; - ) p -- endfor cycle; -\end{smallcode} +\smallmpexternal[firstline=8,lastline=12,xleftmargin=0pt]{curves-astroid.mp} +\noindent Note that you need to use “\mpl{--}†so that the cusps stay neatly pointed.\marginpar{\vskip-38pt\small\noindent -\llap{\hey\,}The geometry of the subtended angles shows that the length of the arc +\hey The geometry of the subtended angles shows that the length of the arc $T\to S$ equals the length of the arc from $T\to P$ on the quarter-sized circle through $T$ and $M$. So the astroid is also the path of a point on the smaller circle rolling around the inside of the base circle.} \newpage -\subsubsection{Astroid and cousins} +\subsubsection*{Astroid and cousins} The geometry of the astroid also allows us to define a simple parametric equation for the point $P$. $$\includegraphics[scale=0.8]{curves-astroid-construction}$$ If the distance $OT = a$, then $OA = BT = a\cos\theta$. -But then $BP = BT\,\cos\theta = a\cos^2\theta$, and the +But then $BP = BT\,\cos\theta = a\cos^2\theta$, and the $x$-coordinate of $P = BP\,\cos\theta=a\cos^3\theta$. By a similar -argument the $y$-coordinate is $a\sin^3\theta$, so the parametric +argument the $y$-coordinate is $a\sin^3\theta$, so the parametric equations for $P = (x, y)$: $$\centerline{$x=a\cos^3\theta$ \quad and \quad $y=a\sin^3\theta$}$$ This is used to make this rather psychedelic family of astroid cousins $\longrightarrow$ \moveright384pt\vbox to 36pt{\vss -$$\includegraphics[scale=0.9]{curves-astroid-family}$$ -\begin{smallcode} -numeric a; a = 144; input colorbrewer-rgb -for n=1 upto 7: - path p; p = a * right for t=6 step 6 until 90: - .. a * (cosd(t) ** n, sind(t) ** n) - endfor; - p := for i=0 upto 3: p rotated 90i & endfor cycle; - fill p withcolor Oranges[9][n]; draw p; -endfor -\end{smallcode}} +$$\includegraphics[scale=0.95]{curves-astroid-family}$$ +\mpexternal[firstline=7,lastline=14]{curves-astroid-family.mp} +} \newpage @@ -6662,102 +5223,47 @@ endfor rolling wheel. In the first diagram the cycloid is drawn in red and the corresponding rolling wheel in blue. The main idea in this diagram is to make the whole drawing depend on just a few parameters; here there are two: the radius $r$ -and the amount of rotation $θ$. If we make $r$ bigger, the drawing will be -scaled up; if we change $θ$, the wheel will appear to have rolled along. -\mpic{-66pt}{cycloids} - +and the amount of rotation $\theta$. If we make $r$ bigger, the drawing will be +scaled up; if we change $\theta$, the wheel will appear to have rolled along. +$$\includegraphics[width=0.9\textwidth]{curves-cycloids}$$ -\marginpar{\par\kern1in \begin{itemize} - \item Near the beginning we define $\pi=3.14159265$, as there’s no such constant - built in, but it makes the source more understandable to write "pi/180" - instead of "0.017453". It would be nice to use the Greek letters themselves - in the source, but \MP\ only lets you use plain ASCII characters, to you - have to write "pi" instead. Later on "t" is used instead of $\theta$. - - \item The path of the cycloid $c$ is defined using an inline "for" loop. There’s a - slight awkwardness to doing this as you have to repeat yourself either at - the beginning or the end, because you can’t have a dangling "--" or ".." at - the end of the path. With a closed path it’s easier because you can just - put "--cycle" after the "endfor". The strange numbers here are because - we are going from a rotation of $-100°$ to $+460°$; $360°$ corresponds to - one hop of the cycloid. + + \item The path of the cycloid is defined using an inline "for" loop, using a + neat trick to avoid a leading "--" in the path. The strange numbers here + are because we are going from a rotation of $-80°$ to $+440°$; $360°$ + corresponds to one hop of the cycloid. \item The axes are done in the usual way, except that we use "xpart" and the "point .. of .." notation to make the $x$-axis neatly line up with the ends of the cycloid path. - \item To label points with dots but no text it’s convenient just to fill a - circle scaled to "dotlabeldiam"; this internal parameter is the current size - to be used for the dots in "dotlabel". - -\end{itemize}} - -\mpexternal[xleftmargin=0pt]{cycloids-code.mp} - -\noindent -You can generalize the picture to make cycloids where the point tracing the -cycloid is not on the circumference doing the rolling; the classic example is the -wheel of the train with a flange. Here I have added $R$ to define the radius of an -outer rim, while the wheel still rolls along a circle of radius $r$. -\mpic{-40pt}{cycloids-extra} -You might like to experiment with making $R<r$. Note also that variable names are -case sensitive in \MP. + \item To label points with dots but no text it’s convenient just to draw + the point with \mpl{pencircle scaled dotlabeldiam}; + this internal parameter is the current size + to be used for the dots in \mpl{dotlabel}. -\mpexternal[xleftmargin=0pt]{cycloids-extra-code.mp} +\end{itemize} -\noindent The output\mpic{-122pt}{cycloids-extra} is repeated at the right to save you flicking pages. +\moveright 384pt\vbox to 0pt{\hsize 320pt\vss +\smallmpexternal[firstline=5,lastline=46,xleftmargin=-10pt]{curves-cycloids.mp} +\vskip -64pt} \newpage -\subsubsection{The cycloid compared to other curves} +\subsubsection*{The cycloid compared to other curves} \noindent\textsc{You can't easily} draw a cycloid through two arbitrary points, but -if you get the size of the generating circle right, you can make it pass through -points at each end of a quarter circle, and then it's easy to draw other curves -between the two points. \vadjust{\moveright5.25in\vbox to 0pt{\vskip-48pt\begin{smallcode} -numeric r; r = 164; -path Y, L, C, P, S; - -Y = origin for t=5 step 5 until 140: - -- (0, r) rotated t shifted (t/57.29577951308232*r, -r) -endfor cutafter (origin -- (4r, 0) rotated -45); - -z0 = point 0 of Y; -z1 = point infinity of Y; - -L = z0 -- z1; -C = quartercircle rotated 180 scaled 2x1 shifted (x1, y0); -% The idea here is to use the derivative as the direction at each point. -% If you treat A as x=-1, and B as x=0 and used x=-1/2 in the middle, -% then three points are enough to make the curves look realistic. -% parabola f = x^2, f' = 2x -P = z0{1,-2} - ... (xpart 1/2[z1, z0], ypart 1/4[z1, z0]){1,-1} ... z1 {1, 0}; -% sixth degree f = x^6, f' = 6x^5 -S = z0{1,-6} - ... (xpart 1/2[z1, z0], ypart 1/64[z1, z0]){1, -6/32} ... z1 {1, 0}; - -draw z0 -- (x0,y1) -- z1 withcolor 3/4; - -drawoptions(withcolor 2/3 red); - draw L; dotlabel.urt("Line", point 1/4 of L); -drawoptions(withcolor 1/2 green); - draw C; dotlabel.urt("Circle", point 1 of C); -drawoptions(withcolor 1/4[red, green]); - draw P; dotlabel.urt("Parabola", point 1/2 of P); -drawoptions(withcolor 3/4[red, green]); - draw S; dotlabel.llft("Sixth degree", point 3/4 of S); -drawoptions(withcolor 1/2 blue); - draw Y; dotlabel.urt("Cycloid", point 22 of Y); -drawoptions(); -dotlabel.ulft(btex $A$ etex, z0); -dotlabel.urt(btex $B$ etex, z1); -\end{smallcode}\vss}} -Here is an example with an inverted cycloid, the -so-called \textit{brachistochrone} (the curve joining two points such that a body -travelling along it under gravity takes a shorter time than is possible along any -other curve between the points). -$$\includegraphics{brachisto}$$ +taking the equations for $x$ and $y$ from the previous page, we can use \mpl{solve} +to find a value $a$ for $\theta>0$ where $\theta-\sin\theta=1-\cos\theta$, and then +you have two points for $\theta=0$ and $\theta=a$ which are +at each end of a quarter circle, and it's easy to draw other curves +through them.\vadjust{\moveright5.25in\vbox to 0pt{\vskip-48pt +\smallmpexternal[firstline=6,lastline=42]{curves-brachisto.mp} +\vss}} +The cycloid is drawn here inverted, to make the \textit{brachistochrone} (the curve +joining two points such that a body travelling along it under gravity takes a +shorter time than is possible along any other curve between the points). +$$\includegraphics{curves-brachisto}$$ \newpage \subsection{Spirals} @@ -6770,7 +5276,7 @@ mathematical terms the radius of the spiral is proportional to the angle turned, $r=a\theta$.\mpic{-36pt}{curves-spiral-archimedes} This is very simple to program in \MP. \begin{code} -numeric a; a = 1/8; path S; +numeric a; a = 1/8; path S; S = origin for t=1 upto 360: .. a * t * dir t endfor; \end{code} except that you are unlikely to need one point for every degree of turn in your spiral, so you are @@ -6783,112 +5289,51 @@ which spreads the points out and gives you eight full turns, or perhaps S = origin for t=1 upto 90: .. 1/12 t * dir 16t endfor; \end{code} which would give you four complete turns with a tighter spacing.\marginpar{\small -The rope was drawn (very slowly) with the \mpl{rope} macro from §\ref{pics-border}.} +The rope was drawn (quite slowly) with the \mpl{rope} macro from §\ref{pics-border}.} -\bigskip\noindent -The next simplest is the logarithmic spiral where you have -$r=a^\theta$.\mwpic{10pt}{curves-spiral-equiangular} This is also very simple to -program in \MP, provided you are careful about the scaling. The complete program -for the spiral shown on the right was: -\begin{code} -numeric a; a = 2.6; path S; -S = right for t=1 upto 360: .. a ** (t/64) * dir 4t endfor; -drawarrow S; -\end{code} +\vfill\noindent +\textsc{The next simplest} is the logarithmic spiral where you have +$r=a^\theta$.\mwpic{-72pt}{curves-spiral-equiangular} This is also very simple to +program in \MP, provided you are careful about the scaling. +For the spiral shown on the right, the complete program was: +\mpexternal[firstline=7,lastline=9,xleftmargin=0pt]{curves-spiral-equiangular.mp} +\noindent Note that $a$ was carefully chosen to get a curve that would fit the page, and that $t$ has been divided by 64 to bring it into a suitable range to work with the -default number system. +default number system. \newpage -\subsubsection{Logarithmic spiral and the golden rectangle} +\subsubsection*{Logarithmic spiral and the golden rectangle} -\textsc{The logarithmic spiral} is connected to growth in nature. If you start with -a small square and keep adding squares scaled to the longer side of the resulting +\textsc{The logarithmic spiral} is connected to growth in nature. If you start with +a small square and keep adding squares scaled to the longer side of the resulting rectangle, you get the golden rectangle and the logarithmic spiral emerges from it.\mpic{-48pt}{curves-spiral-gnomon-sq} -\begin{code}[xleftmargin=0pt, xrightmargin=-20pt] -drawoptions(withpen pencircle scaled 1/4 withcolor 1/4); -path s[]; s0 = unitsquare; -fill s0 withcolor 1/2[2/3 blue, white]; draw s0; -numeric a, b, t, n; a = 1; b = 1; n = 11; -for i = 1 upto n: - t := b; b := b + a; a := t; % Fibonacci sequence - s[i] = unitsquare scaled a; - s[i] := s[i] shifted (point i of s[i-1] - point i-1 of s[i]); - fill s[i] withcolor (1/2 + i/32)[2/3 blue, white]; - draw s[i]; -endfor -% cross hairs -for i = n-1 upto n: - draw point i-2 of s[i-2] -- point i of s[i]; -endfor -drawoptions(); -% Draw the spiral as a red arrow -drawarrow origin for i=0 upto n: .. point i of s[i] endfor - withcolor 2/3 red; -% Show the Fibonacci sizes for the bigger boxes -for i = 5 upto n: - label(TEX(decimal arclength subpath (0, 1) of s[i]) - scaled 0.8 rotated angle point n of s[n], center s[i]); -endfor -% Rotate whole picture to show off the spiral -currentpicture := currentpicture rotated - angle point n of s[n]; -\end{code} +\mpexternal[firstline=6,lastline=33,xleftmargin=0pt]{curves-spiral-gnomon-sq.mp} \moveright 396pt \vbox to 0pt{\vss\hsize 4in\small \noindent\llap{• }You can't assign to a pair literal in \MP, so you cannot write \mpl{(a,b) := (b,a+b)}; use a temporary numeric instead. \noindent\llap{• }The uses of \mpl{point} with the square paths \mpl{s[]} -exploit the fact the the \mpl{unitsquare} path is cyclic, so point 4 is the same +exploit the fact the the \mpl{unitsquare} path is cyclic, so point 4 is the same as point 0, and so on. -\noindent\llap{• }Note also the rotation of the labels, so that they are horizontal +\noindent\llap{• }Note also the rotation of the labels, so that they are horizontal when the whole picture is rotated at the end to show the spiral better. \par} - \newpage -\subsubsection{Logarithmic spiral and similar triangles} +\subsubsection*{Logarithmic spiral and similar triangles} -\textsc{This drawing} starts with a large triangle and transforms it to make +\textsc{This drawing} starts with a large triangle and transforms it to make smaller similar copies. The spiral is drawn through the apex of successive transformed triangles.\mpic{0pt}{curves-spiral-gnomon-trig} -\begin{code}[xleftmargin=0pt, xrightmargin=-80pt] -path t[], base; pair apex; -base = (left--right) scaled 100; -apex = whatever * dir +72 shifted point 0 of base - = whatever * dir -72 shifted point 1 of base; -t0 = (base -- apex -- cycle); - -transform S; -r = arclength subpath (0, 1) of t0 / arclength subpath (2, 3) of t0; -point 0 of t0 transformed S = (r*r)[point 0 of t0, point 2 of t0]; -point 1 of t0 transformed S = point 0 of t0; -point 2 of t0 transformed S = point 1 of t0; - -n = 16; -for i=1 upto n: - t[i] = t[i-1] transformed S; - draw subpath (2,3) of t[i] withpen pencircle scaled 1/4; -endfor - -drawoptions(withpen pencircle scaled 1/8 withcolor blue); -draw point 0 of t0 -- point 3/2 of t0; -draw point 0 of t1 -- point 3/2 of t1; -drawoptions(); -draw t0; -drawarrow point 2 of t[n] for i=n-1 downto 0: - .. point 2 of t[i] endfor withcolor 2/3 red; - -z0 = whatever[point 0 of t0, point 3/2 of t0] - = whatever[point 0 of t1, point 3/2 of t1]; -currentpicture := currentpicture rotated - angle (point 2 of t0 - z0); -\end{code} +\mpexternal[firstline=6,lastline=36,xleftmargin=0pt, xrightmargin=-80pt]{curves-spiral-gnomon-trig.mp} \moveright 396pt \vbox to 0pt{\vss\hsize 4in\small -\noindent The \<transform> $S$ is defined implicitly. It is sufficient -to give equations for three non-collinear points, and \MP\ will work out -the rest. In order to do this, you need to know the ratio of $x/a$, but by -definition $a/b=b/x$, so $x=b^2/a$, hence $x/a=(b/a)^2$. The code shown +\noindent The \<transform> $S$ is defined implicitly. It is sufficient +to give equations for three non-collinear points, and \MP\ will work out +the rest. In order to do this, you need to know the ratio of $x/a$, but by +definition $a/b=b/x$, so $x=b^2/a$, hence $x/a=(b/a)^2$. The code shown sets $r=b/a$, and then uses $r^2$ as the required fraction along $a$. \smallskip\noindent\hey @@ -6901,7 +5346,7 @@ an isosceles with base angles of $72^\circ$ as shown. \newpage \section{Eggs}\label{eggs} -\textsc{Drawing bird's eggs} excites a curious fascination in some people. This +\textsc{Drawing hens' eggs} excites a curious fascination in some people. This section shows some possible ways to make eggs with \MP. The first few compass-and-ruler constructions are taken from Robert Dixon's \textsl{Mathographics}. They all follow the same basic idea of constructing the @@ -6910,135 +5355,57 @@ each egg path has 8 points starting with point 0 at “3 o’clock†like \mpl{ \subsection{Euclidean egg} -The first is made of four circular arcs, defined here as parts of +The first is made of four circular arcs, defined here as parts of circles $a$, $b$, $c$, \& $d$.\mwpic{0pt}{eggs-moss}\marginpar{\par\kern 3in \begin{itemize} \item "eggs-common.mp" defines the colours, and the \mpl{numbered_points} routine that is used to show the points of the "egg" path. \item Note that it is not necessary that the parts of the arcs touch; - in fact it is better to join them with the \mpl{..} connector in case the + in fact it is better to join them with the \mpl{..} connector in case the ends are not close enough for you to use \mpl{&}. - \item The rigmarole with saving the current picture, is to show a copy + \item The rigmarole with saving the current picture, is to show a copy of the egg path with and without the construction lines. \end{itemize} } -\begin{code}[xleftmargin=0pt] -input eggs-common -path a, b, c, d, egg; numeric r; r = 100; -a = fullcircle scaled 2r; -b = fullcircle scaled 4r shifted point 4 of a; -c = fullcircle scaled 4r shifted point 0 of a; -d = fullcircle scaled 2 abs (point 2 of a - point 1 of b) - shifted point 2 of a; -egg = subpath (0, 1) of b .. point 2 of d .. - subpath (3, 4) of c .. subpath (5, 7) of a .. cycle; -beginfig(1); -fill egg withpen pencircle scaled 2 withcolor eggshell; -picture P; P = currentpicture; -drawoptions(withpen pencircle scaled 1/4 withcolor dark_eggshell); -draw a; draw d; -drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); -draw point 1 of egg -- point 4 of egg -- - point 0 of egg -- point 3 of egg; -draw egg; -drawoptions(withpen pencircle scaled 2 withcolor 7/16); -draw center a; -draw center d; -draw numbered_points(egg); -drawoptions(); -draw P shifted 240 right; -endfig; -\end{code} +\mpexternal[firstline=5,lastline=29,xleftmargin=0pt]{eggs-moss.mp} +\noindent \newpage \subsection{Pythagorean egg} The centres of the arcs are determined by the 3-4-5 triangle at the origin.\mwpic{0pt}{eggs-thom} -\begin{code} -numeric r, a, b, t; a = 60; 4b = 3a; r = a ++ b; -path base, cap, egg; -base = subpath (4, 8) of fullcircle scaled 2(2r-b); -cap = subpath (0, 4) of fullcircle scaled 2r shifted (0, a) - cutbefore ((b, 0) -- (b, 2r)) - cutafter ((-b, 0) -- (-b, 2r)); -egg = point 4 of base {up} .. cap .. {down} base & cycle; -% more naturally "base {up} .. cap .. {down} cycle" -% but then point 0 would not be at 3 o'clock -\end{code} +\mpexternal[firstline=8,lastline=17]{eggs-thom.mp} +\noindent Note that you can use $\to$ to create reasonably large circular arcs. -The parts of the drawing for filling the egg, +The parts of the drawing for filling the egg, and showing the construction are similar to the first example. \subsection{A taller Pythagorean egg} A slightly different approach using a $\sqrt3$-$\sqrt4$-$\sqrt7$ triangle.\mwpic{20pt}{eggs-357} -\begin{code} -path base, cup, cap, egg; -base = fullcircle scaled 200; -z1 = point -2/3 of base; -z2 = point 2/3 of base; -z3 = point 10/3 of base; -z4 = point 14/3 of base; -z5 = 1/2[z2, z3]; -z6 = 1/2[z4, z1]; -numeric a, b; -a = abs(z3 - z1) - abs(z4 - z6); -b = abs(z3 - z1) - abs(z4 - z5); -cup = subpath (4, 8) of fullcircle scaled 2a shifted z6; -cap = fullcircle scaled 2b shifted z5 - cutbefore (z5 -- 2[z4, z5]) - cutafter (z5 -- 2[z1, z5]); -egg = point 4 of cup {up} .. cap .. {down} cup & cycle; -\end{code} +\mpexternal[firstline=9,lastline=22]{eggs-357.mp} \newpage \subsection{Golden section egg} -An alternative construction.\mwpic{-10pt}{eggs-gold} -\begin{code}[xleftmargin=0pt] -path base, aa, bb; pair m, n, n'; -base = fullcircle scaled 200; m = 1/2 point 0 of base; -aa = halfcircle scaled 2 abs (point 2 of base - m) - shifted m cutbefore (origin -- 1000 up); -n = point infinity of aa; n' = n reflectedabout(up, down); -bb = subpath (0, 2) of base shifted n cutafter (origin -- 1000 up); - -path dome, cap, cup, egg; -dome = fullcircle - scaled 2 (abs(n - point 0 of base) - abs(n - point 0 of bb)) - shifted point infinity of bb; -cap = dome cutbefore (point 4 of bb -- 2[n, point 4 of bb]) - cutafter (point 4 of bb -- 2[n', point 4 of bb]); -cup = subpath (4, 8) of base; -egg = point 4 of cup {up} .. cap .. {down} cup & cycle; -\end{code} +Another alternative construction, for Callicrates.\mwpic{-10pt}{eggs-gold} +\mpexternal[firstline=9,lastline=23,xleftmargin=0pt]{eggs-gold.mp} \subsection{Four point egg} -% eggs-four-point.mp + So far all the eggs have been drawn with semi-circular big end, but this -can be improved. +can be improved. To get a smoother curve, you can use four different sized arcs with four different -centres of rotation to make up +centres of rotation to make up each side of the egg.\mwpic{-36pt}{eggs-four-point} -\begin{code}[xleftmargin=0pt] -path egg, a, b, c, d; -a = fullcircle scaled 80; -b = a scaled 2 shifted point 6 of a; -c = halfcircle - scaled 2 (abs(point 0 of a - point 5 of b) - abs(point 0 of a)); -d = fullcircle - scaled 2 abs(point 2 of a - point 2 of c) shifted point 2 of c; - -egg = point 0 of c {up} .. subpath (1,3) of d .. {down} point 4 of c - .. subpath (5, 7) of b .. cycle; -\end{code} +\mpexternal[firstline=9,lastline=17,xleftmargin=0pt]{eggs-four-point.mp} \newpage \subsection{Five point egg} -The next level of sophistication is to use five different arcs, -but this is more complex and you lose the +The next level of sophistication is to use five different arcs, +but this is more complex and you lose the points at exactly E, N, W, and S.\mwpic{0pt}{eggs-five-better}\marginpar{\par\vskip 3in \noindent\hey Instead of defining and joining circular arcs, this construction defines the points for the egg and the desired directions at each point; @@ -7047,45 +5414,12 @@ connector. The six symmetrically-arranged rings $r_1$ to $r_6$ are used to defi rotation $o_1$ to $o_8$ which are either points on the rings or intersections of lines between them. Then eight directions $u_1$ to $u_8$ are defined at right angles to lines between pairs of centre points. Finally the handy -\mpl{directionpoint} macro is used to find the points where the relevant circle is -moving in that direction. To make the egg, these points are joined up with $\to$ +\mpl{directionpoint} macro is used to find the points where the relevant circle is +moving in that direction. To make the egg, these points are joined up with $\to$ constrained by the matching direction to make circular arcs.\\ \llap{$\longleftarrow$\ }{\small Like so.} -} -\begin{smallcode}[xleftmargin=0pt] -numeric a; a = 56; -path r[]; % the rings -r1 = fullcircle scaled 2a shifted (0, -3/2 a); -r2 = fullcircle scaled 2a shifted (0, -1/2 a); -r3 = fullcircle scaled 2a shifted (0, +1/2 a); -r4 = fullcircle scaled 2a shifted (0, +3/2 a); -r5 = r2 rotatedabout(point 2 of r2, -60); -r6 = r2 rotatedabout(point 2 of r2, +60); -pair o[]; % the centres of rotation for each arc -o1 = point 6 of r5; -o2 = point 2 of r3; -o3 = point 6 of r6; -o4 = whatever[o3, point 2+4/3 of r2] = whatever[o2, point 2-4/3 of r1]; -o8 = whatever[o1, point 2-4/3 of r2] = whatever[o2, point 2+4/3 of r1]; -o6 = 1/2[point 2-4/3 of r1, point 2+4/3 of r1]; -o5 = whatever[o6, point 2-4/3 of r3] = whatever[o4, point 2+4/3 of r1]; -o7 = whatever[o6, point 2+4/3 of r3] = whatever[o8, point 2-4/3 of r1]; -pair u[], t[]; % directions and points for the egg path -u0 = (o8 - o1) rotated 90; t0 = directionpoint u0 of r6; -u1 = (o2 - o1) rotated 90; t1 = directionpoint u1 of r4; -u2 = (o2 - o3) rotated 90; t2 = directionpoint u2 of r4; -u3 = (o4 - o3) rotated 90; t3 = directionpoint u3 of r5; -u4 = (o5 - o4) rotated 90; -u5 = (o6 - o5) rotated 90; -u6 = (o6 - o7) rotated 90; -u7 = (o7 - o8) rotated 90; -t4 = directionpoint u4 of fullcircle scaled 2 abs (t3 - o4) shifted o4; -t5 = directionpoint u5 of fullcircle scaled 2 abs (t4 - o5) shifted o5; -t6 = directionpoint u6 of fullcircle scaled 2 abs (t5 - o6) shifted o6; -t7 = directionpoint u7 of fullcircle scaled 2 abs (t6 - o7) shifted o7; - -path egg; egg = for i=0 upto 7: t[i] {u[i]} .. endfor cycle; -\end{smallcode} +} +\smallmpexternal[firstline=6,lastline=37,xleftmargin=0pt]{eggs-five-better.mp} \newpage \subsection{A superellipse egg} @@ -7093,27 +5427,18 @@ path egg; egg = for i=0 upto 7: t[i] {u[i]} .. endfor cycle; All this construction is a good exercise in ingenuity, but if you just want a simple quick egg path, then the \mpl{superellipse} macro gives you a \MP-specific option. All you need is this:\mwpic{-36pt}{eggs-super} -\begin{code}[xleftmargin=0pt] -path egg; -egg = superellipse(right, 1.6 up, left, 1.2 down, 0.69); -egg := egg scaled 100; -\end{code} +\mpexternal[firstline=6,lastline=8]{eggs-super.mp} - -\vfill \centerline{\tiny [This space intentionally left blank]} +\vfill +\centerline{\tiny [This space intentionally left blank]} \vfill \subsection{The perfect egg} The last word in egg curve perfection is the algebraic solution provided by the TDCC Laboratory in Japan [{\small \mpl{https://nyjp07.com/index_E.html}}].\mwpic{0pt}{eggs-perfect} -\begin{code} -path egg; -egg = for t=-180 step 15 until 180 - eps: - (0.78 cosd(1/4 t) * sind(t), -cosd(t)) .. - endfor cycle; -egg := egg scaled 128; -\end{code} +\mpexternal[firstline=9,lastline=13]{eggs-perfect.mp} +\noindent Note that, unlike all the others, this path has 24 points and the path starts at the top. You can draw it starting at 3 o’clock, and with only 8 points but the egg is slightly less perfect. Just replace the loop above with: @@ -7127,46 +5452,14 @@ egg = for t=90, 135, 180, -135, -90, -45, 0, 45: \subsection{Egg kitsch} If you want eggs that look solid, then you can use \mpl{interpath}:\mpic{-24pt}{eggs-shaded} -\begin{smallcode}[xleftmargin=0pt] -path egg, spot; -egg = (for t=-180 step 15 until 180 - eps: - (0.78 cosd(1/4 t) * sind(t), -cosd(t)) .. -endfor cycle) scaled 100; -spot = fullcircle scaled 4 shifted 3/4 point 3 of egg; -vardef fade_filled(expr egg, spot, dark, light, n) = image( - for i = 0 upto n: - fill interpath(i/n, egg, spot) withcolor ((i/n)**1/3)[dark,light]; - endfor) -enddef; -beginfig(1); - color a, b; - a = 1/256(150, 100, 60); - b = 1/256(256, 220, 180); - draw fade_filled(egg, spot, a, b, 256) rotated -30; -endfig; -\end{smallcode} +\smallmpexternal[firstline=6,lastline=20,xleftmargin=0pt]{eggs-shaded.mp} +\noindent This works nicely with any of the "egg" paths defined in this section. + +\vfill\noindent And finally, if all that has made you feel peckish, then how about -these?\mwpic{12pt}{eggs-fried} -\begin{smallcode}[xleftmargin=0pt, xrightmargin=-24pt] -path yolk, base; -color cooked_egg_yolk, cooked_egg_white; -cooked_egg_yolk = 1/256(216, 136, 49); -cooked_egg_white = 1/256(235, 237, 233); -vardef fried_egg(expr r) = - save base, yolk; path base, yolk; - yolk = for i=0 upto 17: (r + 1/8 normaldeviate) * dir 20i .. endfor cycle; - base = for i=0 upto 17: (2r + 1/8r * normaldeviate) * dir 20i .. endfor cycle; - base := base shifted (uniformdeviate r/2, uniformdeviate r/2); - image( - fill base withcolor cooked_egg_white; - fill yolk withcolor cooked_egg_yolk; - fill subpath (6.7, 9.6) of yolk scaled 0.8 -- - subpath (9.6, 6.7) of yolk scaled 0.66 -- cycle - withcolor 1/2[cooked_egg_yolk, white]; - ) enddef; -for i=0 upto 1: draw fried_egg(40) shifted 120 dir 120i; endfor -\end{smallcode} +these?\mwpic{0pt}{eggs-fried} +\smallmpexternal[firstline=6,lastline=20,xleftmargin=0pt,xrightmargin=-24pt]{eggs-fried.mp} %=============================================================== \newpage @@ -7175,17 +5468,34 @@ for i=0 upto 1: draw fried_egg(40) shifted 120 dir 120i; endfor \textsc{Graphs and other displays} that show data, rather than a mathematical function, are presented in this section, with a focus on illustrations for books and technical papers. Most of the examples here follow those developed in Edward -Tufte's \textsl{The Visual Display of Quantitative Information}. +Tufte's books on graphics.\vadjust{\moveright5.5in\vbox to 0pt{\vskip-42pt\noindent +\begin{itemize} +\item \textsl{The Visual Display of Quantitative Information} +\item \textsl{Visual Explanations} +\item \textsl{Beautiful Evidence} +\item \dots\ and others, at \texttt{https://edwardtufte.com} +\end{itemize}\vss}} -\bigskip\noindent -Most of them have a pale manilla background, which was added using the technique -from §\ref{backgrounds}, like this: +\vfill\noindent +Most of the drawings in this section have a pale manila background, which was added +using the technique from §\ref{backgrounds}. At the beginning, the background +colour is changed like this: +\begin{code} +background := (1, 1, 31/32); % change at start so "unfill" works +\end{code} +Then at the end of the figure, the background is applied like this: \begin{code} -picture p; p = currentpicture; currentpicture := nullpicture; -bboxmargin := 12; -fill bbox p withcolor 1/32(32, 32, 31); -draw p; +picture p; p = currentpicture; clearit; +bboxmargin := 12; unfill bbox p; draw p; \end{code} +But there are lots of figures in this section, so this “wrapping†is actually +applied using the begin- and end-figure “hooksâ€. If you examine the source code, +you will see that each figure inputs a file +called "tufte-manila-paper" which contains this: +\mpexternal{tufte-manila-paper.mp} +\noindent +The \mpl{beginfig} and \mpl{endfig} macros provided by plain \MP\ automatically apply +anything that is set in the two "extra" strings. \newpage \subsection{Simple time lines} @@ -7197,130 +5507,125 @@ use of "fontspec" to get the Palatino-like font, used in E.\@ Tufte's books. \item The data is stored as \<pair> values in a \<path> variable. This only works if both data values are numeric. If the values are larger than 4096 you either need to scale them or use the "double" number system. - \item Notice how the horizontal unit $u$ is set by measuring the width of a label using + \item Notice how the horizontal unit $u$ is set by measuring the width of a label using the technique discussed in §\ref{textsize}. And that you have to shift the data path left before applying the $x$-scaling to avoid overflow. \end{itemize} } -\begin{texcode}[xleftmargin=0pt] -\documentclass{standalone} -\usepackage{luamplib} -\usepackage{fontspec} -\setmainfont[Numbers=OldStyle]{TeX Gyre Pagella} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -\end{texcode}\vskip -8pt -\begin{smallcode}[xleftmargin=2pt] -beginfig(1); -path data, p; -data = (1978, 18) -- (1979, 19) -- (1980, 20) -- (1981, 22) - -- (1982, 24) -- (1983, 26) -- (1984, 27) -- (1985, 27.5); -numeric u, v; -u = xpart urcorner textext("1980\kern 0.75em"); v = 8; -p = data shifted -(xpart point 0 of data, 0) xscaled u yscaled v; -draw (xpart point 0 of p, 20) -- p -- (xpart point infinity of p, 20); -draw (xpart point 0 of p, 0) -- (xpart point infinity of p, 0); -for t=0 upto length p: - numeric x, y; (x, y) = point t of p; - undraw (x, y) withpen pencircle scaled 2 dotlabeldiam; - draw (x, y) withpen pencircle scaled dotlabeldiam; - label("\strut" & decimal ypart point t of data, (x, y + 8)); - draw (x, 0) -- (x, 4); - label("\strut" & decimal xpart point t of data, (x, 12)); -endfor -dotlabel.rt(btex \vbox to 6pt{\halign{\small #\hss\cr -13.7 mpg, average\cr for all cars on\cr road, 1978\cr}\vss} etex, -(xpart point 0 of p, 13.7v)); -dotlabel.lft(btex \vbox to 6pt{\halign{\small #\hss\cr -19.5 mpg, expected\cr average for all cars\cr on road, 1985\cr}\vss} etex, -(xpart point infinity of p, 19.5v)); -label.top(btex \vbox{\halign{\hss\textsc{#}\hss\cr -required fuel economy standards:\cr -new cars built from 1978 to 1985\cr}} etex, -point 5/2 of bbox currentpicture shifted 21 up); -endfig; -\end{smallcode}\vskip -10pt -\vbox to 0pt{\begin{texcode}[xleftmargin=0pt] -\end{mplibcode} -\end{document} -\end{texcode}\vss} +\enlargethispage{36pt}\vskip-12pt +\smalltexternal[firstline=1,lastline=7,xleftmargin=0pt]{tufte-mpg.mp} +\vskip-12pt +\smallmpexternal[firstline=8,lastline=36,xleftmargin=0pt]{tufte-mpg.mp} +\vskip-12pt +\smalltexternal[firstline=37,lastline=38,xleftmargin=0pt]{tufte-mpg.mp} \newpage \subsection{Time line with minimal annotation} \noindent\mpic{120pt}{tufte-budget}\marginpar{ \begin{itemize} - \item This one has an even sparser frame, and - uses the \mpl{ahangle} trick to make the neat - I-beam annotation mark. + \item This one has an even sparser frame, and dispenses + with the labels on each data point. \item It is suggested that you resist the temptation to make very many - special macros to do charts like this; the ideas here are mainly + special macros to do charts like this; the ideas here are mainly to show that \MP\ makes a good environment for following Tufte’s advice - about charts: to maximize data ink, and minimize chart junk. + about charts: to maximize data ink and minimize chart junk; + albeit at the cost of some pains-taking. \end{itemize}} -\begin{smallcode}[xleftmargin=0pt] -beginfig(1); -path data, p; -data = (1967, 311) -- (1968, 332) -- (1969, 372) -- (1970, 385) - -- (1971, 385) -- (1972, 393) -- (1973, 387) -- (1974, 381) - -- (1975, 387) -- (1976, 400) -- (1977, 380); -numeric u, v; -u = xpart urcorner textext("1980\kern 0.75em"); v = 1.414; -p = data shifted -(xpart point 0 of data, 300) xscaled u yscaled v; -draw p; -for d = 300 step 20 until 400: - numeric y; y = (d - 300) * v; - label.lft("\strut\scriptsize\$\,\small" & decimal d, (-12, y)); - draw (-8, y) -- (-12, y); - if d > 370: - draw (xpart point 3 of p, y) -- (xpart point infinity of p + 8, y) - dashed evenly scaled 1/4 withpen pencircle scaled 1/4; - fi -endfor -path a; a = (xpart point infinity of p + 21, (380 - 300) * v) - -- (xpart point infinity of p + 21, (400 - 300) * v); -interim ahangle := 180; -interim ahlength := 2; -drawdblarrow a withpen pencircle scaled 1/4; -label("\small 5\%", point 1/2 of a shifted 12 right); -for t=0 upto length p: - numeric x, y; (x, y) = point t of p; - undraw (x, y) withpen pencircle scaled 2 dotlabeldiam; - draw (x, y) withpen pencircle scaled dotlabeldiam; - draw (x, -8) -- (x, -12); - label("\strut\small" & decimal xpart point t of data, (x, -20)); -endfor -label.urt(btex \vbox{\halign{\small #\hfill\cr -Per capita\cr budget expenditure\cr in constant dollars\cr}} etex, -(0, (410 - 300) * v)); -endfig; -\end{smallcode} +\smallmpexternal[firstline=10,lastline=44,xleftmargin=0pt,xrightmargin=-30pt]{tufte-budget.mp} \newpage \subsection{Time line with more complex dates} -If the dates in your time line are more granular than years, then you need a -better way to deal with them. This chart shows the £/€ exchange rate by month. -$$\includegraphics[width=\textwidth]{tufte-currency}$$ -The dates on the horizontal axis where transformed from calendar dates to a -serial number using this routine: -\begin{code} -vardef base(expr Y, M, d) = - save m, y; numeric m, y; - if M < 3: m = M + 9; y = Y - 1; - else: m = M - 3; y = Y; fi - 365/1024 y + (floor(y/4) - floor(y/100) + floor(y/400) - + floor((2+3m)/5) + 30m + d - 307) / 1024 -enddef; -\end{code} -which allows you to add events like this: +If the dates in your time line are more granular, then you need a +better way to deal with them. This chart below shows the £/€ exchange rate by month. +The dates on the horizontal axis were transformed from calendar dates to a +serial number using the routine shown on the right, +which allows you to do this: \begin{code} dotlabel.bot("Brexit vote", (base(2016, 6, 24) * u, 78 v)); \end{code} for suitable values of $u$ and $v$. +\vadjust{\moveright5.5in\vbox to 0pt{\vss +\mpexternal[xleftmargin=0pt]{basedate.mp} +}} + +\bigskip +\noindent\hbox to \textwidth{\includegraphics{tufte-currency}\hss} + + +\newpage +\subsection{Daily events with annotation} + +\textsc{This chart} is adapted from Edward Tufte's \textsl{Visual explanations}, +p.33; +it presents the data from John Snow's table of daily deaths in the London +cholera epidemic of 1854 in a simple bar chart form, with annotation pointing out +that the epidemic was already declining when the supposedly decisive intervention of +removing the handle from the water pump at the centre of the outbreak was made. +\vadjust{\moveright5.5in\vbox to 0pt{\hsize=4in\vskip -76pt +\smallmpexternal[firstline=11,lastline=48,xleftmargin=0pt]{tufte-snow.mp} +\noindent\hey +\textit{The code for the annotation and the title was omitted to save space.\\ +See the source file for details}.\vss}} + +\medskip\noindent\includegraphics[width=\textwidth]{tufte-snow} + +\bigskip +\noindent +The data for the chart was edited directly into the \MP\ source, using a text editor +to copy the data from the source table, and format them into lists so that you can use +loops to capture the values in two parallel indexed numeric variables \mpl{deaths[]} +and \mpl{day_number[]}. It is useful to be able to group the data visually into weeks to +reduce the chance of errors, but there is no other significance. + +Note that the bars are drawn with a wide pen and \mpl{cutdraw} in order to get nice square ends +on the bars; then \mpl{undraw} is used to make implicit grid lines. \newpage -\section{Commutative diagrams} +\subsection{Scatter plot with annotations and simple jitter} + +\textsc{This chart} is from Tufte’s analysis of the Challenger space shuttle +disaster. His objective here was to show all the available +data relating launch temperature and damage to the booster rockets, and to point +out that the forecast for 28 January 1986 was very much colder than any other +launch.\vadjust{\moveright5.5in\vbox to 0pt{\hsize 4.2in\vskip -48pt +\begin{smallcode}[xleftmargin=0pt] +numeric r; r = 1/5; % adjustment of the marks where required... +path damage; damage = origin .. (53, 11) .. (57, 4) .. (58, 4) .. + (63, 2).. + (66, 0).. + (67, 0 + 2r) .. % because the data set is quite small + (67, 0) .. % the simplest way to show multiple points + (67, 0 - 2r) .. % at the same (x, y) location is to add + (68, 0).. % this little vertical shift by hand + (69, 0).. + (70, 4 + r).. % the data is captured in a path, but only the + (70, 4 - r).. % points are drawn, not the lines between them + (70, 0 + r).. + (70, 0 - r).. + (72, 0).. + % and so on +\end{smallcode} +\vss}} + +The data was again edited directly into the \MP\ source, but this time captured +as a \<path> variable. One advantage of this is that it allows you to process +all the values in parallel using \mpl{scaled} or \mpl{shifted} on the whole path. +\begin{smallcode}[xleftmargin=0pt] +numeric u, v; u = 10.8; 5u = 4v; +damage := damage xscaled u yscaled v; +\end{smallcode} +The individual points are accessed using the \mpl{point n of p} syntax: +\begin{smallcode}[xleftmargin=0pt, xrightmargin=-36pt] +for i = 1 upto length damage: + draw point i of damage withpen pencircle scaled (3/2r * v) withcolor 2/3 red; +endfor +\end{smallcode} + +\vbox to 0pt{\hbox to \textwidth{\includegraphics{tufte-srm-damage}\hss}\vss} + +\newpage +\section{Commutative diagrams}\label{sec:cd} \textsc{If you want lots} of complex bells and whistles on your commutative diagrams, then you probably want to use specialist tools like "tikz-cd" or "xypic", but if your @@ -7330,62 +5635,21 @@ using it for other illustrations, there is one less thing to learn. Here are two examples to illustrate some general techniques. They may be familiar to readers of the manuals for the tools referred to above. $$ -\includegraphics{tikzcd-example} +\includegraphics{cd-tikzcd-example} \qquad -\includegraphics{xypic-example} +\includegraphics{cd-xypic-example} $$ The complete code used to generate the right-hand picture is shown on the right.\rlap{\rightarrow}% \vadjust{\moveright5.5in\vbox to 0pt{\kern-218pt -\begin{smallcode} -picture U, XY, X, Y, Z; -z1 = -z2 = (-61, 42); - -U = thelabel("$U$", z1); -XY = thelabel("$X\times_ZY$", origin); -X = thelabel("$X$", (x2, 0)); -Y = thelabel("$Y$", (0, y2)); -Z = thelabel("$Z$", z2); - -forsuffixes @=U, XY, X, Y, Z: draw @; endfor - -ahangle := 20; -vardef curved_connect@#(expr s, a, b, d) = - save line, mark; - - path line; - line = center a {d} .. center b; - interim bboxmargin := 4; - drawarrow line cutbefore bbox a cutafter bbox b; - - picture mark; - mark = thelabel@#("$\scriptstyle " & s & "$", point 1/2 of line); - interim bboxmargin := 1; - unfill bbox mark; draw mark; -enddef; - -vardef connect@#(expr s, a, b) = - curved_connect@#(s, a, b, center b - center a) -enddef; - -connect.bot("p", XY, X); -connect.rt ("q", XY, Y); -connect.top("g", Y, Z); -connect.lft("f", X, Z); - -curved_connect.urt("x", U, X, right); -curved_connect.llft("y", U, Y, dir -80); - -drawoptions(dashed withdots scaled 1/2); -connect("(x,y)", U, XY); -drawoptions(); -\end{smallcode} -\noindent\textit{\small This example assumes you are using "mplibtextextlabel" – §\ref{ttlabel}} +\mpexternal[firstline=6,lastline=42,xleftmargin=0pt,xrightmargin=-20pt]{cd-xypic-example.mp} +\noindent +\textit{\small This example assumes you are using "mplibtextextlabel" – §\ref{ttlabel}} \vss}} The approach taken for both examples is first to define the node labels as pictures placed as needed, and then write a special-purpose "connect" macro to make consistent arrows between the nodes, using \mpl{center}, \mpl{bbox}, -\mpl{cutbefore}, and \mpl{cutafter} as appropriate. +\mpl{cutbefore}, and \mpl{cutafter} as appropriate. The $X\times_ZY$ example needs two variations. The "curved_connect" macro takes a string for the label, the two nodes to be connected, and the initial @@ -7397,327 +5661,40 @@ $b$. For the $f^*E$ example, "connect" is simpler, because all the arrows are straight and there are no labels, but needs to allow for arrows crossing: -\begin{smallcode} -vardef connect(expr a, b) = - save line; path line; interim bboxmargin := 4; - line = center a .. center b cutbefore bbox a cutafter bbox b; - cutdraw line withpen pencircle scaled 4 withcolor background; - drawarrow line -enddef; -\end{smallcode} - -\newpage -\section{Tilings and tessellations} - -\textsc{In mathematical terms}, a “tiling†is a countable set of tiles -that cover the plane without gaps or overlaps.\footnote{Adapted from \textsl{Tilings -and Patterns}, Branko Grünbaum \& G.\@ C.\@ Shephard, Freeman, 1987} -This section loosely follows that idea, and presents some ideas and general -techniques for creating tilings and other patterns or textures. - -You can make an effective grid by drawing repeated lines and then clipping to the -size you want:\mpic{-42pt}{tiling-simple} -\begin{code} -for i = -10 upto 10: - draw (left--right) scaled 200 shifted (0, 20i); - draw (down--up) scaled 200 shifted (20i, 0); -endfor -clip currentpicture to fullcircle scaled 200; -\end{code} -but this is a bit limited. If you want to produce more interesting tilings, you -need to define a unit shape or picture, and a pair of vectors to repeat it. -\begin{code} -path unit; pair u, v; color a, b; -unit = unitsquare scaled 24; -u = point 1 of unit - point 0 of unit; -v = point 3 of unit - point 0 of unit; -a = 3/4[red, white]; b = 3/4[blue, white]; -for i=-5 upto 5: - for j=-5 upto 5: - fill unit shifted (i*u + j*v) - withcolor if odd (i+j): a else: b fi; - draw unit shifted (i*u + j*v); - endfor -endfor -clip currentpicture to fullcircle scaled 200; -\end{code} -In tilings with more complex shapes you may find that using \mpl{fill} and -\mpl{draw} in the same loop causes uneven lines because the fill overlaps part of -the line. In these cases it is a good idea to duplicate the loops; use the first -set for filling, the second for drawing. - -\newpage -\subsection{Tiling with regular polygons}\label{sec:regtiling} - -\textsc{After tiling with squares}, the two simplest tilings are with triangles and -hexagons\mwpic{-24pt}{tiling-hex-trig} -(using the regular polygons from §\ref{polygons}). The basic loop is the same as the -previous page except -that the vectors $u$ and $v$ are now at 60° to each other (as shown in blue and -red in the examples to the right). All of these examples where drawn with the same -basic loop as before: -\begin{code} -for i = -n upto n: - for j = -n upto n: - draw P shifted (i * u + j * v); - endfor -endfor; -\end{code} -In the first row, $P$ was set to a simple polygon path: -\begin{code} -triangle = for i=0 upto 2: (0, 16) rotated 120i -- endfor cycle; -hexagon = for i=0 upto 5: (0, 16) rotated 60i -- endfor cycle; -\end{code} -The vectors $u$ (in red) and $v$ (in blue) were defined as (for both tilings): -\begin{code} -u = point 0 of triangle - point 1 of triangle; -v = u rotated -60; -\end{code} -To make the coloured versions, $P$ was defined as an appropriate \<picture>. -For the triangular tiling, it looked like this: $\vcenter{ -\begin{mplibcode} -input colorbrewer-rgb -path t, tt; -t = for i=0 upto 2: (0,8) rotated 120i --endfor cycle; -tt = t reflectedabout(point 2 of t, point 0 of t); - beginfig(0); -fill t withcolor Reds 8 2; fill tt withcolor Blues 8 2; draw t; draw tt; endfig; -\end{mplibcode}}$ so that the tiling actually filled the plane. In the hexagonal -tiling there are no gaps to fill, but in order to get a non-adjacent colouring, the -unit picture was defined as three shifted copies of the hexagon each filled with a -different color. The unit vectors were therefore scaled by $\sqrt3$ and rotated by -30° (as shown). - -The bottom row the unit pictures were replaced with drawings that connect the centre -of each shape to the midpoint of each side (in red), like this: -$$ -\begin{mplibcode} -path p[]; input colorbrewer-rgb -p3 = for i=0 upto 2: (0, 14) rotated 120i -- endfor cycle; -p6 = for i=0 upto 5: (0, 14) rotated 60i -- endfor cycle; -picture P[]; -for i=3,6: - P[i] = image( - for j=1 upto length p[i]: - draw origin -- point j+1/2 of p[i] withcolor Reds 7 6; - endfor - draw p[i]); -endfor - beginfig(0); draw P3; draw P3 reflectedabout(point 0 of p3, point 2 of p3); - draw P6 shifted (60, 3); endfig; -\end{mplibcode} -$$ -This has the effect of -connecting the centres of adjacent shapes in the tiling, which reveals that each -tiling is the dual of the other. - -\newpage -\subsection{Separating filling and drawing} - -\textsc{Repeating a unit image} can sometimes cause unwanted overlaps, so as noted -above, the solution is to make a filler unit and a drawing unit and do the filling -first and the drawing second. In this example\mwpic{-32pt}{arch-4-8-8} the drawing -unit (the octagon) is simple so you can just draw that path instead of making another -\<picture> for it. -\begin{smallcode} -input colorbrewer-rgb -path o, r[]; % o is the octagon, r[] are the "corners" -o = (for i=0 upto 7: 21 dir 45i -- endfor cycle) rotated -90/4; -pair t; t = whatever[point 0 of o, point 1 of o] - = whatever[point 2 of o, point 3 of o]; -r1 = subpath (1,2) of o -- t -- cycle; -r2 = r1 rotated 90; -r3 = r2 rotated 90; -r4 = r3 rotated 90; -picture filler; filler = image( - filldraw r1 withcolor Reds 8 3; - filldraw r3 withcolor Reds 8 3; - filldraw r2 withcolor Blues 8 3; - filldraw r4 withcolor Blues 8 3; - filldraw o withcolor Purples 8 2; -); -pair u, v; -u = point 0 of o - point 5 of o; v = u rotated 90; -beginfig(1); -numeric n; n = 5; -for i=-n upto n: - for j=-n upto n: - draw filler rotated ((i+j) mod 2 * 90) shifted (i*u + j * v); - endfor -endfor -for i=-n upto n: - for j=-n upto n: - draw o shifted (i*u + j * v); - endfor -endfor -\end{smallcode} -Rotating every other \mpl{filler} allows you to get the alternate colours in the squares. -\mpic{-60pt}{arch-4-8-8-parts}% -Using \mpl{filldraw} ensures that there are no gaps between adjacent segments. - -\newpage -\subsection{Tilings with more complex patterns} - -\textsc{The next example} also uses the square lattice,\mwpic{0pt}{arch-3-4-3-4} -but the unit is more complicated, so the drawing needs two \<picture> -variables, one for the colour fill and a second for the grid. -\begin{smallcode} -input colorbrewer-rgb -path s[], t[]; -s1 = unitsquare scaled 21 rotated 15; -s2 = s1 rotated 150; -t1 = subpath (4, 3) of s1 -- point 1 of s2 -- cycle; -t2 = t1 reflectedabout(point 1 of t1, point 2 of t1); -t3 = t1 rotated 150; -t4 = t1 rotated 210; -picture color_unit, grid_unit; -color_unit = image( - fill s1 withcolor Oranges 8 1; - fill s2 withcolor Oranges 8 2; - fill t1 withcolor Blues 8 1; - fill t2 withcolor Blues 8 2; - fill t3 withcolor Blues 8 3; - fill t4 withcolor Blues 8 4; -); -grid_unit = image( - draw s1; draw s2; - draw t2; draw t3; draw t4; -); -pair u, v; -u = point 1 of s1 - point 1 of s2; -v = u rotated 90; -numeric n; n = 4; -forsuffixes $=color_unit, grid_unit: - for i=-n upto n: - for j=-n upto n: - draw $ shifted (i * u + j * v); - endfor - endfor -endfor -\end{smallcode} - - - -\newpage -\subsection{Showing the dual tiling} - -\textsc{These tilings can be classified} by the configuration of the polygons that meet -at each vertex. This one is $(3^4, 6)$ because each vertex has four triangles and one -hexagon. It exists in two enantiomorph forms.\mxpic{-80pt}{3.6in}{arch-snub-hexagon} -The unit pictures look like this: -\par\bigskip -\vbox{\halign{#&\qquad\qquad\vbox to 48pt{\hsize=2.7in\noindent #\par\vss}\cr -\includegraphics[scale=0.75]{arch-snub-hexagon-unit} -&\hey\itshape To reveal the dual of the tiling, you can draw a line from -the median (or centroid if you prefer) of each polygon to the centre of each -edge.\cr}} - -\bigskip -\noindent They are drawn like this, where $h$ is the hexagon, $t_1 \dots\ t_6$ are the blue -triangles surrounding it, and $t_7$ \& $t_8$ are the two “connecting†triangles, -which swap sides to make the enantiomorphs. -\begin{code} -unit[k] = image( - for i=1 upto 6: - fill t[i] withcolor Blues 8 if odd i: 2 else: 3 fi; - endfor - for i=7 upto 8: - fill t[i] withcolor Oranges 8 if odd i: 3 else: 2 fi; - endfor - fill h withcolor Oranges 8 2; - forsuffixes S=h, t1, t2, t3, t4, t5, t6, t7, t8: - draw S withpen pencircle scaled 1/4 withcolor 3/4; - pair m; m = median(S); - for i=1 upto length S: - draw m -- point i - 1/2 of S withcolor 3/4; - endfor - endfor); -\end{code} -The $\id{median}()$ routine is from §\ref{polygons-given-side} and the colours are from -§\ref{colorbrewer}. This tiling is generated using the loop-with-triangular-grid-vectors -from §\ref{sec:regtiling}. - -\newpage -\subsection{Tiling with a dynamic unit} - -\textsc{In order to reveal} patterns in a tiling, you might want to vary the colours -or line styles used in each repeated drawing unit. In this case, you can write a -macro that takes a parameter and returns a picture to draw.\mwpic{-36pt}{arch-3-4-6-4} - -\begin{smallcode} -\mplibsetformat{metafun} % <-- for the "transparent" macro -\begin{mplibcode} -input colorbrewer-rgb -beginfig(1); -numeric r; r = 5; -path d; d = for i=1 upto 12: - (0, r) shifted (r * (sqrt(3)+2), 0) rotated 30i -- -endfor cycle; -color shade[]; -shade0 = Oranges 8 3; shade2 = Greens 8 3; -shade1 = Blues 8 3; shade3 = Reds 8 3; -vardef unit(expr n) = image( - fill d withcolor transparent (2, .9, shade[n mod 4]); - draw d; -) enddef; -pair u, v; -u = point 0 of d - point 3 of d; -v = u rotated 60; -numeric n; n = 6; -for i=-n upto n: - for j=-n upto n: - draw unit(i*j) shifted ((i - floor(j / 2)) * u + j * v); - endfor -endfor -clip currentpicture to unitsquare shifted -(1/2, 1/2) scaled (n * 9 r); -endfig; -\end{mplibcode} -\end{smallcode} -Instead of defining six triangles, six squares, and a hexagon, you can just define -the dodecagon and overlap each one. Using a macro to create the unit, allows you to -choose a different colour for each filler. Using the \mpl{transparent} macro from -Metafun automatically mixes the colours for the overlaps. But the edges don't look -so good, so you need to clip the whole picture to a neat square. - +\mpexternal[firstline=26,lastline=31]{cd-tikzcd-example.mp} \newpage \section{Recursion and iteration} +\vpic{10pt}{rec-bush} + +\noindent \textsc{This chapter is not a tutorial} on recursion or iteration \textit{per se}, but rather more of an exploration of the \MP\ techniques you can use to create some particular types -of drawing such as trees, plane-filling curves, non-periodic tilings, and fractals.\mwpic{-48pt}{rec-bush} +of drawing such as trees, plane-filling curves, fractals, and some types of tiling pattern [§\ref{aperiodic}]. \medskip\noindent -Even so, -it is perhaps useful to review some of the basic programming ideas -involved. -Consider for example the greatest common divisor algorithm presented in +Even so, it is perhaps useful to review some of the basic programming ideas +involved. Consider for example the greatest common divisor algorithm presented in §\ref{sec:gcd}. -\begin{smallcode} -vardef gcd(expr a, b) = if b = 0: a else: gcd(b, a mod b) fi enddef; -\end{smallcode} +\smallmpexternal[firstline=1,lastline=1]{rec-gcd-comparison.mp} +\noindent The reason this works is that we know (mathematically) that $0 \le a \bmod b < b$, and therefore that the arguments to the recursive call must get smaller each time and eventually we must get to $b=0$ when the answer will be $a$. This is the basic recursive approach: ensure at least one argument gets smaller each time and stop -when you get to a given limit. +when you get to a given limit. The examples in this chapter use one of two simple approaches: \begin{itemize} - \item Explicitly pass a \mpl{level} argument that is decremented on each + \item Explicitly pass a \mpl{level} argument that is decremented on each recursive call, and stop the recursion when the level gets to zero \item Pass a \<path> or two \<pair> arguments, and stop the recursion when the path is too short or the pairs are too close together. \end{itemize} If you find recursion confusing, you can nearly always use an iterative approach instead. For example, you can implement the \mpl{gcd} function like this: -\begin{smallcode} -vardef gcd(expr A, B) = save r, a, b; numeric a, b, r; a := A; b := B; - forever: - r := a mod b; exitif r = 0; - a := b; b := r; - endfor b -enddef; -\end{smallcode} +\smallmpexternal[firstline=15,lastline=20]{rec-gcd-comparison.mp} +\noindent Notice that you have to use assignment in the loop to update the variables, and that you cannot assign to the arguments of a macro. Notice also that this version requires both arguments to be positive integers. You need to use your judgement to @@ -7729,25 +5706,13 @@ decide which is the better approach for a given problem. \textsc{The Swedish mathematician} Helge von Koch\mpic{-30pt}{rec-koch-steps} originally devised the Koch curve as an example of a non-differentiable curve that could be constructed with elementary geometry. It makes a good introduction to recursive paths with \MP. The -construction is recursive: each straight line segment in the path is replaced with +construction is recursive: each straight line segment in the path is replaced with four copies of itself, scaled down $\frac13$ and arranged as shown at Level 1 \rightarrowfill\break At each level of the construction, the number of points in the path increases -four-fold and the \mpl{arclength} of the path gets $\frac43$ longer. -\begin{code} -vardef koch(expr level, a, b) = - if level = 0: - a -- b - else: - save p, q, r; pair p, q, r; - p = 1/3[a,b]; r = 2/3[a,b]; q = r rotatedabout(p, 60); - koch(level-1, a, p) & - koch(level-1, p, q) & - koch(level-1, q, r) & - koch(level-1, r, b) - fi -enddef; -\end{code} +four-fold and the \mpl{arclength} of the path gets $\frac43$ longer. +\mpexternal[firstline=7,lastline=18]{rec-koch-steps.mp} +\noindent The five levels were drawing using this function in a loop like this: \begin{code} for n=0 upto 4: @@ -7768,38 +5733,25 @@ detail. \subsection{Sierpinski's gaskets} \textsc{The second example} of recursive construction also dates from the early 20th -century, but unlike von Koch's infinite curve, the area of Sierpinski's gasket tends +century, but unlike the infinite length of von Koch's curve, the area of Sierpinski's gasket tends to zero.\mwpic{-12pt}{rec-sierpinski-triangle} In the original specification, you are supposed to remove the central quarter of each triangle, but this program does it the other way round and delays drawing the triangles until they are small enough. -\begin{code}[xleftmargin=0pt, xrightmargin=-2in] -vardef gasket(expr t, s, limit) = - if length (point 1 of t - point 0 of t) < limit: - fill t; - else: - save little_t; path little_t; little_t = t scaled s; - for i=1 upto length t: - gasket(little_t shifted (point i of t - point i of little_t), s, limit); - endfor - fi -enddef; -\end{code} +\mpexternal[firstline=6,lastline=15,xleftmargin=0pt,xrightmargin=-72pt]{rec-sierpinski-triangle.mp} +\noindent Note the useful idiom \mpl{shifted (point i of t - point i of little_t)} – this neatly tucks a copy of the small triangle into the appropriate corner of the big triangle. You can make this even simpler by coding the scaling parameter $s$ and -\id{limit} as constants in the recursive routine, so that you do not have to pass +\id{limit} as constants in the recursive routine, so that you do not have to pass them down each time. The triangular gasket was generated using the macro like this: -\begin{code}[xleftmargin=0pt, xrightmargin=-2in] -beginfig(1); - path T; T = for i = 1 upto 3: 220 up rotated 120i -- endfor cycle; - gasket(T, 1/2, 20); -endfig; -\end{code} -You can generalize it, for example by making +\mpexternal[firstline=16,lastline=19,xleftmargin=0pt,xrightmargin=-72pt]{rec-sierpinski-triangle.mp} +\noindent +You can generalize this idea, for example by making the path \id{T} into a pentagon with scaling factor $s=(3-\sqrt5)/2$, or a hexagon with $s=1/3$, and so on: -\vbox to 0pt{\vskip-2pt\hsize10in\noindent\includegraphics[width=10in]{rec-sierpinski-pentagon.pdf}\par\vss} +\vbox to +0pt{\vskip-2pt\hsize10in\noindent\includegraphics[width=10in]{rec-sierpinski-garlands.pdf}\par\vss} \newpage \subsection{The Heighway dragon} @@ -7815,32 +5767,15 @@ copies of itself scaled down and arranged as shown.\mwpic{-36pt}{rec-dragon} Note that every other segment is flipped left and right. At each stage, the number of points increases two-fold and the path gets $\sqrt2$ times longer. Here is a recursive routine to generate the curve as a single path. -\begin{smallcode} -numeric r, theta; r = sqrt 1/2; theta = 45; -vardef dragon(expr level, a, b) = - if level > 0: - save p; pair p; - p = r[a, b] rotatedabout(a, theta); - dragon(level - 1, a, p) & reverse dragon(level - 1, b, p) - else: - a .. b - fi -enddef; -\end{smallcode} +\smallmpexternal[firstline=6,lastline=15]{rec-dragon.mp} +\noindent The blue dragon was created with: {\small\mpl{draw dragon(15, origin, 240 right)}}\rlap{\raise1ex\hbox{\ $\smash{\nearrow}$}} After the fourth level the corners of the curve start to touch each other, but they never cross. You can see this if you draw the curve with rounded corners. -\begin{smallcode} -vardef rounded_corners expr p = - save r, n; numeric r, n; r = 1/3; n = length p; - subpath (0, 1-r) of p - for t=1 upto n-1: - .. subpath (t+r, t+1-r) of p - endfor .. subpath (n-r, n) of p -enddef; -\end{smallcode} +\smallmpexternal[firstline=17,lastline=23]{rec-dragon.mp} +\noindent The red dragon was: {\small\mpl{draw rounded_corners dragon(10, origin, 240 right)}}\rlap{\hbox{\ $\smash{\longrightarrow}$}} @@ -7852,7 +5787,7 @@ number system when $n > 11$.} \newpage \subsection{Iterative dragons} -\textsc{The dragon curve} can also be created with iteration instead of recursion. +\textsc{The dragon curve} can also be created with iteration instead of recursion. Another way of viewing the stages of developing the curve is that at each stage the whole curve is replaced by two copies of itself arranged as shown: @@ -7861,16 +5796,8 @@ whole curve is replaced by two copies of itself arranged as shown: \smallskip\noindent We can do this in two steps in a loop, like this:\mpic{-160pt}{ifs-heigh} -\begin{smallcode} -path p; p = origin -- dir 30; -numeric n; -for i=1 upto 12: - n := length p; - p := p rotated 45; - p := p & reverse p rotatedabout(point n of p, 90); -endfor -draw p scaled (384 / xpart (urcorner p - llcorner p)); -\end{smallcode} +\smallmpexternal[firstline=6,lastline=13,xleftmargin=0pt]{ifs-heigh.mp} +\noindent In this approach, instead of scaling down each time, the curve is just allowed to grow $\sqrt2$-times bigger in each loop, then scaled to the desired width (384\unit{pt}) when it is complete. The 12 stages in the loop produce the rotated blue @@ -7878,48 +5805,34 @@ dragon as shown.\rlap{\raise1ex\hbox{\ $\smash{\nearrow}$}} \vfill\noindent With a small adaptation, you can also use this to explore variations. -\begin{smallcode} -path p; p = origin -- dir 30; -numeric n, r; r = 3; -for i=1 upto 12: - n := length p; - p := p rotated (45 - r); - p := p & reverse p rotatedabout(point n of p, 90 + 2r); -endfor -\end{smallcode} +\smallmpexternal[firstline=6,lastline=13,xleftmargin=0pt]{ifs-heigh-open.mp} +\noindent The extra parameter $r$ is used to open up the folds, making it more “organicâ€.\mpic{-200pt}{ifs-heigh-open} \newpage \subsection{The golden dragon} -\textsc{You can also explore variations} with the recursive approach by altering -the scaling and rotation. Here $r\simeq 0.74274$ and -$\theta\simeq 32.893°$ in the initial triangle.\vadjust{\moveright136pt\vbox to -0pt{\vskip 3.16in \hsize 3.6in \noindent +\textsc{You can explore variations} with the recursive approach by altering +the scaling and rotation. Here $r=1/\phi^{1/\phi}\simeq 0.74274$ and +$\theta\simeq 32.893°$ in the initial triangle. + +\medskip +\vbox to 3in{\noindent\hbox to \textwidth{\includegraphics{rec-dragon-golden.pdf}\hss}\vss} + +\moveright136pt\vbox to 0pt{\hsize 3.6in \noindent Because the initial triangle shape is shorter on one side, it is better to adapt the \mpl{dragon} routine to measure the gap between points instead of using a fixed level parameter: -\begin{smallcode} -vardef dragon(expr a, b) = - if abs(a-b) > 1: - save p; pair p; - p = r[a, b] rotatedaround(a, theta); - dragon(a, p) & reverse dragon(b, p) - else: - a .. b - fi -enddef; -\end{smallcode} -\vss}} -$$\hbox to \textwidth{\includegraphics{rec-dragon-golden.pdf}\hss}$$ +\smallmpexternal[firstline=12,lastline=20]{rec-dragon-golden.mp} +\vss} \newpage \subsection{The Peano-Gosper curve, or flow-snake} -\textsc{The Peano-Gosper curve} is a space-filling curve. It is -constructed in the same way as the dragons, but generating shape has seven sections -instead of two, and they are cunningly arranged to fill the space.\mpic{-48pt}{rec-flowsnake-construction} +\textsc{The Peano-Gosper curve} is a space-filling curve. It is +constructed in the same way as the dragons, but the generating shape has seven sections +instead of two, and they are cunningly arranged to fill the space.\mpic{-72pt}{rec-flowsnake-construction} The arrows indicate the reversals so that the scaled-down copies fill the larger part of the hexagons that contain them.\rlap{\hbox{\ $\smash{\rightarrow}$}} $$\includegraphics[width=\textwidth]{rec-flowsnake}$$ @@ -7927,25 +5840,9 @@ This fourth-level curve is the boundary between the filled and unfilled branches \vadjust{\moveright 384pt \vbox to 0pt{\vss\hsize 4in \noindent Given the \id{snake} path scaled to unit length as shown above in \red{red}, the -flow-snake path can be created with: -\begin{smallcode} -vardef rattle(expr level, a, b) = - if level > 0: - save s; path s; s = snake zscaled (b-a) shifted a; - reverse rattle(level - 1, point 1 of s, a) & - rattle(level - 1, point 1 of s, point 2 of s) & - rattle(level - 1, point 2 of s, point 3 of s) & - rattle(level - 1, point 3 of s, point 4 of s) & - reverse rattle(level - 1, point 5 of s, point 4 of s) & - reverse rattle(level - 1, point 6 of s, point 5 of s) & - rattle(level - 1, point 6 of s, b) - else: - a -- b - fi -enddef; -path S; S = rattle(4, origin, 360 right); -\end{smallcode} -}} +flow-snake on the left was created with +\smallmpexternal[firstline=18,lastline=38]{rec-flowsnake.mp} +\vskip -48pt}} \newpage \subsection{Fractal trees} @@ -7955,72 +5852,31 @@ path S; S = rattle(4, origin, 360 right); then make the first branch by scaling the trunk by $r$, rotating it $+\theta$, and moving it to the top of the trunk; make the second in the same way but rotate it by $-\theta$. Then repeat using each branch as a new trunk.\mpic{-114pt}{rec-simple-tree} -And stop after enough levels. +And stop after enough levels. This can be implemented easily in \MP, but requires a slightly different technique. There is no simple way to represent the tree as a single \<path> because a path cannot have branches, so you need to draw each segment separately instead of trying to join them up. Compare this to the \mpl{rattle} routine on the page before. -\begin{code} -vardef make_tree(expr level, bar) = - draw bar; - if level > 0: - for t=-theta, theta: - make_tree(level - 1, bar shifted - point 0 of bar - scaled r rotated t shifted point 1 of bar); - endfor - fi -enddef; -\end{code} +\mpexternal[firstline=7,lastline=16]{rec-simple-tree.mp} +\noindent To combine several such trees in a drawing either move the initial \id{bar} path, or capture the tree as a \<picture> using \mpl{image(make_tree(...))}, like so: -\begin{code} -picture T[]; numeric r, theta; -r = 0.58; theta = 60; T1 = image( - make_tree(3, origin -- 100 up); -); -% update r and theta... -r := 0.75; theta := 14; T2 = image( - make_tree(10, origin -- 100 up); -); -draw T1 shifted 32 up; -draw T2 shifted 128 right; -\end{code} +\mpexternal[firstline=18,lastline=26]{rec-simple-tree.mp} +\noindent Notice that $r$ and $\theta$ are treated as global constants. You could pass them to the \mpl{make_tree} routine instead. Notice also that the smaller tree only has -three levels, but the larger one has 10. And that the labels were omitted. +three levels, but the larger one has 10. \newpage -\subsubsection{More fractal vegetation} +\subsubsection*{More fractal vegetation} \textsc{If you are more interested} in the visual aspect of your tree than the mathematical, you can tweak the \mpl{make_tree} routine a bit.\mpic{-12pt}{rec-general-tree} -\begin{smallcode}[xleftmargin=0pt] -vardef make_tree(expr bar) = - save a; numeric a; a = abs(point 1 of bar - point 0 of bar); - cutdraw bar withpen pencircle scaled 1.2(1/8 a) withcolor background; - cutdraw bar withpen pencircle scaled (1/8 a) withcolor 1/256(57, 35, 32); - if a > leaf: - save s; pair s; - s = 1/32 a * r * unitvector(direction 1 of bar) rotated 90; - make_tree(bar shifted - point 0 of bar - shifted s scaled r rotated theta - shifted point 1 of bar); - make_tree(bar shifted - point 0 of bar - shifted -s scaled r rotated -theta - shifted point 1 of bar); - else: - draw point 1 of bar withpen pencircle scaled 1 withcolor 2/3 green; - fi -enddef; -beginfig(1); - numeric leaf, r, theta; - r = 0.75; theta = 14; leaf = 3; - make_tree(origin -- 100 up); -endfig; -\end{smallcode} +\smallmpexternal[firstline=6,lastline=31,xleftmargin=0pt]{rec-general-tree.mp} +\noindent \begin{itemize} \item The recursion is controlled by measuring the length of the branches instead of using a \id{level} parameter. @@ -8032,7 +5888,7 @@ endfig; \end{itemize} \newpage -\subsubsection{Randomized recursive plants} +\subsubsection*{Randomized recursive plants} \vskip-\baselineskip \noindent\hbox to \linewidth{\includegraphics{rec-general-tree-deviate}\hss} @@ -8040,154 +5896,320 @@ endfig; \noindent \textsc{To get plants that look more natural} you can introduce some random factors. Strictly these are not fractal because they are not -self-similar. The only change from the previous \mpl{make_tree} is to replace -\mpl{scaled r rotated theta} with -\begin{smallcode}[xleftmargin=0pt] -scaled (r + 1/16 normaldeviate) rotated (theta + 8 normaldeviate) -\end{smallcode} -The bush is similar, except that it splits into four branches at each step instead of -two and only the lengths randomized.\mwpic{-96pt}{rec-bush} +self-similar. The only change from the previous \mpl{make_tree} was to replace +\mpl{scaled r rotated theta} with +\smallmpexternal[firstline=17,lastline=17,xleftmargin=0pt]{rec-general-tree-deviate.mp} + +\vfill\noindent +\textsc{The bush} is similar, except that it splits into four branches at each step instead of +two and only the lengths are randomized.\mwpic{-96pt}{rec-bush} The colouring was a happy accident. -\begin{smallcode}[xleftmargin=0pt, xrightmargin=-100pt] +\mpexternal[firstline=8,lastline=17,xleftmargin=0pt,xrightmargin=-150pt]{rec-bush.mp} + +\newpage +\section{Periodic tilings} + +\textsc{In mathematical terms}, a “tiling†is a countable set of tiles +that cover the plane without gaps or overlaps.\footnote{Adapted from \textsl{Tilings +and Patterns}, Branko Grünbaum \& G.\@ C.\@ Shephard, Freeman, 1987} +A \textit{periodic} tiling is one that consists of a unit shape or pattern that is +repeated by translation in two dimensions.\vadjust{\moveright5.5in\vbox to +0pt{\hsize4in\vskip -60pt +\centerline{For notes on drawing \textit{aperiodic} tilings, see below in §\ref{aperiodic}}\vss}} +This section loosely follows that idea, and presents some ideas and general +techniques for creating tilings and other patterns or textures. —— +You can make an effective grid by drawing repeated lines and then clipping to the +size you want:\mpic{-42pt}{tiling-simple} +\mpexternal[firstline=8,lastline=12,xleftmargin=0pt,xrightmargin=-12pt]{tiling-simple.mp} +\noindent +but this is a bit limited. If you want to produce more interesting periodic +tilings, you need to define a unit shape or picture, and a pair of vectors to repeat it. +\mpexternal[firstline=16,lastline=28,xleftmargin=0pt,xrightmargin=-12pt]{tiling-simple.mp} +\noindent +In tilings with more complex shapes you may find that using \mpl{fill} and +\mpl{draw} in the same loop causes uneven lines because the fill overlaps part of +the line. In these cases it is a good idea to duplicate the loops; use the first +set for filling, the second for drawing. + +\newpage +\subsection{Tiling with regular polygons}\label{sec:regtiling} + +\textsc{After tiling with squares}, the next two simplest tilings use triangles and +hexagons\mwpic{-24pt}{tiling-hex-trig} +(made using the routines from §\ref{polygons}). The basic loop is the same as the +previous page except +that the vectors $u$ and $v$ are now at 60° to each other (as shown in blue and +red in the examples to the right). All of these examples were drawn with the same +basic loop as before: +\mpexternal[firstline=11,lastline=15,xleftmargin=0pt]{tiling-hex-trig.mp} +\noindent +In the first row, $P$ was set to a simple polygon path: +\mpexternal[firstline=28,lastline=29,xleftmargin=0pt]{tiling-hex-trig.mp} +\noindent +The vectors $u$ (in red) and $v$ (in blue) were defined as (for both tilings): +\mpexternal[firstline=31,lastline=32,xleftmargin=0pt]{tiling-hex-trig.mp} +\noindent +To make the coloured versions, $P$ was defined as an appropriate \<picture>. +For the triangular tiling, it looked like this: $\vcenter{ +\begin{mplibcode} input colorbrewer-rgb -vardef bush(expr start, aim, level, limit) = - save s, target; numeric s; pair target; s = level / limit; - for a = -32, -8, 8, 16: - target = aim scaled ((32 + 16 normaldeviate) * s) rotated a shifted start; - draw start -- target withpen pencircle scaled s withcolor BrBG[limit][limit-level]; - if level > 1: bush(target, aim rotated a, level - 1, limit); fi - endfor -enddef; -beginfig(1); bush(origin, dir 80, 6, 8); endfig; -\end{smallcode} +path t, tt; +t = for i=0 upto 2: (0,8) rotated 120i --endfor cycle; +tt = t reflectedabout(point 2 of t, point 0 of t); +fill t withcolor Reds 8 2; fill tt withcolor Blues 8 2; draw t; draw tt; +\end{mplibcode}}$ so that the tiling actually filled the plane. In the hexagonal +tiling there are no gaps to fill, but in order to get a non-adjacent colouring, the +unit picture was defined as three shifted copies of the hexagon each filled with a +different color. The unit vectors were therefore scaled by $\sqrt3$ and rotated by +30° (as shown). + +The bottom row the unit pictures were replaced with drawings that connect the centre +of each shape to the midpoint of each side (in red), like this: +$$ +\begin{mplibcode} +path p[]; input colorbrewer-rgb +p3 = for i=0 upto 2: (0, 14) rotated 120i -- endfor cycle; +p6 = for i=0 upto 5: (0, 14) rotated 60i -- endfor cycle; +picture P[]; +for i=3,6: + P[i] = image( + for j=1 upto length p[i]: + draw origin -- point j+1/2 of p[i] withcolor Reds 7 6; + endfor + draw p[i]); +endfor + draw P3; draw P3 reflectedabout(point 0 of p3, point 2 of p3); + draw P6 shifted (60, 3); +\end{mplibcode} +$$ +This has the effect of +connecting the centres of adjacent shapes in the tiling, which reveals that each +tiling is the dual of the other. \newpage -\subsection{Penrose tilings} +\subsection{Separating filling and drawing} -\textsc{Recursion is useful} for generating non-periodic tilings,% -\vadjust{\moveright5.5in\vbox to 0pt{\kern-8pt -\begin{smallcode} -% golden ratio constant -numeric psi; psi = (sqrt 5 - 1) / 2; +\textsc{Repeating a unit image} can sometimes cause unwanted overlaps, so as noted +above, the solution is to make a filler unit and a drawing unit and do the filling +first and the drawing second. In this example\mwpic{-32pt}{tiling-arch-4-8-8} the drawing +unit (the octagon) is simple so you can just draw that path instead of making another +\<picture> for it. +\mpexternal[firstline=5,lastline=31]{tiling-arch-4-8-8.mp} +\noindent +Rotating every other \mpl{filler} allows you to get the alternate colours in the squares. +\mpic{-60pt}{tiling-arch-4-8-8-parts}% +Using \mpl{filldraw} ensures that there are no gaps between adjacent segments. -% inflating tall shape makes two others -vardef inflate_tall(expr level, a, b, c) = - if level = 0: - draw a--b--c withpen pencircle scaled 1/8; - else: - save d; pair d; d = psi[b,a]; - inflate_tall(level - 1, d, c, a); - inflate_wide(level - 1, c, d, b); - fi -enddef; +\newpage +\subsection{Tilings with more complex patterns} -% inflating wide makes three -vardef inflate_wide(expr level, a, b, c) = - if level = 0: - draw a--b--c withpen pencircle scaled 1/8; - else: - save d, e; pair d, e; d = psi[a,b]; e = psi[a,c]; - inflate_tall(level - 1, d, e, b); - inflate_wide(level - 1, e, d, a); - inflate_wide(level - 1, c, e, b); - fi -enddef; +\textsc{The next example} also uses the square lattice,\mwpic{0pt}{tiling-arch-3-4-3-4} +but the unit is more complicated, so the drawing needs two \<picture> +variables, one for the colour fill and a second for the grid. +\mpexternal[firstline=7,lastline=36,xleftmargin=0pt]{tiling-arch-3-4-3-4.mp} -% start with a tall triangle with apex at origin -pair a, b, c; -b = origin; -c = (sind(18), sind(72)) scaled 800; -a = (-xpart c, ypart c); +\newpage +\subsection{Showing the dual tiling} -% make an inflated "wedge" -picture P; P = image(inflate_tall(7, a, b, c)); +\textsc{These tilings can be classified} by the configuration of the polygons that meet +at each vertex. This one is $(3^4, 6)$ because each vertex has four triangles and one +hexagon. It exists in two enantiomorph forms.\mpic{-80pt}{tiling-arch-snub-hexagon} +The unit pictures look like this: +\par\bigskip +\vbox{\halign{#&\qquad\qquad\vbox to 48pt{\hsize=2.7in\noindent #\par\vss}\cr +\includegraphics[scale=0.75]{tiling-arch-snub-hexagon-unit} +&\hey\itshape To reveal the dual of the tiling, you can draw a line from +the centroid of each polygon to the midpoint of each edge.\cr}} -% then exploit the five-fold symmetry to make the picture -for t = 0 upto 9: - draw P if odd t: reflectedabout(b, c) fi rotated 72t; -endfor; -\end{smallcode} +\bigskip +\noindent They are drawn like this, where $h$ is the hexagon, $t_1 \dots\ t_6$ are the blue +triangles surrounding it, and $t_7$ \& $t_8$ are the two “connecting†triangles, +which swap sides to make the enantiomorphs. +\mpexternal[firstline=23,lastline=37,xleftmargin=0pt]{tiling-arch-snub-hex-parts.mp} +\noindent +The $\id{centroid}()$ routine is from §\ref{polygons} and the colours are from +§\ref{colorbrewer}. This tiling is generated using the loop-with-triangular-grid-vectors +from §\ref{sec:regtiling}. + +\newpage +\subsection{Tiling with a dynamic unit} + +\textsc{In order to reveal} patterns in a tiling, you might want to vary the colours +or line styles used in each repeated drawing unit. In this case, you can write a +macro that takes a parameter and returns a picture to draw.\mwpic{-48pt}{tiling-arch-3-4-6-4} +\smallmpexternal[firstline=6,lastline=30]{tiling-arch-3-4-6-4.mp} +\noindent +Instead of defining six triangles, six squares, and a hexagon, you can just define +the dodecagon and overlap each one. Using a macro to create the unit, allows you to +choose a different colour for each filler. Using the transparency support from +"luamplib" automatically mixes the colours for the overlaps. But the edges don't look +so good, so you need to clip the whole picture to a neat square. + +\newpage +\subsection{Colouring with a set number of colours} -\qquad\hey \textit{\small Colouring the tiling is left as an exercise for the -reader.}\par\vss}} -like those discovered in the 1970s by the British polymath Sir Roger Penrose. -$$\includegraphics[width=\textwidth]{penrose-P3.pdf}$$ -By definition, there is no periodic unit to repeat; but there are well-known -expansion rules to split each shape in the tiling into smaller congruent copies. So -you can start with a single large shape and apply the rules recursively to make the -tiling. The tiling above is made from two rhombus shapes, but each of these shapes can be -split in half into two triangles, and the expansion process actually works on these: -$$\includegraphics{penrose-stages.pdf}$$ +\textsc{This “attractive and ingenious†pattern of squares} is given in Grünbaum \& +Shephard, chapter 8, and is shown here coloured with three colours so that no two +squares with the same colour touch each other.\mpic{-12pt}{tiling-pp48a} + +\mpexternal[firstline=7,lastline=26,xleftmargin=0pt]{tiling-pp48a.mp} +\noindent +The points of interest here are +\begin{itemize} + \item The use of the \mpl{sind} function to position the square in the unit so + that it makes the six-pointed star when rotated. + \item The expression “\mpl{t mod 3 + 3}†which cycles through 3, 4, and 5 for + different values of $t$. +\end{itemize} +Many different colourings are possible but you might need to make a more complex +unit drawing for some of them. + + +\newpage +\section{Aperiodic tilings}\label{aperiodic} + +\textsc{Mathematical research in the 1960s and 1970s} established that it is also +possible to tile an infinite plane with polygons that do not have any periodic +repeating pattern. There are various mathematical approaches to creating these +tilings; this section explores substitution tilings, which lend themselves to +recursive programming. The rules for a substitution define a dissection for each +shape that makes up the tiling. + +The idea is to define a recursive macro for each shape in the tiling, with +parameters for the recursion level and points that define the shape. If +$\id{level}=0$, draw or decorate that particular shape, otherwise work out +the points for the dissection and call the appropriate macros for each shape with +$level-1$. Here is an example:\mpic{-123pt}{tiling-subs-triangle.pdf} + +\mpexternal[firstline=7,lastline=28]{tiling-subs-triangle.mp} \vbox to 0pt{\noindent -Each expansion of half the thick rhombus, produces two more thick halves and one -thin half; each expansion of half the thin rhombus produces a thick half and a thin -half. No other shapes are produced, so the recursive process can be repeated -indefinitely. At the desired lowest level the triangles are patched back into -rhombus shapes simply by \textit{not} drawing the edges shown with dots.\par\vss} +These procedures are illustrated on the right. The completed +tiling was drawn with \mpl{tall(6, 173 dir 210, 173 dir 330, 173 dir 90)}. +\par\vss} \newpage \subsection{Pinwheel tiling} -\textsc{Another non-periodic tiling} is the so-called pinwheel tiling, devised in 1994 +\textsc{The second aperiodic tiling example} is the so-called pinwheel tiling, devised in 1994 by Charles Radin, based on -this dissection by John Conway.\mpic{-22pt}{pinwheel} -$$\includegraphics{conway.pdf}$$ +this dissection by John Conway.\mpic{-22pt}{tiling-subs-pinwheel} +$$\includegraphics[scale=0.8]{tiling-conway}$$ Starting with a triangle of this shape, the tiling recursively divides into five smaller copies of itself. The colouring is passed down each level but only used on the lowest. -\begin{smallcode} -input colorbrewer-rgb -vardef pinwheel(expr level, a, b, c, s) = - if level = 0: - fill a--b--c--cycle withcolor s; - draw a--b--c--cycle withpen pencircle scaled 1/8 withcolor white; - else: - save d, e, f, g; pair d, e, f, g; - d = 2/5[b, c]; e = 4/5[b,c]; f = 1/2[e, a]; g = 1/2[a, b]; - pinwheel(level - 1, e, a, c, Blues 9 4); - pinwheel(level - 1, f, g, a, Blues 9 3); - pinwheel(level - 1, f, g, e, Blues 9 2); - pinwheel(level - 1, d, e, g, Blues 9 5); - pinwheel(level - 1, d, b, g, Blues 9 6); - fi -enddef; -beginfig(1); - pinwheel(5, origin, 200 right, 100 up, ""); - pinwheel(5, (200,100), 100 up, 200 right, ""); -endfig; -\end{smallcode} -Notice that to make the dissection work, it is important to pass the three -\<pair> arguments in the right order. +\smallmpexternal[firstline=1,lastline=15]{tiling-pinwheel-macro.mp} +\vskip -\baselineskip + +\smallmpexternal[firstline=7,lastline=14]{tiling-subs-pinwheel.mp} + +\enlargethispage{24pt} + +\noindent +\hey To make the dissection work, it is important to pass the three +\<pair> arguments in the right order. Note also the manipulation of +\mpl{currentpicture} at the end. \newpage -\tableofcontents +\subsection{Ammann A5 tiling} + +\textsc{Of the various sets} of aperiodic tiles discovered by Robert Ammann in 1977, +the best known and probably most attractive is the set known as A5. The recursive +substitutions for the tiling are usually given as follows, + +\smallskip +\centerline{\includegraphics{tiling-ammann-substitutions-overlapping.pdf}} +\smallskip\noindent +with the square shapes overlapping the edges of the parent shapes. This can be +implemented with two co-operating recursive macros \rightarrowfill +\vadjust{\moveright384pt\vbox to 0pt{\vskip -138pt +\centerline{\small\textit{This needs the \mpl{withalpha} macro given in §\ref{sec:transparent}}.} +\smallmpexternal[firstline=10, lastline=48, xleftmargin=0pt, xrightmargin=-30pt]{tiling-ammann-procedures.mp} +\vss}} + +The overlaps mean that much of the tiling is overlaid by other expansions which +makes the resulting PDF rather large, and that you need to clip the final picture to +the original shape. The uneven texture is apparent if you colour the tiles with +transparent colours (although this is not unattractive): + +\noindent +\vbox to 0pt{\noindent +\centerline{\includegraphics{tiling-ammann.pdf}} +\vss} \newpage -\section*{To do...} +\subsection{Ammann A5 tiling improved} -- angle marks, including curved angle marks +\textsc{With some extra thought}, you can devise a substitution pattern that avoids +the overlaps and makes a smaller tiling. The idea is to split the square in half, +and make a macro that can do the top half or the bottom half as required. -- drawing knots, double lines, ropes +\smallskip +\centerline{\includegraphics{tiling-ammann-substitutions-bounded.pdf}} +\smallskip\noindent +This requires an extra parameter for the new "half_square" macro to tell it which +half to do, and two triangular paths for the upper and lower halves. Note that +the second of these paths is reversed, which simplifies the macro. +\vadjust{\moveright384pt\vbox to 0pt{\vskip -172pt +\smallmpexternal[firstline=10, lastline=14, xleftmargin=0pt, xrightmargin=-30pt]{tiling-ammann-procedures.mp} +\smallmpexternal[firstline=50, lastline=81, xleftmargin=0pt, xrightmargin=-30pt]{tiling-ammann-procedures.mp} +\vss}} -- decorating lines +Now there is no overlapping of any of the tiles and the tiling does not overflow outside the original +shape, and the colouring is uniform. +$$\includegraphics[width=\textwidth]{tiling-ammann-bounded.pdf}$$ +In general, aperiodic tilings work best if you can find a set of recursive +substitutions that are bounded within each parent shape. -- the eye, hand +\noindent\hey{\small Notice also the useful idiom \mpl{zscaled (b-a) shifted a} used +with a “unit†shape.} -- physics diagrams, pendulum, indicating movement and vibration +\newpage +\subsection{Penrose P2 tiling} -- examining a glyph +\textsc{The same techniques are useful} for generating the well-known aperiodic +tilings discovered in the 1970s by the British polymath Sir Roger Penrose. +This P2 tiling is also known as the “kite and dart†tiling. +\vadjust{\moveright384pt\vbox to 0pt{\vskip +-36pt\smallmpexternal[firstline=7, lastline=46, xleftmargin=0pt]{tiling-penrose-tatham-p2-kite-dart.mp}\vss}} +The expansion rules used here are those documented by Simon Tatham. +$$\includegraphics{tiling-penrose-tatham-p2-kite-dart-construction.pdf}$$ +Each of the shapes is split into two opposite triangles and the expansion rules +applied separately. Only part of the edge of each triangle is drawn, so that the +proper shapes appear in the final result. The patch below was clipped to a +rectangle. -- all sorts of arrow, arrows between arrows, arrows next to a path (handles) +\bigskip +\vbox to 2.4in{\noindent +\includegraphics[width=\textwidth]{tiling-penrose-tatham-p2-kite-dart.pdf} +\vss} +\newpage +\subsection{Penrose P3 tiling} -- faking 3d +\textsc{The final example} is Penrose's P3 tiling, composed of thick and thin +rhombus shapes. There is no new \MP\ technique, but it is perhaps of mathematical +interest that the code for P3 is so similar to P2 on the previous page. +\vadjust{\moveright384pt\vbox to 0pt{\vskip -36pt +\smallmpexternal[firstline=7, lastline=46, xleftmargin=0pt]{tiling-penrose-tatham-p3-rhombs.mp} +\vss}} +$$\includegraphics[scale=0.9]{tiling-penrose-tatham-p3-rhombs-construction.pdf}$$ +Each of the shapes is again split into two opposite triangles and the expansion rules +applied separately, and only part of the edge of each triangle is drawn, so that the +proper shapes appear in the final result. + +\bigskip +\vbox to 2.4in{\noindent +\includegraphics[width=\textwidth]{tiling-penrose-tatham-p3-rhombs.pdf} +\vss} -- functions, def, vardef, recursion, primarydef etc, of syntax, expr suffix text -- four box model charts - Tufte charts - Venn diagrams +% \newpage{Physics and engineering} +% - the eye, hand +% - physics diagrams, pendulum, indicating movement and vibration -- tour of the plain format +\newpage +\tableofcontents \end{document} diff --git a/info/drawing-with-metapost/src/angles-lines.mp b/info/drawing-with-metapost/src/angles-lines.mp deleted file mode 100644 index 5b2f3be14c..0000000000 --- a/info/drawing-with-metapost/src/angles-lines.mp +++ /dev/null @@ -1,78 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - % define a unit - numeric u; - u = 1cm; - - % define the axes - path xx, yy; - xx = (2 left -- 10 right) scaled u; - yy = (down -- 7 up) scaled u; - - % and the angles - numeric theta, psi; - psi = 28; - theta = 50; - - % and some points - pair P, Q, H, N, M, T, L; - P = (4, 3) scaled 1cm; - - % now some lines - path ell, tee, arc; - ell = (left--right) scaled 10u rotated theta shifted P cutbefore xx; - tee = (left--right) scaled 10u rotated psi shifted P cutbefore xx; - - % this is a bit if a fiddle, but gets us a circular arc tangent to - % the line tee at point P, which appears to be what is wanted.... - arc = subpath (1.6, 3.2) of halfcircle rotated -180 shifted 1/2 up - scaled 10u shifted P rotatedabout(P, psi); - - % the rest of the points then follow... - Q = ell intersectionpoint subpath (1.5, 3) of arc; - H = P + whatever * dir psi; - xpart H = xpart Q = xpart M; ypart M = ypart N = 0; - xpart N = xpart P; - L = point 0 of ell; - T = point 0 of tee; - - % now we can get with the drawing - draw arc dashed withdots scaled 1/4 withcolor 1/2 red; - draw P--N dashed withdots scaled 1/2; - draw Q--M dashed withdots scaled 1/2; - - drawarrow xx; label.rt("$x$", point 1 of xx); - drawarrow yy; label.top("$y$", point 1 of yy); - - drawoptions(withcolor 2/3 blue); - draw fullcircle scaled 32 shifted T cutafter tee; - draw fullcircle scaled 28 shifted L cutafter ell; - label("$\psi$", 24 right rotated 1/2 psi shifted T); - label("$\theta$", 20 right rotated 1/2 theta shifted L); - drawoptions(); - - path boundary; - z1 = point .95 of xx; - z2 = point .95 of yy; - boundary = z1--(x1,y2)--z2; - - draw ell cutafter boundary; - draw tee cutafter boundary; - - % and finally label the points. - label.bot("$T$", T); - label.bot("$L$", L); - label.bot("$N$", N); - label.bot("$M$", M); - dotlabel.ulft("$P$", P); - dotlabel.lrt("$Q$", Q); - dotlabel.lrt("$H$", H); - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/arbelos.mp b/info/drawing-with-metapost/src/arbelos.mp deleted file mode 100644 index 7fe9bfc796..0000000000 --- a/info/drawing-with-metapost/src/arbelos.mp +++ /dev/null @@ -1,63 +0,0 @@ -\RequirePackage{luatex85} -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -% invert path or pair P in circle C -vardef invert(expr P, C) = - save I, r; pair I; numeric r; - I = center C; - r = abs(point 0 of C shifted -I); - if pair P: if abs(P-I) > 0: unitvector(P-I) scaled (r/abs(P-I)*r) shifted fi I - elseif path P: - save T; numeric T; - T = length P; - for t=0 upto T-1: invert(point t of P, C) .. endfor if cycle P: cycle else: invert(point T of P, C) fi - fi -enddef; -beginfig(1); - pair A,B,C; - A = origin; C = 244 right; B = 7/8[A, C]; - - path c[]; - c1 = fullcircle scaled 2 abs(A-C); % large circle for the inversions - c2 = fullcircle scaled abs(A-C) shifted 1/2[A,C]; - c3 = fullcircle scaled abs(A-B) shifted 1/2[A,B]; - c4 = fullcircle scaled abs(B-C) shifted 1/2[B,C]; - c5 = invert(c4,c1); - - numeric d; d = abs(point 0 of c5 - point 4 of c5); % diameter of c5 - - drawoptions(withcolor 3/4 white); - draw c4; draw c5; - draw invert(subpath(0, 3/2) of c2, c1); - draw invert(subpath(0, 3/2) of c3, c1); - drawoptions(); - - draw subpath(-1/4,1) of c1 withcolor 3/4[1/2 red,white]; - label.bot("\textit{circle of inversion}", point -1/4 of c1) withcolor 1/4[1/2 red, white]; - - for i=1 upto 72: - path c, c'; - c = c5 shifted (0, i*d); - c' = invert(c, c1); - if i<5: - drawoptions(withcolor 3/4 white); - draw c; draw origin -- center c; - fill fullcircle scaled dotlabeldiam shifted center c; - fill fullcircle scaled dotlabeldiam shifted center c'; - drawoptions(); - fi - draw c' withpen pencircle scaled 1/4 withcolor 2/3 blue; - endfor - - forsuffixes $=2,3,4: draw subpath (0,4) of c$ - withpen pencircle scaled 1/4 withcolor 2/3 blue; - endfor - - draw A--C; - dotlabel.lft("$A$", A); dotlabel.llft("$B$", B); dotlabel.rt("$C$", C); -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/arbelos.pdf b/info/drawing-with-metapost/src/arbelos.pdf Binary files differdeleted file mode 100644 index df5f9a957f..0000000000 --- a/info/drawing-with-metapost/src/arbelos.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-3-4-3-4.mp b/info/drawing-with-metapost/src/arch-3-4-3-4.mp deleted file mode 100644 index 42b01cb7eb..0000000000 --- a/info/drawing-with-metapost/src/arch-3-4-3-4.mp +++ /dev/null @@ -1,62 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -vardef median(expr p) = origin for i=1 upto length p: + point i of p / length p endfor enddef; -beginfig(1); - path s[], t[]; - s1 = unitsquare scaled 21 rotated 15; - s2 = s1 rotated 150; - t1 = subpath (4, 3) of s1 -- point 1 of s2 -- cycle; - t2 = t1 reflectedabout(point 1 of t1, point 2 of t1); - t3 = t1 rotated 150; - t4 = t1 rotated 210; - - picture color_unit, grid_unit; - color_unit = image( - fill s1 withcolor Oranges 8 1; - fill s2 withcolor Oranges 8 2; - fill t1 withcolor Blues 8 1; - fill t2 withcolor Blues 8 2; - fill t3 withcolor Blues 8 3; - fill t4 withcolor Blues 8 4; - ); - grid_unit = image( - forsuffixes $=s1, s2, t1, t2, t3, t4: - draw $; - % pair m; m = median($); - % for i=1 upto length $: - % draw m -- point i - 1/2 of $ - % withpen pencircle scaled 1/4; - % endfor - endfor - ); - - pair u, v; - u = point 1 of s1 - point 1 of s2; - v = u rotated 90; - - numeric n; n = 3; - forsuffixes $=color_unit, grid_unit: - for i=-n upto n: - for j=-n upto n: - draw $ shifted (i * u + j * v); - endfor - endfor - endfor - label.bot("The arrangement of polygons in the units was carefully", point 1/2 of bbox currentpicture - shifted 21 down); - label.bot("chosen to give the tiling neat edges." , point 1/2 of bbox currentpicture); - - path b; b = bbox currentpicture shifted 34 down; - draw color_unit shifted point 1/4 of b; - draw grid_unit shifted point 3/4 of b; - path b; b = bbox currentpicture shifted 13 down; - label("\texttt{color\_unit}", point 1/4 of b); - label("\texttt{grid\_unit}", point 3/4 of b); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/arch-3-4-3-4.pdf b/info/drawing-with-metapost/src/arch-3-4-3-4.pdf Binary files differdeleted file mode 100644 index 1ceea33b78..0000000000 --- a/info/drawing-with-metapost/src/arch-3-4-3-4.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-3-4-6-4.mp b/info/drawing-with-metapost/src/arch-3-4-6-4.mp deleted file mode 100644 index 0a7094be3b..0000000000 --- a/info/drawing-with-metapost/src/arch-3-4-6-4.mp +++ /dev/null @@ -1,54 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\mplibsetformat{metafun} -\begin{mplibcode} -input colorbrewer-rgb -beginfig(1); - numeric r; r = 5; - path d; d = for i=1 upto 12: - up scaled r - shifted (r * (sqrt(3)+2), 0) - rotated 30i -- - endfor cycle; - - color shade[]; - shade0 = Oranges 8 3; - shade1 = Blues 8 3; - shade2 = Greens 8 3; - shade3 = Reds 8 3; - - vardef unit(expr n) = image( - fill d withcolor transparent (2, .9, shade[n mod 4]); - draw d; - ) enddef; - pair u, v; - u = point 0 of d - point 3 of d; - v = u rotated 60; - numeric n; n = 6; - for i=-n upto n: - for j=-n upto n: - draw unit(i*j) shifted ((i - floor(j / 2)) * u + j * v); - endfor - endfor - clip currentpicture to unitsquare shifted -(1/2, 1/2) scaled (n * 9 r); - picture p; p = image( - draw d; draw point 0 of d withpen pencircle scaled 2; - drawoptions(withcolor 3/4[red, white]); - draw d shifted u; draw point 0 of d shifted u withpen pencircle scaled 2; - drawoptions(withcolor 3/4[blue, white]); - draw d shifted v; draw point 0 of d shifted v withpen pencircle scaled 2; - drawoptions(); - drawarrow origin -- u withcolor red; - drawarrow origin -- v withcolor blue; - ); - label.bot(p, point 1/2 of bbox currentpicture shifted 13 down); - label.bot(btex \vbox{\hsize 3.4in\noindent - The vectors are chosen so that the dodecagons overlap to make - the required triangles, squares, and hexagons.} etex, - point 1/2 of bbox currentpicture shifted 13 down); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/arch-3-4-6-4.pdf b/info/drawing-with-metapost/src/arch-3-4-6-4.pdf Binary files differdeleted file mode 100644 index e145578609..0000000000 --- a/info/drawing-with-metapost/src/arch-3-4-6-4.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-4-6-12.mp b/info/drawing-with-metapost/src/arch-4-6-12.mp deleted file mode 100644 index 8d8ddf2684..0000000000 --- a/info/drawing-with-metapost/src/arch-4-6-12.mp +++ /dev/null @@ -1,65 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input archimedean-tools -input colorbrewer-rgb -beginfig(1); - path dodo, h[], s[]; - dodo = poly 12 of (origin -- 21 up); - for i=1 upto 3: - s[i] = poly 4 of subpath(2i, 2i-1) of dodo; - endfor - h1 = poly 6 of subpath (4, 3) of s1; - h2 = poly 6 of subpath (2, 1) of s3; - - picture cols, lines; - cols = image( - fill dodo withcolor Greens 9 2; - for i=1 upto 2: - fill h[i] withcolor Greens 9 3; - endfor - for i=1 upto 3: - fill s[i] withcolor Greens 9 4; - endfor - ); - lines = image( - forsuffixes $=dodo, s1, s2, s3, h1, h2: - if known $: - draw $ withpen pencircle scaled 1/4; - pair m; m = median($); - for i=1 upto length $: - cutdraw m -- point i - 1/2 of $ - if odd i: cutbefore fullcircle scaled (length $ / 4) shifted m fi - withpen pencircle scaled 1/4 - withcolor Reds 4 3; - ; - endfor - fi - endfor - ); - - pair u, v; - u = point 2 of s1 - point 8 of dodo; - v = u rotated 60; - - numeric n; - n = 2; - - forsuffixes @ = cols, lines: - for i=-n upto n+1: - for j=-n upto n: - draw @ shifted (i*u + j*v - floor(i/2) * v); - endfor - endfor - endfor - - clip currentpicture to unitsquare xscaled ((2n+1) * xpart u) yscaled (2n * ypart v) - shifted median(s2 shifted (-n*u - n*v + floor(n/2) * v)); - - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/arch-4-6-12.pdf b/info/drawing-with-metapost/src/arch-4-6-12.pdf Binary files differdeleted file mode 100644 index 4868f44da3..0000000000 --- a/info/drawing-with-metapost/src/arch-4-6-12.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-4-8-8.mp b/info/drawing-with-metapost/src/arch-4-8-8.mp deleted file mode 100644 index 117588ff02..0000000000 --- a/info/drawing-with-metapost/src/arch-4-8-8.mp +++ /dev/null @@ -1,40 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -beginfig(1); -input colorbrewer-rgb -path o, r[]; -o = (for i=0 upto 7: 21 dir 45i -- endfor cycle) rotated -90/4; -pair t; t = whatever[point 0 of o, point 1 of o] - = whatever[point 2 of o, point 3 of o]; -r1 = subpath (1,2) of o -- t -- cycle; -r2 = r1 rotated 90; -r3 = r2 rotated 90; -r4 = r3 rotated 90; - -picture filler; -filler = image( - filldraw r1 withcolor Reds 8 3; - filldraw r2 withcolor Blues 8 3; - filldraw r3 withcolor Reds 8 3; - filldraw r4 withcolor Blues 8 3; - filldraw o withcolor Purples 8 2; -); -pair u, v; -u = point 0 of o - point 5 of o; v = u rotated 90; -beginfig(1); -numeric n; n = 5; -for i=-n upto n: - for j=-n upto n: - draw filler rotated ((i+j) mod 2 * 90) shifted (i*u + j * v); - endfor -endfor -for i=-n upto n: - for j=-n upto n: - draw o shifted (i*u + j * v); - endfor -endfor -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/arch-4-8-8.pdf b/info/drawing-with-metapost/src/arch-4-8-8.pdf Binary files differdeleted file mode 100644 index e5fa45dde0..0000000000 --- a/info/drawing-with-metapost/src/arch-4-8-8.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-hexagon.mp b/info/drawing-with-metapost/src/arch-hexagon.mp deleted file mode 100644 index 0cb259d124..0000000000 --- a/info/drawing-with-metapost/src/arch-hexagon.mp +++ /dev/null @@ -1,59 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -input archimedean-tools -beginfig(1); - - path h[]; - % 42/sqrt(3) \simeq 24.2487; - for i=0 upto 2: - h[i] = poly 6 of (origin -- 42 / sqrt(3) * dir (30 + 120i)); - endfor - - picture unit; - unit = image( - % fill h0 withcolor Purples 8 3; - % fill h1 withcolor Oranges 8 3; - % fill h2 withcolor Blues 8 2; - numeric i; i = -1; - forsuffixes $ = Purples, Oranges, Blues: - pair m; m = median(h[incr i]); - for j=1 upto 3: - fill subpath (-2i+2j, 2-2i+2j) of h[i] -- m -- cycle withcolor $[8][1+j]; - endfor - for j=1 upto 3: - draw m -- point 2j of h[i] withcolor $[8][1]; - endfor - endfor - - % for i=0 upto 2: - % pair m; m = median(h[i]); - % for j=0 upto 2: - % draw point 2j+1/2 of h[i] -- m -- point 2j+3/2 of h[i]; - % endfor - % endfor - ); - - pair u, v; - u = point 3 of h1 - point 1 of h0; - v = u rotated 60; - - numeric n; - n = 4; - - for i=-n upto n: - for j=-n upto n: - draw unit shifted (i*u + j*v); - endfor - endfor - - clip currentpicture to superellipse(168 right, 168 up, 168 left, 168 down, 0.78); - - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/arch-hst.mp b/info/drawing-with-metapost/src/arch-hst.mp deleted file mode 100644 index ebcf5668d2..0000000000 --- a/info/drawing-with-metapost/src/arch-hst.mp +++ /dev/null @@ -1,62 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -input archimedean-tools -beginfig(1); - path t[], s[], h; - h = poly 6 of (origin -- 42 dir 30); - for i=1 upto 3: - s[i] = poly 4 of subpath (2i, 2i-1) of h; - endfor - t1 = poly 3 of subpath (4, 3) of s1; - t2 = poly 3 of subpath (2, 1) of s2; - - picture unit; - unit = image( - for i=1 upto 2: - fill t[i] withcolor Blues 8 4; - endfor - for i=1 upto 3: - fill s[i] withcolor Greens 8 1; - endfor - fill h withcolor Oranges 9 4; - forsuffixes $=t1, t2: - pair m; m = median($); - for i=1 upto length $: - draw m -- point i - 1/2 of $ withcolor Blues 8 8; - endfor - endfor - forsuffixes $=s1, s2, s3: - draw point 1/2 of $ -- point 5/2 of $ withcolor Oranges 8 8; - draw point 3/2 of $ -- point 7/2 of $ withcolor Blues 8 8; - endfor - for i=1 upto 3: - draw point i-1/2 of h -- point i+5/2 of h withcolor Oranges 8 8; - endfor - ); - - pair u, v; - u = point 2 of s1 - point -1 of h; - v = u rotated 60; - - numeric n; n=4; - for i=-n upto n: - for j=-n upto n: - draw unit rotated 0 shifted (i*u + j*v - floor (j/2) * u); - endfor - endfor - %draw bbox unit withcolor red; - - clip currentpicture to fullcircle scaled (3/2n * abs(v)); - - % picture p; p = currentpicture; - % (wd, ht) = (urcorner p - llcorner p); - % currentpicture := nullpicture; - % p := p scaled (148.5mm / wd); - % draw p; -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/arch-hst.pdf b/info/drawing-with-metapost/src/arch-hst.pdf Binary files differdeleted file mode 100644 index 6d973adde9..0000000000 --- a/info/drawing-with-metapost/src/arch-hst.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-snub-hex-parts.mp b/info/drawing-with-metapost/src/arch-snub-hex-parts.mp deleted file mode 100644 index bf3ff14355..0000000000 --- a/info/drawing-with-metapost/src/arch-snub-hex-parts.mp +++ /dev/null @@ -1,49 +0,0 @@ -input colorbrewer-rgb -input archimedean-tools -path t[], h; -h = poly 6 of (origin -- 21 dir 30); -for i=1 upto 6: - t[i] = poly 3 of subpath (i, i-1) of h; -endfor -picture P[], unit[]; -for k=1 upto 2: - pair u, v; - if k=1: - u = point 2 of h - point 2 of t6; - t7 := poly3 of subpath (0, -1) of t6; - t8 := poly3 of subpath (0, -1) of t3; - else: - u = point 3 of h - point 2 of t6; - t7 := poly3 of subpath (2, 1) of t6; - t8 := poly3 of subpath (2, 1) of t3; - fi - - v = u rotated -60; - - unit[k] = image( - for i=1 upto 6: - fill t[i] withcolor Blues 8 if odd i: 2 else: 3 fi; - endfor - for i=7 upto 8: - fill t[i] withcolor Oranges 8 if odd i: 3 else: 2 fi; - endfor - fill h withcolor Oranges 8 2; - forsuffixes $=h, t1, t2, t3, t4, t5, t6, t7, t8: - draw $ withpen pencircle scaled 1/4 withcolor 3/4; - pair m; m = median($); - for i=1 upto length $: - draw m -- point i - 1/2 of $ withcolor 3/4; - endfor - endfor - ); - - numeric n; n=4; - P[k] = image( - for i=-n upto n: - for j=-n upto n: - draw unit[k] shifted (i*u + j*v - floor (j/2) * u); - endfor - endfor - clip currentpicture to superellipse(168 right, 168 up, 168 left, 168 down, 0.78); - ); -endfor diff --git a/info/drawing-with-metapost/src/arch-snub-hexagon-unit.mp b/info/drawing-with-metapost/src/arch-snub-hexagon-unit.mp deleted file mode 100644 index b5200f6a6f..0000000000 --- a/info/drawing-with-metapost/src/arch-snub-hexagon-unit.mp +++ /dev/null @@ -1,12 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input arch-snub-hex-parts -beginfig(1); - draw unit1 rotated 210; - draw unit2 rotated 210 shifted 100 left; -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/arch-snub-hexagon-unit.pdf b/info/drawing-with-metapost/src/arch-snub-hexagon-unit.pdf Binary files differdeleted file mode 100644 index 1dd83c0b0d..0000000000 --- a/info/drawing-with-metapost/src/arch-snub-hexagon-unit.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-snub-hexagon.pdf b/info/drawing-with-metapost/src/arch-snub-hexagon.pdf Binary files differdeleted file mode 100644 index aed6e4d102..0000000000 --- a/info/drawing-with-metapost/src/arch-snub-hexagon.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-snub-square.pdf b/info/drawing-with-metapost/src/arch-snub-square.pdf Binary files differdeleted file mode 100644 index 4cc73ce6e5..0000000000 --- a/info/drawing-with-metapost/src/arch-snub-square.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/arch-square.mp b/info/drawing-with-metapost/src/arch-square.mp deleted file mode 100644 index 3511abf4e9..0000000000 --- a/info/drawing-with-metapost/src/arch-square.mp +++ /dev/null @@ -1,39 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -input archimedean-tools -beginfig(1); - - path s; - s = poly 4 of (origin -- 42 right); - pair m; - m = median(s); - - picture unit[]; - unit0 = image( - fill s withcolor Oranges 8 5; - for i=1 upto length s: - draw m -- point i-1/2 of s; - endfor<D-`> - - ); - unit1 = image(fill s withcolor Blues 8 4); - - - pair u, v; - u = point 1 of s - point 0 of s; - v = point 3 of s - point 0 of s; - - - numeric n; - n = 4 - - - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/arch-triangle.mp b/info/drawing-with-metapost/src/arch-triangle.mp deleted file mode 100644 index cc80674664..0000000000 --- a/info/drawing-with-metapost/src/arch-triangle.mp +++ /dev/null @@ -1,45 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -input archimedean-tools -beginfig(1); - - path s, t; - s = poly 3 of (origin -- 42 right); - t = poly 3 of subpath(2,1) of s; - pair ms, mt; - ms = median(s); - mt = median(t); - - picture unit; - unit = image( - fill s withcolor Oranges 8 3; - fill t withcolor Blues 8 2; - draw point 5/2 of s -- ms; - draw point 3/2 of t -- mt; - draw point 1/2 of s -- ms -- mt -- point 5/2 of t; - ); - - pair u, v; - u = point 1 of s - point 0 of s; - v = point 2 of s - point 0 of s; - - numeric n; - n = 0; - - for i=-n upto n: - for j=-n upto n: - draw unit shifted (i*u + j*v); - endfor - endfor - - clip currentpicture to superellipse(168 right, 168 up, 168 left, 168 down, 0.78); - - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/archimedean-tools.mp b/info/drawing-with-metapost/src/archimedean-tools.mp deleted file mode 100644 index e10c8f447f..0000000000 --- a/info/drawing-with-metapost/src/archimedean-tools.mp +++ /dev/null @@ -1,33 +0,0 @@ -% a polygon of n sides on a given path -vardef poly expr n of p = - save x, y; - z0 = point 0 of p; - z1 = point 1 of p; - for i=2 upto n-1: - z[i] = z[i-2] rotatedabout(z[i-1], 180(2/n-1)); - endfor - for i=0 upto n-1: z[i] -- endfor cycle -enddef; -vardef polyc expr n of p = - save x, y; - z0 = point 0 of p; - z1 = point 1 of p; - for i=2 upto n-1: - z[i] = z[i-2] rotatedabout(z[i-1], 180(2/n-1)); - endfor - for i=0 upto n-1: z[i] ... endfor cycle -enddef; - -% a polygon of n sides of a given length -vardef polya(expr n, s) = - save r, x, y; numeric r, x, y; - (x, y) = dir (180/n); - 2r = s * x / y; - for i=0 upto n-1: - (left * s/2) shifted (r * down) rotated (360 / n * i) -- - endfor cycle -enddef; -vardef median(expr P) = - (origin for i=1 upto length P: + point i of P endfor) / length P -enddef; - diff --git a/info/drawing-with-metapost/src/archimedes.pdf b/info/drawing-with-metapost/src/archimedes.pdf Binary files differdeleted file mode 100644 index ead562d6f9..0000000000 --- a/info/drawing-with-metapost/src/archimedes.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/area-under-graph.mp b/info/drawing-with-metapost/src/area-under-graph.mp deleted file mode 100644 index e9dc5f5886..0000000000 --- a/info/drawing-with-metapost/src/area-under-graph.mp +++ /dev/null @@ -1,37 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -ahangle := 30; -beginfig(1); - numeric u; - u = 1cm; - path xx, yy, f; - xx = (1/4 left -- 17/4 right) scaled u; - yy = (1/4 down -- 9/4 up) scaled u; - - f = ((15/32,32/15) for x = 1/2 step 1/8 until 33/8: .. (x,1/x) endfor) scaled u; - - path A; - A = buildcycle(yy shifted (u,0), f, yy shifted (2.71828u,0), xx); - fill A withcolor Blues 8 2; - - drawoptions(withcolor 3/4); - for x=1 upto 4: - draw yy shifted (x*u,0) cutafter (xx shifted (0, ypart point 0 of f)); - endfor - for y=1 upto 2: - draw xx shifted (0,y*u) cutafter (yy shifted (xpart point infinity of f,0)); - endfor - - drawoptions(); - draw f withcolor Reds 8 7; - drawarrow xx; - drawarrow yy; - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/area-under-graph.pdf b/info/drawing-with-metapost/src/area-under-graph.pdf Binary files differdeleted file mode 100644 index 8230d85b40..0000000000 --- a/info/drawing-with-metapost/src/area-under-graph.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/automatic-grid.mp b/info/drawing-with-metapost/src/automatic-grid.mp new file mode 100644 index 0000000000..a6a59ced16 --- /dev/null +++ b/info/drawing-with-metapost/src/automatic-grid.mp @@ -0,0 +1,16 @@ +vardef grid(expr p, grid_unit) = + save llx, lly, urx, ury; + (llx, lly) = llcorner p - (bboxmargin, bboxmargin); + (urx, ury) = urcorner p + (bboxmargin, bboxmargin); + image( + for x = 1 + floor(llx / grid_unit) upto floor(urx / grid_unit): + draw (x * grid_unit, lly) -- (x * grid_unit, ury); + endfor + for y = 1 + floor(lly / grid_unit) upto floor(ury / grid_unit): + draw (llx, y * grid_unit) -- (urx, y * grid_unit); + endfor + if (llx < 0) and (lly < 0) and (urx > 0) and (ury > 0): + draw fullcircle scaled 3; % show origin if in range + fi + ) +enddef; diff --git a/info/drawing-with-metapost/src/basedate.mp b/info/drawing-with-metapost/src/basedate.mp index f91c360894..f355ce991f 100644 --- a/info/drawing-with-metapost/src/basedate.mp +++ b/info/drawing-with-metapost/src/basedate.mp @@ -1,11 +1,7 @@ vardef base(expr Y, M, d) = - save m, y; numeric m, y; - if M < 3: - m = M + 9; - y = Y - 1; - else: - m = M - 3; - y = Y; - fi - 365/1024 y + (floor(y/4) - floor(y/100) + floor(y/400) + floor((2+3m)/5) + 30m + d - 307) / 1024 + save m, y; + if M < 3: m = M + 9; y = Y - 1; + else: m = M - 3; y = Y; fi + 365/1024 y + (floor(y/4) - floor(y/100) + floor(y/400) + + floor((2+3m)/5) + 30m + d - 307) / 1024 enddef; diff --git a/info/drawing-with-metapost/src/blended-color-circles.mp b/info/drawing-with-metapost/src/blended-color-circles.mp deleted file mode 100644 index 4da586d64b..0000000000 --- a/info/drawing-with-metapost/src/blended-color-circles.mp +++ /dev/null @@ -1,44 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\usepackage{fontspec} -\setmainfont{Helvetica} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - -path C[], B[]; - -% arrange each circle so that point 0 is outside the others -C1 = fullcircle scaled 120 rotated 90 shifted 40 up; -C2 = C1 rotated 120; -C3 = C2 rotated 120; - -B0 = buildcycle(C1, C2, C3); -B1 = buildcycle(C1, C2); -B2 = buildcycle(C2, C3); -B3 = buildcycle(C3, C1); - -picture P; -for x=0 upto 1: - for y=0 upto 1: - P := image( - s := 1/4 + x/2; - k := 0 + y/4; - fill C1 withcolor s*(1,0,0,k); - fill C2 withcolor s*(0,1,0,k); - fill C3 withcolor s*(0,0,1,k); - fill B3 withcolor s*(1,0,1,k); - fill B2 withcolor s*(0,1,1,k); - fill B1 withcolor s*(1,1,0,k); - fill B0 withcolor s*(1,1,1,k); - undraw C1; undraw C2; undraw C3; - ) shifted -(200x, 200y); - draw P; - label.bot(("shade: " & decimal s & ", k: " & decimal k) - infont "phvr8r", point 1/2 of bbox P); - endfor -endfor -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/blended-color-circles.pdf b/info/drawing-with-metapost/src/blended-color-circles.pdf Binary files differdeleted file mode 100644 index d5b4b4c631..0000000000 --- a/info/drawing-with-metapost/src/blended-color-circles.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/border-dashed.pdf b/info/drawing-with-metapost/src/border-dashed.pdf Binary files differdeleted file mode 100644 index 0f46ba0340..0000000000 --- a/info/drawing-with-metapost/src/border-dashed.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/border-shadow.pdf b/info/drawing-with-metapost/src/border-shadow.pdf Binary files differdeleted file mode 100644 index 5ba2540848..0000000000 --- a/info/drawing-with-metapost/src/border-shadow.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/border.mp b/info/drawing-with-metapost/src/border.mp deleted file mode 100644 index 71dd27309b..0000000000 --- a/info/drawing-with-metapost/src/border.mp +++ /dev/null @@ -1,50 +0,0 @@ -\documentclass[border=2mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -input rope -beginfig(1); - - interim ahangle := 30; - - z0 = 42 left rotated normaldeviate; - z1 = 30 up rotated normaldeviate; - z2 = 31 right rotated normaldeviate; - z3 = 34 down rotated normaldeviate; - - path s[]; - for i=0 upto 3: - s[i] = unitsquare zscaled (z[(i+1) mod 4] - z[i]) shifted z[i]; - fill s[i] withcolor if odd i: Blues else: Oranges fi 8 1; - draw point 3 of s[i] -- subpath (1,4) of s[i] -- point 2 of s[i] withcolor 3/4; - drawarrow subpath (0, 1) of s[i]; - z[i+4] = 1/2[point 0 of s[i], point 2 of s[i]]; - endfor - - z8 = whatever[z4, z6] = whatever[z5, z7]; - - draw unitsquare scaled 5 rotated angle (z4-z6) shifted z8 withcolor 3/4; - - drawarrow z4--z6; - drawarrow z5--z7; - - vardef with_rounded_corners expr p = - for i=1 upto length p: - subpath (i-15/16, i-1/16) of p .. - endfor cycle - enddef; - - interim bboxmargin := 16; - draw rope with_rounded_corners bbox currentpicture; - % dashed evenly scaled 3/4; - %picture P; P = currentpicture; - %fill bbox P shifted (3,-3) withcolor 3/4; - %unfill bbox P; draw bbox P; - %draw P; - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/border.pdf b/info/drawing-with-metapost/src/border.pdf Binary files differdeleted file mode 100644 index 3b1e9fcd6f..0000000000 --- a/info/drawing-with-metapost/src/border.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/braces.mp b/info/drawing-with-metapost/src/braces.mp deleted file mode 100644 index 454adfb42a..0000000000 --- a/info/drawing-with-metapost/src/braces.mp +++ /dev/null @@ -1,44 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -vardef do_brace(expr a,b,m,r) = - save d, e, n, bb; - numeric d, n; pair e; path bb; - d = angle (b-a); - e = up scaled m rotated d shifted r[a,b]; - n = 1/2 m; - bb = ( - (origin {0,n} .. {right} (abs n,n)) - rotated d shifted a - -- - ((-abs n,-n) {right} .. {0,n} origin {0,-n} .. {right}(abs n,-n)) - rotated d shifted e - -- - ((-abs n,n){right}..{0,-n}origin) - rotated d shifted b - ) shifted (up scaled n rotated d); - draw bb withpen pencircle yscaled .6 xscaled .1666 rotated d; - point 3 of bb -enddef; -beginfig(1); - -z1 = origin; -z2 = 180 right rotated 13; -draw z1--z2 withcolor .7 white; -dotlabel.llft("$z_1$",z1); -dotlabel.urt("$z_2$",z2); - -begingroup; interim ahangle := 180; interim ahlength := 3; -drawdblarrow (z1--z2) shifted (12 up rotated angle (z2-z1)) withcolor 2/3 blue; -endgroup; - -drawoptions(withcolor 2/3 red); -label.lrt("Here",do_brace(z1,z2,-12,3/4)); -drawoptions(); - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/brachisto.mp b/info/drawing-with-metapost/src/brachisto.mp deleted file mode 100644 index aab584db00..0000000000 --- a/info/drawing-with-metapost/src/brachisto.mp +++ /dev/null @@ -1,56 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - - path Y, L, C, P, S; - - % cycloid - numeric r, s; r = 160; - def sin(expr x) = sind( 57.29577951308232 x) enddef; - def cos(expr x) = cosd( 57.29577951308232 x) enddef; - vardef u(expr x) = x - sin(x) enddef; - vardef v(expr x) = 1 - cos(x) enddef; - vardef f(expr t) = u(t) < v(t) enddef; - tolerance := epsilon; - numeric a; a = solve f(2,3); - - Y = (origin for t = 1 upto 128: -- (u(t / 128 * a), -v(t / 128 * a)) endfor) scaled r; - - % Y = origin for t=5 step 5 until 140: - % -- (0, r) rotated t shifted (t / 57.29577951308232 * r, -r) - % endfor cutafter (origin -- 4r * dir -45); - - z0 = point 0 of Y; - z1 = point infinity of Y; - - % line - L = z0 -- z1; - - % circle - C = quartercircle rotated 180 scaled 2x1 shifted (x1, y0); - - % parabola f = x^2, f' = 2x - P = z0{1,-2} ... (xpart 1/2[z1, z0], ypart 1/4[z1, z0]){1,-1} ... z1 {1, 0}; - - % sixth degree f = x^6, f' = 6x^5 - S = z0{1,-6} ... (xpart 1/2[z1, z0], ypart 1/64[z1, z0]){1, -6/32} ... z1 {1, 0}; - - % axes - draw z0 -- (x0,y1) -- z1 withcolor 3/4; - - drawoptions(withcolor 2/3 red); draw L; dotlabel.urt("Line", point 1/4 of L); - drawoptions(withcolor 1/2 green); draw C; dotlabel.urt("Circle", point 1 of C); - drawoptions(withcolor 1/4[red, green]); draw P; dotlabel.urt("Parabola", point 1/2 of P); - drawoptions(withcolor 3/4[red, green]); draw S; dotlabel.llft("Sixth degree", point 3/4 of S); - drawoptions(withcolor 1/2 blue); draw Y; dotlabel.urt("Cycloid", point 100 of Y); - drawoptions(); - - dotlabel.ulft("$A$", z0); - dotlabel.urt("$B$", z1); - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/brexit-map.mp b/info/drawing-with-metapost/src/brexit-map.mp deleted file mode 100644 index 5f3f68d6b4..0000000000 --- a/info/drawing-with-metapost/src/brexit-map.mp +++ /dev/null @@ -1,99 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\mplibtextextlabel{enable} -\begin{document} -\begin{mplibcode} -input london-boroughs -input colorbrewer-rgb -vardef median(expr p) = - save n; numeric n; n = length p; - 1/n * point 0 of p for i=1 upto n: + 1/n * point i of p endfor -enddef; - -beginfig(1); - -fill Barking_and_Dagenham withcolor 0.638 [white, RdYlBu 9 3]; draw Barking_and_Dagenham; -fill Barnet withcolor 0.721 [white, RdYlBu 9 6]; draw Barnet; -fill Bexley withcolor 0.752 [white, RdYlBu 9 3]; draw Bexley; -fill Brent withcolor 0.650 [white, RdYlBu 9 5]; draw Brent; -fill Bromley withcolor 0.788 [white, RdYlBu 9 5]; draw Bromley; -fill Camden withcolor 0.654 [white, RdYlBu 9 7]; draw Camden; -fill City_of_London withcolor 0.735 [white, RdYlBu 9 7]; draw City_of_London; -fill Croydon withcolor 0.698 [white, RdYlBu 9 5]; draw Croydon; -fill Ealing withcolor 0.700 [white, RdYlBu 9 5]; draw Ealing; -fill Enfield withcolor 0.690 [white, RdYlBu 9 5]; draw Enfield; -fill Greenwich withcolor 0.695 [white, RdYlBu 9 5]; draw Greenwich; -fill Hackney withcolor 0.651 [white, RdYlBu 9 7]; draw Hackney; -fill Hammersmith_and_Fulham withcolor 0.699 [white, RdYlBu 9 6]; draw Hammersmith_and_Fulham; -fill Haringey withcolor 0.705 [white, RdYlBu 9 7]; draw Haringey; -fill Harrow withcolor 0.722 [white, RdYlBu 9 5]; draw Harrow; -fill Havering withcolor 0.760 [white, RdYlBu 9 3]; draw Havering; -fill Hillingdon withcolor 0.689 [white, RdYlBu 9 4]; draw Hillingdon; -fill Hounslow withcolor 0.697 [white, RdYlBu 9 5]; draw Hounslow; -fill Islington withcolor 0.703 [white, RdYlBu 9 7]; draw Islington; -fill Kensington_and_Chelsea withcolor 0.659 [white, RdYlBu 9 6]; draw Kensington_and_Chelsea; -fill Kingston_upon_Thames withcolor 0.783 [white, RdYlBu 9 6]; draw Kingston_upon_Thames; -fill Lambeth withcolor 0.673 [white, RdYlBu 9 7]; draw Lambeth; -fill Lewisham withcolor 0.630 [white, RdYlBu 9 6]; draw Lewisham; -fill Merton withcolor 0.734 [white, RdYlBu 9 6]; draw Merton; -fill Newham withcolor 0.592 [white, RdYlBu 9 5]; draw Newham; -fill Redbridge withcolor 0.675 [white, RdYlBu 9 5]; draw Redbridge; -fill Richmond_upon_Thames withcolor 0.820 [white, RdYlBu 9 6]; draw Richmond_upon_Thames; -fill Southwark withcolor 0.661 [white, RdYlBu 9 7]; draw Southwark; -fill Sutton withcolor 0.760 [white, RdYlBu 9 4]; draw Sutton; -fill Tower_Hamlets withcolor 0.645 [white, RdYlBu 9 6]; draw Tower_Hamlets; -fill Waltham_Forest withcolor 0.666 [white, RdYlBu 9 5]; draw Waltham_Forest; -fill Wandsworth withcolor 0.719 [white, RdYlBu 9 7]; draw Wandsworth; -fill Westminster withcolor 0.649 [white, RdYlBu 9 6]; draw Westminster; - -label("\tiny Barking \& Dagenham", median(Barking_and_Dagenham)); -label("\tiny Barnet", median(Barnet)); -label("\tiny Bexley", median(Bexley)); -label("\tiny Brent", median(Brent)); -label("\tiny Bromley", median(Bromley)); -label("\tiny Camden", median(Camden)); -label("\tiny City of London", median(City_of_London)); -label("\tiny Croydon", median(Croydon)); -label("\tiny Ealing", median(Ealing)); -label("\tiny Enfield", median(Enfield)); -label("\tiny Greenwich", median(Greenwich)); -label("\tiny Hackney", median(Hackney)); -label(TEX("\tiny Hammersmith \& Fulham") rotated -62, median(Hammersmith_and_Fulham)); -label("\tiny Haringey", median(Haringey)); -label("\tiny Harrow", median(Harrow)); -label("\tiny Havering", median(Havering)); -label("\tiny Hillingdon", median(Hillingdon)); -label("\tiny Hounslow", median(Hounslow) shifted 12 left); -label("\tiny Islington", median(Islington)); -label(TEX("\tiny Kensington \& Chelsea") rotated -54, median(Kensington_and_Chelsea)); -label(TEX("\tiny Kingston upon Thames") rotated 66, median(Kingston_upon_Thames)); -label("\tiny Lambeth", median(Lambeth)); -label("\tiny Lewisham", median(Lewisham)); -label("\tiny Merton", median(Merton)); -label("\tiny Newham", median(Newham)); -label("\tiny Redbridge", median(Redbridge)); -label("\tiny Richmond upon Thames", median(Richmond_upon_Thames)); -label("\tiny Southwark", median(Southwark)); -label("\tiny Sutton", median(Sutton)); -label("\tiny Tower Hamlets", median(Tower_Hamlets)); -label("\tiny Waltham Forest", median(Waltham_Forest)); -label("\tiny Wandsworth", median(Wandsworth)); -label("\tiny Westminster", median(Westminster)); - -label("\tiny Barking \& Dagenham", median(Barking_and_Dagenham)); -picture legend; legend = image( -numeric s; s = 10; -for i = 1 upto 9: - fill unitsquare scaled s shifted (i*s, 0) withcolor RdYlBu [9][i]; - if i > 1: draw (i*s, 0) -- (i*s, s); fi -endfor -draw unitsquare xscaled 9s yscaled s shifted (s,0); -label.top("Remain" infont "phvr8r", (10s, s)); -label.top("Leave" infont "phvr8r", (s, s));); -label.ulft(legend, point 1 of bbox currentpicture); -label.lrt("Brexit vote in London 2016" infont "phvr8r", point 3 of bbox currentpicture); - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/brexit-map.pdf b/info/drawing-with-metapost/src/brexit-map.pdf Binary files differdeleted file mode 100644 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+\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); +r = 0.9; +z0 = (0, 0); +z1 = r*(89, -55); +z2 = r*(42, 30); +z3 = z1 + z2; + +picture FE, FEV, E, EV, M, N, U, V; +FE = thelabel("$f^*E$", (x0, y0)); +M = thelabel("$M$", (x0, y1)); +E = thelabel("$E$", (x1, y0)); +N = thelabel("$N$", (x1, y1)); +FEV = thelabel("$f^*E_V$", (x2, y2)); +U = thelabel("$U$", (x2, y3)); +EV = thelabel("$E_V$", (x3, y2)); +V = thelabel("$V$", (x3, y3)); + +forsuffixes @=E, M, N, U, V, EV, FE, FEV: draw @; endfor + +ahangle := 20; +vardef connect(expr a, b) = + save line; path line; interim bboxmargin := 3; + line = center a .. center b cutbefore bbox a cutafter bbox b; + cutdraw line withpen pencircle scaled 4 withcolor background; + drawarrow line +enddef; + +connect(FEV, EV); +connect(FEV, U); +connect(EV, V); +connect(U, V); + +connect(FEV, FE); +connect(EV, E); +connect(U, M); +connect(V, N); + +connect(FE, E); +connect(FE, M); +connect(E, N); +connect(M, N); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tikzcd-example.pdf b/info/drawing-with-metapost/src/cd-tikzcd-example.pdf Binary files differindex c2b95990db..eb212b3cdf 100644 --- a/info/drawing-with-metapost/src/tikzcd-example.pdf +++ b/info/drawing-with-metapost/src/cd-tikzcd-example.pdf diff --git a/info/drawing-with-metapost/src/cd-xypic-example.mp b/info/drawing-with-metapost/src/cd-xypic-example.mp new file mode 100644 index 0000000000..672fa7c278 --- /dev/null +++ b/info/drawing-with-metapost/src/cd-xypic-example.mp @@ -0,0 +1,44 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + picture U, XY, X, Y, Z; + z1 = -z2 = (-61, 42); + U = thelabel("$U$", z1); + XY = thelabel("$X\times_ZY$", origin); + X = thelabel("$X$", (x2, 0)); + Y = thelabel("$Y$", (0, y2)); + Z = thelabel("$Z$", z2); + + forsuffixes @=U, XY, X, Y, Z: draw @; endfor + + ahangle := 20; + vardef connect@#(expr s, a, b) = + curved_connect@#(s, a, b, center b - center a) + enddef; + vardef curved_connect@#(expr s, a, b, d) = + save line, mark; path line; picture mark; + line = center a {d} .. center b; + interim bboxmargin := 4; + drawarrow line cutbefore bbox a cutafter bbox b; + mark = thelabel@#("$\scriptstyle " & s & "$", + point 1/2 of line); + interim bboxmargin := 1; + unfill bbox mark; draw mark; + enddef; + + connect.bot("p", XY, X); + connect.rt ("q", XY, Y); + connect.top("g", Y, Z); + connect.lft("f", X, Z); + curved_connect.urt("x", U, X, right); + curved_connect.llft("y", U, Y, dir -80); + + drawoptions(dashed withdots scaled 1/2); + connect("(x,y)", U, XY); + drawoptions(); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/xypic-example.pdf b/info/drawing-with-metapost/src/cd-xypic-example.pdf Binary files differindex fb5cb9d295..6348da43c1 100644 --- a/info/drawing-with-metapost/src/xypic-example.pdf +++ b/info/drawing-with-metapost/src/cd-xypic-example.pdf diff --git a/info/drawing-with-metapost/src/circumcircle.mp b/info/drawing-with-metapost/src/circumcircle.mp deleted file mode 100644 index b4cca18faa..0000000000 --- a/info/drawing-with-metapost/src/circumcircle.mp +++ /dev/null @@ -1,49 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -vardef through(expr a, b, o) = - save t; numeric t; t = 1+o/abs(a-b); - t[b,a] -- t[a,b] -enddef; - -beginfig(1); - path T; T = origin -- 377 dir 10 -- 233 dir 70 -- cycle; - pair m; - m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T - = whatever * (point 1 of T - point 2 of T) rotated 90 shifted point 3/2 of T - = whatever * (point 2 of T - point 3 of T) rotated 90 shifted point 5/2 of T; - - drawoptions(withcolor 3/4); - draw unitsquare scaled 5 rotated angle (point 1 of T-point 0 of T) shifted point 1/2 of T; - draw unitsquare scaled 5 rotated angle (point 2 of T-point 1 of T) shifted point 3/2 of T; - draw unitsquare scaled 5 rotated angle (point 0 of T-point 2 of T) shifted point 5/2 of T; - drawoptions(dashed evenly scaled 1/4 withcolor 1/2); - draw through(point 1/2 of T, m, 10); - draw through(point 3/2 of T, m, 10); - draw through(point 5/2 of T, m, 10); - drawoptions(); - draw fullcircle scaled 2 abs (point 0 of T - m) shifted m withcolor 2/3 red; - draw T; - - draw m withpen pencircle scaled dotlabeldiam; label("$m$", m + 10 dir 12); - -vardef mark_equal(expr a, b, n) = - save m, s; picture m; m = image( - numeric s; 2s = n - 1; for t=-s upto s: - draw (down--up) scaled 2 rotated -13 shifted (t,0) withpen pencircle scaled 1/4; - endfor - ); - draw m rotated angle (b-a) shifted 1/4[a,b]; - draw m rotated angle (b-a) shifted 3/4[a,b]; -enddef; - - mark_equal(point 0 of T, point 1 of T, 1); - mark_equal(point 1 of T, point 2 of T, 2); - mark_equal(point 2 of T, point 0 of T, 3); - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/clocks.mp b/info/drawing-with-metapost/src/clocks.mp index 045c0f1682..16a412e93d 100644 --- a/info/drawing-with-metapost/src/clocks.mp +++ b/info/drawing-with-metapost/src/clocks.mp @@ -7,11 +7,14 @@ vardef clock_roman primary h = enddef; path hand[]; -hand1 = origin .. (.257,1/50) .. (.377,1/60) & (.377,1/60) {up} .. (.40,3/50) .. (.60, 1/40) .. {right} (.75,0); -hand1 := (hand1 .. reverse hand1 reflectedabout(left,right) .. cycle) scaled 50; - +hand1 = origin .. (.257,1/50) .. (.377,1/60) + & (.377,1/60) {up} .. (.40,3/50) + .. (.60, 1/40) .. {right} (.75,0); +hand1 := (hand1 .. reverse hand1 reflectedabout(left,right) + .. cycle) scaled 50; hand2 = origin .. (.60, 1/64) .. {right} (.925,0); -hand2 := (hand2 .. reverse hand2 reflectedabout(left,right) .. cycle) scaled 50; +hand2 := (hand2 .. reverse hand2 reflectedabout(left,right) + .. cycle) scaled 50; % hour of the day to degrees vardef htod(expr hours) = 30*((15-hours) mod 12) enddef; @@ -31,17 +34,13 @@ vardef clock(expr hours, minutes) = image( endfor % numerals for h=1 upto 12: - label( - if known roman_numerals_please: - clock_roman h infont "bchr8r" rotated ((12-h)*30) - else: - decimal h infont "bchr8r" - fi, (40,0) rotated htod(h)); + label(decimal h infont "bchr8r", (40,0) rotated htod(h)); endfor % hands rotated to the given time - filldraw hand1 rotated htod(hours+minutes/60) withpen pencircle scaled 7/8; - filldraw hand2 rotated mtod(minutes) withpen pencircle scaled 7/8; + pickup pencircle scaled 7/8; + filldraw hand1 rotated htod(hours+minutes/60); + filldraw hand2 rotated mtod(minutes); % draw the center on top - fill fullcircle scaled 5; - fill fullcircle scaled 3 withcolor .4 white; + draw origin withpen pencircle scaled 5; + undraw origin withpen pencircle scaled 3; ) enddef; diff --git a/info/drawing-with-metapost/src/closed-antireuleaux-set.mp b/info/drawing-with-metapost/src/closed-antireuleaux-set.mp deleted file mode 100644 index 8d8da6b507..0000000000 --- a/info/drawing-with-metapost/src/closed-antireuleaux-set.mp +++ /dev/null @@ -1,27 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -\mplibtextextlabel{enable} -vardef reuleaux(expr n, r) = - save a; numeric a; a = 90/n; - for t = 0 step 4a until 359: - (0, r) rotated t {left rotated (3a + t)} .. {left rotated (a + t)} - endfor cycle -enddef; -vardef median(expr p) = origin for i=1 upto length p: + point i of p / length p endfor enddef; -input colorbrewer-rgb -beginfig(1); - for n = 3 upto 7: - path p; p = reuleaux(n, 42) shifted (90n, 0); - pair m; m = point (n+1)/2 of p; - fill p withcolor if odd n: Oranges else: Blues fi 8 2; - % draw tensepath(p) withcolor Blues 8 6; - %draw p rotatedabout(median(p), 180/n) withcolor Blues 8 6; - draw p; - endfor - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/closed-antireuleaux-set.pdf b/info/drawing-with-metapost/src/closed-antireuleaux-set.pdf Binary files differdeleted file mode 100644 index 9c0606cfd3..0000000000 --- a/info/drawing-with-metapost/src/closed-antireuleaux-set.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/closed-polygon-chain.mp b/info/drawing-with-metapost/src/closed-polygon-chain.mp deleted file mode 100644 index 14f9b28738..0000000000 --- a/info/drawing-with-metapost/src/closed-polygon-chain.mp +++ /dev/null @@ -1,18 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input archimedean-tools -beginfig(1); - path P[]; P3 = for i=0 upto 2: 6 up rotated 120i -- endfor cycle; - fill P3 withcolor 3/4 red; draw P3; - for n = 4 upto 23: - numeric m; m = floor(n / 2); - P[n] = poly n of subpath (m, m-1) of P[n-1]; - fill P[n] withcolor (n/32)[3/4 if odd n: red else: blue fi, white]; - draw P[n]; label(decimal n, median(P[n])); - endfor -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/closed-polygon-chain.pdf b/info/drawing-with-metapost/src/closed-polygon-chain.pdf Binary files differdeleted file mode 100644 index 4034d6a359..0000000000 --- a/info/drawing-with-metapost/src/closed-polygon-chain.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/color-blend-toy.mp b/info/drawing-with-metapost/src/color-blend-toy.mp index d712791230..336f7db64f 100644 --- a/info/drawing-with-metapost/src/color-blend-toy.mp +++ b/info/drawing-with-metapost/src/color-blend-toy.mp @@ -3,19 +3,19 @@ \begin{document} \begin{mplibcode} beginfig(1); - color brg, pbr; - brg = 1/256 (1, 66, 37); - pbr = 1/256 (223, 52, 57); - N = 5; n = 0; - for y=1 upto N: - for x=1 upto N: - fill fullcircle scaled 16 shifted 20(x,y) - withpen pencircle scaled 2 - withcolor (n/N/N)[pbr, brg]; - label(decimal incr n infont "phvr8r", 20(x,y)) - withcolor white; - endfor +color brg, pbr; +brg = 1/256 (1, 66, 37); % British Racing Green +pbr = 1/256 (223, 52, 57); % Pillar Box Red +N = 5; n = 0; +for y=1 upto N: + for x=1 upto N: + fill fullcircle scaled 16 shifted 20(x,y) + withpen pencircle scaled 2 + withcolor (n/N/N)[pbr, brg]; + label(decimal incr n infont "phvr8r", 20(x,y)) + withcolor white; endfor +endfor endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/color-blended-circles.mp b/info/drawing-with-metapost/src/color-blended-circles.mp new file mode 100644 index 0000000000..b3e89974fd --- /dev/null +++ b/info/drawing-with-metapost/src/color-blended-circles.mp @@ -0,0 +1,44 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\usepackage{fontspec} +\setmainfont{Helvetica} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); +path C[], B[]; + +% arrange each circle so that point 0 is outside the others +C1 = fullcircle scaled 100 rotated 90 shifted 40 up; +C2 = C1 rotated 120; +C3 = C2 rotated 120; + +% the illusion of blended colours is helped by buildcycle +B0 = buildcycle(C1, C2, C3); +B1 = buildcycle(C1, C2); +B2 = buildcycle(C2, C3); +B3 = buildcycle(C3, C1); + +picture P; +for x=0 upto 1: + for y=0 upto 1: + P := image( + s := 1/2 + x/4; + k := 0 + y/4; + fill C1 withcolor s*(1,0,0,k); + fill C2 withcolor s*(0,1,0,k); + fill C3 withcolor s*(0,0,1,k); + fill B3 withcolor s*(1,0,1,k); + fill B2 withcolor s*(0,1,1,k); + fill B1 withcolor s*(1,1,0,k); + fill B0 withcolor s*(1,1,1,k); + undraw C1; undraw C2; undraw C3; + ) shifted (200x, 180y); + draw P; + label.bot(("shade: " & decimal s & ", k: " & decimal k) + infont "phvr8r", point 1/2 of bbox P); + endfor +endfor +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/color-blended-circles.pdf b/info/drawing-with-metapost/src/color-blended-circles.pdf Binary files differnew file mode 100644 index 0000000000..b2893e08b2 --- /dev/null +++ b/info/drawing-with-metapost/src/color-blended-circles.pdf diff --git a/info/drawing-with-metapost/src/color-brexit-map.mp b/info/drawing-with-metapost/src/color-brexit-map.mp new file mode 100644 index 0000000000..54ca1c23ff --- /dev/null +++ b/info/drawing-with-metapost/src/color-brexit-map.mp @@ -0,0 +1,104 @@ +\documentclass{standalone} +\usepackage{luamplib} +\mplibtextextlabel{enable} +\usepackage{fontspec} +\setmainfont{TeX Gyre Heros} +\begin{document} +\begin{mplibcode} +input london-boroughs +input colorbrewer-rgb +picture legend; legend = image( +for i = 1 upto 9: + path s; s = unitsquare scaled 12 shifted (12i, 0); + fill s withcolor RdYlBu[9][i]; draw s; + if i = 1: + label.top("Leave", point 5/2 of s); + elseif i = 9: + label.top("Remain", point 5/2 of s); + fi +endfor +); +vardef median(expr p) = + save n; numeric n; n = length p; + 1/n * point 0 of p for i=1 upto n: + 1/n * point i of p endfor +enddef; + +beginfig(1); + +fill Barking_and_Dagenham withcolor 0.756 [RdYlBu 9 3, RdYlBu 9 4]; draw Barking_and_Dagenham; +fill Barnet withcolor 0.223 [RdYlBu 9 6, RdYlBu 9 7]; draw Barnet; +fill Bexley withcolor 0.705 [RdYlBu 9 3, RdYlBu 9 4]; draw Bexley; +fill Brent withcolor 0.974 [RdYlBu 9 5, RdYlBu 9 6]; draw Brent; +fill Bromley withcolor 0.065 [RdYlBu 9 5, RdYlBu 9 6]; draw Bromley; +fill Camden withcolor 0.494 [RdYlBu 9 7, RdYlBu 9 8]; draw Camden; +fill City_of_London withcolor 0.529 [RdYlBu 9 7, RdYlBu 9 8]; draw City_of_London; +fill Croydon withcolor 0.429 [RdYlBu 9 5, RdYlBu 9 6]; draw Croydon; +fill Ealing withcolor 0.040 [RdYlBu 9 6, RdYlBu 9 7]; draw Ealing; +fill Enfield withcolor 0.582 [RdYlBu 9 5, RdYlBu 9 6]; draw Enfield; +fill Greenwich withcolor 0.559 [RdYlBu 9 5, RdYlBu 9 6]; draw Greenwich; +fill Hackney withcolor 0.848 [RdYlBu 9 7, RdYlBu 9 8]; draw Hackney; +fill Hammersmith_and_Fulham withcolor 0.002 [RdYlBu 9 7, RdYlBu 9 8]; draw Hammersmith_and_Fulham; +fill Haringey withcolor 0.557 [RdYlBu 9 7, RdYlBu 9 8]; draw Haringey; +fill Harrow withcolor 0.463 [RdYlBu 9 5, RdYlBu 9 6]; draw Harrow; +fill Havering withcolor 0.034 [RdYlBu 9 3, RdYlBu 9 4]; draw Havering; +fill Hillingdon withcolor 0.363 [RdYlBu 9 4, RdYlBu 9 5]; draw Hillingdon; +fill Hounslow withcolor 0.106 [RdYlBu 9 5, RdYlBu 9 6]; draw Hounslow; +fill Islington withcolor 0.522 [RdYlBu 9 7, RdYlBu 9 8]; draw Islington; +fill Kensington_and_Chelsea withcolor 0.869 [RdYlBu 9 6, RdYlBu 9 7]; draw Kensington_and_Chelsea; +fill Kingston_upon_Thames withcolor 0.161 [RdYlBu 9 6, RdYlBu 9 7]; draw Kingston_upon_Thames; +fill Lambeth withcolor 0.862 [RdYlBu 9 7, RdYlBu 9 8]; draw Lambeth; +fill Lewisham withcolor 0.986 [RdYlBu 9 6, RdYlBu 9 7]; draw Lewisham; +fill Merton withcolor 0.294 [RdYlBu 9 6, RdYlBu 9 7]; draw Merton; +fill Newham withcolor 0.284 [RdYlBu 9 5, RdYlBu 9 6]; draw Newham; +fill Redbridge withcolor 0.397 [RdYlBu 9 5, RdYlBu 9 6]; draw Redbridge; +fill Richmond_upon_Thames withcolor 0.929 [RdYlBu 9 6, RdYlBu 9 7]; draw Richmond_upon_Thames; +fill Southwark withcolor 0.281 [RdYlBu 9 7, RdYlBu 9 8]; draw Southwark; +fill Sutton withcolor 0.628 [RdYlBu 9 4, RdYlBu 9 5]; draw Sutton; +fill Tower_Hamlets withcolor 0.746 [RdYlBu 9 6, RdYlBu 9 7]; draw Tower_Hamlets; +fill Waltham_Forest withcolor 0.910 [RdYlBu 9 5, RdYlBu 9 6]; draw Waltham_Forest; +fill Wandsworth withcolor 0.503 [RdYlBu 9 7, RdYlBu 9 8]; draw Wandsworth; +fill Westminster withcolor 0.897 [RdYlBu 9 6, RdYlBu 9 7]; draw Westminster; + +% scaling represents turnout +label(TEX("Barking \& Dagenham") scaled 0.637 rotated 15, median(Barking_and_Dagenham)); +label(TEX("Barnet") scaled 0.720, median(Barnet) shifted 12 up); +label(TEX("Bexley") scaled 0.752, median(Bexley) shifted 12 left); +label(TEX("Brent") scaled 0.649, median(Brent) shifted 12 left); +label(TEX("Bromley") scaled 0.788, median(Bromley)); +label(TEX("Camden") scaled 0.654, median(Camden) shifted 6 left); +label(TEX("City") scaled 0.734, median(City_of_London)); +label(TEX("Croydon") scaled 0.697, median(Croydon)); +label(TEX("Ealing") scaled 0.699, median(Ealing)); +label(TEX("Enfield") scaled 0.690, median(Enfield)); +label(TEX("Greenwich") scaled 0.694, median(Greenwich) shifted 6 right); +label(TEX("Hackney") scaled 0.650, median(Hackney) shifted 8 right); +label(TEX("Hammersmith \& Fulham") scaled 0.698 rotated -62, median(Hammersmith_and_Fulham)); +label(TEX("Haringey") scaled 0.705, median(Haringey)); +label(TEX("Harrow") scaled 0.721, median(Harrow)); +label(TEX("Havering") scaled 0.759, median(Havering)); +label(TEX("Hillingdon") scaled 0.689, median(Hillingdon) shifted 6 right); +label(TEX("Hounslow") scaled 0.697, median(Hounslow) shifted 12 left); +label(TEX("Islington") scaled 0.703, median(Islington) shifted 4 right); +label(TEX("Kensington \& Chelsea") scaled 0.659 rotated -54, median(Kensington_and_Chelsea)); +label(TEX("Kingston upon Thames") scaled 0.783 rotated 66, median(Kingston_upon_Thames)); +label(TEX("Lambeth") scaled 0.673, median(Lambeth) shifted 4 left); +label(TEX("Lewisham") scaled 0.630, median(Lewisham) shifted 8 right); +label(TEX("Merton") scaled 0.734, median(Merton)); +label(TEX("Newham") scaled 0.591, median(Newham)); +label(TEX("Redbridge") scaled 0.675, median(Redbridge)); +label.lft(TEX("Richmond") scaled 0.820, median(Richmond_upon_Thames) shifted (-1,4)); +label.rt(TEX("upon Thames") scaled 0.820, median(Richmond_upon_Thames) shifted (-9,-6)); +label(TEX("Southwark") scaled 0.661, median(Southwark) shifted 4 left); +label(TEX("Sutton") scaled 0.759, median(Sutton)); +label(TEX("Tower Hamlets") scaled 0.644, median(Tower_Hamlets) shifted 8 left); +label(TEX("Waltham Forest") scaled 0.666 rotated 50, median(Waltham_Forest)); +label(TEX("Wandsworth") scaled 0.719, median(Wandsworth) shifted 8 left); +label(TEX("Westminster") scaled 0.648, median(Westminster)); + +label.ulft(legend, point 1 of bbox currentpicture); +label.lrt("\large Brexit vote in London 2016", point 3 of bbox currentpicture shifted (4,-4)); + + +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/color-brexit-map.pdf b/info/drawing-with-metapost/src/color-brexit-map.pdf Binary files differnew file mode 100644 index 0000000000..df81e61574 --- /dev/null +++ b/info/drawing-with-metapost/src/color-brexit-map.pdf diff --git a/info/drawing-with-metapost/src/color-grey-escher.mp b/info/drawing-with-metapost/src/color-grey-escher.mp new file mode 100644 index 0000000000..b8f57e44d2 --- /dev/null +++ b/info/drawing-with-metapost/src/color-grey-escher.mp @@ -0,0 +1,38 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); + numeric s; s = 8; + path atom; + atom = origin + -- (2s,0) rotated -30 -- (2s,0) rotated -30 + (0,s) + -- ( s,0) rotated 30 -- ( s,0) rotated 30 + (0,s) + -- (0,2s) -- cycle; + + picture p[]; + for i=0 upto 2: + p[i] = image( + fill atom rotated -120i withcolor (7/8 - 1/8i) ; + draw atom rotated -120i; + ); + endfor + + pair u, v; + u = point 3 of atom - point 1 of atom rotated -120; + v = u rotated 60; + + n = 13; + for i=-n upto n: + for j=-n upto n: + forsuffixes $=0,1,2: + draw p$ shifted (i*u + j*v); + endfor + endfor + endfor + + clip currentpicture to + unitsquare shifted -(1/2,1/2) scaled 5in yscaled 0.618; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/color-grey-escher.pdf b/info/drawing-with-metapost/src/color-grey-escher.pdf Binary files differnew file mode 100644 index 0000000000..3fd8a6e0e2 --- /dev/null +++ b/info/drawing-with-metapost/src/color-grey-escher.pdf diff --git a/info/drawing-with-metapost/src/color-grey-shadows.mp b/info/drawing-with-metapost/src/color-grey-shadows.mp new file mode 100644 index 0000000000..36396c63b8 --- /dev/null +++ b/info/drawing-with-metapost/src/color-grey-shadows.mp @@ -0,0 +1,34 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); +path b, w; +b = ((-3,-4)--(3,-2)--(3,+2)--(-3,4)--cycle) scaled 5; +w = b reflectedabout(up, down); + +picture B, W; +B = image( + for i=0 step 1/64 until 1: + draw point 4-i of b -- point 1+i**2 of b withcolor 1-i**8; + endfor +); + +W = image( + for i=0 step 1/64 until 1: + draw point 4-i of w -- point 1+i**2 of w withcolor 3/4-i**8; + endfor +); + +for i=-7 upto 7: + for j=-4 upto 4: + draw if odd (i+j): W else: B fi shifted ((i,j) scaled 30); + endfor +endfor + +clip currentpicture to + unitsquare shifted -(.5,.5) scaled 5in yscaled 0.618; + +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/color-grey-shadows.pdf b/info/drawing-with-metapost/src/color-grey-shadows.pdf Binary files differnew file mode 100644 index 0000000000..b4e8142470 --- /dev/null +++ b/info/drawing-with-metapost/src/color-grey-shadows.pdf diff --git a/info/drawing-with-metapost/src/color-hsv-bathymetric.mp b/info/drawing-with-metapost/src/color-hsv-bathymetric.mp index 057e923edd..6dad717199 100644 --- a/info/drawing-with-metapost/src/color-hsv-bathymetric.mp +++ b/info/drawing-with-metapost/src/color-hsv-bathymetric.mp @@ -3,40 +3,40 @@ \begin{document} \begin{mplibcode} input color-hsv-macro -beginfig(2); - defaultfont := "phvr8r"; - defaultscale := 3/4; - path h,d,b; numeric n; - h = ((-2,0)--(0,0)--(-1,3)--(-2,3)--cycle) scaled 60; - d = h rotated 180; - n = 10; - b = subpath (0,1) of h -- point 1+1/n of d -- (xpart point 0 of h, ypart point 1+1/n of d) -- cycle; - fill b withcolor hsv_color(123, 1/8, 7/8); - draw subpath (2.13,4) of b; - - for i=1 upto n: - fill point 4-(i-1)/n of h -- point 1+(i-1)/n of h - -- point 1+i/n of h -- point 4-i/n of h -- cycle - withcolor hsv_color(42, 1/4 + 3/4 * i/n, 1 - i/3n); - fill point 4-(i-1)/n of d -- point 1+(i-1)/n of d - -- point 1+i/n of d -- point 4-i/n of d -- cycle - withcolor hsv_color(200, i/n - 1/n, 1 - i/3n); - endfor - string s; - for i=1 upto n-1: - draw point 4-i/n of h -- point 1+i/n of h; - draw point 4-i/n of d -- point 1+i/n of d; - s := decimal if i < 4: (i**2+1) else: (10 + (i-3)*10) fi & "00"; - label.rt(s, point 1+i/n of h); - label.lft(s, point 1+i/n of d); - endfor - label.rt("Metres", point 2 of h); - label.lft("Metres", point 2 of d); - label.lft("Hypsometric tints" infont defaultfont scaled defaultscale rotated 90, point 7/2 of h); - label.rt("Bathymetric tints" infont defaultfont scaled defaultscale rotated -90, point 7/2 of d); - label.lft("sea level", point 0 of h); - label("areas below sea level", center b); - draw h; draw d; +beginfig(1); +defaultfont := "phvr8r"; defaultscale := 3/4; +path h,d,b; numeric n; n = 10; +h = ((-2,0)--(0,0)--(-1,3)--(-2,3)--cycle) scaled 64; +d = h rotated 180; +b = subpath (0,1) of h -- point 1+1/n of d -- + (xpart point 0 of h, ypart point 1+1/n of d) -- cycle; +fill b withcolor hsv_color(123, 1/8, 7/8); +draw subpath (2.13,4) of b; +for i=1 upto n: + fill point 4-(i-1)/n of h -- point 1+(i-1)/n of h -- + point 1+i/n of h -- point 4-i/n of h -- cycle + withcolor hsv_color(42, 1/4 + 3/4 * i/n, 1 - i/3n); + fill point 4-(i-1)/n of d -- point 1+(i-1)/n of d -- + point 1+i/n of d -- point 4-i/n of d -- cycle + withcolor hsv_color(200, i/n - 1/n, 1 - i/3n); +endfor +string s; +for i=1 upto n-1: + draw point 4-i/n of h -- point 1+i/n of h; + draw point 4-i/n of d -- point 1+i/n of d; + s := decimal if i < 4: (i**2+1) else: (10 + (i-3)*10) fi & "00"; + label.rt(s, point 1+i/n of h); + label.lft(s, point 1+i/n of d); +endfor +label.rt("Metres", point 2 of h); +label.lft("Metres", point 2 of d); +label.lft("Hypsometric tints" infont defaultfont + scaled defaultscale rotated 90, point 7/2 of h); +label.rt("Bathymetric tints" infont defaultfont + scaled defaultscale rotated -90, point 7/2 of d); +label.lft("sea level", point 0 of h); +label("areas below sea level", center b); +draw h; draw d; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/color-hsv-bathymetric.pdf b/info/drawing-with-metapost/src/color-hsv-bathymetric.pdf Binary files differindex 8f03ce2b73..4898820243 100644 --- a/info/drawing-with-metapost/src/color-hsv-bathymetric.pdf +++ b/info/drawing-with-metapost/src/color-hsv-bathymetric.pdf diff --git a/info/drawing-with-metapost/src/color-hsv-gamut.mp b/info/drawing-with-metapost/src/color-hsv-gamut.mp index 392853e7bc..71a62ef031 100644 --- a/info/drawing-with-metapost/src/color-hsv-gamut.mp +++ b/info/drawing-with-metapost/src/color-hsv-gamut.mp @@ -4,24 +4,30 @@ \begin{mplibcode} input color-hsv-macro beginfig(1); - defaultfont := "phvr8r"; - numeric s[], v[]; - s0 = 1/2; v0 = 7/8; - s1 = 7/8; v1 = 7/8; - s2 = 7/8; v2 = 1/2; - for y=0 upto 2: - for h=0 step 15 until 360: - fill fullcircle scaled 24 shifted (h, -32y) withcolor hsv_color(h, s[y], v[y]); - draw fullcircle scaled 24 shifted (h, -32y) withcolor white; - if y=1: label(decimal h infont defaultfont scaled 1/2, (h,-16)); fi - endfor + defaultfont := "phvr8r"; + + numeric s[], v[]; + s0 = 1/2; v0 = 7/8; + s1 = 7/8; v1 = 7/8; + s2 = 7/8; v2 = 1/2; + + path r; + for y=0, 1, 2: + for h=0 step 15 until 360: + r := fullcircle scaled 24 shifted (h, -36y if y=2: +8 fi); + fill r withcolor hsv_color(h, s[y], v[y]); + draw r withcolor white; + if y=1: + label(decimal h infont defaultfont scaled 0.7, (h,-18)); + fi endfor + endfor - label.urt("Less saturation", (-20,12)); - label.lrt("Lower value", (-20,-76)); + label.urt("Less saturation", (-20,14)); + label.lrt("Lower value", (-20,-78)); - drawarrow (-15, -12) -- (-15,12); - drawarrow (-15, -52) -- (-15,-76); + drawarrow (-15, -21) -- (-15,12); + drawarrow (-15, -43) -- (-15,-76); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/color-hsv-gamut.pdf b/info/drawing-with-metapost/src/color-hsv-gamut.pdf Binary files differindex a2a2d68a08..5ca16508e3 100644 --- a/info/drawing-with-metapost/src/color-hsv-gamut.pdf +++ b/info/drawing-with-metapost/src/color-hsv-gamut.pdf diff --git a/info/drawing-with-metapost/src/color-hsv-macro.mp b/info/drawing-with-metapost/src/color-hsv-macro.mp index 1ec265a055..243725fbe4 100644 --- a/info/drawing-with-metapost/src/color-hsv-macro.mp +++ b/info/drawing-with-metapost/src/color-hsv-macro.mp @@ -1,15 +1,14 @@ -vardef hsv_color(expr h,s,v) = - % following wikipedia article on "HSL and HSV" - save chroma, hh, x, m; - chroma = v*s; - hh = h/60; - x = chroma * (1-abs(hh mod 2 - 1)); - m = v - chroma; - if hh < 1: (chroma,x,0)+(m,m,m) - elseif hh < 2: (x,chroma,0)+(m,m,m) - elseif hh < 3: (0,chroma,x)+(m,m,m) - elseif hh < 4: (0,x,chroma)+(m,m,m) - elseif hh < 5: (x,0,chroma)+(m,m,m) - else: (chroma,0,x)+(m,m,m) - fi +vardef hsv_color(expr h, s, v) = + save chroma, hh, x, m; + chroma = v * s; + hh = h / 60; + x = chroma * (1 - abs(hh mod 2 - 1)); + m = v - chroma; + if hh < 1: (chroma,x,0)+(m,m,m) + elseif hh < 2: (x,chroma,0)+(m,m,m) + elseif hh < 3: (0,chroma,x)+(m,m,m) + elseif hh < 4: (0,x,chroma)+(m,m,m) + elseif hh < 5: (x,0,chroma)+(m,m,m) + else: (chroma,0,x)+(m,m,m) + fi enddef; diff --git a/info/drawing-with-metapost/src/compass-rose.mp b/info/drawing-with-metapost/src/compass-rose.mp deleted file mode 100644 index 26952e26e2..0000000000 --- a/info/drawing-with-metapost/src/compass-rose.mp +++ /dev/null @@ -1,35 +0,0 @@ -vardef compass_rose(expr shade, highlight) = - save currentpicture, s; - picture currentpicture; currentpicture := nullpicture; - drawoptions(withcolor shade); - draw fullcircle scaled 144 withpen pencircle scaled 2; - draw fullcircle scaled 138; - draw thelabel("NW" infont defaultfont scaled 3/4, 64 up) rotated +45; - draw thelabel("NE" infont defaultfont scaled 3/4, 64 up) rotated -45; - draw thelabel("SE" infont defaultfont scaled 3/4, 64 down) rotated +45; - draw thelabel("SW" infont defaultfont scaled 3/4, 64 down) rotated -45; - draw fullcircle scaled 120; - draw fullcircle scaled 118; - draw fullcircle scaled 108; - draw fullcircle scaled 106; - for t=0 step 15 until 350: draw ((53,0) -- (60,0)) rotated t; endfor - for t=0 step 45 until 350: draw ((69,0) -- (80,0)) rotated t; endfor - path s; s = 8 right -- 60 up -- 8 left -- cycle; - for t=0 upto 3: filldraw s rotated (45 + 90t); endfor - s := s scaled 1.414; - for t=0 upto 3: - s := s rotated 90t; - fill s withcolor background; - fill subpath (-1/2, 1) of s -- cycle if t=0: withcolor highlight fi; - draw s; - endfor - fill fullcircle scaled 28 withcolor background; - draw fullcircle scaled 28; - fill fullcircle scaled dotlabeldiam; - label.top("N" infont "cmbx12", 84 up); - label.bot("S" infont "cmbx12", 84 down); - label.rt("E" infont "cmbx12", 84 right); - label.lft("W" infont "cmbx12", 84 left); - drawoptions(); - currentpicture -enddef; diff --git a/info/drawing-with-metapost/src/complex-inverse-and-sqrt.mp b/info/drawing-with-metapost/src/complex-inverse-and-sqrt.mp deleted file mode 100644 index 3b187fad26..0000000000 --- a/info/drawing-with-metapost/src/complex-inverse-and-sqrt.mp +++ /dev/null @@ -1,48 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -picture axes, dot, opendot, P[]; -numeric u; u = 42; -interim ahangle := 30; -axes = image( - path xx, yy; xx = (left--right) scaled 1.2 u; yy = xx rotated 90; - draw fullcircle scaled 2u; - drawarrow xx; label.rt("$\Re$", point 1 of xx); - drawarrow yy; label.top("$\Im$", point 1 of yy); -); -dot = image(fill fullcircle scaled dotlabeldiam); -opendot = image(draw dot; unfill fullcircle scaled 3/4 dotlabeldiam); -z1 = 0.7 dir 76; -z2 = 1.5 dir 60; -z3 = 1 dir 42; - -vardef connect(expr a, b, shade) = - path c; c = (a -- origin -- b) scaled u; - drawarrow c cutafter fullcircle scaled 5 shifted point 2 of c withcolor shade; - draw dot shifted point 0 of c; draw opendot shifted point 2 of c; -enddef; - -vardef zinverse(expr z) = 1/abs z * dir - angle z enddef; -vardef zsqrt(expr z) = if abs z > 0: sqrt(abs z) * dir 1/2 angle fi z enddef; - -input colorbrewer-rgb -P1 = image( -draw axes withcolor 3/4; -label.lrt("\small\texttt{zinverse()}", ulcorner axes shifted 10 left); -for i=1 upto 3: connect(z[i], zinverse(z[i]), SetTwo[7][2+i]); endfor -); -P2 = image( -draw axes withcolor 3/4; -label.lrt("\small\texttt{zsqrt()}", ulcorner axes); -for i=1 upto 3: connect(z[i], zsqrt(z[i]), SetTwo[7][2+i]); endfor -); -beginfig(1); - interim labeloffset := 12; - label.lft(P1, origin); - label.rt(P2, origin); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/complex-operators.mp b/info/drawing-with-metapost/src/complex-operators.mp deleted file mode 100644 index a1510bc64b..0000000000 --- a/info/drawing-with-metapost/src/complex-operators.mp +++ /dev/null @@ -1,32 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - numeric u; u = 1cm; - z1 = 2 dir 15; z2 = 1.2 dir 60; - z3 = z1+z2; z4 = z1 zscaled z2; z5 = (x1,-y1); - drawoptions(withcolor 2/3 white); - draw (1/2 left -- 3 right) scaled u ; - draw (1/2 down -- 3 up ) scaled u ; - draw subpath (0,3) of fullcircle scaled 2u rotated -22.5; - drawoptions(); - dotlabel.lrt (btex $\scriptstyle 1$ etex, (u,0)); - dotlabel.ulft(btex $\scriptstyle i$ etex, (0,u)); - interim ahangle := 30; - forsuffixes @=1,2,3,4,5: - x@ := x@ * u; y@ := y@ * u; - drawarrow origin -- z@ - cutafter fullcircle scaled 5 shifted z@ - withcolor 2/3 if @ < 3: blue else: red fi; - endfor - fill fullcircle scaled dotlabeldiam; - dotlabel.rt (btex $A$ etex, z1); - dotlabel.urt(btex $B$ etex, z2); - dotlabel.top(btex $A+B$ etex, z3); - dotlabel.top(btex $A \times B$ etex, z4); - dotlabel.rt (btex $\bar{A}$ etex, z5); -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/curves-astroid-family.mp b/info/drawing-with-metapost/src/curves-astroid-family.mp index 340144f721..083784f960 100644 --- a/info/drawing-with-metapost/src/curves-astroid-family.mp +++ b/info/drawing-with-metapost/src/curves-astroid-family.mp @@ -3,17 +3,15 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -input colorbrewer-rgb beginfig(1); - numeric a; a = 144; - for n=1 upto 7: - path p; p = a * right for t=6 step 6 until 90: - .. a * (cosd(t) ** n, sind(t) ** n) - endfor; - p := for i=0 upto 3: p rotated 90i & endfor cycle; - fill p withcolor Oranges[9][n]; draw p; - endfor +input colorbrewer-rgb +for n=1 upto 7: + path p; p = (right for t=6 step 6 until 90: + .. (cosd(t) ** n, sind(t) ** n) + endfor) scaled 144; + p := for i=0 upto 3: p rotated 90i & endfor cycle; + fill p withcolor Blues[9][n]; draw p; +endfor endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/curves-astroid-family.pdf b/info/drawing-with-metapost/src/curves-astroid-family.pdf Binary files differindex 18eb3b64d9..50a407f380 100644 --- a/info/drawing-with-metapost/src/curves-astroid-family.pdf +++ b/info/drawing-with-metapost/src/curves-astroid-family.pdf diff --git a/info/drawing-with-metapost/src/curves-astroid.mp b/info/drawing-with-metapost/src/curves-astroid.mp index b572205217..6fe4896108 100644 --- a/info/drawing-with-metapost/src/curves-astroid.mp +++ b/info/drawing-with-metapost/src/curves-astroid.mp @@ -4,17 +4,16 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - path base; base = fullcircle scaled 300; - path astroid; astroid = - for t=0 step 1/16 until 8: - hide(pair a, b, p; - a = (xpart point t of base, 0); - b = (0, ypart point t of base); - draw a -- b withpen pencircle scaled 1/4 withcolor 3/4; - p = whatever[a, b]; p - point t of base = whatever * (a - b) rotated 90; - ) p -- - endfor cycle; - draw astroid withcolor 2/3 red; + path base; base = fullcircle scaled 300; + path astroid; astroid = for t=0 step 1/16 until 8: + hide(pair a, b, p; + a = (xpart point t of base, 0); b = (0, ypart point t of base); + p = whatever[a,b]; p - point t of base = whatever * (a-b) rotated 90; + ) p -- endfor cycle; + for t=0 step 1/16 until 8: + draw (xpart point t of base, 0) -- (0, ypart point t of base) withcolor 7/8; + endfor + draw astroid withcolor 2/3 red; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-astroid.pdf b/info/drawing-with-metapost/src/curves-astroid.pdf Binary files differindex 550b18858a..d9ec00252d 100644 --- a/info/drawing-with-metapost/src/curves-astroid.pdf +++ b/info/drawing-with-metapost/src/curves-astroid.pdf diff --git a/info/drawing-with-metapost/src/curves-brachisto.mp b/info/drawing-with-metapost/src/curves-brachisto.mp new file mode 100644 index 0000000000..eb41d1965d --- /dev/null +++ b/info/drawing-with-metapost/src/curves-brachisto.mp @@ -0,0 +1,44 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + path Y, L, C, P, S; + + % solve parameters for cycloid + vardef u(expr x) = x - sind(57.295779513 x) enddef; + vardef v(expr x) = 1 - cosd(57.295779513 x) enddef; + vardef f(expr t) = u(t) < v(t) enddef; + tolerance := epsilon; a = solve f(2,3); + s = 1/64 a; + Y = (origin for t = s step s until a+eps: + -- (u(t), -v(t)) % negative v(t) so curve is inverted + endfor) scaled 160; + z0 = point 0 of Y; + z1 = point infinity of Y; + + % define the four other paths + L = z0 -- z1; + C = quartercircle rotated 180 scaled 2x1 shifted (x1, y0); + P = z0{1,-2} ... (1/2[x1, x0], 1/4[y1, y0]){1,-1} ... z1 {1, 0}; + S = z0{1,-6} ... (1/2[x1, x0], 1/64[y1, y0]){1, -6/32} ... z1 {1, 0}; + + draw z0 -- (x0,y1) -- z1 withcolor 3/4; + drawoptions(withcolor 2/3 red); + draw L; dotlabel.urt("Line", point 1/4 of L); + drawoptions(withcolor 1/2 green); + draw C; dotlabel.urt("Circle", point 1 of C); + drawoptions(withcolor 1/4[red, green]); + draw P; dotlabel.urt("Parabola", point 1/2 of P); + drawoptions(withcolor 3/4[red, green]); + draw S; dotlabel.llft("Sixth degree", point 3/4 of S); + drawoptions(withcolor 1/2 blue); + draw Y; dotlabel.urt("Cycloid", point 50 of Y); + drawoptions(); + + dotlabel.urt("$A$", z0); + dotlabel.urt("$B$", z1); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/brachisto.pdf b/info/drawing-with-metapost/src/curves-brachisto.pdf Binary files differindex 9535832c97..cae7e3db5b 100644 --- a/info/drawing-with-metapost/src/brachisto.pdf +++ b/info/drawing-with-metapost/src/curves-brachisto.pdf diff --git a/info/drawing-with-metapost/src/curves-cardioid-construction.mp b/info/drawing-with-metapost/src/curves-cardioid-construction.mp index 4336fa7ab7..0dd5a9011a 100644 --- a/info/drawing-with-metapost/src/curves-cardioid-construction.mp +++ b/info/drawing-with-metapost/src/curves-cardioid-construction.mp @@ -5,48 +5,49 @@ \begin{mplibcode} beginfig(1); - numeric u; u = 144; - - path base; base = fullcircle rotated 180 scaled u; - - path cardioid; - cardioid = for t = 0 step 1/4 until length base: - point 0 of base reflectedabout(precontrol t of base, postcontrol t of base) .. - endfor cycle; - - numeric t; t = 5.4; - pair A, M, P, P', Q, Q', R; - A = point 0 of base; - Q = point t of base; - Q' = point t-4 of base; - P = A reflectedabout(precontrol t of base, postcontrol t of base); - P' = A reflectedabout(precontrol t-4 of base, postcontrol t-4 of base); - M = 1/2[P, P']; - R = whatever[P, Q] = whatever[P', Q']; - - %draw Q' -- R -- Q withcolor 3/4; - draw 3[postcontrol t of base, precontrol t of base] - -- 5[precontrol t of base, postcontrol t of base] withcolor 3/4; - %draw 5[postcontrol t-4 of base, precontrol t-4 of base] - % -- 3[precontrol t-4 of base, postcontrol t-4 of base] withcolor 3/4; - - draw fullcircle scaled 2 abs (Q-A) shifted Q withcolor 7/8; - - % - %draw P' -- Q' -- Q -- P -- cycle; - draw A -- Q -- P -- cycle; - - draw base withcolor 2/3 blue; - draw origin withpen pencircle scaled dotlabeldiam withcolor 2/3 blue; - draw cardioid withcolor 1/4[white, 1/2 red]; - - dotlabel.ulft("$A$", A); - %dotlabel.ulft("$M$", M); - dotlabel.top ("$P$", P); - %dotlabel.llft("$P'$", P'); - dotlabel.urt ("$Q$", Q); - %dotlabel.bot ("$Q'$", Q'); - %dotlabel.lrt ("$R$", R); +numeric u; u = 144; + +path base; base = fullcircle rotated 180 scaled u; +numeric s; s = 1/8; + +pair A; A = point 0 of base; +path cardioid; cardioid = for t = 0 step s until length base: + A reflectedabout(precontrol t of base, postcontrol t of base) .. +endfor cycle; + +numeric t; t = 5.4; +pair A, M, P, P', Q, Q', R; +A = point 0 of base; +Q = point t of base; +Q' = point t-4 of base; +P = A reflectedabout(precontrol t of base, postcontrol t of base); +P' = A reflectedabout(precontrol t-4 of base, postcontrol t-4 of base); +M = 1/2[P, P']; +R = whatever[P, Q] = whatever[P', Q']; + +%draw Q' -- R -- Q withcolor 3/4; +draw 3[postcontrol t of base, precontrol t of base] + -- 5[precontrol t of base, postcontrol t of base] withcolor 3/4; +%draw 5[postcontrol t-4 of base, precontrol t-4 of base] +% -- 3[precontrol t-4 of base, postcontrol t-4 of base] withcolor 3/4; + +draw fullcircle scaled 2 abs (Q-A) shifted Q withcolor 7/8; + +% +%draw P' -- Q' -- Q -- P -- cycle; +draw A -- Q -- P -- cycle; + +draw base withcolor 2/3 blue; +draw origin withpen pencircle scaled dotlabeldiam withcolor 2/3 blue; +draw cardioid withcolor 1/4[white, 1/2 red]; + +dotlabel.ulft("$A$", A); +%dotlabel.ulft("$M$", M); +dotlabel.top ("$P$", P); +%dotlabel.llft("$P'$", P'); +dotlabel.urt ("$Q$", Q); +%dotlabel.bot ("$Q'$", Q'); +%dotlabel.lrt ("$R$", R); endfig; \end{mplibcode} diff --git a/info/drawing-with-metapost/src/curves-cardioid-construction.pdf b/info/drawing-with-metapost/src/curves-cardioid-construction.pdf Binary files differindex cab8862bc7..88b94918bd 100644 --- a/info/drawing-with-metapost/src/curves-cardioid-construction.pdf +++ b/info/drawing-with-metapost/src/curves-cardioid-construction.pdf diff --git a/info/drawing-with-metapost/src/cycloids-extra-code.mp b/info/drawing-with-metapost/src/curves-cycloids-extra.mp index 15ea28144f..bef1884e3d 100644 --- a/info/drawing-with-metapost/src/cycloids-extra-code.mp +++ b/info/drawing-with-metapost/src/curves-cycloids-extra.mp @@ -1,3 +1,9 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); numeric R, r, pi; R = 1.8cm; % radius of the outer part r = 1.3cm; % radius of the inner part @@ -59,3 +65,6 @@ dotlabel.top(btex $(\pi r,R+r)$ etex, (pi*r,R+r)); label(btex $\vcenter{\halign{&$#$\hfil\cr x=r\theta-R\sin\theta\cr y=r-R\cos\theta\cr}}$ etex,(4.75r,r)); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/cycloids-extra.pdf b/info/drawing-with-metapost/src/curves-cycloids-extra.pdf Binary files differindex 80daf06271..76250155cb 100644 --- a/info/drawing-with-metapost/src/cycloids-extra.pdf +++ b/info/drawing-with-metapost/src/curves-cycloids-extra.pdf diff --git a/info/drawing-with-metapost/src/curves-cycloids.mp b/info/drawing-with-metapost/src/curves-cycloids.mp new file mode 100644 index 0000000000..21c2f6c535 --- /dev/null +++ b/info/drawing-with-metapost/src/curves-cycloids.mp @@ -0,0 +1,48 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); + numeric pi, r, theta; pi = 3.141592653589793; r = 42; theta = 81; + path cycloid; + for t=-80 step 5 until 440: + cycloid := if known cycloid: cycloid -- fi + (0, -r) rotated -t shifted (t/180*pi*r, r); + endfor; + path wheel; + z1 = (theta/180*pi*r, r); + wheel = reverse fullcircle scaled 2r rotated -(90 + theta) shifted z1; + z2 = point 0 of wheel; + path a[]; u = 1/16; % u = a little shortening + a1 = subpath -(theta/45-u,u) of wheel shifted -z1 scaled 5/8 shifted z1; + a2 = subpath (.3, 1.4) of wheel shifted -z1 scaled 1.08 shifted z1; + a3 = a2 rotatedabout(z1, 170); + path xx, yy; + xx = (xpart point 0 of cycloid, 0) -- (xpart point infinity of cycloid,0); + yy = (down -- 5 up) scaled 1/2 r; + + ahangle := 30; + drawarrow xx withcolor 1/2; label.rt (btex $x$ etex, point 1 of xx); + drawarrow yy withcolor 1/2; label.top(btex $y$ etex, point 1 of yy); + + draw cycloid withcolor .67 red; + draw wheel withcolor .67 blue; + drawarrow a1; drawarrow a2; drawarrow a3; + draw (0,y2) -- z2 -- (x2,0) dashed withdots scaled 1/4; + draw z2 -- z1 -- (x1,0); + draw z1 withpen pencircle scaled dotlabeldiam; + draw z2 withpen pencircle scaled dotlabeldiam; + + label(btex $\theta$ etex, z1 + 3/4r * dir (270 - 1/2 theta)); + label.bot(btex $\mathstrut 2\pi r$ etex, (2pi*r,0)); + label.bot(btex $\mathstrut r\theta$ etex, (x1,0)); + label.bot(btex $\mathstrut x$ etex, (x2,0)); + label.lft(btex $y$ etex, (0,y2)); + label.top(btex $r$ etex, 1/2[z1, z2]); + dotlabel.top(btex $(\pi r,2r)$ etex, (pi*r,2r)); + label.rt(btex $\vcenter{\halign{&$#$\hfil\cr + x=r(\theta-\sin\theta)\cr + y=r(1-\cos\theta)\cr}}$ etex, (pi*r,r)); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/cycloids.pdf b/info/drawing-with-metapost/src/curves-cycloids.pdf Binary files differindex 6334dd9ed2..16fa0f7628 100644 --- a/info/drawing-with-metapost/src/cycloids.pdf +++ b/info/drawing-with-metapost/src/curves-cycloids.pdf diff --git a/info/drawing-with-metapost/src/curves-ellipse-family.mp b/info/drawing-with-metapost/src/curves-ellipse-family.mp new file mode 100644 index 0000000000..d2f7487ed4 --- /dev/null +++ b/info/drawing-with-metapost/src/curves-ellipse-family.mp @@ -0,0 +1,34 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef dp(expr x) = substring(0, 5) of decimal x enddef; +beginfig(1); + + pair F[], o; + + -F1 = F2 = 55 dir 34; + + o = 1/2[F1, F2]; + + dotlabel.lrt("$F_1$", F1); + dotlabel.lrt("$F_2$", F2); + + 2d = abs(F1 - F2); + r = angle(F1 - F2); + + for i = 0 upto 8: + a := d * (1 + 1/4 i); + b := a +-+ d; + e := 1 +-+ b/a; + path ee; ee = fullcircle xscaled 2a yscaled 2b rotated r shifted o; + draw ee; + picture tl; tl = thelabel.top(TEX("$e=" & dp(e) & "$"), origin); + draw tl rotated angle direction 2 of ee shifted point 2 of ee; + endfor + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/curves-ellipse-family.pdf b/info/drawing-with-metapost/src/curves-ellipse-family.pdf Binary files differnew file mode 100644 index 0000000000..00b6d563bb --- /dev/null +++ b/info/drawing-with-metapost/src/curves-ellipse-family.pdf diff --git a/info/drawing-with-metapost/src/curves-ellipse-tangents.mp b/info/drawing-with-metapost/src/curves-ellipse-tangents.mp index a94e38463f..696c06b0a8 100644 --- a/info/drawing-with-metapost/src/curves-ellipse-tangents.mp +++ b/info/drawing-with-metapost/src/curves-ellipse-tangents.mp @@ -3,53 +3,47 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -secondarydef a through b = - begingroup; save d; numeric d; d = abs(a-b); (1+12/d)[b,a]--(1+12/d)[a,b] endgroup -enddef; beginfig(1); -path ellipse; ellipse = fullcircle scaled 300 yscaled 5/8 rotated 13; -z0 = 1/2[point 4 of ellipse, point 0 of ellipse]; -numeric a, b, e; -2a = abs (point 4 of ellipse - point 0 of ellipse); -2b = abs (point 6 of ellipse - point 2 of ellipse); +path ellipse; ellipse = fullcircle scaled 300 yscaled 5/8 rotated 8; +2a = abs (point 0 of ellipse - point 4 of ellipse); +2b = abs (point 2 of ellipse - point 6 of ellipse); e = 1 +-+ b/a; -z1 = e[z0, point 0 of ellipse]; -z2 = e[z0, point 4 of ellipse]; -z3 = 240 dir 25; -path pp, qq; -pp = fullcircle scaled 2 abs (z1 - z3) shifted z3; -qq = fullcircle scaled 4a shifted z2; -z4 = pp intersectionpoint qq; -z5 = reverse pp intersectionpoint qq; -numeric t, u; -(t, whatever) = ellipse intersectiontimes (z2 -- z4); -(u, whatever) = ellipse intersectiontimes (z2 -- z5); + +pair F[], A; +F1 = (1/2-e/2)[point 0 of ellipse, point 4 of ellipse]; +F2 = (1/2+e/2)[point 0 of ellipse, point 4 of ellipse]; +A = 240 dir 25; + +path pp; pp = fullcircle scaled 2 abs (F1-A) shifted A; +path qq; qq = fullcircle scaled 4a shifted F2; +pair P, Q, T, T'; +z1 = pp intersectiontimes qq; P = point x1 of pp; +z2 = reverse pp intersectiontimes qq; Q = point -x2 of pp; +z3 = ellipse intersectiontimes (F2 -- P); T = point x3 of ellipse; +z4 = ellipse intersectiontimes (F2 -- Q); T' = point x4 of ellipse; vardef f(expr x) = - angle (z3 - point x of ellipse) + 90 > angle direction x of ellipse + angle (A-point x of ellipse) + 90 > angle direction x of ellipse enddef; -drawarrow z3 -- point solve f(0, t) of ellipse withcolor 2/3 blue; +drawarrow A -- point solve f(0, x3) of ellipse withcolor 2/3 blue; -drawoptions(dashed evenly withcolor 7/8); -draw point 0 of ellipse through point 4 of ellipse; -draw point 2 of ellipse through point 6 of ellipse; -drawoptions(withcolor 3/4); -draw z4 -- z1 -- z5; -draw z2 -- z4 -- z3 -- z5 -- cycle; -draw point t of ellipse -- z1 -- point u of ellipse; -drawoptions(); -draw point t of ellipse -- z3 -- point u of ellipse withcolor 2/3 red; -dotlabel.llft("$F_1$", z1); dotlabel.llft("$F_2$", z2); -dotlabel.urt("$A$", z3); -dotlabel.ulft("$P$", z4); dotlabel.lrt ("$Q$", z5); -dotlabel.ulft("$T$", point t of ellipse); -dotlabel.lrt("$T'$", point u of ellipse); +draw subpath (x1 - 1/2, 17/2 - x2) of pp dashed withdots scaled 1/2; +draw subpath (y2 - 33/4, y1 + 1/4) of qq dashed withdots scaled 1/2; +draw T -- F1 -- P -- F2 -- Q -- F1 -- T' withcolor 1/2; +draw P -- A -- Q withcolor 1/2; +draw T -- A -- T' withcolor 2/3 red; draw ellipse; -picture P; P = currentpicture; currentpicture := nullpicture; -draw pp dashed withdots scaled 1/2; -draw qq dashed withdots scaled 1/2; -bboxmargin := 24; clip currentpicture to bbox P; -draw P; + +def dotlabelx(expr t, z, o) = + draw z withpen pencircle scaled dotlabeldiam; label(t, z + o); +enddef; +dotlabelx("$F_1$", F1, 10 dir 241); +dotlabelx("$F_2$", F2, 8 dir 260); +dotlabelx("$A$", A, 8 dir 30); +dotlabelx("$P$", P, 10 dir 94); dotlabelx("$Q$", Q, 10 dir 300); +dotlabelx("$T$", T, 10 dir 120); dotlabelx("$T'$", T', 10 dir -45); + +input show_name endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-ellipse-tangents.pdf b/info/drawing-with-metapost/src/curves-ellipse-tangents.pdf Binary files differindex 7cb7034ead..431da32bc3 100644 --- a/info/drawing-with-metapost/src/curves-ellipse-tangents.pdf +++ b/info/drawing-with-metapost/src/curves-ellipse-tangents.pdf diff --git a/info/drawing-with-metapost/src/curves-ellipse.mp b/info/drawing-with-metapost/src/curves-ellipse.mp index f08f6ee204..4c6c7a84c4 100644 --- a/info/drawing-with-metapost/src/curves-ellipse.mp +++ b/info/drawing-with-metapost/src/curves-ellipse.mp @@ -4,45 +4,57 @@ \mplibtextextlabel{enable} \begin{mplibcode} secondarydef a through b = - begingroup; save d; numeric d; d = abs(a-b); (1+12/d)[b,a] -- (1+12/d)[a,b] endgroup + begingroup; save d; d = abs(a-b); (1+12/d)[b,a] -- (1+12/d)[a,b] endgroup enddef; beginfig(1); - path ellipse; ellipse = fullcircle scaled 300 yscaled 5/8 rotated 13; - numeric a, b, e; - 2a = abs (point 4 of ellipse - point 0 of ellipse); - 2b = abs (point 6 of ellipse - point 2 of ellipse); - e = 1 +-+ b/a; - - z0 = 1/2[point 0 of ellipse, point 4 of ellipse]; - z1 = e[z0, point 0 of ellipse]; - z2 = e[z0, point 4 of ellipse]; - - drawoptions(withcolor 3/4); - draw point 0 of ellipse through point 4 of ellipse; - draw point 2 of ellipse through point 6 of ellipse; - drawoptions(withcolor 1/2); - label.top("$a$", 1/2[z0, point 0 of ellipse]); - label.bot("$ae$", 1/2[z0, z1]); - label.rt("$b$", 1/2[z0, point 2 of ellipse]); - drawoptions(); - - numeric t; t = 1.732; - draw z1 -- point t of ellipse -- z2; - drawoptions(withcolor 1/2); - draw (left--right) scaled 21 - rotated angle direction t of ellipse - shifted point t of ellipse; - draw (1/2 down--up) scaled 21 - rotated angle direction t of ellipse - shifted point t of ellipse; - drawoptions(); - - draw ellipse withcolor 3/4 red; - - dotlabel.urt("$T$", point t of ellipse); - dotlabel.lrt("$F_1$", z1); - dotlabel.lrt("$F_2$", z2); + path ellipse; + ellipse = fullcircle scaled 300 yscaled 5/8 rotated 13; + numeric a, b; + 2a = abs (point 4 of ellipse - point 0 of ellipse); + 2b = abs (point 6 of ellipse - point 2 of ellipse); + + numeric e; e = 1 +-+ b/a; % Pythagorean difference + + z0 = 1/2[point 0 of ellipse, point 4 of ellipse]; + z1 = e[z0, point 0 of ellipse]; + z2 = e[z0, point 4 of ellipse]; + + drawoptions(withcolor 3/4[blue, white]); + draw point 0 of ellipse through point 4 of ellipse; + draw point 2 of ellipse through point 6 of ellipse; + + vardef arrowlabel(expr s, a, b, offset) = + save p, t; interim ahangle := 28; + path p; p = (a--b) shifted (offset * unitvector(b-a) rotated 90); + picture t; t = thelabel(s, point 1/2 of p); + drawdblarrow p; unfill bbox t; draw t; + enddef; + + label.lrt("$a$", 1/2[z0, point 4 of ellipse]); + label.rt("$b$", 1/2[z0, point 6 of ellipse]); + arrowlabel("$ae$", z0, z1, -6); + drawoptions(); + + numeric t; t = 1.732; + drawoptions(withcolor 1/2); + draw (left--right) scaled 34 + rotated angle direction t of ellipse + shifted point t of ellipse; + draw (1/2 down--up) scaled 34 + rotated angle direction t of ellipse + shifted point t of ellipse; + drawoptions(); + + draw z1 -- point t of ellipse -- z2; + draw ellipse withcolor 3/4 red; + + labeloffset := 6; + dotlabel.urt("$T$", point t of ellipse); + dotlabel.top("$F_1$", z1); + dotlabel.ulft("$F_2$", z2); + + input show_name endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-ellipse.pdf b/info/drawing-with-metapost/src/curves-ellipse.pdf Binary files differindex 0da741f270..64fb3be1fe 100644 --- a/info/drawing-with-metapost/src/curves-ellipse.pdf +++ b/info/drawing-with-metapost/src/curves-ellipse.pdf diff --git a/info/drawing-with-metapost/src/curves-limacon-simple.mp b/info/drawing-with-metapost/src/curves-limacon-simple.mp index 9647c805a4..5707b65535 100644 --- a/info/drawing-with-metapost/src/curves-limacon-simple.mp +++ b/info/drawing-with-metapost/src/curves-limacon-simple.mp @@ -5,34 +5,28 @@ \begin{mplibcode} beginfig(1); - numeric a; 2a = 144; + numeric a; 2a = 144; - path base; base = fullcircle rotated 180 scaled 2a shifted (2a, 0); - path c[]; numeric n; n = -1; - numeric s; s = 1/4; - pair A; A = 2[center base, point 0 of base]; - for t = 0 step s until length base: - c[incr n] = fullcircle - scaled 2 abs (point t of base - A) - shifted point t of base; - draw c[n] withpen pencircle scaled 1/4 withcolor 3/4; - endfor + path base; base = fullcircle rotated 180 scaled 2a shifted (2a, 0); + numeric s; s = 1/4; + pair A; A = 2[center base, point 0 of base]; + path limacon; limacon = for t = 0 step s until length base: + A reflectedabout(precontrol t of base, postcontrol t of base) .. + endfor cycle; - path limacon; - limacon = for t = 0 step s until length base: - A reflectedabout(precontrol t of base, postcontrol t of base) .. - endfor cycle; + path c[]; numeric n; n = -1; + for t = 0 step s until length base: + c[incr n] = fullcircle scaled 2 abs (point t of base - A) shifted point t of base; + draw c[n] withpen pencircle scaled 1/4 withcolor 3/4; + endfor - % path polar; - % polar = for t=0 upto 359: 2a * (1 + 2 cosd(t)) * dir t .. endfor cycle; - % draw polar withpen pencircle scaled 5/4 withcolor 3/4[green, white]; + draw base withcolor 2/3 blue; + draw center base withpen pencircle scaled 2 withcolor 2/3 blue; + draw limacon withcolor 2/3 red; - draw base withcolor 2/3 blue; draw center base withpen pencircle scaled 2 withcolor 2/3 blue; - draw limacon withcolor 2/3 red; - - dotlabel.lft("$A$", A); - dotlabel.urt("$Q$", point 5.4 of base); - dotlabel.ulft("$P$", A reflectedabout(precontrol 5.4 of base, postcontrol 5.4 of base)); + dotlabel.lft("$A$", A); + dotlabel.urt("$Q$", point 5.4 of base); + dotlabel.ulft("$P$", A reflectedabout(precontrol 5.4 of base, postcontrol 5.4 of base)); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-limacon-simple.pdf b/info/drawing-with-metapost/src/curves-limacon-simple.pdf Binary files differindex 8ceb70b520..62bb6589f5 100644 --- a/info/drawing-with-metapost/src/curves-limacon-simple.pdf +++ b/info/drawing-with-metapost/src/curves-limacon-simple.pdf diff --git a/info/drawing-with-metapost/src/curves-parabola-directrix.mp b/info/drawing-with-metapost/src/curves-parabola-directrix.mp index 52f3f8c3cc..8fe141c4a4 100644 --- a/info/drawing-with-metapost/src/curves-parabola-directrix.mp +++ b/info/drawing-with-metapost/src/curves-parabola-directrix.mp @@ -12,64 +12,63 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} - + % A--B = directrix, S = focus vardef parabola(expr A, B, S) = - save m, q, n, parabola; - pair n; - n = whatever[A, B]; - n - S = whatever * (A-B) rotated 90; - path parabola; - for t=0 step 1/64 until 1: - pair m, q; - m = 1/2[S, t[A, B]]; - q = whatever[S, n]; q - m = whatever * (S - m) rotated 90; - parabola := if known parabola: parabola -- fi q reflectedabout(S, m); - endfor - parabola + save m, q, n, parabola; + pair n; % the point on A--B nearest to S + n = whatever[A, B]; + n - S = whatever * (A-B) rotated 90; + path parabola; + for t=0 step 1/64 until 1: + pair m, q; + m = 1/2[S, t[A, B]]; + q = whatever[S, n]; q - m = whatever * (S - m) rotated 90; + parabola := if known parabola: parabola -- fi + q reflectedabout(S, m); + endfor + parabola enddef; input colorbrewer-rgb beginfig(1); - numeric i; i = 16; - pair a, b, s; a = 160 up rotated 5; b = 160 down rotated 5; s = 60 * right; - draw a--b; + numeric i; i = 16; + pair a, b, s; a = 160 up rotated 5; b = 160 down rotated 5; s = 60 * right; + draw a--b; + + path ff; ff = (-1, 1){1, -2} .. (-1/2, 1/4){1, -1} .. + (0, 0){right} .. (1/2, 1/4){1, 1} .. (1, 1){1, 2}; + + path p; p = parabola(a, b, s); + pair tab; tab = whatever[a, b]; point i of p - tab = whatever * (a-b) rotated 90; + pair q; q = point i of p reflectedabout(s, tab); + pair n; n = whatever[a,b] = whatever[q, s]; + pair o; o = 1/2[n, s]; - path ff; ff = (-1, 1){1, -2} .. (-1/2, 1/4){1, -1} .. (0, 0){right} .. (1/2, 1/4){1, 1} .. (1, 1){1, 2}; + % draw ff scaled 4 abs(s-o) rotated angle (b-a) shifted o; - path p; p = parabola(a, b, s); - pair tab; tab = whatever[a, b]; point i of p - tab = whatever * (a-b) rotated 90; - pair q; q = point i of p reflectedabout(s, tab); - pair n; n = whatever[a,b] = whatever[q, s]; - pair o; o = 1/2[n, s]; + interim ahangle := 24; + drawarrow (b--a) shifted (o-n) withcolor 3/4; + drawarrow (1/2[a, n] --b) rotatedabout(n, 90) withcolor 3/4; - % draw ff scaled 4 abs(s-o) - % rotated angle (b-a) - % shifted o - % withpen pencircle scaled 2 withcolor 7/8[red, white]; - - interim ahangle := 24; - drawarrow (b--a) shifted (o-n) withcolor 3/4; - drawarrow (1/2[a, n] --b) rotatedabout(n, 90) withcolor 3/4; + draw tab -- point i of p -- q -- tab -- s withcolor 3/4; - draw tab -- point i of p -- q -- tab -- s withcolor 3/4; - - drawarrow s -- point i of p - -- s reflectedabout(precontrol i of p rotatedabout(point i of p, 90), - postcontrol i of p rotatedabout(point i of p, 90)) - withcolor Blues 8 4; + drawarrow s -- point i of p + -- s reflectedabout(precontrol i of p rotatedabout(point i of p, 90), + postcontrol i of p rotatedabout(point i of p, 90)) + withcolor Blues 8 4; - draw p withcolor Blues 8 6; - dotlabel.lrt("$S$", s); - dotlabel.urt("$A$", a); - dotlabel.lrt("$B$", b); - dotlabel.ulft("\kw{point} $i$ \kw{of} $p$", point i of p); - interim dotlabeldiam := 2; - dotlabel.bot("$\scriptstyle q$", q); - dotlabel.llft("$\scriptstyle n$", n); - dotlabel.llft("$\scriptstyle o$", o); - dotlabel.lft("$\scriptstyle m\:$", 1/2[tab, s]); - dotlabel.lft("$\scriptstyle t[A, B]$", tab); + draw p withcolor Blues 8 6; + dotlabel.lrt("$S$", s); + dotlabel.urt("$A$", a); + dotlabel.lrt("$B$", b); + dotlabel.ulft("\kw{point} $i$ \kw{of} $p$", point i of p); + interim dotlabeldiam := 2; + dotlabel.bot("$\scriptstyle q$", q); + dotlabel.llft("$\scriptstyle n$", n); + dotlabel.llft("$\scriptstyle o$", o); + dotlabel.lft("$\scriptstyle m\:$", 1/2[tab, s]); + dotlabel.lft("$\scriptstyle t[A, B]$", tab); endfig; \end{mplibcode}\llap{\tiny\texttt{\jobname}} diff --git a/info/drawing-with-metapost/src/curves-parabola-directrix.pdf b/info/drawing-with-metapost/src/curves-parabola-directrix.pdf Binary files differindex ab70182803..6c0c010dff 100644 --- a/info/drawing-with-metapost/src/curves-parabola-directrix.pdf +++ b/info/drawing-with-metapost/src/curves-parabola-directrix.pdf diff --git a/info/drawing-with-metapost/src/curves-parabola.mp b/info/drawing-with-metapost/src/curves-parabola.mp index 98c166560b..8c836dfab3 100644 --- a/info/drawing-with-metapost/src/curves-parabola.mp +++ b/info/drawing-with-metapost/src/curves-parabola.mp @@ -4,38 +4,25 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - pair O, S; O = origin; S = 66 right; - path parabola, last; - for q = -144 step 8 until 144: - pair Q; Q = (0, q); - path ray; - ray = (origin -- unitvector(S - Q)) scaled 300 - rotated if q < 0: - fi 90 shifted Q; - draw S -- ray withcolor 7/8; - if known last: - pair t; - t = whatever[point 0 of ray, point 1 of ray] - = whatever[point 0 of last, point 1 of last]; - parabola := if known parabola: parabola .. fi t; - fi - last := ray; - endfor - - draw parabola withcolor 3/4[red, white]; - for t=0 upto length parabola: - draw point t of parabola withpen pencircle scaled 3/2 withcolor red; - endfor - draw (up--down) scaled 300; - - dotlabel.lft("$A$", O); - dotlabel.rt("$S$", S); - - % vardef signum(expr x) = if x=0: 1 else: abs(x) / x fi enddef; - % path cart; - % cart = subpath (1, infinity) of (origin for x=-304 step 8 until 304: - % .. (x, 16 sqrt abs(x)) scaled signum(x) endfor); - - % drawarrow cart withcolor 1/3 green; + pair A, S; A = origin; S = 66 right; + path parabola, last; + for q = -144 step 8 until 144: + pair Q; Q = q * up; path ray; + ray = Q -- Q + 300 unitvector(S - Q) rotated if q < 0: - fi 90; + draw S -- ray withcolor 7/8; + if known last: + pair t; t = whatever[point 0 of ray, point 1 of ray] + = whatever[point 0 of last, point 1 of last]; + parabola := if known parabola: parabola .. fi t; + fi + last := ray; + endfor + draw parabola withcolor 3/4[red, white]; + for t=0 upto length parabola: + draw point t of parabola withpen pencircle scaled 3/2 withcolor red; + endfor + draw (up--down) scaled 300; + dotlabel.lft("$A$", A); dotlabel.rt("$S$", S); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-parabola.pdf b/info/drawing-with-metapost/src/curves-parabola.pdf Binary files differindex 2889b2a82b..445f686496 100644 --- a/info/drawing-with-metapost/src/curves-parabola.pdf +++ b/info/drawing-with-metapost/src/curves-parabola.pdf diff --git a/info/drawing-with-metapost/src/curves-spiral-archimedes.mp b/info/drawing-with-metapost/src/curves-spiral-archimedes.mp index ba9b37122c..505ea129d4 100644 --- a/info/drawing-with-metapost/src/curves-spiral-archimedes.mp +++ b/info/drawing-with-metapost/src/curves-spiral-archimedes.mp @@ -5,12 +5,12 @@ \mplibnumbersystem{decimal} \begin{mplibcode} beginfig(1); - path S; S = origin for t=1 upto 360: .. 1/12 t * dir 8t endfor; - drawarrow S; - input rope - draw rope S shifted 64 right; - z0 = urcorner currentpicture - llcorner currentpicture; - currentpicture := currentpicture scaled (300 / x0); + path S; S = origin for t=1 upto 360: .. 1/12 t * dir 8t endfor; + drawarrow S; + input rope + draw rope S shifted 64 right; + z0 = urcorner currentpicture - llcorner currentpicture; + currentpicture := currentpicture scaled (300 / x0); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-spiral-archimedes.pdf b/info/drawing-with-metapost/src/curves-spiral-archimedes.pdf Binary files differindex a74df7785a..fd8534c7e2 100644 --- a/info/drawing-with-metapost/src/curves-spiral-archimedes.pdf +++ b/info/drawing-with-metapost/src/curves-spiral-archimedes.pdf diff --git a/info/drawing-with-metapost/src/curves-spiral-equiangular.mp b/info/drawing-with-metapost/src/curves-spiral-equiangular.mp index 81e45147c7..b343717d51 100644 --- a/info/drawing-with-metapost/src/curves-spiral-equiangular.mp +++ b/info/drawing-with-metapost/src/curves-spiral-equiangular.mp @@ -4,10 +4,10 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - numeric a; a = 2.6; path S; - S = right for t=1 upto 360: .. a ** (t/64) * dir 4t endfor; - drawarrow S; -% input ruler-cm + numeric a; a = 2.6; path S; + S = right for t=1 upto 360: .. a ** (t/64) * dir 4t endfor; + drawarrow S; + % input ruler-cm endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.mp b/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.mp index 5347da9484..4be5a0a55c 100644 --- a/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.mp +++ b/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.mp @@ -4,28 +4,32 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - drawoptions(withpen pencircle scaled 1/4 withcolor 1/4); + drawoptions(withpen pencircle scaled 1/4 withcolor 1/4); path s[]; s0 = unitsquare; fill s0 withcolor 1/2[2/3 blue, white]; draw s0; numeric a, b, t, n; a = 1; b = 1; n = 11; for i = 1 upto n: - t := b; b := b + a; a := t; - s[i] = unitsquare scaled a; - s[i] := s[i] shifted (point i of s[i-1] - point i-1 of s[i]); - fill s[i] withcolor (1/2 + i/32)[2/3 blue, white]; - draw s[i]; + t := b; b := b + a; a := t; % Fibonacci sequence + s[i] = unitsquare scaled a; + s[i] := s[i] shifted (point i of s[i-1] - point i-1 of s[i]); + fill s[i] withcolor (1/2 + i/32)[2/3 blue, white]; + draw s[i]; endfor + % cross hairs for i = n-1 upto n: - draw point i-2 of s[i-2] -- point i of s[i]; + draw point i-2 of s[i-2] -- point i of s[i]; endfor - drawoptions(); - drawarrow origin for i=0 upto n: .. point i of s[i] endfor withcolor 2/3 red; - for i = 5 upto n: - label(TEX(decimal arclength subpath (0, 1) of s[i]) - scaled 0.8 rotated angle point n of s[n], center s[i]); - endfor - currentpicture := currentpicture rotated - angle point n of s[n]; - + drawoptions(); + % Draw the spiral as a red arrow + drawarrow origin for i=0 upto n: .. point i of s[i] endfor + withcolor 2/3 red; + % show the Fibonacci sizes for the larger boxes + for i = 5 upto n: + label(TEX(decimal arclength subpath (0, 1) of s[i]) + scaled 0.8 rotated angle point n of s[n], center s[i]); + endfor + % Rotate the whole picture to show off the spiral + currentpicture := currentpicture rotated - angle point n of s[n]; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.pdf b/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.pdf Binary files differindex 0863722fc3..a2d05f2a9f 100644 --- a/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.pdf +++ b/info/drawing-with-metapost/src/curves-spiral-gnomon-sq.pdf diff --git a/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.mp b/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.mp index 5bf37d00b7..014d5c82fc 100644 --- a/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.mp +++ b/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.mp @@ -4,36 +4,35 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - path t[], base; pair apex; - base = (left--right) scaled 100; - apex = whatever * dir +72 shifted point 0 of base - = whatever * dir -72 shifted point 1 of base; - t0 = (base -- apex -- cycle); - transform S; - r = arclength subpath (0, 1) of t0 / arclength subpath (2, 3) of t0; - point 0 of t0 transformed S = (r*r)[point 0 of t0, point 2 of t0]; - point 1 of t0 transformed S = point 0 of t0; - point 2 of t0 transformed S = point 1 of t0; - - n = 16; - for i=1 upto n: - t[i] = t[i-1] transformed S; - draw subpath (2,3) of t[i] withpen pencircle scaled 1/4; - endfor - draw point 0 of t0 -- point 3/2 of t0 withpen pencircle scaled 1/8 withcolor blue; - draw point 0 of t1 -- point 3/2 of t1 withpen pencircle scaled 1/8 withcolor blue; - draw t0; - drawarrow point 2 of t[n] for i=n-1 downto 0: .. point 2 of t[i] endfor withcolor 2/3 red; - - z0 = whatever[point 0 of t0, point 3/2 of t0] - = whatever[point 0 of t1, point 3/2 of t1]; - numeric a; a = angle (point 2 of t0 - z0); - drawoptions(withcolor 1/2 green); - label.lft(TEX("$a$") rotated a, point 5/2 of t0); - label.bot(TEX("$b$") rotated a, point 1/2 of t0); - label.rt(TEX("$x$") rotated a, point 1/2 of t1); - drawoptions(); - currentpicture := currentpicture rotated -a; + path t[], base; pair apex; + base = (left--right) scaled 100; + apex = whatever * dir +72 shifted point 0 of base + = whatever * dir -72 shifted point 1 of base; + t0 = (base -- apex -- cycle); + transform S; + r = arclength subpath (0, 1) of t0 / arclength subpath (2, 3) of t0; + point 0 of t0 transformed S = (r*r)[point 0 of t0, point 2 of t0]; + point 1 of t0 transformed S = point 0 of t0; + point 2 of t0 transformed S = point 1 of t0; + n = 16; + for i=1 upto n: + t[i] = t[i-1] transformed S; + draw subpath (2,3) of t[i] withpen pencircle scaled 1/4; + endfor + drawoptions(withpen pencircle scaled 1/8 withcolor blue); + draw point 0 of t0 -- point 3/2 of t0; + draw point 0 of t1 -- point 3/2 of t1; + drawoptions(); + draw t0; + drawarrow point 2 of t[n] for i=n-1 downto 0: + .. point 2 of t[i] endfor withcolor 2/3 red; + z0 = whatever[point 0 of t0, point 3/2 of t0] + = whatever[point 0 of t1, point 3/2 of t1]; + numeric a; a = angle (point 2 of t0 - z0); + label.lft(TEX("$a$") rotated a, point 5/2 of t0); + label.bot(TEX("$b$") rotated a, point 1/2 of t0); + label.rt(TEX("$x$") rotated a, point 1/2 of t1); + currentpicture := currentpicture rotated -a; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.pdf b/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.pdf Binary files differindex 24cf426568..afa7e4705e 100644 --- a/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.pdf +++ b/info/drawing-with-metapost/src/curves-spiral-gnomon-trig.pdf diff --git a/info/drawing-with-metapost/src/cycloids-code.mp b/info/drawing-with-metapost/src/cycloids-code.mp deleted file mode 100644 index f81c74ae6e..0000000000 --- a/info/drawing-with-metapost/src/cycloids-code.mp +++ /dev/null @@ -1,63 +0,0 @@ -numeric r, pi; -r = 1.25cm; % radius of the wheel -pi = 3.14159265; % constant -% -% define the cycloid -path c; -c = (0,-r) rotated 100 shifted (r*-100/180*pi,r) - for t=-99 upto 460: - -- (0,-r) rotated -t shifted (r*t/180*pi,r) - endfor; -% and the axes -drawoptions(withcolor .5 white); -path xx, yy; -yy = (down -- 5 up) scaled 1/2 r; -xx = (xpart point 0 of c, 0) -- (xpart point infinity of c,0); -draw fullcircle scaled 1/4r; drawarrow xx; drawarrow yy; -drawoptions(); -label.rt (btex $x$ etex, point 1 of xx); -label.top(btex $y$ etex, point 1 of yy); -% draw the cycloid on top of the axes -draw c withcolor .67 red; - -% define a couple of related points: -% z1 center of the blue wheel -% z2 intersection of rim and cycloid -t = 84; % if you change t then the wheel will "roll" along... -z1 = (r*t/180*pi,r); -z2 = (0,-r) rotated -t shifted z1; - -% draw the auxiliary lines -draw (0,y2) -- z2 -- (x2,0) dashed withdots scaled .6; -draw z2 -- z1 -- (x1,0); - -% draw the rolling circle -draw fullcircle scaled 2r shifted z1 withcolor .67 blue; -% mark the centre and intersection with cycloid -fill fullcircle scaled dotlabeldiam shifted z1; -fill fullcircle scaled dotlabeldiam shifted z2; - -% some arc arrows and labels -path a[]; -z3 = (x1,5/12y1); -a1 = z3 {left} .. {left rotatedabout(z1,-t)} z3 rotatedabout(z1,-t); -drawarrow subpath (.05,.95) of a1; -label.llft(btex $\theta$ etex, point .5 of a1); - -a2 = subpath (0,1) of reverse quartercircle scaled 2.2r shifted z1; -drawarrow a2 rotatedabout(z1,-100); -drawarrow a2 rotatedabout(z1,80); - -% finally all the other labels -label.top(btex $r$ etex, .5[z1,z2]); -label.lft(btex $y$ etex, (0,y2)); -% give all the x-axis labels a common baseline with mathstrut -label.bot(btex $\mathstrut x$ etex, (x2,0)); -label.bot(btex $\mathstrut r\theta$ etex, (x1,0)); -label.bot(btex $\mathstrut 2\pi r$ etex, (r*2pi,0)); -% notice how nicely the coordinates work... -dotlabel.top(btex $(\pi r,2r)$ etex, (pi*r,2r)); -% and a little alignment to finish -label(btex $\vcenter{\halign{&$#$\hfil\cr -x=r(\theta-\sin\theta)\cr -y=r(1-\cos\theta)\cr}}$ etex,(4.2r,r)); diff --git a/info/drawing-with-metapost/src/cycloids-extra.mp b/info/drawing-with-metapost/src/cycloids-extra.mp deleted file mode 100644 index af41bcdf46..0000000000 --- a/info/drawing-with-metapost/src/cycloids-extra.mp +++ /dev/null @@ -1,10 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); -input cycloids-extra-code -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/cycloids.mp b/info/drawing-with-metapost/src/cycloids.mp deleted file mode 100644 index 86788b5c46..0000000000 --- a/info/drawing-with-metapost/src/cycloids.mp +++ /dev/null @@ -1,10 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - input cycloids-code -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/deco-borders.mp b/info/drawing-with-metapost/src/deco-borders.mp new file mode 100644 index 0000000000..3f00de1a9d --- /dev/null +++ b/info/drawing-with-metapost/src/deco-borders.mp @@ -0,0 +1,58 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef plain_dots(expr boxpath, gap, radius, shade) = + save wd, ht, u, v; numeric wd, ht, u, v; + wd = arclength subpath (0,1) of boxpath; + ht = arclength subpath (1,2) of boxpath; + u = wd / round(wd/gap); + v = ht / round(ht/gap); + save B, R; picture B, R; + B = image( + draw (down -- right) xscaled 1/2u yscaled 1/2v + withpen pencircle scaled 1/4 radius + withcolor blue; + for x=1 upto round(wd/u): + pair p; p = point arctime x * u of boxpath of boxpath; + draw p + withpen pencircle scaled radius + withcolor shade; + draw p shifted -1/2(u, v) + withpen pencircle scaled radius + withcolor shade; + draw (left--down--right) xscaled 1/2u yscaled 1/2v shifted p + withpen pencircle scaled 1/4 radius + withcolor blue; + endfor); + R = image(for y=0 upto round(ht/v) - 1: + pair p; p = point arctime y * v of reverse boxpath of reverse boxpath; + draw p + withpen pencircle scaled radius + withcolor shade; + draw p + shifted 1/2(-u, v) + withpen pencircle scaled radius + withcolor shade; + draw (up -- left -- down) xscaled 1/2u yscaled 1/2v shifted p + withpen pencircle scaled 1/4 radius + withcolor blue; + endfor + draw p shifted 1/2(0, v) -- p shifted (-1/2u, v) + withpen pencircle scaled 1/4 radius + withcolor blue; + ); + image( + draw B; draw B rotatedabout(center boxpath, 180); + draw R; draw R rotatedabout(center boxpath, 180); + ) +enddef; + +beginfig(1); + path bb; bb = unitsquare xscaled 233 yscaled 144; + draw plain_dots(bb, 8, 3, red); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/deco-borders.pdf b/info/drawing-with-metapost/src/deco-borders.pdf Binary files differnew file mode 100644 index 0000000000..b75e2d8daf --- /dev/null +++ b/info/drawing-with-metapost/src/deco-borders.pdf diff --git a/info/drawing-with-metapost/src/desargues.mp b/info/drawing-with-metapost/src/desargues.mp deleted file mode 100644 index 27203d4961..0000000000 --- a/info/drawing-with-metapost/src/desargues.mp +++ /dev/null @@ -1,56 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); -beginfig(1); - z.P = 200 up rotated 21; z.A = 100 left rotated -21; - z.B = origin; z.C = 90 right rotated 42; - - z.A' = 3/8[z.P, z.A]; - z.B' = 1/2[z.P, z.B]; - z.C' = 5/8[z.P, z.C]; - - z.R = whatever [z.A, z.B] = whatever [z.A', z.B']; - z.S = whatever [z.B, z.C] = whatever [z.B', z.C']; - z.T = whatever [z.C, z.A] = whatever [z.C', z.A']; - - path t[]; - t1 = z.A--z.B--z.C--cycle; - t2 = z.A'--z.B'--z.C'--cycle; - - fill t1 withcolor 7/8[red, white]; - fill t2 withcolor 7/8[blue, white]; - draw t1 withcolor 1/2 white; - draw t2 withcolor 1/2 white; - - drawoptions(dashed withdots scaled 1/2); - draw z.P--z.A; - draw z.P--z.B; - draw z.P--z.C; - - drawoptions(dashed evenly scaled 1/2); - draw z.B--z.R--z.B'; - draw z.C--z.S--z.C'; - undraw subpath (1/4, 3/4) of (z.C'--z.T) withpen - pencircle scaled 5; - draw z.C--z.T--z.C'; - drawoptions(withcolor 2/3 red); - draw 9/8[z.S,z.R] -- 9/8[z.R,z.S]; - picture pp; pp = thelabel("perspectrix", origin); - draw pp shifted 7 down rotated angle (z.S-z.R) - shifted 1/2[z.R, z.T]; - dotlabel.urt("perspector", z.P); - - drawoptions(); - dotlabel.lft (btex $A$ etex, z.A); - dotlabel.llft(btex $B$ etex, z.B); - dotlabel.lrt (btex $C$ etex, z.C); - dotlabel.lft (btex $A'$ etex, z.A'); - dotlabel.llft(btex $B'$ etex, z.B'); - dotlabel.bot (btex $C'$ etex, z.C'); - label.rt(btex Desargues' Theorem etex, (x.C', 1/2(y.P+y.C'))); -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/dice.mp b/info/drawing-with-metapost/src/dice.mp deleted file mode 100644 index a68153004e..0000000000 --- a/info/drawing-with-metapost/src/dice.mp +++ /dev/null @@ -1,41 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -beginfig(1); -vardef dice(expr pip_count, pip_color) = - save d,r,p, ul, ur, lr, ll; - r=1/8; path d; picture p; - %d = (for i=0 upto 3: subpath (r+i,1+i-r) of unitsquare .. endfor cycle) scaled 30; - d = for i=0 upto 3: quartercircle scaled 3 shifted (15,15) rotated 90i -- endfor cycle; - p = image(draw fullcircle scaled 6; fill fullcircle scaled 6 withcolor pip_color); - pair ul, ur, ll, lr; - ul = 1/5[ulcorner d, lrcorner d]; - lr = 4/5[ulcorner d, lrcorner d]; - ur = 1/5[urcorner d, llcorner d]; - ll = 4/5[urcorner d, llcorner d]; - image(fill d withcolor background; draw d; - if odd(pip_count): - draw p shifted center d; - fi; - if pip_count > 1: - draw p shifted ul; - draw p shifted lr; - fi; - if pip_count > 3: - draw p shifted ur; - draw p shifted ll; - fi; - if pip_count = 6: - draw p shifted 1/2[ul,ur]; - draw p shifted 1/2[ll,lr]; - fi) -enddef; - -beginfig(1); -for i=0 upto 4: - draw dice(1+floor uniformdeviate 6, red) rotated (2 normaldeviate) shifted (36i,0); -endfor -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/dice.pdf b/info/drawing-with-metapost/src/dice.pdf Binary files differdeleted file mode 100644 index e5fc396365..0000000000 --- a/info/drawing-with-metapost/src/dice.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/double-dragon.mp b/info/drawing-with-metapost/src/double-dragon.mp deleted file mode 100644 index a701cbe8a0..0000000000 --- a/info/drawing-with-metapost/src/double-dragon.mp +++ /dev/null @@ -1,57 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\mplibnumbersystem{double} -\begin{mplibcode} -beginfig(1); - -vardef zinverse(expr z) = 1/abs z * dir - angle z enddef; - -vardef fizz(expr X) = - pair m, n; - m = right; - n = origin; - numeric a, x; - x = X; - forever: - exitif x = 0; - m := m zscaled zinverse((-1, 1)); - a := x mod 2; - n := n + a * m; - x := x div 2; - endfor - n -enddef; -input colorbrewer-rgb -color shade[]; -shade0 = Reds 5 4; shade1 = Oranges 5 4; -shade2 = Greens 5 4; shade3 = Blues 5 4; - -beginfig(1); - numeric s, t; s = 256; t = 4; - for n=0 upto (s/t*s/t-1): - numeric h, v; - h = floor 1/8 (n mod 32); - v = n mod 4; - fill fullcircle scaled t shifted (fizz(n) scaled s) - withcolor (1/2 + 1/8 v)[white, shade[h]]; - endfor; - path xx, yy; - xx = (left--right) scaled (s+8); - yy = xx rotated 90; - for i=-1 upto 1: - draw xx shifted (0, s*i) withpen pencircle scaled 1/8; - draw yy shifted (s*i, 0) withpen pencircle scaled 1/8; - endfor - dotlabel.lrt(btex $-1-i$ etex, (-1, -1) scaled s); - dotlabel.lrt(btex $-1$ etex, (-1, 0) scaled s); - dotlabel.lrt(btex $-1+i$ etex, (-1, 1) scaled s); - dotlabel.lrt(btex $-i$ etex, (0, -1) scaled s); - dotlabel.lrt(btex $+i$ etex, (0, 1) scaled s); - dotlabel.lrt(btex $+1-i$ etex, (1, -1) scaled s); - dotlabel.lrt(btex $+1$ etex, (1, 0) scaled s); - dotlabel.lrt(btex $+1+i$ etex, (1, 1) scaled s); -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/double-dragon.pdf b/info/drawing-with-metapost/src/double-dragon.pdf Binary files differdeleted file mode 100644 index ccede3d7c5..0000000000 --- a/info/drawing-with-metapost/src/double-dragon.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/draw-picture.mp b/info/drawing-with-metapost/src/draw-picture.mp deleted file mode 100644 index 16c40d8a49..0000000000 --- a/info/drawing-with-metapost/src/draw-picture.mp +++ /dev/null @@ -1,73 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - numeric s; s = 21; - path alpha; - alpha = ((-2s, s) {right} - .. halfcircle rotated -90 scaled 2s shifted (2s, 0) - .. {left} (-2s, -s)) shifted (s*left); - - vardef overdraw(expr a, b, r, P, shade) = - linecap := butt; - undraw subpath (a+r, b-r) of P withpen pencircle scaled 2; - draw subpath (a, b) of P withcolor shade; - enddef; - - picture cb; cb = image( - draw alpha withcolor 2/3 red; - undraw alpha rotated 180 withpen pencircle scaled 2; - draw alpha rotated 180 withcolor 2/3 blue; - overdraw(0.21, 0.36, 0.02, alpha, 2/3 red); - overdraw(0.67, 0.86, 0.02, alpha, 2/3 red); - overdraw(3.4, 4.3, 0.1, alpha, 2/3 red); - overdraw(5.4, 5.6, 0.02, alpha, 2/3 red); - overdraw(5.4, 5.6, 0.02, alpha rotated 180, 2/3 blue); - ); - - picture P[]; - - P1 = image(draw cb; label.rt("\texttt{draw cb;}", point 3/2 of bbox currentpicture)); - P2 = image(draw cb withpen pencircle scaled 4; label.rt("\texttt{draw cb withpen pencircle scaled 4;}", point 3/2 of bbox currentpicture)); - P3 = image(draw cb withcolor 1/2; label.rt("\texttt{draw cb withcolor 1/2;}", point 3/2 of bbox currentpicture)); - P4 = image(draw cb withpen pencircle scaled 4 withcolor 1/2; label.rt("\texttt{draw cb withpen pencircle scaled 4 withcolor 1/2;}", point 3/2 of bbox currentpicture)); - P5 = image( - color bagel; bagel = 1/256(187, 146, 79); - for i=4 step -1/4 until 1/2: - draw cb withpen pencircle scaled i - withcolor (i/4)[white, bagel]; - endfor - label.rt(btex \vbox{\halign{\texttt{#}\cr - for i=4 step -1/4 until 1/2:\cr - \quad draw cb withpen pencircle scaled i \cr - \qquad withcolor sqrt(i/4)[white, bagel];\cr - endfor\cr}} etex, point 3/2 of bbox currentpicture); - ); - - P6 = image( - for e within cb: - draw pathpart e withpen penpart e scaled 4 - withcolor 7/8[colorpart e, background]; - endfor - label.rt(btex \vbox{\halign{\texttt{#}\cr - for e within cb:\cr - \quad draw pathpart e withpen penpart e scaled 4\cr - \qquad withcolor 7/8[colorpart e, background];\cr - endfor\cr}} etex, point 3/2 of bbox currentpicture); - ); - - for i=1 upto 6: - if known P[i]: - pair p; p = 60i * down; - label.rt(P[i], p); - fill superellipse(right, up, left, down, 0.8) scaled 6 shifted p - withcolor 2/3; - label("\textsf{" & decimal i & "}", p) withcolor white; - fi; - endfor - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/draw-picture.pdf b/info/drawing-with-metapost/src/draw-picture.pdf Binary files differdeleted file mode 100644 index 6eb8f7dbff..0000000000 --- a/info/drawing-with-metapost/src/draw-picture.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/dwmpcode.sty b/info/drawing-with-metapost/src/dwmpcode.sty index ccc13d95a8..35efab9489 100644 --- a/info/drawing-with-metapost/src/dwmpcode.sty +++ b/info/drawing-with-metapost/src/dwmpcode.sty @@ -2,11 +2,13 @@ \ProvidesPackage{dwmpcode}[2021/12/30 v0.01 Code setting in DwMP] \RequirePackage{listings} \RequirePackage{xcolor} +\RequirePackage{luamplib} \definecolor{textblue}{rgb}{.2,.2,.7} \definecolor{textred}{rgb}{0.54,0,0} \definecolor{textgreen}{rgb}{0,0.43,0} \definecolor{squash}{rgb}{0.793, 0.359, 0.05} \definecolor{carrot}{rgb}{0.934, 0.445, 0.082} +\definecolor{purple}{rgb}{0.398, 0.008, 0.234} \def\red#1{\textcolor{textred}{#1}} \def\blue#1{\textcolor{textblue}{#1}} \def\green#1{\textcolor{textgreen}{#1}} @@ -16,6 +18,7 @@ basicstyle=\ttfamily, keywordstyle=\color{textblue}, keywordstyle=[5]\color{squash}, keywordstyle=[6]\color{carrot}, +keywordstyle=[7]\color{purple}, commentstyle=\color{textred}, stringstyle=\color{textgreen}, frame=none, @@ -23,13 +26,85 @@ columns=fullflexible, keepspaces=true, xleftmargin=\parindent, showstringspaces=false, -morekeywords={cmykcolor, step, eps, exitif, rotatedabout}, -morestring=[s]{btex}{etex} +% keywords[1] = Syntax primitive + plain sugar +keywords=[1]{beginfig, begingroup, bye, controls, curl, verbatimtex,% + cycle, def, delimiters, downto, else, elseif, end, enddef, endfig,% + endfor, endgroup, etex, exitif, exitunless, expr, fi, for, forever,% + forsuffixes, if, input, numtok, outer, primary, primarydef, range,% + relax, scantokens, secondary, secondarydef, step, suffix, tension,% + tertiary, tertiarydef, text, thru, until, upto, vardef, within},% +% keywords[2] = Operators - nullary, unary, binary, thing x of y +keywords=[2]{abs, and, angle, arclength, arctime, ASCII, bbox,% + blackpart, bluepart, bounded, byte, ceiling, center, char,% + clipped, colormodel, colorpart, cosd, counterclockwise, cutafter,% + cutbefore, cyanpart, dashpart, decimal, dir, direction,% + directionpoint, directiontime, div, dotprod, false, filled, floor,% + fontpart, fontsize, glyph, gobbled, greenpart, greypart, hex,% + infont, intersectionpoint, intersectiontimes, inverse, known,% + length, llcorner, lrcorner, magentapart, makepath, makepen,% + mexp, mlog, mod, normaldeviate, not, nullpen, nullpicture, oct,% + odd, of, or, pathpart, pencircle, penoffset, penpart, point,% + postcontrol, precontrol, readfrom, redpart, reflectedabout,% + reverse, rotated, rotatedabout, rotatedaround, round, scaled,% + shifted, sind, slanted, softjoin, sqrt, str, stroked, subpath,% + substring, textpart, textual, transformed, true,% + turningnumber, ulcorner, uniformdeviate, unitvector, unknown,% + urcorner, whatever, xpart, xscaled, xxpart, xypart, yellowpart,% + ypart, yscaled, yxpart, yypart, zscaled, + top, bot, lft, rt, ulft, urt, llft, lrt},% +% keywords[3] = Commands +keywords=[3]{addto, also, batchmode, clearit, clearpen, clearxy,% + clear_pen_memory, clip, closefrom, contour, cutdraw, dotlabel,% + doublepath, draw, drawarrow, drawdblarrow, drawdot, drawoptions,% + errhelp, errmessage, errorstopmode, filenametemplate, fill,% + filldraw, fontmapfile, fontmapline, interim, label, let,% + loggingall, makelabel, message, newinternal, nonstopmode,% + penstroke, pickup, randomseed, readstring, save, savepen,% + scrollmode, setbounds, shipit, shipout, show, showdependencies,% + showtoken, showvariable, special, to, tracingall, tracingnone,% + undraw, undrawdot, unfill, unfilldraw, write},% +% keywords[4] = Specials, fancy macros, etc +keywords=[4]{boxit, boxjoin, bpath, buildcycle, circleit, dashed,% + dashpattern, decr, dotlabels, drawboxed, drawboxes, drawunboxed,% + erase, fixpos, fixsize, flex, gobble, hide, image, incr, interact,% + interpath, labels, magstep, max, min, off, on, penlabels, penpos,% + solve, stop, superellipse, takepower, tensepath, thelabel,% + withcmykcolor, withcolor, withgreyscale, withoutcolor, withpen,% + withpostscript, withprescript, withrgbcolor, withalpha, z},% +% keywords[5] = Predefined variables +keywords=[5]{ahangle, ahlength, arrowhead, background, bboxmargin,% + charcode, circmargin, currentpen, currentpicture, cuttings, day,% + defaultcolormodel, defaultdx, defaultdy, defaultfont, defaultpen,% + defaultscale, dotlabeldiam, eps, extra_beginfig, extra_endfig,% + hour, hppp, jobname, join_radius, labeloffset, laboff, labxf,% + labyf, linecap, linejoin, minute, miterlimit, month, mpprocset,% + numberprecision, numbersystem, outputfilename, outputformat,% + outputformatoptions, outputtemplate, pausing, pen_bot, pen_lft,% + pen_rt, pen_top, prologues, restoreclipcolor, showstopping, time,% + tolerance, tracingcapsules, tracingchoices, tracingcommands,% + tracingequations, tracinglostchars, tracingmacros, tracingonline,% + tracingoutput, tracingrestores, tracingspecs, tracingstats,% + tracingtitles, troffmode, truecorners, vppp, warningcheck, year},% +% keywords[6] = Constants +keywords=[6]{base_name, base_version, beveled, black,% + blankpicture, blue, bp, butt, cc, cm, dd, ditto, down, EOF,% + epsilon, evenly, fullcircle, green, halfcircle, identity, in, left,% + mitered, mm, mpversion, origin, pc, penrazor, penspeck,% + pensquare, pt, quartercircle, red, right, rounded, squared,% + unitsquare, up, white, withdots, infinity},% +% keywords[7] = Types +keywords=[7]{boolean, cmykcolor, color, numeric, pair, path, pen,% + picture, rgbcolor, string, transform},% +sensitive=true,% +alsoother={0123456789$@},% +morestring=[s]{verbatimtex}{etex},% +morestring=[s]{btex}{etex}% }} \lstnewenvironment{smallcode}[1][]{\mpstyle\lstset{basicstyle=\small\ttfamily,#1}}{} \lstnewenvironment{code}[1][]{\mpstyle\lstset{#1}}{} \newcommand\mpexternal[2][]{{\mpstyle\lstinputlisting[#1]{#2}}} -\newcommand\mpl[1]{{\mpstyle\lstinline!#1!}} +\newcommand\smallmpexternal[2][]{{\mpstyle\lstinputlisting[basicstyle=\small\ttfamily,#1]{#2}}} +\newcommand\mpl[1]{{\normalfont\mpstyle\lstinline!#1!}} % \newcommand\texstyle{\lstset{ language=[LaTeX]Tex, @@ -42,8 +117,21 @@ columns=fullflexible, keepspaces=true, xleftmargin=\parindent, showstringspaces=false, +morekeywords={everymplib, everyendmplib, setmainfont, +mplibtextextlabel, mplibnumbersystem, mplibsetformat, mplibshowlog}, }} \lstnewenvironment{texcode}[1][]{\texstyle\lstset{basicstyle=\small\ttfamily,#1}}{} \newcommand\txl[1]{{\texstyle\lstinline!#1!}} +\newcommand\texternal[2][]{{\texstyle\lstinputlisting[#1]{#2}}} +\newcommand\smalltexternal[2][]{{\texstyle\lstinputlisting[basicstyle=\small\ttfamily,#1]{#2}}} +% +% Labels.. +% +\newcommand\sep[1]{$\vcenter{\begin{mplibcode} +picture T; T = thelabel(TEX("\ttfamily " & #1), origin); interim bboxmargin := 3; path p; p = bbox T; +path S; S = superellipse(point 3/2 of p, point 5/2 of p, point 7/2 of p, point 1/2 of p, 0.78); +string x; x = substring (0, 1) of #1; +fill S withcolor if x = "m": 7/8[red, white] elseif x = "c": 7/8[blue, white] else: white fi; +draw S; draw T;\end{mplibcode}}$} % \endinput diff --git a/info/drawing-with-metapost/src/eggs-357.mp b/info/drawing-with-metapost/src/eggs-357.mp index 746638a83c..0b3117dde4 100644 --- a/info/drawing-with-metapost/src/eggs-357.mp +++ b/info/drawing-with-metapost/src/eggs-357.mp @@ -7,26 +7,18 @@ input eggs-common beginfig(1); path base, cup, cap, egg; - base = fullcircle scaled 180; -z0 = origin; z1 = point -2/3 of base; z2 = point 2/3 of base; z3 = point 10/3 of base; z4 = point 14/3 of base; -z5 = 1/2[z2, z3]; -z6 = 1/2[z4, z1]; - -numeric a, b, c; -a = abs(z3 - z1); -b = a - abs(z4 - z6); -c = a - abs(z4 - z5); - -cup = subpath (4, 8) of fullcircle scaled 2b shifted z6; -cap = fullcircle scaled 2c shifted z5 - cutbefore (z5 -- 2[z4, z5]) - cutafter (z5 -- 2[z1, z5]); - +z5 = 1/2[z2, z3]; z6 = 1/2[z4, z1]; +numeric a, b; +a = abs(z3-z1) - abs(z4-z6); +b = abs(z3-z1) - abs(z4-z5); +cup = subpath (4, 8) of fullcircle scaled 2a shifted z6; +cap = fullcircle scaled 2b shifted z5 + cutbefore (z5 -- 2[z4, z5]) cutafter (z5 -- 2[z1, z5]); egg = point 4 of cup {up} .. cap .. {down} cup & cycle; fill egg withpen pencircle scaled 2 withcolor eggshell; @@ -39,7 +31,7 @@ label.lft("$\scriptstyle \sqrt 4 $", 10 down); label.ulft("$\scriptstyle \sqrt 7$", 7/16[z4, z5]); draw base; draw z1 -- z2 -- z3 -- z4 -- z6 -- z5; -draw z0 withpen pencircle scaled 2; +draw origin withpen pencircle scaled 2; drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); draw point 0 of egg -- point 4 of egg; draw z4 -- point 1 of egg; diff --git a/info/drawing-with-metapost/src/eggs-357.pdf b/info/drawing-with-metapost/src/eggs-357.pdf Binary files differindex 1f445d9698..0d6c73c8d5 100644 --- a/info/drawing-with-metapost/src/eggs-357.pdf +++ b/info/drawing-with-metapost/src/eggs-357.pdf diff --git a/info/drawing-with-metapost/src/eggs-five-better.mp b/info/drawing-with-metapost/src/eggs-five-better.mp index 472f3ab0a3..1a4d232335 100644 --- a/info/drawing-with-metapost/src/eggs-five-better.mp +++ b/info/drawing-with-metapost/src/eggs-five-better.mp @@ -3,7 +3,7 @@ \mplibtextextlabel{enable} \begin{document} \begin{mplibcode} -numeric a; a = 56; +numeric a; a = 56; path r[]; % the rings r1 = fullcircle scaled 2a shifted (0, -3/2 a); r2 = fullcircle scaled 2a shifted (0, -1/2 a); @@ -11,7 +11,6 @@ r3 = fullcircle scaled 2a shifted (0, +1/2 a); r4 = fullcircle scaled 2a shifted (0, +3/2 a); r5 = r2 rotatedabout(point 2 of r2, -60); r6 = r2 rotatedabout(point 2 of r2, +60); - pair o[]; % the centres of rotation for each arc o1 = point 6 of r5; o2 = point 2 of r3; @@ -21,13 +20,11 @@ o8 = whatever[o1, point 2-4/3 of r2] = whatever[o2, point 2+4/3 of r1]; o6 = 1/2[point 2-4/3 of r1, point 2+4/3 of r1]; o5 = whatever[o6, point 2-4/3 of r3] = whatever[o4, point 2+4/3 of r1]; o7 = whatever[o6, point 2+4/3 of r3] = whatever[o8, point 2-4/3 of r1]; - pair u[], t[]; % directions and points for the egg u0 = (o8 - o1) rotated 90; t0 = directionpoint u0 of r6; u1 = (o2 - o1) rotated 90; t1 = directionpoint u1 of r4; u2 = (o2 - o3) rotated 90; t2 = directionpoint u2 of r4; u3 = (o4 - o3) rotated 90; t3 = directionpoint u3 of r5; - u4 = (o5 - o4) rotated 90; u5 = (o6 - o5) rotated 90; u6 = (o6 - o7) rotated 90; @@ -37,8 +34,7 @@ t5 = directionpoint u5 of fullcircle scaled 2 abs (t4 - o5) shifted o5; t6 = directionpoint u6 of fullcircle scaled 2 abs (t5 - o6) shifted o6; t7 = directionpoint u7 of fullcircle scaled 2 abs (t6 - o7) shifted o7; -path egg; -egg = for i=0 upto 7: t[i] {u[i]} .. endfor cycle; +path egg; egg = for i=0 upto 7: t[i] {u[i]} .. endfor cycle; input eggs-common diff --git a/info/drawing-with-metapost/src/eggs-five-better.pdf b/info/drawing-with-metapost/src/eggs-five-better.pdf Binary files differindex bf092abbca..3a94369729 100644 --- a/info/drawing-with-metapost/src/eggs-five-better.pdf +++ b/info/drawing-with-metapost/src/eggs-five-better.pdf diff --git a/info/drawing-with-metapost/src/eggs-four-point.mp b/info/drawing-with-metapost/src/eggs-four-point.mp index e168217aad..13b67c08fe 100644 --- a/info/drawing-with-metapost/src/eggs-four-point.mp +++ b/info/drawing-with-metapost/src/eggs-four-point.mp @@ -9,13 +9,16 @@ beginfig(1); path egg, a, b, c, d; a = fullcircle scaled 80; b = a scaled 2 shifted point 6 of a; -c = halfcircle scaled 2 (abs(point 0 of a - point 5 of b) - abs(point 0 of a)); -d = fullcircle scaled 2 abs(point 2 of a - point 2 of c) shifted point 2 of c; -egg = point 0 of c {up} .. subpath (1,3) of d .. {down} point 4 of c .. subpath (5, 7) of b .. cycle; +c = halfcircle + scaled 2 (abs(point 0 of a - point 5 of b) - abs(point 0 of a)); +d = fullcircle + scaled 2 abs(point 2 of a - point 2 of c) shifted point 2 of c; +egg = point 0 of c {up} .. subpath (1,3) of d .. {down} point 4 of c + .. subpath (5, 7) of b .. cycle; fill egg withpen pencircle scaled 2 withcolor 3/4[1/4[red, green], white]; picture P; P = currentpicture; -drawoptions(withpen pencircle scaled 1/4 withcolor darker_eggshell); +drawoptions(withpen pencircle scaled 1/4 withcolor dark_eggshell); draw a; draw b; draw c; draw d; drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); draw point 0 of c -- point 3 of egg; diff --git a/info/drawing-with-metapost/src/eggs-four-point.pdf b/info/drawing-with-metapost/src/eggs-four-point.pdf Binary files differindex ffbf1a3438..d86353034b 100644 --- a/info/drawing-with-metapost/src/eggs-four-point.pdf +++ b/info/drawing-with-metapost/src/eggs-four-point.pdf diff --git a/info/drawing-with-metapost/src/eggs-fried.mp b/info/drawing-with-metapost/src/eggs-fried.mp index 2c8c6d7226..6acf838c55 100644 --- a/info/drawing-with-metapost/src/eggs-fried.mp +++ b/info/drawing-with-metapost/src/eggs-fried.mp @@ -4,29 +4,20 @@ \begin{mplibcode} beginfig(1); path yolk, base; -color cooked_egg_yolk, cooked_egg_white; -cooked_egg_yolk = 1/256(216, 136, 49); -cooked_egg_white = 1/256(235, 237, 233); - -vardef fried_egg(expr r) = +color cooked_egg_yolk; cooked_egg_yolk = 1/256(216, 136, 49); +color cooked_egg_white; cooked_egg_white = 1/256(235, 237, 233); +vardef fried_egg(expr r) = image( save base, yolk; path base, yolk; yolk = for i=0 upto 17: (r + 1/8 normaldeviate) * dir 20i .. endfor cycle; base = (for i=0 upto 17: (2r + 1/8r * normaldeviate) * dir 20i .. endfor cycle) - shifted (uniformdeviate r/2, uniformdeviate r/2); - image( - fill base withcolor cooked_egg_white; - fill yolk withcolor cooked_egg_yolk; - fill subpath (6.7, 9.6) of yolk scaled 0.8 -- - subpath (9.6, 6.7) of yolk scaled 0.66 -- cycle - withcolor 1/2[cooked_egg_yolk, white]; - ) -enddef; - -for i=0 upto 1: - draw fried_egg(40) shifted 120 dir 120i; -endfor - - + shifted (uniformdeviate r/2, uniformdeviate r/2); + fill base withcolor cooked_egg_white; + fill yolk withcolor cooked_egg_yolk; + fill subpath (6.7, 9.6) of yolk scaled 0.8 -- + subpath (9.6, 6.7) of yolk scaled 0.66 -- cycle + withcolor 1/2[cooked_egg_yolk, white] +) enddef; +for i=0 upto 1: draw fried_egg(40) shifted 120 dir 120i; endfor endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/eggs-fried.pdf b/info/drawing-with-metapost/src/eggs-fried.pdf Binary files differindex b75e01b5bb..62e9a8c6dd 100644 --- a/info/drawing-with-metapost/src/eggs-fried.pdf +++ b/info/drawing-with-metapost/src/eggs-fried.pdf diff --git a/info/drawing-with-metapost/src/eggs-gold.mp b/info/drawing-with-metapost/src/eggs-gold.mp index 6c13a6afb3..f41b8dc3be 100644 --- a/info/drawing-with-metapost/src/eggs-gold.mp +++ b/info/drawing-with-metapost/src/eggs-gold.mp @@ -6,29 +6,21 @@ input eggs-common beginfig(1); -path base; -base = fullcircle scaled 200; - -pair m, n, n', p; -path aa, bb; - -m = 1/2 point 0 of base; -aa = halfcircle scaled 2 abs (point 2 of base - m) shifted m cutbefore (origin -- 1000 up); -n = point infinity of aa; -n' = n reflectedabout(up, down); +path base, aa, bb; pair m, n, n'; +base = fullcircle scaled 200; m = 1/2 point 0 of base; +aa = halfcircle scaled 2 abs (point 2 of base - m) + shifted m cutbefore (origin -- 1000 up); +n = point infinity of aa; n' = n reflectedabout(up, down); bb = subpath (0, 2) of base shifted n cutafter (origin -- 1000 up); -p = point infinity of bb; - -path dome; -path cap, cup, egg; +path dome, cap, cup, egg; dome = fullcircle scaled 2 (abs(n - point 0 of base) - abs(n - point 0 of bb)) - shifted p; + shifted point length bb of bb; cap = dome cutbefore (point 4 of bb -- 2[n, point 4 of bb]) cutafter (point 4 of bb -- 2[n', point 4 of bb]); cup = subpath (4, 8) of base; -path egg; egg = point 4 of cup {up} .. cap .. {down} cup & cycle; +egg = point 4 of cup {up} .. cap .. {down} cup & cycle; fill egg withpen pencircle scaled 2 withcolor eggshell; picture P; P = currentpicture; @@ -40,7 +32,6 @@ draw base; draw dome; label.bot("$m$", m); label.ulft("$n$", n); label.urt("$n'$", n'); -% label.lft("$p$", p); drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); draw n -- point 1 of egg; @@ -48,7 +39,7 @@ draw n' -- point 3 of egg; draw point 0 of egg -- point 4 of egg; draw egg; -forsuffixes $=n, n', p, origin: draw $ withpen pencircle scaled 2; endfor +forsuffixes $=n, n', origin: draw $ withpen pencircle scaled 2; endfor draw m withpen pencircle scaled 2 withcolor dark_eggshell; draw numbered_points(egg); diff --git a/info/drawing-with-metapost/src/eggs-gold.pdf b/info/drawing-with-metapost/src/eggs-gold.pdf Binary files differindex 171112387e..b13c73d735 100644 --- a/info/drawing-with-metapost/src/eggs-gold.pdf +++ b/info/drawing-with-metapost/src/eggs-gold.pdf diff --git a/info/drawing-with-metapost/src/eggs-moss.mp b/info/drawing-with-metapost/src/eggs-moss.mp index 6bd228dd4f..314d6959cf 100644 --- a/info/drawing-with-metapost/src/eggs-moss.mp +++ b/info/drawing-with-metapost/src/eggs-moss.mp @@ -11,21 +11,21 @@ d = fullcircle scaled 2 abs (point 2 of a - point 1 of b) shifted point 2 of a; egg = subpath (0, 1) of b .. point 2 of d .. subpath (3, 4) of c .. subpath (5, 7) of a .. cycle; + beginfig(1); -fill egg withpen pencircle scaled 2 withcolor eggshell; -picture P; P = currentpicture; -drawoptions(withpen pencircle scaled 1/4 withcolor dark_eggshell); -draw a; draw d; -drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); -draw point 1 of egg -- point 4 of egg -- - point 0 of egg -- point 3 of egg; -draw egg; -drawoptions(withpen pencircle scaled 2 withcolor 7/16); -draw center a; -draw center d; -draw numbered_points(egg); -drawoptions(); -draw P shifted 240 right; + fill egg withpen pencircle scaled 2 withcolor eggshell; + picture plain_egg; plain_egg = currentpicture; + drawoptions(withpen pencircle scaled 1/4 withcolor dark_eggshell); + draw a; draw d; + drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); + draw point 1 of egg -- point 4 of egg -- + point 0 of egg -- point 3 of egg; + draw egg; + drawoptions(withpen pencircle scaled 2 withcolor 7/16); + draw center a; draw center d; + draw numbered_points(egg); + drawoptions(); + draw plain_egg shifted 240 right; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/eggs-perfect.mp b/info/drawing-with-metapost/src/eggs-perfect.mp index 8f63cd6e8b..5388bf13b9 100644 --- a/info/drawing-with-metapost/src/eggs-perfect.mp +++ b/info/drawing-with-metapost/src/eggs-perfect.mp @@ -5,9 +5,8 @@ \begin{mplibcode} input eggs-common beginfig(1); + path egg; -%egg = for t=90,105,120,135,150,165,-180,-165,-150,-135,-120,-105,-90,-75,-60,-45,-30,-15,0,15,30,45,60,75: -%egg = for t=90, 135, 180, -135, -90, -45, 0, 45: egg = for t=-180 step 15 until 180 - eps: (0.78 cosd(1/4 t) * sind(t), -cosd(t)) .. endfor cycle; diff --git a/info/drawing-with-metapost/src/eggs-perfect.pdf b/info/drawing-with-metapost/src/eggs-perfect.pdf Binary files differindex 9a291f9059..82364951ee 100644 --- a/info/drawing-with-metapost/src/eggs-perfect.pdf +++ b/info/drawing-with-metapost/src/eggs-perfect.pdf diff --git a/info/drawing-with-metapost/src/eggs-shaded.mp b/info/drawing-with-metapost/src/eggs-shaded.mp index 3eeca4babe..dd4a6fd782 100644 --- a/info/drawing-with-metapost/src/eggs-shaded.mp +++ b/info/drawing-with-metapost/src/eggs-shaded.mp @@ -5,22 +5,18 @@ \begin{mplibcode} path egg, spot; egg = (for t=-180 step 15 until 180 - eps: - (0.78 cosd(1/4 t) * sind(t), -cosd(t)) .. + (0.78 cosd(1/4 t) * sind(t), -cosd(t)) .. endfor cycle) scaled 100; - spot = fullcircle scaled 4 shifted 3/4 point 3 of egg; - vardef fade_filled(expr egg, spot, dark, light, n) = image( - for i = 0 upto n: - fill interpath(i/n, egg, spot) withcolor ((i/n)**1/3)[dark,light]; - endfor) + for i = 0 upto n: + fill interpath(i/n, egg, spot) withcolor ((i/n)**1/3)[dark,light]; + endfor) enddef; - beginfig(1); - color a, b; - a = 1/256(150, 100, 60); - b = 1/256(256, 220, 180); - draw fade_filled(egg, spot, a, b, 256) rotated -30; + color a; a = 1/256(150, 100, 60); + color b; b = 1/256(256, 220, 180); + draw fade_filled(egg, spot, a, b, 256) rotated -30; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/eggs-shaded.pdf b/info/drawing-with-metapost/src/eggs-shaded.pdf Binary files differindex ec2143cdc2..3f1a19b8cc 100644 --- a/info/drawing-with-metapost/src/eggs-shaded.pdf +++ b/info/drawing-with-metapost/src/eggs-shaded.pdf diff --git a/info/drawing-with-metapost/src/eggs-super.mp b/info/drawing-with-metapost/src/eggs-super.mp index 89f8dda5b4..ae6e25bfa8 100644 --- a/info/drawing-with-metapost/src/eggs-super.mp +++ b/info/drawing-with-metapost/src/eggs-super.mp @@ -4,7 +4,8 @@ \begin{document} \begin{mplibcode} path egg; -egg = (superellipse(right, 1.6 up, left, 1.2 down, 0.69)) scaled 100; +egg = (superellipse(right, 1.6 up, left, 1.2 down, 0.69)); +egg := egg scaled 100; input eggs-common beginfig(1); fill egg withpen pencircle scaled 2 withcolor eggshell; diff --git a/info/drawing-with-metapost/src/eggs-super.pdf b/info/drawing-with-metapost/src/eggs-super.pdf Binary files differindex 2022f1ed2d..f7530d2ff8 100644 --- a/info/drawing-with-metapost/src/eggs-super.pdf +++ b/info/drawing-with-metapost/src/eggs-super.pdf diff --git a/info/drawing-with-metapost/src/eggs-thom.mp b/info/drawing-with-metapost/src/eggs-thom.mp index f38d86fcad..bbe2de4476 100644 --- a/info/drawing-with-metapost/src/eggs-thom.mp +++ b/info/drawing-with-metapost/src/eggs-thom.mp @@ -13,8 +13,7 @@ cap = subpath (0, 4) of fullcircle scaled 2r shifted (0, a) cutbefore ((b, 0) -- (b, 2r)) cutafter ((-b, 0) -- (-b, 2r)); egg = point 4 of base {up} .. cap .. {down} base & cycle; -% more naturally -% base {up} .. cap .. {down} & cycle +% more naturally "base {up} .. cap .. {down} & cycle" % but then point 0 would not be at 3 o'clock beginfig(1); diff --git a/info/drawing-with-metapost/src/escher.mp b/info/drawing-with-metapost/src/escher.mp deleted file mode 100644 index eac172d4f3..0000000000 --- a/info/drawing-with-metapost/src/escher.mp +++ /dev/null @@ -1,38 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -beginfig(1); - -numeric s; s = 13; -path atom; -atom = origin - -- (2s,0) rotated -30 -- (2s,0) rotated -30 + (0,s) - -- ( s,0) rotated 30 -- ( s,0) rotated 30 + (0,s) - -- (0,2s) -- cycle; - -picture p[]; -for i=0 upto 2: - p[i] = image( - fill atom rotated -120i withcolor (7/8 - 1/8i) ; - draw atom rotated -120i; - ); -endfor - -n = 13; -for i=-n upto n: - for j=-n upto n: - forsuffixes $=0,1,2: - draw p$ shifted ((3i*s,0) rotated -30 - + (0,floor(1/2i)*3s + 3j*s)); - endfor - endfor -endfor - -clip currentpicture to (unitsquare shifted -(1/2,1/2) - xscaled 55.425s yscaled 30s); - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/escher.pdf b/info/drawing-with-metapost/src/escher.pdf Binary files differdeleted file mode 100644 index 391fc26d5d..0000000000 --- a/info/drawing-with-metapost/src/escher.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/excircle.mp b/info/drawing-with-metapost/src/excircle.mp deleted file mode 100644 index 01307ce3d0..0000000000 --- a/info/drawing-with-metapost/src/excircle.mp +++ /dev/null @@ -1,39 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -vardef through(expr a, b, o) = - save t; numeric t; t = 1+o/abs(a-b); - t[b,a] -- t[a,b] -enddef; - -beginfig(1); - pair A, B, C; - A = origin; B = 233 dir 10; C = 144 dir 70; - pair a, b, m, t; - a = A + 22 unitvector (C-A) - 22 unitvector (B-A); - b = B + 22 unitvector (A-B) + 22 unitvector (C-B); - m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; - t-m = whatever * (B-A) rotated 90; - - drawoptions(dashed evenly scaled 1/4 withcolor 1/2 white); - draw t -- m; - draw unitsquare scaled 5 rotated angle (B-A) shifted t; - draw through(A, m, 10); - draw through(A, t, 10); - draw through(B, m, 10); - drawoptions(); - draw fullcircle scaled 2 abs (t-m) shifted m withcolor 2/3 blue; - draw A--B--C--cycle; - dotlabel.urt(btex $m$ etex, m); - dotlabel.bot(btex $t$ etex, t); - dotlabel.bot(btex $A$ etex, A); - dotlabel.urt(btex $B$ etex, B); - dotlabel.top(btex $C$ etex, C); - dotlabel.urt(btex $a$ etex, a); - dotlabel.top(btex $b$ etex, b); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/explode.mp b/info/drawing-with-metapost/src/explode.mp deleted file mode 100644 index 8d03d94846..0000000000 --- a/info/drawing-with-metapost/src/explode.mp +++ /dev/null @@ -1,31 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\usepackage{fontspec} -\setmainfont{PlayfairDisplay-Black} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -randomseed:=2128.5073; -beginfig(1); -n = 40; r = 7 ; s = 44; -path explosion, splash; -explosion = for i=1 upto n: - (s if odd(i): - else: + fi r + uniformdeviate r,0) rotated (i*360/n) -- -endfor cycle; - -splash = for i=1 upto n: - (s if odd(i): - else: + fi r + uniformdeviate r,0) rotated (i*360/n) .. -endfor cycle; -splash := splash shifted (3s,0); - -fill explosion withcolor Oranges 7 4; -draw explosion withpen pencircle scaled 2 withcolor Reds 7 7; -label(TEX("\textbf{BOOM!}") scaled 1.6, center explosion) withcolor Reds 7 7; - -fill splash withcolor Blues 7 2; -draw splash withpen pencircle scaled 2 withcolor Blues 7 7; -label(TEX("\bfseries SPLAT!") scaled 1.6, center splash) withcolor Blues 7 7; -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/explode.pdf b/info/drawing-with-metapost/src/explode.pdf Binary files differdeleted file mode 100644 index d5c1c094d9..0000000000 --- a/info/drawing-with-metapost/src/explode.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/func-addition-of-sines.mp b/info/drawing-with-metapost/src/func-addition-of-sines.mp index d7f9a41db5..7b651e831d 100644 --- a/info/drawing-with-metapost/src/func-addition-of-sines.mp +++ b/info/drawing-with-metapost/src/func-addition-of-sines.mp @@ -19,40 +19,41 @@ vardef pi_sixths(expr n) = enddef; beginfig(1); - numeric u, pi; u = 50; pi = 3.141592653589793; + numeric u, pi; u = 50; pi = 3.141592653589793; - path xx, yy; - xx = (3.5 left -- 4 right) scaled u; - yy = (1.2 down -- 1.3 up) scaled u; - - path ss, tt, uu; - ss = origin for x=1 upto 360: -- (x, sind(x)) endfor; - tt = origin for x=1 upto 360: -- (x, 1/2 sind(3x)) endfor; - uu = origin for x=1 upto 360: -- (x, ypart point x of ss + ypart point x of tt) endfor; + path xx, yy; + xx = (3.5 left -- 4 right) scaled u; + yy = (1.2 down -- 1.3 up) scaled u; + + path ss, tt, uu; + ss = origin for x=1 upto 360: -- (x, sind(x)) endfor; + tt = origin for x=1 upto 360: -- (x, 1/2 sind(3x)) endfor; + uu = origin for x=1 upto 360: + -- (x, ypart point x of ss + ypart point x of tt) + endfor; - forsuffixes $=ss, tt, uu: - $ := $ shifted 360 left & $; - $ := $ xscaled (pi/180) scaled u; - $ := $ cutbefore yy shifted point 0 of xx - cutafter yy shifted point 1 of xx; - endfor + forsuffixes $=ss, tt, uu: + $ := $ shifted 360 left & $; + $ := $ xscaled (pi/180) scaled u; + $ := $ cutbefore yy shifted point 0 of xx + cutafter yy shifted point 1 of xx; + endfor - draw ss withcolor 1/2[blue, white]; - draw tt withcolor 1/2[red, white]; - draw uu withcolor 1/4 green; - - label.top("$f(x)=sin(x)$", point 290 of ss) withcolor 1/2[blue, white]; - label.bot("$g(x)=\frac12 sin(3x)$", point 295 of tt) withcolor 1/2[red, white]; - label.urt("$f(x) + g(x)$", point 350 of uu) withcolor 1/4 green; - - drawarrow xx; label.rt("$x$", point 1 of xx); - drawarrow yy; label.top("$y$", point 1 of yy); - - for i=-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7: - draw (down--up) scaled 2 shifted (pi * i/6 * u, 0); - label.bot(pi_sixths(i), (pi * i/6 * u, -2)); - endfor + drawoptions(withcolor 3/4 blue); + draw ss; label.top("$f(x)=\sin(x)$", point 290 of ss); + drawoptions(withcolor 2/3 red); + draw tt; label.bot("$g(x)=\frac12 \sin(3x)$", point 295 of tt); + drawoptions(withcolor 1/4 green); + draw uu; label.urt("$f(x) + g(x)$", point 350 of uu); + drawoptions(); + + drawarrow xx; label.rt("$x$", point 1 of xx); + drawarrow yy; label.top("$y$", point 1 of yy); + for i=-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7: + draw (down--up) scaled 2 shifted (pi * i/6 * u, 0); + label.bot(pi_sixths(i), (pi * i/6 * u, -2)); + endfor endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/func-addition-of-sines.pdf b/info/drawing-with-metapost/src/func-addition-of-sines.pdf Binary files differindex 29973d3b2a..2b992fb3ff 100644 --- a/info/drawing-with-metapost/src/func-addition-of-sines.pdf +++ b/info/drawing-with-metapost/src/func-addition-of-sines.pdf diff --git a/info/drawing-with-metapost/src/func-angles-lines.mp b/info/drawing-with-metapost/src/func-angles-lines.mp new file mode 100644 index 0000000000..7c7c0a7dad --- /dev/null +++ b/info/drawing-with-metapost/src/func-angles-lines.mp @@ -0,0 +1,53 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + numeric u; u = 1cm; + path xx; xx = (2 left -- 10 right) scaled u; + path yy; yy = (down -- 7 up) scaled u; + + numeric theta, psi; psi = 28; theta = 50; + pair P, Q, H, N, M, T, L; P = (4, 3) scaled u; + + path ell, tee, arc; + ell = (left--right) scaled 10u rotated theta shifted P cutbefore xx; + tee = (left--right) scaled 10u rotated psi shifted P cutbefore xx; + arc = subpath (1.6, 3.2) of halfcircle rotated -180 shifted 1/2 up + scaled 10u shifted P rotatedabout(P, psi); + + Q = ell intersectionpoint subpath (1.5, 3) of arc; + H = P + whatever * dir psi; + xpart H = xpart Q = xpart M; ypart M = ypart N = 0; + xpart N = xpart P; + L = point 0 of ell; + T = point 0 of tee; + + % now we can get with the drawing + draw arc withcolor 1/2 red; + draw P--N dashed withdots scaled 1/2; + draw Q--M dashed withdots scaled 1/2; + drawarrow xx; label.rt("$x$", point 1 of xx); + drawarrow yy; label.top("$y$", point 1 of yy); + drawoptions(withcolor 2/3 blue); + draw fullcircle scaled 32 shifted T cutafter tee; + draw fullcircle scaled 28 shifted L cutafter ell; + label("$\psi$", 24 right rotated 1/2 psi shifted T); + label("$\theta$", 20 right rotated 1/2 theta shifted L); + drawoptions(); + + % draw the lines trimmed neatly + path invisible_boundary; + z1 = point .95 of xx; + z2 = point .95 of yy; + invisible_boundary = z1--(x1,y2)--z2; + draw ell cutafter invisible_boundary; + draw tee cutafter invisible_boundary; + + % and finally label the points. + forsuffixes @ = T, L, N, M: label.bot("$" & str @ & "$", @); endfor + forsuffixes @ = H, P, Q: dotlabel.lrt("$" & str @ & "$", @); endfor +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/angles-lines.pdf b/info/drawing-with-metapost/src/func-angles-lines.pdf Binary files differindex e894f32f21..03b6f20b0e 100644 --- a/info/drawing-with-metapost/src/angles-lines.pdf +++ b/info/drawing-with-metapost/src/func-angles-lines.pdf diff --git a/info/drawing-with-metapost/src/func-epi-v-pie.mp b/info/drawing-with-metapost/src/func-epi-v-pie.mp index cb36f02f6d..ba5cfcdc5b 100644 --- a/info/drawing-with-metapost/src/func-epi-v-pie.mp +++ b/info/drawing-with-metapost/src/func-epi-v-pie.mp @@ -6,8 +6,7 @@ beginfig(1); numeric minx, maxx, s, u, v; -minx = 13/8; s = 1/16; maxx = 19/4; -u = 89; v = 3072; +minx = 13/8; s = 1/16; maxx = 19/4; u = 89; v = 3072; def f(expr x) = 1/256 mlog(x) / x enddef; @@ -22,11 +21,9 @@ yy := yy shifted point 0 of ff shifted 20 left; numeric pi, e, fpi, fe; pi = 3.141592653589793 u; fpi = f(3.141592653589793) * v; e = 2.718281828459045 u; fe = f(2.718281828459045) * v; - path ee, pp; ee = (e, ypart point 0 of xx) -- (e, fe) -- (xpart point 0 of yy, fe); pp = (pi, ypart point 0 of xx) -- (pi, fpi) -- (xpart point 0 of yy, fpi); - draw ee dashed withdots scaled 1/4 withcolor 2/3 red; draw pp dashed withdots scaled 1/2 withcolor 2/3 red; draw ff withcolor 3/4 blue; @@ -37,11 +34,11 @@ for x=2 upto 4: draw (down--up) scaled 2 shifted (x * u, ypart point 0 of xx); label.bot("$" & decimal x & "$", (x * u, ypart point 0 of xx - 2)); endfor -for y=31 upto 38: - draw (left--right) scaled 2 shifted (xpart point 0 of yy, y/100*v); +for y=.31, .32, .33, .34, .35, .36, .37, .38: + draw (left--right) scaled 2 shifted (xpart point 0 of yy, y*v); endfor -for y=32, 35, 38: - label.lft("$" & decimal (y/100) & "$", (xpart point 0 of yy-2, y/100*v)); +for y=.32, .35, .38: + label.lft("$" & decimal y & "$", (xpart point 0 of yy-2, y*v)); endfor drawoptions(withcolor 1/2 red); diff --git a/info/drawing-with-metapost/src/func-epi-v-pie.pdf b/info/drawing-with-metapost/src/func-epi-v-pie.pdf Binary files differindex 175bde4577..1f2319e7ab 100644 --- a/info/drawing-with-metapost/src/func-epi-v-pie.pdf +++ b/info/drawing-with-metapost/src/func-epi-v-pie.pdf diff --git a/info/drawing-with-metapost/src/func-exponential.mp b/info/drawing-with-metapost/src/func-exponential.mp index bfea46f174..be627f057f 100644 --- a/info/drawing-with-metapost/src/func-exponential.mp +++ b/info/drawing-with-metapost/src/func-exponential.mp @@ -4,46 +4,39 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); -numeric u; u = 42; - -path xx, yy; -xx = (-3u, 0) -- (5u, 0); -yy = xx rotated 90; - -path ee, ll, nn; -numeric minx, maxx, s; -minx = -3; maxx = 1/256 mlog(4.5); s = 1/4; -ee = (for x = minx step s until maxx - s: + numeric u, minx, s, maxx; + u = 42; minx = -3; s = 1/4; maxx = 1/256 mlog(4.5); + path xx; xx = (-3u, 0) -- (5u, 0); + path yy; yy = xx rotated 90; + path ee, ll, nn; + ee = (for x = minx step s until maxx - s: (x, mexp(256x)){1, mexp(256x)} ... -endfor (maxx, mexp(256 maxx)){1, mexp(256 maxx)}) scaled u; -ll = ee reflectedabout(origin, dir 45); -nn = (for x=1 step s until 4-s: (x, 1/x) ... endfor (4, 1/4)) scaled u; -nn := reverse nn reflectedabout(origin, dir 45) & nn; - -draw unitsquare xscaled mexp(256) scaled u withcolor 7/8; -draw unitsquare yscaled mexp(256) scaled u withcolor 7/8; - -path T[]; -numeric p; p = directiontime dir 45 of ee; -T1 = (precontrol p of ee -- postcontrol p of ee) shifted - point p of ee scaled 1/2 u shifted point p of ee; -T2 = (precontrol p of ll -- postcontrol p of ll) shifted - point p of ll scaled 1/2 u shifted point p of ll; -drawoptions(withpen pencircle scaled 1/4 withcolor 1/2); -draw T1; draw T2; draw interpath(1/2, T1, T2) dashed evenly; -drawoptions(); - -draw nn; label.urt("$1/x$", point 0 of nn); -draw ee withcolor 2/3 blue; label.top("$e^x$", point infinity of ee) withcolor 2/3 blue; -draw ll withcolor 3/4 red; label.top("$\ln(x)$", point infinity of ll) withcolor 3/4 red; -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); - -dotlabel.lft("$e$", (0, mexp(256) * u)); -dotlabel.bot("$e$", (mexp(256) * u, 0)); -dotlabel.ulft("$1$", (0, u)); -dotlabel.lrt("$1$", (u, 0)); - - + endfor (maxx, mexp(256 maxx)){1, mexp(256 maxx)}) scaled u; + ll = ee reflectedabout(origin, dir 45); + nn = (for x=1 step s until 4-s: (x, 1/x) ... endfor (4, 1/4)) scaled u; + nn := reverse nn reflectedabout(origin, dir 45) & nn; + drawoptions(withcolor 7/8); + draw unitsquare xscaled mexp(256) scaled u; + draw unitsquare yscaled mexp(256) scaled u; + drawoptions(withcolor 3/4); + forsuffixes $ = ee, ll: + path T$; T$ = (left--right) scaled 2u rotated 45 + shifted directionpoint dir 45 of $; + draw T$; + endfor + draw interpath(1/2, T.ee, T.ll) dashed evenly; + drawoptions(withcolor 2/3 blue); + draw ee; label.top("$e^x$", point infinity of ee); + drawoptions(withcolor 2/3 red); + draw ll; label.top("$\ln(x)$", point infinity of ll); + drawoptions(); + draw nn; label.urt("$1/x$", point 0 of nn); + drawarrow xx; label.rt("$x$", point 1 of xx); + drawarrow yy; label.top("$y$", point 1 of yy); + dotlabel.lft("$e$", (0, mexp(256) * u)); + dotlabel.bot("$e$", (mexp(256) * u, 0)); + dotlabel.ulft("$1$", (0, u)); + dotlabel.lrt("$1$", (u, 0)); endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/func-exponential.pdf b/info/drawing-with-metapost/src/func-exponential.pdf Binary files differindex eab1af76ed..0a40cec1fe 100644 --- a/info/drawing-with-metapost/src/func-exponential.pdf +++ b/info/drawing-with-metapost/src/func-exponential.pdf diff --git a/info/drawing-with-metapost/src/func-lemniscate.mp b/info/drawing-with-metapost/src/func-lemniscate.mp index cf56cede6b..d22fff62d2 100644 --- a/info/drawing-with-metapost/src/func-lemniscate.mp +++ b/info/drawing-with-metapost/src/func-lemniscate.mp @@ -4,22 +4,20 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); -numeric a, c; c = 100; a = sqrt(2) * c; -vardef f(expr x) = a * cosd(x) / (1 + sind(x) ** 2) enddef; -vardef g(expr x) = f(x) * sind(x) enddef; -numeric mint, maxt, s; mint = 0; s = 30; maxt = 360; -path p; -p = for t = mint step s until maxt - s: + numeric a, c; c = 100; a = sqrt(2) * c; + vardef f(expr x) = a * cosd(x) / (1 + sind(x) ** 2) enddef; + vardef g(expr x) = f(x) * sind(x) enddef; + numeric mint, maxt, s; mint = 0; s = 30; maxt = 360; + path p; p = for t = mint step s until maxt - s: (f(t), g(t)) ... -endfor cycle; -draw p withcolor 3/4 blue; -path xx, yy; -xx = (left -- right) scaled 150; -yy = (down -- up) scaled 55; -drawarrow xx; label.rt("$x$", point 1 of xx); -drawarrow yy; label.top("$y$", point 1 of yy); -dotlabel.bot("$F_1$", c * left); -dotlabel.bot("$F_2$", c * right); + endfor cycle; + draw p withcolor 3/4 blue; + path xx; xx = (left -- right) scaled 150; + path yy; yy = (down -- up) scaled 55; + drawarrow xx; label.rt("$x$", point 1 of xx); + drawarrow yy; label.top("$y$", point 1 of yy); + dotlabel.bot("$F_1$", c * left); + dotlabel.bot("$F_2$", c * right); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/func-linear-graph.mp b/info/drawing-with-metapost/src/func-linear-graph.mp new file mode 100644 index 0000000000..fc71ccf60e --- /dev/null +++ b/info/drawing-with-metapost/src/func-linear-graph.mp @@ -0,0 +1,51 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); % Using \mplibtextextlabel{enable} ... + numeric u, m, m', b, b'; + u = 1.44cm; + b = 3.6u; b' = b + 1/2 u; + m = -1; m' = 3/4 m; + + path xx, yy; + xx = (left -- 5 right) scaled u; + yy = xx rotated 90; + + numeric minx, maxx; path ff, gg; + minx = xpart point 1/16 of xx; + maxx = xpart point 15/16 of xx; + ff = (minx, minx * m + b) -- (maxx, maxx * m + b); + gg = (minx, minx * m' + b') -- (maxx, maxx * m' + b'); + + z0 = point 0.4 of ff; + z1 = point 0.54 of ff; + z1 0 = whatever [point 0 of gg, point 1 of gg]; x1 0 = x0; + z1 1 = whatever [point 0 of gg, point 1 of gg]; x1 1 = x1; + + forsuffixes @=0, 1: + draw (x@, 0) -- z@ -- (0, y@) dashed evenly scaled 3/4; + draw z@ -- z1 @ -- (0, y1 @) dashed withdots scaled 1/2; + label.bot("$x_{" & decimal @ & "}$", (x@, 0)); + label.lft("$y_{" & decimal @ & "}$", (0, y@)); + label.lft("$y'_{" & decimal @ & "}$", (0, y1 @)); + endfor + + draw ff withcolor 2/3 red; + draw gg withcolor 3/4 blue; + drawarrow xx; drawarrow yy; + + label.rt("$x$", point 1 of xx); + label.top("$y$", point 1 of yy); + + dotlabel.urt("$b$", (0, b)); + dotlabel.urt("$b'$", (0, b')); + + draw thelabel("slope: $m=" & decimal m & "$", 7 up) + rotated angle (1, m) shifted point 2/3 of ff; + draw thelabel("slope: $m'=" & decimal m' & "$", 7 up) + rotated angle (1, m') shifted point 2/3 of gg; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/linear-graph.pdf b/info/drawing-with-metapost/src/func-linear-graph.pdf Binary files differindex 5e511e976c..6397849ee3 100644 --- a/info/drawing-with-metapost/src/linear-graph.pdf +++ b/info/drawing-with-metapost/src/func-linear-graph.pdf diff --git a/info/drawing-with-metapost/src/func-maurer-rose.mp b/info/drawing-with-metapost/src/func-maurer-rose.mp index afa0d85467..3ceb59ad41 100644 --- a/info/drawing-with-metapost/src/func-maurer-rose.mp +++ b/info/drawing-with-metapost/src/func-maurer-rose.mp @@ -4,28 +4,22 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); + path r, k; + r = for t = 1 upto 360: cosd 2t * dir t .. endfor cycle; + r := r scaled 150; + k = for t = 1 upto 360: point 29t of r -- endfor cycle; - numeric n; n = 2; - path r; r = (for t=0 upto 360: - cosd(n * t) * dir t ... - endfor cycle) scaled 150; + draw k dashed withdots scaled 1/8 + withpen pencircle scaled 1/4 + withcolor 1/2[blue, white]; - numeric d; d = 29; - path k; k = for t = 0 upto 360: - point d * t mod 360 of r -- - endfor cycle; - - draw k dashed withdots scaled 1/8 - withpen pencircle scaled 1/4 - withcolor 1/2[blue, white]; - draw r withcolor 2/3 red; - - path xx, yy; - xx = (left -- right) scaled 160; - yy = (down -- up) scaled 160; - drawarrow xx; label.rt("$x$", point 1 of xx); - drawarrow yy; label.top("$y$", point 1 of yy); + draw r withcolor 2/3 red; + path xx, yy; % you might nor need the axes... + xx = (left -- right) scaled 160; + yy = (down -- up) scaled 160; + drawarrow xx; label.rt("$x$", point 1 of xx); + drawarrow yy; label.top("$y$", point 1 of yy); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/func-maurer-rose.pdf b/info/drawing-with-metapost/src/func-maurer-rose.pdf Binary files differindex a4a94febe5..9fe81b5440 100644 --- a/info/drawing-with-metapost/src/func-maurer-rose.pdf +++ b/info/drawing-with-metapost/src/func-maurer-rose.pdf diff --git a/info/drawing-with-metapost/src/func-numbered-axes.mp b/info/drawing-with-metapost/src/func-numbered-axes.mp new file mode 100644 index 0000000000..6e1ac43466 --- /dev/null +++ b/info/drawing-with-metapost/src/func-numbered-axes.mp @@ -0,0 +1,25 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\begin{mplibcode} +beginfig(1); +numeric u, v; u = 40; v = 29; path xx, yy; +xx = (3/2 left -- 5 right) scaled u; +yy = (3/2 down -- 4 up) scaled v; +for x=-1, 1, 2, 3, 4: + draw yy shifted (x * u, 0) withcolor 7/8; % grid + draw (down--up) shifted (x * u, 0); % ticks + label(TEX("$" & decimal x & "$"), (x * u, -8)); +endfor +for y=-1, 1, 2, 3: + draw xx shifted (0, y * v) withcolor 7/8; % grid + draw (left--right) shifted (0, y * v); % ticks + label(TEX("$" & decimal y & "$"), (-10, y * v)); +endfor +drawarrow xx; label.rt(TEX("$x$"), point 1 of xx); +drawarrow yy; label.top(TEX("$y$"), point 1 of yy); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/numbered-axes.pdf b/info/drawing-with-metapost/src/func-numbered-axes.pdf Binary files differindex d8e68dab34..cbe7473d9c 100644 --- a/info/drawing-with-metapost/src/numbered-axes.pdf +++ b/info/drawing-with-metapost/src/func-numbered-axes.pdf diff --git a/info/drawing-with-metapost/src/func-parametric.mp b/info/drawing-with-metapost/src/func-parametric.mp index 7d86c3b2ab..6702b94d14 100644 --- a/info/drawing-with-metapost/src/func-parametric.mp +++ b/info/drawing-with-metapost/src/func-parametric.mp @@ -4,20 +4,14 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); -path p; -numeric a, b, j, k; a = 144; b = 89; j = 3; k = 2; -p = for t = 0 upto 360: - (a * cosd(j * t), b * sind(k * t)) ... -endfor cycle; - -draw p withcolor 2/3 red; - path xx, yy; xx = (left -- right) scaled 150; yy = (down -- up) scaled 100; drawarrow xx; label.rt("$x$", point 1 of xx); drawarrow yy; label.top("$y$", point 1 of yy); - +path p; +p = for t = 0 upto 360: (144 cosd(3t), 89 sind(2t)) ... endfor cycle; +draw p withcolor 2/3 red; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/func-parametric.pdf b/info/drawing-with-metapost/src/func-parametric.pdf Binary files differindex 8f7bed75f4..d99f060b73 100644 --- a/info/drawing-with-metapost/src/func-parametric.pdf +++ b/info/drawing-with-metapost/src/func-parametric.pdf diff --git a/info/drawing-with-metapost/src/func-plain-axes.mp b/info/drawing-with-metapost/src/func-plain-axes.mp new file mode 100644 index 0000000000..9e3bc3d5c5 --- /dev/null +++ b/info/drawing-with-metapost/src/func-plain-axes.mp @@ -0,0 +1,14 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); +path xx, yy; +xx = (left -- right) scaled 130; +yy = (down -- up) scaled 80; +drawarrow xx; label.rt(TEX("$x$"), point 1 of xx); +drawarrow yy; label.top(TEX("$y$"), point 1 of yy); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/plain-axes.pdf b/info/drawing-with-metapost/src/func-plain-axes.pdf Binary files differindex fc1a766613..b26770c505 100644 --- a/info/drawing-with-metapost/src/plain-axes.pdf +++ b/info/drawing-with-metapost/src/func-plain-axes.pdf diff --git a/info/drawing-with-metapost/src/func-pulse.mp b/info/drawing-with-metapost/src/func-pulse.mp index ae07cfd570..e5f5fd6073 100644 --- a/info/drawing-with-metapost/src/func-pulse.mp +++ b/info/drawing-with-metapost/src/func-pulse.mp @@ -3,33 +3,29 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} - +beginfig(1); vardef pulse(expr w, h, d) = -for i=0 upto 4: x[i] = w/4 * i; endfor - y0 = y1 = 0; - y3 = y4 = d; - y2 = h; - z0 .. 1/2[z0, z1] .. controls z1 - .. 1/2[z1, z2] .. controls z2 - .. 1/2[z2, z3] .. controls z3 - .. 1/2[z3, z4] .. z4 + clearxy; % protect (x,y) values + x0 = 0; x1 = 1/4w; x2 = 1/2w; x3 = 3/4w; x4 = w; + y0 = 0; y1 = 0; y2 = h; y3 = d; y4 = d; + z0 .. 1/2[z0, z1] .. controls z1 + .. 1/2[z1, z2] .. controls z2 + .. 1/2[z2, z3] .. controls z3 + .. 1/2[z3, z4] .. z4 enddef; +path p; p = pulse(300, 100, -40); draw p withcolor 1/2 blue; -beginfig(1); - path p; p = pulse(300, 100, -40); - - draw point 0 of p -- postcontrol 1 of p -- postcontrol 2 of p -- postcontrol 3 of p -- point 5 of p - dashed withdots scaled 1/2 withcolor 2/3 red; - for i=1 upto 3: draw postcontrol i of p withpen pencircle scaled 2 withcolor 2/3 red; endfor - label.lrt("$z_1$", postcontrol 1 of p) withcolor 2/3 red; - label.top("$z_2$", postcontrol 2 of p) withcolor 2/3 red; - label.llft("$z_3$", postcontrol 3 of p) withcolor 2/3 red; - - draw p withcolor 1/2 blue; - draw p shifted 120 up withcolor 1/2 blue; - for i=0 upto length p: draw point i of p withpen pencircle scaled 2; endfor +picture pcon; pcon = image( + draw point 0 of p -- postcontrol 1 of p -- postcontrol 2 of p -- postcontrol 3 of p -- point 5 of p + dashed withdots scaled 1/2 withcolor 2/3 red; + for i=1 upto 3: draw postcontrol i of p withpen pencircle scaled 2 withcolor 2/3 red; endfor + label.lrt("$z_1$", postcontrol 1 of p) withcolor 2/3 red; + label.top("$z_2$", postcontrol 2 of p) withcolor 2/3 red; + label.llft("$z_3$", postcontrol 3 of p) withcolor 2/3 red; + draw p withcolor 1/2 blue; + for i=0 upto length p: draw point i of p withpen pencircle scaled 2; endfor +); draw pcon shifted 120 down; endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/func-pulse.pdf b/info/drawing-with-metapost/src/func-pulse.pdf Binary files differindex 6b60a628bd..a458c56e47 100644 --- a/info/drawing-with-metapost/src/func-pulse.pdf +++ b/info/drawing-with-metapost/src/func-pulse.pdf diff --git a/info/drawing-with-metapost/src/func-reflection.mp b/info/drawing-with-metapost/src/func-reflection.mp index a9bbf7f85e..20bd808f6a 100644 --- a/info/drawing-with-metapost/src/func-reflection.mp +++ b/info/drawing-with-metapost/src/func-reflection.mp @@ -7,20 +7,22 @@ beginfig(1); path xx, yy; xx = (left -- right) scaled 150; yy = (down -- up) scaled 150; +for i=-6 upto 6: + draw xx shifted (0, 24i) withpen pencircle scaled 1/4 withcolor 7/8; + draw yy shifted (24i, 0) withpen pencircle scaled 1/4 withcolor 7/8; +endfor path ff, negative_ff; + ff = (1,1) for x = 3/2 step 1/2 until 6: ... (x, 1/x) endfor; ff := reverse ff reflectedabout(origin, dir 45) & ff; ff := ff scaled 24; negative_ff = ff reflectedabout(origin, dir -45); -for i=-6 upto 6: - draw xx shifted (0, 24i) withpen pencircle scaled 1/4 withcolor 7/8; - draw yy shifted (24i, 0) withpen pencircle scaled 1/4 withcolor 7/8; -endfor +draw ff withcolor 2/3 red; +draw negative_ff withcolor 2/3 red; forsuffixes @ = ff, negative_ff: - draw @ withcolor 2/3 red; for i=0 upto length @: draw point i of @ withpen pencircle scaled 1; endfor diff --git a/info/drawing-with-metapost/src/func-sines.mp b/info/drawing-with-metapost/src/func-sines.mp index 2a854ede62..a1b2896fb4 100644 --- a/info/drawing-with-metapost/src/func-sines.mp +++ b/info/drawing-with-metapost/src/func-sines.mp @@ -4,54 +4,49 @@ \mplibtextextlabel{enable} \begin{mplibcode} vardef pi_quarters(expr n) = - save s, f, q; string s, f; numeric q; - s = if n < 0: "-" else: "" fi; q = abs(n); - if q mod 4 = 0: - f = if q > 4: decimal 1/4 q else: "" fi; - elseif q mod 2 = 0: - f = "\frac{" & decimal 1/2 q & "}{2}"; - else: - f = "\frac{" & decimal q & "}{4}"; - fi - "$\scriptstyle" & s & f & "\pi$" + save s, f, q; string s, f; numeric q; + s = if n < 0: "-" else: "" fi; q = abs(n); + if q mod 4 = 0: f = if q > 4: decimal 1/4 q else: "" fi; + elseif q mod 2 = 0: f = "\frac{" & decimal 1/2 q & "}{2}"; + else: f = "\frac{" & decimal q & "}{4}"; + fi TEX("$\scriptstyle" & s & f & "\pi$") enddef; beginfig(1); - numeric u, pi; u = 50; pi = 3.141592653589793; - - path xx, yy; - xx = (3.5 left -- 3.6 right) scaled u; - yy = (1.1 down -- 1.2 up) scaled u; - - path ss; - ss = origin for t=1 upto 360: -- (t, sind(t)) endfor; - ss := ss shifted 360 left & ss; - ss := ss xscaled (pi/180) scaled u; - - drawoptions(dashed withdots scaled 1/4); - draw ((1/4 pi, 0) .. (1/4 pi, sind(45))) scaled u; - draw ((1/2 pi, 0) .. (1/2 pi, sind(90))) scaled u; - draw ((3/4 pi, 0) .. (3/4 pi, sind(135))) scaled u; - drawoptions(); - - draw ss cutbefore yy shifted point 0 of xx - cutafter yy shifted point 1 of xx - withcolor 3/4 blue; - draw ss shifted (-1/2 pi * u ,0) - cutbefore yy shifted point 0 of xx - cutafter yy shifted point 1 of xx - withcolor 2/3 red; - - drawarrow xx; label.rt("$t$", point 1 of xx); - drawarrow yy; label.top("$u(t)$", point 1 of yy); - - for i=-4, -3, -2, -1, 1, 2, 3, 4: - draw (down--up) scaled 2 shifted (pi * i/4 * u, 0); - label.bot(pi_quarters(i), (pi * i/4 * u, -2)); - endfor - - + numeric u, pi; u = 50; pi = 3.141592653589793; + + path xx, yy; + xx = (3.5 left -- 3.6 right) scaled u; + yy = (1.1 down -- 1.2 up) scaled u; + + path ss; + ss = origin for t=1 upto 360: -- (t, sind(t)) endfor; + ss := ss shifted 360 left & ss; + ss := ss xscaled (pi/180) scaled u; + + drawoptions(dashed withdots scaled 1/4); + draw ((1/4 pi, 0) .. (1/4 pi, sind(45))) scaled u; + draw ((1/2 pi, 0) .. (1/2 pi, sind(90))) scaled u; + draw ((3/4 pi, 0) .. (3/4 pi, sind(135))) scaled u; + drawoptions(); + + draw ss + cutbefore yy shifted point 0 of xx + cutafter yy shifted point 1 of xx + withcolor 3/4 blue; + + draw ss shifted (-1/2 pi * u ,0) + cutbefore yy shifted point 0 of xx + cutafter yy shifted point 1 of xx + withcolor 2/3 red; + + drawarrow xx; label.rt(TEX("$t$"), point 1 of xx); + drawarrow yy; label.top(TEX("$u(t)$"), point 1 of yy); + + for i=-4, -3, -2, -1, 1, 2, 3, 4: + draw (down--up) scaled 2 shifted (pi * i/4 * u, 0); + label.bot(pi_quarters(i), (pi * i/4 * u, -2)); + endfor endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/func-sines.pdf b/info/drawing-with-metapost/src/func-sines.pdf Binary files differindex cce783b5bd..c9d33e9be9 100644 --- a/info/drawing-with-metapost/src/func-sines.pdf +++ b/info/drawing-with-metapost/src/func-sines.pdf diff --git a/info/drawing-with-metapost/src/func-stress.mp b/info/drawing-with-metapost/src/func-stress.mp index a22b39a783..aeeee43a56 100644 --- a/info/drawing-with-metapost/src/func-stress.mp +++ b/info/drawing-with-metapost/src/func-stress.mp @@ -4,40 +4,39 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - z1 = 377 right; z2 = 233 up; - - path ff; - ff = origin .. (72, 144){1,2} .. (84, 144) .. (96, 144){1,1} .. (220, 220){right} .. (370, 160){2,-1.3}; - - for t=2, 4, 4.9: - draw point t of ff -- (xpart point t of ff, y2 + 6) dashed evenly scaled 1/2; - endfor - label.top("Strain hardening", (1/2 (xpart point 2 of ff + xpart point 4 of ff), y2)); - label.top("Necking", (1/2 (xpart point 4 of ff + xpart point 4.9 of ff), y2)); - - path rr; - rr = point 0.4 of ff -- (xpart point 0.8 of ff, ypart point 0.4 of ff) -- point 0.8 of ff; - draw rr; label.bot("Run", point 1/2 of rr); label.rt("Rise", point 3/2 of rr); - - vardef pin_label@#(expr p, a, b)= - draw a -- b cutbefore fullcircle scaled 8 shifted a withpen pencircle scaled 1/4 withcolor 1/2 white; - label@#(p, b); - enddef; - - pin_label.lrt("Yield strength", point 1.2 of ff, point 2 of ff + (8, -18)); - pin_label.bot("Ultimate strength", point 4 of ff, point 4 of ff + (4, -24)); - pin_label.bot("Fracture", point 5 of ff, point 5 of ff + (-8, -18)); - - draw ff withpen pencircle scaled 1 withcolor 2/3 blue; - clip currentpicture to unitsquare scaled 400; % clip thick pen at origin - - drawdblarrow z1 -- origin -- z2; - label.ulft("Strain, $\epsilon$", z1); - label.urt("Stress, $\sigma$", z2); - - label("$\displaystyle\hbox{Young's modulus} = \hbox{Slope} = {\hbox{Rise}\over\hbox{Run}}$", - 1/2 z1 shifted 36 up) withcolor 2/3 blue; - + z1 = 377 right; z2 = 233 up; + path ff; ff = origin .. (72, 144){1,2} .. (84, 144) .. + (96, 144){1,1} .. (220, 220){right} .. (370, 160){2,-1.3}; + + for t=2, 4, 4.9: + draw point t of ff -- (xpart point t of ff, y2 + 6) d + ashed evenly scaled 1/2; + endfor + label.top("Strain hardening", + (1/2 (xpart point 2 of ff + xpart point 4 of ff), y2)); + label.top("Necking", + (1/2 (xpart point 4 of ff + xpart point 4.9 of ff), y2)); + + path rr; + rr = point 0.4 of ff -- (xpart point 0.8 of ff, ypart point 0.4 of ff) -- point 0.8 of ff; + draw rr; label.bot("Run", point 1/2 of rr); label.rt("Rise", point 3/2 of rr); + + vardef pin_label@#(expr p, a, b)= + draw a -- b cutbefore fullcircle scaled 8 shifted a withpen pencircle scaled 1/4 withcolor 1/2 white; + label@#(p, b); + enddef; + pin_label.lrt("Yield strength", point 1.2 of ff, point 2 of ff + (8, -18)); + pin_label.bot("Ultimate strength", point 4 of ff, point 4 of ff + (4, -24)); + pin_label.bot("Fracture", point 5 of ff, point 5 of ff + (-8, -18)); + + draw ff withpen pencircle scaled 1 withcolor 2/3 blue; + clip currentpicture to unitsquare scaled 400; % clip thick pen at origin + + drawdblarrow z1 -- origin -- z2; + label.ulft("Strain, $\epsilon$", z1); + label.urt("Stress, $\sigma$", z2); + + label("$\displaystyle\hbox{Young's modulus} = \hbox{Slope} = {\hbox{Rise}\over\hbox{Run}}$", 1/2 z1 shifted 36 up) withcolor 2/3 blue; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/apollonius.mp b/info/drawing-with-metapost/src/geometry-apollonius.mp index 91ed22b600..94fb28dcb7 100644 --- a/info/drawing-with-metapost/src/apollonius.mp +++ b/info/drawing-with-metapost/src/geometry-apollonius.mp @@ -15,8 +15,6 @@ vardef radical_axis(expr ca, cb) = shifted t[center ca, center cb] enddef; -input tangent-times - vardef invert_point(expr P, o, r) = save p, d; pair p; numeric d; p = P - o; d = abs p; diff --git a/info/drawing-with-metapost/src/apollonius.pdf b/info/drawing-with-metapost/src/geometry-apollonius.pdf Binary files differindex 7de0b11b20..bfcfa7621a 100644 --- a/info/drawing-with-metapost/src/apollonius.pdf +++ b/info/drawing-with-metapost/src/geometry-apollonius.pdf diff --git a/info/drawing-with-metapost/src/geometry-arbelos.mp b/info/drawing-with-metapost/src/geometry-arbelos.mp new file mode 100644 index 0000000000..8c2b67b4a8 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-arbelos.mp @@ -0,0 +1,54 @@ +\RequirePackage{luatex85} +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef invert(expr P, C) = % invert path P or pair P in circle C + save I, r, s, T; pair I; I = center C; r = abs(point 0 of C-I); + if pair P: s = abs(P-I); I if s > eps: + (P-I) / s * r / s * r fi + elseif path P: T = length P; for t=0 upto T-1: + invert(point t of P, C) .. endfor + if cycle P: cycle else: invert(point T of P, C) fi + fi +enddef; +beginfig(1); + pair A,B,C; A = origin; C = 254 right; B = 7/8[A, C]; + path c[]; + c1 = fullcircle scaled 2 abs(A-C); % large circle for the inversions + c2 = fullcircle scaled abs(A-C) shifted 1/2[A,C]; + c3 = fullcircle scaled abs(A-B) shifted 1/2[A,B]; + c4 = fullcircle scaled abs(B-C) shifted 1/2[B,C]; + c5 = invert(c4,c1); + + drawoptions(withcolor 3/4 white); + draw c4; draw c5; + draw invert(subpath(-3/8, 3/2) of c2, c1); % vertical lines + draw invert(subpath(-3/8, 3/2) of c3, c1); + + drawoptions(withcolor 1/2 red); + draw subpath(-1/4,7/8) of c1 withpen pencircle scaled 1/4; + label.lft("\textit{circle of inversion}", point 7/8 of c1); + + numeric d; d = abs(point 0 of c5 - point 4 of c5); % diameter of c5 + for i=1 upto 48: + path c, c'; c = c5 shifted (0, i*d); c' = invert(c, c1); + draw c' withpen pencircle scaled 1/4 withcolor 2/3 blue; + if i<5: + drawoptions(withcolor 3/4 white); + draw c; draw origin -- center c; + draw center c withpen pencircle scaled dotlabeldiam; + draw center c' withpen pencircle scaled dotlabeldiam; + drawoptions(); + fi + endfor + + drawoptions(withcolor 2/3 blue); + draw A--C; + draw subpath (0,4) of c2 withpen pencircle scaled 1/4; + draw subpath (0,4) of c3 withpen pencircle scaled 1/4; + draw subpath (0,4) of c4 withpen pencircle scaled 1/4; + dotlabel.lft("$A$", A); dotlabel.llft("$B$", B); dotlabel.rt("$C$", C); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/geometry-arbelos.pdf b/info/drawing-with-metapost/src/geometry-arbelos.pdf Binary files differnew file mode 100644 index 0000000000..2852f1a1ef --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-arbelos.pdf diff --git a/info/drawing-with-metapost/src/axis-of-similitude.mp b/info/drawing-with-metapost/src/geometry-axis-of-similitude.mp index 94ad49f695..94ad49f695 100644 --- a/info/drawing-with-metapost/src/axis-of-similitude.mp +++ b/info/drawing-with-metapost/src/geometry-axis-of-similitude.mp diff --git a/info/drawing-with-metapost/src/axis-of-similitude.pdf b/info/drawing-with-metapost/src/geometry-axis-of-similitude.pdf Binary files differindex 422e03717c..422e03717c 100644 --- a/info/drawing-with-metapost/src/axis-of-similitude.pdf +++ b/info/drawing-with-metapost/src/geometry-axis-of-similitude.pdf diff --git a/info/drawing-with-metapost/src/bisection-euclidean.mp b/info/drawing-with-metapost/src/geometry-bisection-euclidean.mp index 742d762011..7e63bde25b 100644 --- a/info/drawing-with-metapost/src/bisection-euclidean.mp +++ b/info/drawing-with-metapost/src/geometry-bisection-euclidean.mp @@ -17,7 +17,7 @@ enddef; \end{code} \cr\kern 64pt \begin{mplibcode} -input bisection +input geometry-bisection beginfig(1); z0 = euclidean_bisector(A,B,C,100); draw B -- 1.2[B,z0] withcolor .67 red; diff --git a/info/drawing-with-metapost/src/bisection-euclidean.pdf b/info/drawing-with-metapost/src/geometry-bisection-euclidean.pdf Binary files differindex c5d2971ec7..c5d2971ec7 100644 --- a/info/drawing-with-metapost/src/bisection-euclidean.pdf +++ b/info/drawing-with-metapost/src/geometry-bisection-euclidean.pdf diff --git a/info/drawing-with-metapost/src/bisection-interior.mp b/info/drawing-with-metapost/src/geometry-bisection-interior.mp index c39c6fd5a9..c39c6fd5a9 100644 --- a/info/drawing-with-metapost/src/bisection-interior.mp +++ b/info/drawing-with-metapost/src/geometry-bisection-interior.mp diff --git a/info/drawing-with-metapost/src/bisection-interior.pdf b/info/drawing-with-metapost/src/geometry-bisection-interior.pdf Binary files differindex f58a457e9f..f58a457e9f 100644 --- a/info/drawing-with-metapost/src/bisection-interior.pdf +++ b/info/drawing-with-metapost/src/geometry-bisection-interior.pdf diff --git a/info/drawing-with-metapost/src/bisection-vector.mp b/info/drawing-with-metapost/src/geometry-bisection-vector.mp index 55a8166df9..2ec8f8017c 100644 --- a/info/drawing-with-metapost/src/bisection-vector.mp +++ b/info/drawing-with-metapost/src/geometry-bisection-vector.mp @@ -4,15 +4,10 @@ \mplibtextextlabel{enable} \begin{document} \vbox{\openup 1pt \halign to 4in{#\cr -\begin{code} -vardef vector_bisector(expr a,b,c,r) = - b + unitvector (a-b) scaled r - + unitvector (c-b) scaled r -enddef; -\end{code} +\mpexternal[firstline=21,lastline=24]{geometry-bisection.mp} \cr\kern 64pt \begin{mplibcode} -input bisection +input geometry-bisection beginfig(1); z0 = vector_bisector(A,B,C,50); drawarrow B--A cutafter fullcircle scaled 5 shifted A; diff --git a/info/drawing-with-metapost/src/bisection-vector.pdf b/info/drawing-with-metapost/src/geometry-bisection-vector.pdf Binary files differindex a3afc5aee0..72e3d95268 100644 --- a/info/drawing-with-metapost/src/bisection-vector.pdf +++ b/info/drawing-with-metapost/src/geometry-bisection-vector.pdf diff --git a/info/drawing-with-metapost/src/bisection.mp b/info/drawing-with-metapost/src/geometry-bisection.mp index 895fdefb20..895fdefb20 100644 --- a/info/drawing-with-metapost/src/bisection.mp +++ b/info/drawing-with-metapost/src/geometry-bisection.mp diff --git a/info/drawing-with-metapost/src/geometry-circumcircle.mp b/info/drawing-with-metapost/src/geometry-circumcircle.mp new file mode 100644 index 0000000000..ae266aa656 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-circumcircle.mp @@ -0,0 +1,59 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef through(expr a, b, o) = + save t; numeric t; t = 1+o/abs(a-b); + t[b,a] -- t[a,b] +enddef; + +vardef circumcircle(expr T) = + save m; pair m; + m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T + = whatever * (point 1 of T - point 2 of T) rotated 90 shifted point 3/2 of T; + fullcircle scaled 2 abs (point 0 of T - m) shifted m +enddef; + +beginfig(1); + path T; T = origin -- 377 dir 10 -- 233 dir 70 -- cycle; + pair m; + m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T + = whatever * (point 2 of T - point 3 of T) rotated 90 shifted point 5/2 of T; + + drawoptions(withcolor 3/4); + draw unitsquare scaled 5 rotated angle (point 1 of T-point 0 of T) shifted point 1/2 of T; + draw unitsquare scaled 5 rotated angle (point 2 of T-point 1 of T) shifted point 3/2 of T; + draw unitsquare scaled 5 rotated angle (point 0 of T-point 2 of T) shifted point 5/2 of T; + drawoptions(dashed evenly scaled 1/4 withcolor 1/2); + draw through(point 1/2 of T, m, 10); + draw through(point 3/2 of T, m, 10); + draw through(point 5/2 of T, m, 10); + drawoptions(); + draw circumcircle(T) withcolor 2/3 red; + draw T; + + draw m withpen pencircle scaled dotlabeldiam; label("$m$", m + 10 dir 12); + + vardef mark_equal(expr a, b, n) = + save m, s; picture m; m = image( + numeric s; 2s = n - 1; for t=-s upto s: + draw (down--up) scaled 2 rotated -13 shifted (t,0) + withpen pencircle scaled 1/4; + endfor + ); + draw m rotated angle (b-a) shifted 1/4[a,b]; + draw m rotated angle (b-a) shifted 3/4[a,b]; + enddef; + + mark_equal(point 0 of T, point 1 of T, 1); + mark_equal(point 1 of T, point 2 of T, 2); + mark_equal(point 2 of T, point 0 of T, 3); + + numeric wd; wd = xpart (urcorner currentpicture - llcorner currentpicture); + currentpicture := currentpicture scaled (303/wd); + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/circumcircle.pdf b/info/drawing-with-metapost/src/geometry-circumcircle.pdf Binary files differindex a1ce79e196..1969467d9f 100644 --- a/info/drawing-with-metapost/src/circumcircle.pdf +++ b/info/drawing-with-metapost/src/geometry-circumcircle.pdf diff --git a/info/drawing-with-metapost/src/drawing-circles.mp b/info/drawing-with-metapost/src/geometry-drawing-circles.mp index 014541eb18..014541eb18 100644 --- a/info/drawing-with-metapost/src/drawing-circles.mp +++ b/info/drawing-with-metapost/src/geometry-drawing-circles.mp diff --git a/info/drawing-with-metapost/src/drawing-circles.pdf b/info/drawing-with-metapost/src/geometry-drawing-circles.pdf Binary files differindex e7e8f22f0a..e7e8f22f0a 100644 --- a/info/drawing-with-metapost/src/drawing-circles.pdf +++ b/info/drawing-with-metapost/src/geometry-drawing-circles.pdf diff --git a/info/drawing-with-metapost/src/geometry-examples-desargues.mp b/info/drawing-with-metapost/src/geometry-examples-desargues.mp new file mode 100644 index 0000000000..34a6249529 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-examples-desargues.mp @@ -0,0 +1,55 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + pair P, A, B, C, A', B', C', R, S, T; + P = 200 dir 102; + A = 100 dir 159; B = origin; C = 90 dir 42; + + A' = 3/8[P, A]; % the factors should not + B' = 1/2[P, B]; % be the same! + C' = 5/8[P, C]; + + R = whatever [A, B] = whatever [A', B']; + S = whatever [B, C] = whatever [B', C']; + T = whatever [C, A] = whatever [C', A']; + + path t[]; + t1 = A -- B -- C -- cycle; + t2 = A' -- B' -- C' -- cycle; + fill t1 withcolor 7/8[red, white]; + fill t2 withcolor 7/8[blue, white]; + draw t1 withcolor 1/2 white; + draw t2 withcolor 1/2 white; + + drawoptions(dashed withdots scaled 1/2); + draw P--A; + draw P--B; + draw P--C; + + drawoptions(dashed evenly scaled 1/2); + draw B--R--B'; + draw C--S--C'; + undraw subpath (1/4, 3/4) of (C'--T) withpen + pencircle scaled 5; + draw C--T--C'; + + drawoptions(withcolor 2/3 red); + draw 9/8[S,R] -- 9/8[R,S]; + draw thelabel.bot("perspectrix", origin) + rotated angle (T-R) shifted 1/2[T, R]; + dotlabel.urt("perspector", P); + drawoptions(); + + dotlabel.lft ("$A$ ", A); + dotlabel.llft("$B$ ", B); + dotlabel.lrt ("$C$ ", C); + dotlabel.lft ("$A'$ ", A'); + dotlabel.llft("$B'$ ", B'); + dotlabel.bot ("$C'$ ", C'); + label.rt("\textsc{Desargues' Theorem}", 1/2[P, C'] shifted 10 right); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/desargues.pdf b/info/drawing-with-metapost/src/geometry-examples-desargues.pdf Binary files differindex bbb38bb28b..b5aba7a97c 100644 --- a/info/drawing-with-metapost/src/desargues.pdf +++ b/info/drawing-with-metapost/src/geometry-examples-desargues.pdf diff --git a/info/drawing-with-metapost/src/geometry-examples-napoleon.mp b/info/drawing-with-metapost/src/geometry-examples-napoleon.mp new file mode 100644 index 0000000000..c9697f1db0 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-examples-napoleon.mp @@ -0,0 +1,40 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +def equilateral_triangle_point(expr a, b) = + a rotatedabout(b, 60) +enddef; +primarydef o beyond z = z scaled (1+o/abs(z)) enddef; +beginfig(1); + randomseed := 543.01811; + + pair A, B, C, D, E, F, G, H, I; + A = 91 dir ( 0 + 18 normaldeviate); + B = 92 dir (120 + 18 normaldeviate); + C = 93 dir (240 + 18 normaldeviate); + + D = equilateral_triangle_point(A, B); + E = equilateral_triangle_point(B, C); + F = equilateral_triangle_point(C, A); + + G = 1/3(A + B + D); + H = 1/3(B + C + E); + I = 1/3(C + A + F); + + draw A -- B -- C -- cycle withcolor blue; + draw A -- D -- B -- E -- C -- F -- cycle withcolor 3/4; + draw G -- H -- I -- cycle withcolor 2/3 red; + + forsuffixes @ = A, B, C, D, E, F, G, H, I: + draw @ withpen pencircle scaled dotlabeldiam; + label("$" & str @ & "$", 10 beyond @); + endfor + + label.bot("\textsc{Napoleon's Theorem}", + point 1/2 of bbox currentpicture); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/geometry-examples-napoleon.pdf b/info/drawing-with-metapost/src/geometry-examples-napoleon.pdf Binary files differnew file mode 100644 index 0000000000..35665758b3 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-examples-napoleon.pdf diff --git a/info/drawing-with-metapost/src/projections-code.mp b/info/drawing-with-metapost/src/geometry-examples-projections.mp index e10619e2b6..781f953e1a 100644 --- a/info/drawing-with-metapost/src/projections-code.mp +++ b/info/drawing-with-metapost/src/geometry-examples-projections.mp @@ -1,3 +1,9 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); % define the end points of the three rays z1 = right scaled 200 rotated 10; z2 = right scaled 100 rotated 135; @@ -29,6 +35,9 @@ drawoptions(); dotlabel.urt(btex $Q$ etex, Q); dotlabel.top(btex $A$ etex, A); dotlabel.lrt(btex $R$ etex, R) withcolor .67 blue; -label.top (btex $B$ etex, B); -label.llft(btex $P$ etex, P); -label.llft(btex $O$ etex, origin); +dotlabel.top (btex $B$ etex, B); +dotlabel.llft(btex $P$ etex, P); +dotlabel.llft(btex $O$ etex, origin); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/projections.pdf b/info/drawing-with-metapost/src/geometry-examples-projections.pdf Binary files differindex 327f5caf95..3dc0599d04 100644 --- a/info/drawing-with-metapost/src/projections.pdf +++ b/info/drawing-with-metapost/src/geometry-examples-projections.pdf diff --git a/info/drawing-with-metapost/src/trisection-triangles.mp b/info/drawing-with-metapost/src/geometry-examples-trisections.mp index 400934e647..400934e647 100644 --- a/info/drawing-with-metapost/src/trisection-triangles.mp +++ b/info/drawing-with-metapost/src/geometry-examples-trisections.mp diff --git a/info/drawing-with-metapost/src/trisection-triangles.pdf b/info/drawing-with-metapost/src/geometry-examples-trisections.pdf Binary files differindex 2bf044ad78..c344f5bcc3 100644 --- a/info/drawing-with-metapost/src/trisection-triangles.pdf +++ b/info/drawing-with-metapost/src/geometry-examples-trisections.pdf diff --git a/info/drawing-with-metapost/src/geometry-excircle.mp b/info/drawing-with-metapost/src/geometry-excircle.mp new file mode 100644 index 0000000000..1f6a324e73 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-excircle.mp @@ -0,0 +1,50 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef through(expr a, b, o) = + save t; numeric t; t = 1+o/abs(a-b); + t[b,a] -- t[a,b] +enddef; + +vardef excircle(expr A, B, C) = + save a, b, m, t; pair a, b, m, t; + a = A + unitvector (C-A) - unitvector (B-A); + b = B + unitvector (A-B) + unitvector (C-B); + m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; + t-m = whatever * (B-A) rotated 90; + fullcircle scaled 2 abs (t-m) shifted m +enddef; + +beginfig(1); + pair A, B, C; + A = origin; B = 233 dir 10; C = 144 dir 70; + pair a, b, m, t; + a = A + 22 unitvector (C-A) - 22 unitvector (B-A); + b = B + 22 unitvector (A-B) + 22 unitvector (C-B); + m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; + t-m = whatever * (B-A) rotated 90; + + drawoptions(dashed evenly scaled 1/4 withcolor 1/2 white); + draw t -- m; + draw unitsquare scaled 5 rotated angle (B-A) shifted t; + draw through(A, m, 10); + draw through(A, t, 10); + draw through(B, m, 10); + drawoptions(); + draw excircle(A, B, C) withcolor 2/3 blue; + draw A--B--C--cycle; + dotlabel.urt(btex $m$ etex, m); + dotlabel.bot(btex $t$ etex, t); + dotlabel.bot(btex $A$ etex, A); + dotlabel.urt(btex $B$ etex, B); + dotlabel.top(btex $C$ etex, C); + dotlabel.urt(btex $a$ etex, a); + dotlabel.top(btex $b$ etex, b); + numeric wd; wd = xpart (urcorner currentpicture - llcorner currentpicture); + currentpicture := currentpicture scaled (333/wd); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/excircle.pdf b/info/drawing-with-metapost/src/geometry-excircle.pdf Binary files differindex 817cd59350..533d3c6b38 100644 --- a/info/drawing-with-metapost/src/excircle.pdf +++ b/info/drawing-with-metapost/src/geometry-excircle.pdf diff --git a/info/drawing-with-metapost/src/geometry-incircle.mp b/info/drawing-with-metapost/src/geometry-incircle.mp new file mode 100644 index 0000000000..119c729fdb --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-incircle.mp @@ -0,0 +1,50 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef through(expr a, b, o) = + save t; numeric t; t = 1+o/abs(a-b); + t[b,a] -- t[a,b] +enddef; + +vardef incircle(expr A, B, C) = + save a, b, m, t; pair a, b, m, t; + a = A + unitvector (C-A) + unitvector (B-A); + b = B + unitvector (A-B) + unitvector (C-B); + m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; + t-m = whatever * (B-A) rotated 90; + fullcircle scaled 2 abs (t-m) shifted m +enddef; + +beginfig(1); + pair A, B, C; + A = origin; B = 377 dir 10; C = 233 dir 70; + pair a, b, m, t; + a = A + 22 unitvector (C-A) + 22 unitvector (B-A); + b = B + 22 unitvector (A-B) + 22 unitvector (C-B); + m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; + t-m = whatever * (B-A) rotated 90; + + drawoptions(dashed evenly scaled 1/4 withcolor 1/2 white); + draw t -- m; + draw unitsquare scaled 5 rotated angle (B-A) shifted t; + draw through(A, m, 10); + draw through(B, m, 10); + drawoptions(); + draw incircle(A, B, C) withcolor 2/3 red; + draw A--B--C--cycle; + dotlabel.top(btex $m$\thinspace\strut etex, m); + dotlabel.bot(btex $t$ etex, t); + dotlabel.bot(btex $A$ etex, A); + dotlabel.urt(btex $B$ etex, B); + dotlabel.top(btex $C$ etex, C); + dotlabel.top(btex $a$ etex, a); + dotlabel.top(btex $b$ etex, b); + + numeric wd; wd = xpart (urcorner currentpicture - llcorner currentpicture); + currentpicture := currentpicture scaled (333/wd); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/incircle.pdf b/info/drawing-with-metapost/src/geometry-incircle.pdf Binary files differindex fe062e227e..6a914e7e5b 100644 --- a/info/drawing-with-metapost/src/incircle.pdf +++ b/info/drawing-with-metapost/src/geometry-incircle.pdf diff --git a/info/drawing-with-metapost/src/intersection-AB-or-BA.mp b/info/drawing-with-metapost/src/geometry-intersection-AB-or-BA.mp index e7f5e902cc..e7f5e902cc 100644 --- a/info/drawing-with-metapost/src/intersection-AB-or-BA.mp +++ b/info/drawing-with-metapost/src/geometry-intersection-AB-or-BA.mp diff --git a/info/drawing-with-metapost/src/intersection-AB-or-BA.pdf b/info/drawing-with-metapost/src/geometry-intersection-AB-or-BA.pdf Binary files differindex 8cf9d43814..8cf9d43814 100644 --- a/info/drawing-with-metapost/src/intersection-AB-or-BA.pdf +++ b/info/drawing-with-metapost/src/geometry-intersection-AB-or-BA.pdf diff --git a/info/drawing-with-metapost/src/intersection-algorithm.mp b/info/drawing-with-metapost/src/geometry-intersection-algorithm.mp index 2915dc737c..2915dc737c 100644 --- a/info/drawing-with-metapost/src/intersection-algorithm.mp +++ b/info/drawing-with-metapost/src/geometry-intersection-algorithm.mp diff --git a/info/drawing-with-metapost/src/intersection-algorithm.pdf 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b/info/drawing-with-metapost/src/geometry-intersection-only-two.mp index 9ed3a02c93..9ed3a02c93 100644 --- a/info/drawing-with-metapost/src/intersection-only-two.mp +++ b/info/drawing-with-metapost/src/geometry-intersection-only-two.mp diff --git a/info/drawing-with-metapost/src/intersection-only-two.pdf b/info/drawing-with-metapost/src/geometry-intersection-only-two.pdf Binary files differindex cb3c6d5570..cb3c6d5570 100644 --- a/info/drawing-with-metapost/src/intersection-only-two.pdf +++ b/info/drawing-with-metapost/src/geometry-intersection-only-two.pdf diff --git a/info/drawing-with-metapost/src/magic-square-14.mp b/info/drawing-with-metapost/src/geometry-magic-square-14.mp index 09be4d36cd..09be4d36cd 100644 --- a/info/drawing-with-metapost/src/magic-square-14.mp +++ b/info/drawing-with-metapost/src/geometry-magic-square-14.mp diff --git a/info/drawing-with-metapost/src/magic-square-14.pdf b/info/drawing-with-metapost/src/geometry-magic-square-14.pdf Binary files differindex a3c04cebae..e98b8b74f0 100644 --- a/info/drawing-with-metapost/src/magic-square-14.pdf +++ b/info/drawing-with-metapost/src/geometry-magic-square-14.pdf diff --git a/info/drawing-with-metapost/src/mediation-pitfall.mp b/info/drawing-with-metapost/src/geometry-mediation-pitfall.mp index 84c3839f64..84c3839f64 100644 --- a/info/drawing-with-metapost/src/mediation-pitfall.mp +++ b/info/drawing-with-metapost/src/geometry-mediation-pitfall.mp diff --git a/info/drawing-with-metapost/src/mediation-pitfall.pdf b/info/drawing-with-metapost/src/geometry-mediation-pitfall.pdf Binary files differindex d56116c5b3..d56116c5b3 100644 --- a/info/drawing-with-metapost/src/mediation-pitfall.pdf +++ b/info/drawing-with-metapost/src/geometry-mediation-pitfall.pdf diff --git a/info/drawing-with-metapost/src/mediation-sallows.mp b/info/drawing-with-metapost/src/geometry-mediation-sallows.mp index 6814522e77..6814522e77 100644 --- a/info/drawing-with-metapost/src/mediation-sallows.mp +++ b/info/drawing-with-metapost/src/geometry-mediation-sallows.mp diff --git a/info/drawing-with-metapost/src/mediation-sallows.pdf b/info/drawing-with-metapost/src/geometry-mediation-sallows.pdf Binary files differindex de8d8d3a74..de8d8d3a74 100644 --- a/info/drawing-with-metapost/src/mediation-sallows.pdf +++ b/info/drawing-with-metapost/src/geometry-mediation-sallows.pdf diff --git a/info/drawing-with-metapost/src/mediation-shapes.mp b/info/drawing-with-metapost/src/geometry-mediation-shapes.mp index 77e2825dfa..77e2825dfa 100644 --- a/info/drawing-with-metapost/src/mediation-shapes.mp +++ b/info/drawing-with-metapost/src/geometry-mediation-shapes.mp diff --git a/info/drawing-with-metapost/src/mediation-shapes.pdf b/info/drawing-with-metapost/src/geometry-mediation-shapes.pdf Binary files differindex 4b40c2506a..4b40c2506a 100644 --- a/info/drawing-with-metapost/src/mediation-shapes.pdf +++ b/info/drawing-with-metapost/src/geometry-mediation-shapes.pdf diff --git a/info/drawing-with-metapost/src/geometry-nine-point-circle.mp b/info/drawing-with-metapost/src/geometry-nine-point-circle.mp new file mode 100644 index 0000000000..12a25f0b98 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-nine-point-circle.mp @@ -0,0 +1,54 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + pair A, B, C, D, N, M, p, q, r; + A = origin; B = 343 dir 10; C = 212 dir 70; + % pedal points (not labelled) + p = whatever[B, C]; A - p = whatever * (B-C) rotated 90; + q = whatever[C, A]; B - q = whatever * (C-A) rotated 90; + r = whatever[A, B]; C - r = whatever * (A-B) rotated 90; + + D = whatever[A, p] = whatever[B, q]; + N = 1/4(A + B + C + D); % remarkably... + M = D rotatedabout(N, 180); % M is also the circumcentre + + path circumcircle, nine_point_circle; + nine_point_circle = fullcircle scaled 2 abs(N - 1/2[A, B]) shifted N; + circumcircle = fullcircle scaled 2 abs(M - A) shifted M; + + draw nine_point_circle withcolor 3/4 red; + draw circumcircle withcolor 1/2[3/4 blue, white]; + + drawoptions(dashed evenly scaled 1/4 withcolor 1/2); + draw 1/2[A,B] -- M -- 1/2[B, C]; + draw 1/2[C,A] -- M -- D; + draw A -- p; + draw B -- q; + draw C -- r; + + % mark the nine points with small circles + drawoptions(withpen pencircle scaled 1/4); + draw fullcircle scaled 2 shifted 1/2[A, B]; + draw fullcircle scaled 2 shifted 1/2[A, C]; + draw fullcircle scaled 2 shifted 1/2[A, D]; + draw fullcircle scaled 2 shifted 1/2[B, C]; + draw fullcircle scaled 2 shifted 1/2[B, D]; + draw fullcircle scaled 2 shifted 1/2[C, D]; + draw fullcircle scaled 2 shifted p; + draw fullcircle scaled 2 shifted q; + draw fullcircle scaled 2 shifted r; + + drawoptions(); + draw A--B--C--cycle; + dotlabel.llft("$A$", A); + dotlabel.rt("$B$", B); + dotlabel.ulft("$C$", C); + dotlabel.urt("\ $D$", D); + dotlabel.llft("$M$", M); + dotlabel.llft("$N$", N); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/nine-point-circle.pdf b/info/drawing-with-metapost/src/geometry-nine-point-circle.pdf Binary files differindex 8436ae129b..9eb9c67f12 100644 --- a/info/drawing-with-metapost/src/nine-point-circle.pdf +++ b/info/drawing-with-metapost/src/geometry-nine-point-circle.pdf diff --git a/info/drawing-with-metapost/src/parallel.mp b/info/drawing-with-metapost/src/geometry-parallel.mp index 802b1b1801..802b1b1801 100644 --- a/info/drawing-with-metapost/src/parallel.mp +++ b/info/drawing-with-metapost/src/geometry-parallel.mp diff --git a/info/drawing-with-metapost/src/parallel.pdf b/info/drawing-with-metapost/src/geometry-parallel.pdf Binary files differindex 0fd68348c0..0fd68348c0 100644 --- a/info/drawing-with-metapost/src/parallel.pdf +++ b/info/drawing-with-metapost/src/geometry-parallel.pdf diff --git a/info/drawing-with-metapost/src/geometry-pole-and-polar.mp b/info/drawing-with-metapost/src/geometry-pole-and-polar.mp new file mode 100644 index 0000000000..f1c43ac19d --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-pole-and-polar.mp @@ -0,0 +1,68 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef invert(expr P, C) = + save o; pair o; o = 1/2[point 0 of C, point 4 of C]; + save r; numeric r; r = abs (point 0 of C - o); + save s; numeric s; s = abs (P - o); + o + (P - o) * r / s * r / s +enddef; +beginfig(1); + path C, L; + numeric r; + r = 89; + C = fullcircle scaled 2r; + L = (up--down) scaled 120 shifted 184 right rotated 38; + pair a, b, o; + a = point 0 of L; b = point 1 of L; o = center C; + + pair P, Q, R, P', m; + P = whatever[a, b]; o - P = whatever * (a - b) rotated 90; + Q = C intersectionpoint halfcircle zscaled (P-o) shifted 1/2[P, o]; + R = C intersectionpoint halfcircle zscaled (o-P) shifted 1/2[P, o]; + P' = whatever[o, P] = whatever [Q, R]; + + draw subpath (-3.5,3.5) of fullcircle zscaled (P'-o) shifted 1/2[o, P'] + dashed withdots scaled 1/4 + withcolor 1/3 blue; + + draw unitsquare scaled 5 rotated (270 + angle (P-Q)) shifted Q withcolor 3/4 white; + draw unitsquare scaled 5 rotated (90 + angle (P-o)) shifted P withcolor 3/4 white; + draw unitsquare scaled 5 rotated (90 + angle (P-o)) shifted P' withcolor 3/4 white; + + draw P -- Q -- o -- R -- cycle withcolor 1/2 white; + draw Q--R; draw o -- P; + draw L withcolor 2/3 blue; + + draw C dashed evenly scaled 1/2 withcolor 1/2[2/3 blue, white]; + + dotlabel.top("$Q$", Q); + dotlabel.lrt("$R$", R); + dotlabel.urt("$P$", P); + dotlabel.llft("$O$", o); fill fullcircle scaled 3/4 dotlabeldiam shifted o withcolor white; + label.lft("$r$", 1/2[o, Q]); + + drawdot P' withpen pencircle scaled dotlabeldiam; + label("$P'$", P' shifted 10 dir 68) withcolor 2/3 blue; + + drawoptions(withcolor 2/3 blue); + label.bot("\textit{circle of inversion}", point 6 of C); + label.top(TEX("\textit{polar}") rotated angle direction 0 of L, point 1/4 of L); + z0 = P' + 20 dir -20; draw z0 -- P' cutafter fullcircle scaled 8 shifted P' + withpen pencircle scaled 1/4; + label.rt("\textit{pole}", z0); + drawoptions(withpen pencircle scaled 2 withcolor 2/3 blue); + for i = 1/8, 1/4, 3/8, 5/8, 3/4, 7/8: + draw point i of L; + draw invert(point i of L, C); + endfor + drawoptions(); + + label("$\displaystyle {r\over OP} = {OP' \over r}$", 1/2[point 0 of C, point 1 of L] + 12 down); + label("$\displaystyle r^2 = OP \times OP'$", 1/2[point 0 of C, point 1 of L] + 36 down); + +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pole-and-polar.pdf b/info/drawing-with-metapost/src/geometry-pole-and-polar.pdf Binary files differindex 5bb43987cc..70c6fd5e02 100644 --- a/info/drawing-with-metapost/src/pole-and-polar.pdf +++ b/info/drawing-with-metapost/src/geometry-pole-and-polar.pdf diff --git a/info/drawing-with-metapost/src/geometry-radical-axis.mp b/info/drawing-with-metapost/src/geometry-radical-axis.mp new file mode 100644 index 0000000000..82ae651e3e --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-radical-axis.mp @@ -0,0 +1,53 @@ +\documentclass[border=1mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef radical_axis(expr ca, cb) = + numeric t, d, ra, rb; + ra = abs(center ca - point 0 of ca); + rb = abs(center cb - point 0 of cb); + d = abs(center cb - center ca); + 2t = 1 + (ra+rb) / d * (ra-rb) / d; + (up -- down) scaled 89 + rotated angle (center cb - center ca) + shifted t[center ca, center cb] +enddef; +beginfig(1); + z1 = origin; z2 = 233 dir 4; z3 = 209 dir -42; + path c[], a[]; + c1 = fullcircle scaled 202 shifted z1; + c2 = fullcircle scaled 106 shifted z2; + c3 = fullcircle scaled 62 shifted z3; + a1 = radical_axis(c1, c2); + a2 = radical_axis(c2, c3); + a3 = radical_axis(c3, c1); + + pair radix, t; path orthogonal_circle; + radix = whatever[point 0 of a1, point 1 of a1] + = whatever[point 0 of a2, point 1 of a2]; + t = c1 intersectionpoint + halfcircle zscaled (radix-z1) shifted 1/2[radix, z1]; + orthogonal_circle = fullcircle + scaled 2 abs (t - radix) shifted radix; + + draw z1 -- z2 -- z3 -- cycle withpen pencircle scaled 1/4; + draw a1; draw a2; draw a3; + drawoptions(withcolor 3/4[blue, white]); + draw c1; draw c2; draw c3; + draw z1 -- t dashed evenly; + drawoptions(withcolor 2/3 red); + draw orthogonal_circle; + draw radix -- t dashed evenly; + draw radix withpen pencircle scaled dotlabeldiam; + drawoptions(withcolor 1/4[blue, white]); + draw z1 withpen pencircle scaled dotlabeldiam; + draw z2 withpen pencircle scaled dotlabeldiam; + draw z3 withpen pencircle scaled dotlabeldiam; + + label.urt(btex $C_1$ etex, point 1 of c1); + label.urt(btex $C_2$ etex, point 1 of c2); + label.rt (btex $C_3$ etex, point 0 of c3); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/radical-axis.pdf b/info/drawing-with-metapost/src/geometry-radical-axis.pdf Binary files differindex fc643c1d71..849f5c8375 100644 --- a/info/drawing-with-metapost/src/radical-axis.pdf +++ b/info/drawing-with-metapost/src/geometry-radical-axis.pdf diff --git a/info/drawing-with-metapost/src/tangent-times-on-circle.mp b/info/drawing-with-metapost/src/geometry-tangent-times-on-circle.mp index b59986110c..65eefc8a4e 100644 --- a/info/drawing-with-metapost/src/tangent-times-on-circle.mp +++ b/info/drawing-with-metapost/src/geometry-tangent-times-on-circle.mp @@ -3,7 +3,7 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -input tangent-times +input geometry-tangent-times beginfig(1); path C; pair p; numeric a, b; diff --git a/info/drawing-with-metapost/src/tangent-times-on-circle.pdf b/info/drawing-with-metapost/src/geometry-tangent-times-on-circle.pdf Binary files differindex 074d756042..33ec3df639 100644 --- a/info/drawing-with-metapost/src/tangent-times-on-circle.pdf +++ b/info/drawing-with-metapost/src/geometry-tangent-times-on-circle.pdf diff --git a/info/drawing-with-metapost/src/geometry-tangent-times.mp b/info/drawing-with-metapost/src/geometry-tangent-times.mp new file mode 100644 index 0000000000..bcf12d3e5d --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-tangent-times.mp @@ -0,0 +1,12 @@ +% return a <pair> with the two times on C that +% correspond to the external tangents from p to C +vardef tangent_times(expr C, p) = + save m, o, G, H, a, b; + pair m, o; path G, H; numeric a, b; + o = center C; m = 1/2[o, p]; + H = halfcircle zscaled (p-o) shifted m; + G = halfcircle zscaled (o-p) shifted m; + (a, whatever) = C intersectiontimes H; + (b, whatever) = C intersectiontimes G; + (a, b if b < a: + 8 fi) +enddef; diff --git a/info/drawing-with-metapost/src/tangents-on-path.mp b/info/drawing-with-metapost/src/geometry-tangents-on-path.mp index c93dc1d1d6..01c55cffe3 100644 --- a/info/drawing-with-metapost/src/tangents-on-path.mp +++ b/info/drawing-with-metapost/src/geometry-tangents-on-path.mp @@ -37,8 +37,9 @@ P2 = image( P3 = image( draw p withcolor 0.54 red; drawoptions(withcolor 1/2); + pair s; for t=0 step 1/4 until length p: - pair s; s = 16 unitvector(direction t of p); + s := 16 unitvector(direction t of p); drawarrow (-s -- s) shifted point t of p; draw point t of p withpen pencircle scaled 2; endfor diff --git a/info/drawing-with-metapost/src/tangents-on-path.pdf b/info/drawing-with-metapost/src/geometry-tangents-on-path.pdf Binary files differindex 6fdd9064a2..af18bcd238 100644 --- a/info/drawing-with-metapost/src/tangents-on-path.pdf +++ b/info/drawing-with-metapost/src/geometry-tangents-on-path.pdf diff --git a/info/drawing-with-metapost/src/tangents-point-to-circle.mp b/info/drawing-with-metapost/src/geometry-tangents-point-to-circle.mp index 500e009160..718ba17c2f 100644 --- a/info/drawing-with-metapost/src/tangents-point-to-circle.mp +++ b/info/drawing-with-metapost/src/geometry-tangents-point-to-circle.mp @@ -4,30 +4,28 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); -path C, C'; pair p, t, t'; +path C; pair p; C = fullcircle scaled 100; p = 189 right rotated 30; -C' = fullcircle zscaled p shifted 1/2 p; -% t = C intersectionpoint C'; -% t' = reverse C intersectionpoint C'; -t = C intersectionpoint halfcircle zscaled p shifted 1/2 p; -t' = C intersectionpoint halfcircle zscaled -p shifted 1/2 p; +pair o, m, t, t'; o = center C; m = 1/2[o, p]; +t = C intersectionpoint halfcircle zscaled (p-o) shifted m; +t' = C intersectionpoint halfcircle zscaled (o-p) shifted m; drawoptions(dashed withdots scaled 1/4 withcolor (.2, .2, .7)); -draw C'; draw t -- center C -- p; + draw fullcircle zscaled p shifted 1/2 p; + draw t -- center C -- p; drawoptions(withcolor (.2, .2, .7)); -dotlabel.lrt("$m$", 1/2 p); -dotlabel.llft("$o$", center C); + dotlabel.lrt("$m$", 1/2 p); + dotlabel.llft("$o$", center C); drawoptions(dashed evenly); -draw t -- p -- t'; + draw t -- p -- t'; drawoptions(); -draw C; -label.llft("$C$", point 5 of C); +draw C; label.llft("$C$", point 5 of C); dotlabel.urt("$p$", p); dotlabel.ulft("$t$", t); dotlabel.bot("\strut $t'$", t'); diff --git a/info/drawing-with-metapost/src/tangents-point-to-circle.pdf b/info/drawing-with-metapost/src/geometry-tangents-point-to-circle.pdf Binary files differindex 6991303955..f80a7b7b7d 100644 --- a/info/drawing-with-metapost/src/tangents-point-to-circle.pdf +++ b/info/drawing-with-metapost/src/geometry-tangents-point-to-circle.pdf diff --git a/info/drawing-with-metapost/src/tangents-two-circles-exterior.mp b/info/drawing-with-metapost/src/geometry-tangents-two-circles-exterior.mp index 504fdf19e0..6e718beba4 100644 --- a/info/drawing-with-metapost/src/tangents-two-circles-exterior.mp +++ b/info/drawing-with-metapost/src/geometry-tangents-two-circles-exterior.mp @@ -3,7 +3,7 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -input tangent-times +input geometry-tangent-times color tb; tb = (0.2, 0.2, 0.7); beginfig(1); path A, B; @@ -20,11 +20,12 @@ C = fullcircle scaled (2R-2r) shifted center A; draw A withpen pencircle scaled 2 withcolor 3/4[blue, white]; draw B withpen pencircle scaled 2 withcolor 3/4[blue, white]; -draw C withpen pencircle scaled 1 withcolor 7/8[blue, white]; -draw subpath (t, u) of C -- center B -- cycle dashed evenly withcolor 1/2; draw subpath (t, u) of A -- subpath (u-8, t) of B -- cycle; +draw C withpen pencircle scaled 1 withcolor 7/8[blue, white]; +draw subpath (t, u) of C -- center B -- cycle dashed evenly withcolor 1/2; + drawoptions(dashed withdots scaled 1/2 withcolor 1/4); forsuffixes $=t, u: draw point $ of C -- point $ of A; @@ -39,11 +40,11 @@ drawdot center B withpen pencircle scaled dotlabeldiam; drawoptions(); dotlabel.lrt("$t$", point t of C); -dotlabel.ulft("$t'$", point t of A); -dotlabel.ulft("$t''$", point t of B); +dotlabel.ulft("$t$", point t of A); +dotlabel.ulft("$t$", point t of B); dotlabel.ulft("$u$", point u of C); -dotlabel.lrt("$u'$", point u of A); -dotlabel.lrt("$u''$", point u of B); +dotlabel.lrt("$u$", point u of A); +dotlabel.lrt("$u$", point u of B); label.rt("$r$", 1/2[center B, point t of B]); label.rt("$r$", 1/2[point t of C, point t of A]); diff --git a/info/drawing-with-metapost/src/geometry-tangents-two-circles-exterior.pdf b/info/drawing-with-metapost/src/geometry-tangents-two-circles-exterior.pdf Binary files differnew file mode 100644 index 0000000000..5d0be6748d --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-tangents-two-circles-exterior.pdf diff --git a/info/drawing-with-metapost/src/tangents-two-circles-interior.mp b/info/drawing-with-metapost/src/geometry-tangents-two-circles-interior.mp index afa46790e6..68383929c7 100644 --- a/info/drawing-with-metapost/src/tangents-two-circles-interior.mp +++ b/info/drawing-with-metapost/src/geometry-tangents-two-circles-interior.mp @@ -3,13 +3,13 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -input tangent-times +input geometry-tangent-times vardef adjust_time(expr tt, AA, BB) = - tt + 1/45 angle (point 0 of AA - center AA) - - 1/45 angle (point 0 of BB - center BB) + tt + 1/45 angle (point 0 of AA - center AA) + - 1/45 angle (point 0 of BB - center BB) enddef; beginfig(1); -path A, B; +path A, B; % randomly rotated to show off "adjust_time" A = fullcircle scaled 144 rotated uniformdeviate 360; B = fullcircle scaled 60 shifted 240 right rotated 36; @@ -48,11 +48,10 @@ dotlabel.ulft(btex $u''$ etex, point u'' of B); drawdot center B withpen pencircle scaled dotlabeldiam; drawoptions(withcolor 1/2[blue, white]); - label.urt(btex $A$ etex, point 1/2(t'+u'- 7.6) of A); - label.rt (btex $B$ etex, point 1/2(t''+u''- 2) of B); - label.urt(btex $C$ etex, point 1/2(t+u-8) of C); + label.urt(btex $A$ etex, point 1/2(t'+u'- 7.6) of A); + label.rt (btex $B$ etex, point 1/2(t''+u''- 2) of B); + label.urt(btex $C$ etex, point 1/2(t+u-8) of C); drawoptions(); - endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/tangents-two-circles-interior.pdf b/info/drawing-with-metapost/src/geometry-tangents-two-circles-interior.pdf Binary files differindex f9faedbd97..5228c93172 100644 --- a/info/drawing-with-metapost/src/tangents-two-circles-interior.pdf +++ b/info/drawing-with-metapost/src/geometry-tangents-two-circles-interior.pdf diff --git a/info/drawing-with-metapost/src/geometry-triangles-on-circle.mp b/info/drawing-with-metapost/src/geometry-triangles-on-circle.mp index 16852ad54e..07720f553a 100644 --- a/info/drawing-with-metapost/src/geometry-triangles-on-circle.mp +++ b/info/drawing-with-metapost/src/geometry-triangles-on-circle.mp @@ -6,18 +6,18 @@ vardef equilateral_triangle_point(expr a, b) = b shifted -a rotated 60 shifted a enddef; beginfig(1); -path c; c = fullcircle scaled 144; -numeric n; n = 8; -for i=0 upto n-1: - pair a,b,p,q; - a = point 8/n * i of c; - b = point 8/n * (i + 1) of c; - p = equilateral_triangle_point(a,b); - q = equilateral_triangle_point(b,a); - draw a -- p -- b withcolor .67 green; - draw a -- q -- b withcolor .67 red; -endfor -draw c withcolor .53 blue; + path c; c = fullcircle scaled 144; + numeric n; n = 11; + for i=0 upto n-1: + pair a,b,p,q; + a = point 8/n * i of c; + b = point 8/n * (i + 1) of c; + p = equilateral_triangle_point(a,b); + q = equilateral_triangle_point(b,a); + draw a -- p -- b withcolor .67 green; + draw a -- q -- b withcolor .67 red; + endfor + draw c withcolor .53 blue; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/geometry-triangles-on-circle.pdf b/info/drawing-with-metapost/src/geometry-triangles-on-circle.pdf Binary files differindex fce9394170..86cc5cdd0e 100644 --- a/info/drawing-with-metapost/src/geometry-triangles-on-circle.pdf +++ b/info/drawing-with-metapost/src/geometry-triangles-on-circle.pdf diff --git a/info/drawing-with-metapost/src/trisection-classical.mp b/info/drawing-with-metapost/src/geometry-trisection-classical.mp index 980ceae25e..980ceae25e 100644 --- a/info/drawing-with-metapost/src/trisection-classical.mp +++ b/info/drawing-with-metapost/src/geometry-trisection-classical.mp diff --git a/info/drawing-with-metapost/src/trisection-classical.pdf b/info/drawing-with-metapost/src/geometry-trisection-classical.pdf Binary files differindex 7dc1d031e2..7dc1d031e2 100644 --- a/info/drawing-with-metapost/src/trisection-classical.pdf +++ b/info/drawing-with-metapost/src/geometry-trisection-classical.pdf diff --git a/info/drawing-with-metapost/src/geometry-trisection-simple.mp b/info/drawing-with-metapost/src/geometry-trisection-simple.mp new file mode 100644 index 0000000000..e8c17334a4 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-trisection-simple.mp @@ -0,0 +1,20 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + path ray; ray = origin -- 200 right; + numeric theta; theta = 42; + draw ray; + draw ray rotated 1/3 theta withcolor 2/3 red; + draw ray rotated 2/3 theta withcolor 2/3 red; + draw ray rotated theta; + dotlabel.llft("$0$", origin); + label("$\theta/3$", 72 right rotated 1/6 theta) withcolor 2/3 blue; + label("$\theta/3$", 72 right rotated 3/6 theta) withcolor 2/3 blue; + label("$\theta/3$", 72 right rotated 5/6 theta) withcolor 2/3 blue; +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/trisection-simple.pdf b/info/drawing-with-metapost/src/geometry-trisection-simple.pdf Binary files differindex 7a63ce3cf3..7a63ce3cf3 100644 --- a/info/drawing-with-metapost/src/trisection-simple.pdf +++ b/info/drawing-with-metapost/src/geometry-trisection-simple.pdf diff --git a/info/drawing-with-metapost/src/geometry-whatever.mp b/info/drawing-with-metapost/src/geometry-whatever.mp new file mode 100644 index 0000000000..21d0de8950 --- /dev/null +++ b/info/drawing-with-metapost/src/geometry-whatever.mp @@ -0,0 +1,26 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\hbox to 5in{$\vcenter{% +\begin{mplibcode} +beginfig(1); + z1 = (10, 50); + z2 = (80, 190); + z3 = (0, 170); + z4 = (60, 10); + + z0 = whatever [z1, z2] = whatever [z3, z4]; + + draw z1--z2; draw z3--z4; + + forsuffixes @=0,1,2,3,4: + dotlabel.rt(TEX("$z_" & decimal @ & "$"), z@) + withcolor 2/3 if @=0: red else: blue fi; + endfor +endfig; +\end{mplibcode} +}\quad\vcenter{ +\smallmpexternal[firstline=7,lastline=21]{geometry-whatever.mp} +}$\hss} +\end{document} diff --git a/info/drawing-with-metapost/src/whatever.pdf b/info/drawing-with-metapost/src/geometry-whatever.pdf Binary files differindex e02bd9c354..8b641cef45 100644 --- a/info/drawing-with-metapost/src/whatever.pdf +++ b/info/drawing-with-metapost/src/geometry-whatever.pdf diff --git a/info/drawing-with-metapost/src/gons.mp b/info/drawing-with-metapost/src/gons.mp deleted file mode 100644 index 417c598690..0000000000 --- a/info/drawing-with-metapost/src/gons.mp +++ /dev/null @@ -1,28 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -vardef gcd(expr a, b) = - if b = 0: a else: gcd(b, a mod b) fi -enddef; -beginfig(1); -for n=2 upto 24: - for s=1 upto floor n/2: - pair p; p = (12n - 24s, -24n); - path gon; gon = ( - for t=0 upto n/gcd(s,n) - 1: - 10 up rotated (360/n * s * t) -- - endfor cycle); - if (n mod s = 0): - fill gon shifted p withcolor PuBuGn[9][1+floor (n/s/6)]; - label("$" & decimal (n/s) & "$", p); - fi - draw gon shifted p withpen pencircle scaled 1/8; - endfor -endfor -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/graph-paper.mp b/info/drawing-with-metapost/src/graph-paper.mp deleted file mode 100644 index b4fc2b8f1b..0000000000 --- a/info/drawing-with-metapost/src/graph-paper.mp +++ /dev/null @@ -1,34 +0,0 @@ -\documentclass[border=1mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -vardef grid(expr ll, ur, grid_unit) = - save llx, lly, urx, ury, G; numeric llx, lly, urx, ury; - (llx, lly) = ll; (urx, ury) = ur; - picture G; G = image( - for x = floor(llx / grid_unit) + 1 upto floor(urx / grid_unit): - draw (x * grid_unit, lly) -- (x * grid_unit, ury); - endfor - for y = floor(lly / grid_unit) + 1 upto floor(ury / grid_unit): - draw (llx, y * grid_unit) -- (urx, y * grid_unit); - endfor - fill fullcircle; % <-- you might not want this - ); G enddef; - -input colorbrewer-rgb -beginfig(1); - path C; - C = fullcircle scaled 120 shifted 12 up rotated 6; - for t=0, 1.23, 4: draw center C -- point t of C withcolor Blues 8 8; endfor - draw C withcolor Reds 8 8; - dotlabel.urt("Start", point 0 of C); - - picture P; P = currentpicture; currentpicture := nullpicture; - draw grid(llcorner P, urcorner P, 1mm) withpen pencircle scaled 1/4 withcolor Blues 8 1; - draw grid(llcorner P, urcorner P, 1cm) withpen pencircle scaled 1/4 withcolor Blues 8 2; - draw P; -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/graph-paper.pdf b/info/drawing-with-metapost/src/graph-paper.pdf Binary files differdeleted file mode 100644 index d6cd20458e..0000000000 --- a/info/drawing-with-metapost/src/graph-paper.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/greek-default-encoding.mp b/info/drawing-with-metapost/src/greek-default-encoding.mp deleted file mode 100644 index 76bbe6b86c..0000000000 --- a/info/drawing-with-metapost/src/greek-default-encoding.mp +++ /dev/null @@ -1,29 +0,0 @@ -%\documentclass[border=5mm]{standalone} -%\usepackage{luamplib} -%\begin{document} -%\begin{mplibcode} -prologues := 3; -outputtemplate := "%j.%{outputformat}"; -beginfig(1); -string ab, AB; - -ab = ("" for i=11 upto 23: & char i endfor - & "o" for i=24 upto 33: & char i endfor); - -AB = ("AB" & char 0 & char 1 & "EZH" & char 2 & "IK" - & char 3 & "MNO" & char 4 & char 5 & "P" - & char 6 & "T" & char 7 & char 8 & "X" - & char 9 & char 10); - -draw ab infont "cmmi10"; -draw AB infont "cmmi10" shifted 12 down; -draw ab infont "eurm10" shifted 32 down; -draw AB infont "eurm10" shifted 44 down; - -undraw (6 left -- 180 right) shifted 12 up; -undraw (6 left -- 180 right) shifted 50 down; - -endfig; -%\end{mplibcode} -%\end{document} -end diff --git a/info/drawing-with-metapost/src/greek-default-encoding.pdf b/info/drawing-with-metapost/src/greek-default-encoding.pdf Binary files differdeleted file mode 100644 index a98ad701dc..0000000000 --- a/info/drawing-with-metapost/src/greek-default-encoding.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/icosahedron.pdf b/info/drawing-with-metapost/src/icosahedron.pdf Binary files differdeleted file mode 100644 index 48a513c8ff..0000000000 --- a/info/drawing-with-metapost/src/icosahedron.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/ifs-heigh-open.mp b/info/drawing-with-metapost/src/ifs-heigh-open.mp index 337bef2e61..39104b44e7 100644 --- a/info/drawing-with-metapost/src/ifs-heigh-open.mp +++ b/info/drawing-with-metapost/src/ifs-heigh-open.mp @@ -6,9 +6,9 @@ beginfig(1); path p; p = origin -- dir 30; numeric n, r; r = 3; for i=1 upto 12: - n := length p; - p := p rotated (45 - r); - p := p & reverse p rotatedabout(point n of p, 90 + 2r); + n := length p; + p := p rotated (45 - r); + p := p & reverse p rotatedabout(point n of p, 90 + 2r); endfor draw p scaled (384 / xpart (urcorner p - llcorner p)) withcolor .54 red; endfig; diff --git a/info/drawing-with-metapost/src/ifs-heigh-open.pdf b/info/drawing-with-metapost/src/ifs-heigh-open.pdf Binary files differindex 5f26760b2e..7a9bfab1a1 100644 --- a/info/drawing-with-metapost/src/ifs-heigh-open.pdf +++ b/info/drawing-with-metapost/src/ifs-heigh-open.pdf diff --git a/info/drawing-with-metapost/src/ifs-heigh.mp b/info/drawing-with-metapost/src/ifs-heigh.mp index 6ff5b94df0..cfe96940d3 100644 --- a/info/drawing-with-metapost/src/ifs-heigh.mp +++ b/info/drawing-with-metapost/src/ifs-heigh.mp @@ -3,15 +3,14 @@ \begin{document} \begin{mplibcode} beginfig(1); -path p; p = origin -- right rotated 30; +path p; p = origin -- dir 30; numeric n; for i=1 upto 12: - n := length p; - p := p rotated 45; - p := p & reverse p rotatedabout(point n of p, 90); + n := length p; + p := p rotated 45; + p := p & reverse p rotatedabout(point n of p, 90); endfor -draw p scaled (384 / xpart (urcorner p - llcorner p)) - withcolor (.2, .2, .7); +draw p scaled (384 / xpart (urcorner p - llcorner p)) withcolor (.2,.2,.7); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/ifs-heigh.pdf b/info/drawing-with-metapost/src/ifs-heigh.pdf Binary files differindex d779719752..30924f4d0a 100644 --- a/info/drawing-with-metapost/src/ifs-heigh.pdf +++ b/info/drawing-with-metapost/src/ifs-heigh.pdf diff --git a/info/drawing-with-metapost/src/illusions-cafe-wall.mp b/info/drawing-with-metapost/src/illusions-cafe-wall.mp index da81df2963..061ff235ed 100644 --- a/info/drawing-with-metapost/src/illusions-cafe-wall.mp +++ b/info/drawing-with-metapost/src/illusions-cafe-wall.mp @@ -3,22 +3,21 @@ \begin{document} \begin{mplibcode} beginfig(1); - numeric u; u = 21; -picture strip; -strip = image( + numeric u; u = 21; + picture strip; + strip = image( for i=-10 upto 10: - fill unitsquare shifted (2i,0) scaled u; - draw unitsquare shifted (2i,0) scaled u withcolor 1/2; + fill unitsquare shifted (2i,0) scaled u; + draw unitsquare shifted (2i,0) scaled u withcolor 1/2; endfor for i=0, 1: - draw ((-20, i) -- (20, i)) scaled u withcolor 1/2; + draw ((-20, i) -- (20, i)) scaled u withcolor 1/2; endfor -); -for i=0 upto 9: + ); + for i=0 upto 9: draw strip shifted (4 normaldeviate, i*u); -endfor -clip currentpicture to unitsquare shifted 1/2 left xscaled 29.2 yscaled 10 scaled u; + endfor + clip currentpicture to unitsquare shifted 1/2 left xscaled 29.2 yscaled 10 scaled u; endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/illusions-cafe-wall.pdf b/info/drawing-with-metapost/src/illusions-cafe-wall.pdf Binary files differnew file mode 100644 index 0000000000..c5fd7f90fc --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-cafe-wall.pdf diff --git a/info/drawing-with-metapost/src/illusions-cubes.mp b/info/drawing-with-metapost/src/illusions-cubes.mp index 2b083debb1..501aae3081 100644 --- a/info/drawing-with-metapost/src/illusions-cubes.mp +++ b/info/drawing-with-metapost/src/illusions-cubes.mp @@ -5,42 +5,41 @@ \begin{mplibcode} input colorbrewer-rgb beginfig(2); - numeric u, v; - u = 60; - v = 21 * sqrt(3); - path face[]; + numeric u, v; + u = 60; + v = 21 * sqrt(3); + path face[]; + for i=0 upto 2: + face[i] = unitsquare scaled u rotated 45 yscaled (1/sqrt(3)) rotated (120-120i); + endfor + picture cube, sides; + cube = image( for i=0 upto 2: - face[i] = unitsquare scaled u rotated 45 yscaled (1/sqrt(3)) rotated (120-120i); + fill face[i] withcolor Oranges[8][i+1]; endfor - picture cube, sides; - cube = image( - for i=0 upto 2: - fill face[i] withcolor Oranges[8][i+1]; - endfor - for i=0 upto 2: - draw subpath (1, 4) of face[i]; - endfor - ); - sides = image( - for i=0, 2: - fill face[i] withcolor Oranges[8][i+1]; - endfor - for i=0, 2: - draw face[i]; - endfor - ); - draw cube shifted (0u, 2v); - draw cube shifted (0u, 4v); - draw cube shifted (0u, 6v); - draw cube shifted (1u, 5v); - draw cube shifted (2u, 4v); - draw cube shifted (3u, 3v); - draw cube shifted (2u, 2v); - draw cube shifted (u, v); - draw cube; - draw sides shifted (0u, 2v); + for i=0 upto 2: + draw subpath (1, 4) of face[i]; + endfor + ); + sides = image( + for i=0, 2: + fill face[i] withcolor Oranges[8][i+1]; + endfor + for i=0, 2: + draw face[i]; + endfor + ); + draw cube shifted (0u, 2v); + draw cube shifted (0u, 4v); + draw cube shifted (0u, 6v); + draw cube shifted (1u, 5v); + draw cube shifted (2u, 4v); + draw cube shifted (3u, 3v); + draw cube shifted (2u, 2v); + draw cube shifted (u, v); + draw cube; + draw sides shifted (0u, 2v); endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/illusions-cubes.pdf b/info/drawing-with-metapost/src/illusions-cubes.pdf Binary files differnew file mode 100644 index 0000000000..e9c20264a7 --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-cubes.pdf diff --git a/info/drawing-with-metapost/src/illusions-fraser-spiral.mp b/info/drawing-with-metapost/src/illusions-fraser-spiral.mp deleted file mode 100644 index 850d957e79..0000000000 --- a/info/drawing-with-metapost/src/illusions-fraser-spiral.mp +++ /dev/null @@ -1,26 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\mplibsetformat{metafun} -\begin{mplibcode} -beginfig(1); - path s; - s = origin for i=1 upto 90: .. (30i, 0) rotated 4i endfor; - - path e[], f[]; - for i = 0 upto 17: - e[i] = s rotated 20i; - f[i] = s reflectedabout(left, right) rotated 20i; - endfor - - for i=0 upto 8: - fill e[2i] -- reverse e[2i+1] .. cycle withcolor 1/2; - endfor - for i=0 upto 8: - fill f[2i] -- reverse f[2i+1] .. cycle withcolor transparent(2, 1/2, 0); - endfor -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/illusions-fraser-spiral.pdf b/info/drawing-with-metapost/src/illusions-fraser-spiral.pdf Binary files differnew file mode 100644 index 0000000000..be04c02985 --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-fraser-spiral.pdf diff --git a/info/drawing-with-metapost/src/illusions-impossible-ring.mp b/info/drawing-with-metapost/src/illusions-impossible-ring.mp deleted file mode 100644 index 85aaa6492f..0000000000 --- a/info/drawing-with-metapost/src/illusions-impossible-ring.mp +++ /dev/null @@ -1,42 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\usepackage{graphicx} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); -%label("$\includegraphics{ring-11.png}$", origin); -path S; -S = (-117, 4) {dir 30} .. {right} 30 up .. {dir -36} (117, -4) .. {left} 88 down - .. (-200, -50) .. {up} (-266, 30) {down} -- (-266, -50) - .. (-200, -108) {dir -28} .. 148 down {right} - .. (200, -108) .. {up} (266, -30); -S := S & subpath (5, 2) of S rotated 180 & cycle; -input colorbrewer-rgb - -fill S withcolor Greens 8 3; -fill S rotated 180 withcolor Reds 8 3; - -picture rules; rules = image( - for t=0 step 1/32 until directiontime down of subpath(12, 13) of S: - draw point 12+t of S -- point 12+t of S shifted 100 down - cutafter S; - endfor - for t=3 step 1/16 until 5: - draw point t of S -- point t of S shifted 100 down cutafter subpath (6, 8) of S; - endfor - for t=8+1/16 step 1/16 until 12: - draw point t of S -- 1/2[point 1 of S, point 3 of S] cutafter subpath (1, 3) of S; - endfor -); - -for r = 0, 180: - draw rules rotated r; - draw S rotated r; -endfor - - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/illusions-impossible-ring.pdf b/info/drawing-with-metapost/src/illusions-impossible-ring.pdf Binary files differnew file mode 100644 index 0000000000..d8b8a7d735 --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-impossible-ring.pdf diff --git a/info/drawing-with-metapost/src/illusions-impossible-triangle.mp b/info/drawing-with-metapost/src/illusions-impossible-triangle.mp index 370a4800af..951f5c2979 100644 --- a/info/drawing-with-metapost/src/illusions-impossible-triangle.mp +++ b/info/drawing-with-metapost/src/illusions-impossible-triangle.mp @@ -6,35 +6,33 @@ input colorbrewer-rgb beginfig(1); - numeric u; - - u = 42; - - z0 = (0, 3u); - z1 = z0 rotated 120; - z2 = z1 rotated 120; - - z3 = z0 shifted (1/2u, 3/2u * sqrt(3)); - z4 = z3 shifted (-u,0); - - z5-z4 = whatever * (z0-z1); - z6 = whatever [z0, z2]; - y5 = y6 = y2 - sqrt(3) * 1/2 u; - - z7-z3 = whatever * (z0-z1); - z7 = whatever [z1, z2]; - - %dotlabels.top(0, 1, 2, 3, 4, 5, 6, 7); - - path vii; - vii = z3--z4--z5--z6--z2--z7--cycle; - - for i=0 upto 2: - fill vii rotated 120i withcolor Blues[9][i+2]; - endfor - for i=0 upto 2: - draw vii rotated 120i; - endfor + numeric u; + + u = 42; + + z0 = (0, 3u); + z1 = z0 rotated 120; + z2 = z1 rotated 120; + + z3 = z0 shifted (1/2u, 3/2u * sqrt(3)); + z4 = z3 shifted (-u,0); + + z5-z4 = whatever * (z0-z1); + z6 = whatever [z0, z2]; + y5 = y6 = y2 - sqrt(3) * 1/2 u; + + z7-z3 = whatever * (z0-z1); + z7 = whatever [z1, z2]; + + path vii; + vii = z3--z4--z5--z6--z2--z7--cycle; + + for i=0 upto 2: + fill vii rotated 120i withcolor Blues[9][i+2]; + endfor + for i=0 upto 2: + draw vii rotated 120i; + endfor endfig; \end{mplibcode} diff --git a/info/drawing-with-metapost/src/illusions-impossible-triangle.pdf b/info/drawing-with-metapost/src/illusions-impossible-triangle.pdf Binary files differnew file mode 100644 index 0000000000..8e90a30227 --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-impossible-triangle.pdf diff --git a/info/drawing-with-metapost/src/illusions-pinna.mp b/info/drawing-with-metapost/src/illusions-pinna.mp index 070802a5d9..06ac610f53 100644 --- a/info/drawing-with-metapost/src/illusions-pinna.mp +++ b/info/drawing-with-metapost/src/illusions-pinna.mp @@ -1,23 +1,20 @@ \documentclass[border=5mm]{standalone} \usepackage{luamplib} \begin{document} -\mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - path s; s = unitsquare shifted -(1/2, 1/2) scaled 23; - for n = 1 upto 4: - numeric N; N = 10n + 8; - numeric a; a = 30 normaldeviate; - for t=0 upto N-1: - draw s rotated if odd n: - fi 13 shifted (5N * right) rotated (360 / N * t + a) - withcolor t mod 2; - endfor + path s; s = unitsquare shifted -(1/2, 1/2) scaled 21; + for n = 1 upto 4: + numeric N; N = 9n + 8; + numeric a; a = 30 normaldeviate; + for t=0 upto N-1: + draw s rotated if odd n: - fi 13 shifted (5N * right) rotated (360 / N * t + a) + withpen pencircle scaled 1 withcolor t mod 2; endfor - picture P; - P = currentpicture; currentpicture := nullpicture; - fill bbox P withcolor 0.42; - draw P; + endfor + picture P; + P = currentpicture; clearit; + fill bbox P withcolor 0.52; draw P; endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/illusions-pinna.pdf b/info/drawing-with-metapost/src/illusions-pinna.pdf Binary files differnew file mode 100644 index 0000000000..0c9ae9aee1 --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-pinna.pdf diff --git a/info/drawing-with-metapost/src/illusions-shaded-diamonds.mp b/info/drawing-with-metapost/src/illusions-shaded-diamonds.mp index adb4b003a6..17b2475534 100644 --- a/info/drawing-with-metapost/src/illusions-shaded-diamonds.mp +++ b/info/drawing-with-metapost/src/illusions-shaded-diamonds.mp @@ -6,27 +6,24 @@ input colorbrewer-rgb path diamond; picture shaded; diamond = (left -- 3 down -- right -- 3 up -- cycle) scaled 13; -shaded = image( -for i=0 upto 256: - draw (left--right) scaled 15 shifted (0, 78/256 i - 39) - withpen pencircle scaled 0.32 - withcolor (i/256)[white, Greens 8 8]; +shaded = image(for i=0 upto 256: + draw (left--right) scaled 15 shifted (0, 78/256 i - 39) + withpen pencircle scaled 0.32 + withcolor (i/256)[white, Greens 8 8]; endfor); clip shaded to diamond; - - pair u, v; - u = point 2 of diamond - point 0 of diamond; - v = point 3 of diamond - point 0 of diamond; + +pair u, v; +u = point 2 of diamond - point 0 of diamond; +v = point 3 of diamond - point 0 of diamond; beginfig(1); - for i=0 upto 8: - for j=0 upto min(8-i, 4): - draw shaded shifted (i * u + j * v); - endfor + for i=0 upto 8: + for j=0 upto min(8-i, 4): + draw shaded shifted (i * u + j * v); endfor - clip currentpicture to -1/2u -- 9u -- 5u + 4v -- 4v - 1/2u -- cycle; - - draw currentpicture rotated 180; - + endfor + clip currentpicture to -1/2u -- 9u -- 5u + 4v -- 4v - 1/2u -- cycle; + draw currentpicture rotated 180; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/illusions-shaded-diamonds.pdf b/info/drawing-with-metapost/src/illusions-shaded-diamonds.pdf Binary files differnew file mode 100644 index 0000000000..4e01066e5c --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-shaded-diamonds.pdf diff --git a/info/drawing-with-metapost/src/illusions-wonky-grid.mp b/info/drawing-with-metapost/src/illusions-wonky-grid.mp index 74fe8ddf99..fa40371a17 100644 --- a/info/drawing-with-metapost/src/illusions-wonky-grid.mp +++ b/info/drawing-with-metapost/src/illusions-wonky-grid.mp @@ -4,22 +4,22 @@ \begin{mplibcode} input colorbrewer-rgb beginfig(1); - path o; numeric r; r = 1/4; - o = (for i=0 upto 3: subpath (i+r, i+1-r) of unitsquare shifted -(1/2, 1/2) -- endfor cycle) scaled 42; - picture unit; path s; s = unitsquare scaled arclength subpath (1, 3/2) of o - rotated -45 shifted point 3/2 of o; - unit = image( - fill o withcolor Blues 8 5; - for i=0 upto 3: fill s rotated 90i; endfor - ); + path o; numeric r; r = 1/4; + o = (for i=0 upto 3: subpath (i+r, i+1-r) of unitsquare shifted -(1/2, 1/2) -- endfor cycle) scaled 42; + picture unit; path s; s = unitsquare scaled arclength subpath (1, 3/2) of o + rotated -45 shifted point 3/2 of o; + unit = image( + fill o withcolor Blues 8 5; + for i=0 upto 3: fill s rotated 90i; endfor + ); - pair u, v; u = 42 right; v = u rotated 90; numeric n; n = 3; - for i=-n upto n: - for j=-2n upto 2n: - draw unit if (i+j) mod 4 < 2: reflectedabout (dir 135, dir -45) fi - shifted ((2i + j mod 2)*u + j*v); - endfor + pair u, v; u = 42 right; v = u rotated 90; numeric n; n = 3; + for i=-n upto n: + for j=-2n upto 2n: + draw unit if (i+j) mod 4 < 2: reflectedabout (dir 135, dir -45) fi + shifted ((2i + j mod 2)*u + j*v); endfor + endfor endfig; \end{mplibcode} diff --git a/info/drawing-with-metapost/src/illusions-wonky-grid.pdf b/info/drawing-with-metapost/src/illusions-wonky-grid.pdf Binary files differnew file mode 100644 index 0000000000..1b709dff61 --- /dev/null +++ b/info/drawing-with-metapost/src/illusions-wonky-grid.pdf diff --git a/info/drawing-with-metapost/src/incircle.mp b/info/drawing-with-metapost/src/incircle.mp deleted file mode 100644 index 050beebf22..0000000000 --- a/info/drawing-with-metapost/src/incircle.mp +++ /dev/null @@ -1,38 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -vardef through(expr a, b, o) = - save t; numeric t; t = 1+o/abs(a-b); - t[b,a] -- t[a,b] -enddef; - -beginfig(1); - pair A, B, C; - A = origin; B = 377 dir 10; C = 233 dir 70; - pair a, b, m, t; - a = A + 22 unitvector (C-A) + 22 unitvector (B-A); - b = B + 22 unitvector (A-B) + 22 unitvector (C-B); - m = whatever[A,a] = whatever [B,b]; t = whatever[A,B]; - t-m = whatever * (B-A) rotated 90; - - drawoptions(dashed evenly scaled 1/4 withcolor 1/2 white); - draw t -- m; - draw unitsquare scaled 5 rotated angle (B-A) shifted t; - draw through(A, m, 10); - draw through(B, m, 10); - drawoptions(); - draw fullcircle scaled 2 abs (t-m) shifted m withcolor 2/3 red; - draw A--B--C--cycle; - dotlabel.top(btex $m$\thinspace\strut etex, m); - dotlabel.bot(btex $t$ etex, t); - dotlabel.bot(btex $A$ etex, A); - dotlabel.urt(btex $B$ etex, B); - dotlabel.top(btex $C$ etex, C); - dotlabel.top(btex $a$ etex, a); - dotlabel.top(btex $b$ etex, b); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/line-caps-and-joins.mp b/info/drawing-with-metapost/src/line-caps-and-joins.mp deleted file mode 100644 index cf52919d6e..0000000000 --- a/info/drawing-with-metapost/src/line-caps-and-joins.mp +++ /dev/null @@ -1,56 +0,0 @@ -\documentclass[border=2mm]{standalone} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -beginfig(1); -numeric u; u = 32; -z1 = right scaled u; -z2 = z1 rotated 90; -z3 = z2 rotated 90; -z4 = z3 rotated 90; -z5 = 1/2[z1,z2]; -z6 = 1/2[z2,z3]; -z7 = 1/2[z3,z4]; -z8 = 1/2[z4,z1]; - -color tb, tr; -tb = (.2,.2,.7); -tr = 0.54 red; - -drawoptions (withpen pencircle scaled 2); -picture p; -for i=0 upto 2: - for j=0 upto 2: - linecap := i; - linejoin := j; - p := image( - draw unitsquare shifted -(1/2,1/2) scaled 2u withcolor 7/8; - label(decimal linecap, z7) withcolor tb; - label(decimal linejoin, z8) withcolor tr; - drawarrow z1--z3; - draw z2--z4; - drawdot(z5); - drawdot(z6); - drawarrow halfcircle scaled u rotated 180 shifted z4; - ) shifted (5/2u*i, -11/4u*j); - draw p; - if (i=1) and (j=1): draw bbox p dashed withdots scaled 3/4 - withpen pencircle scaled 1/2 - ; fi - endfor - endfor - - label("linecap" infont "cmtt10" scaled 1.2, (5/2u, 7/4u)); - label("butt" infont "cmtt10" , ( 0, 5/4u)) withcolor tb; - label("rounded" infont "cmtt10" , (5/2u, 5/4u)) withcolor tb; - label("squared" infont "cmtt10" , (5/1u, 5/4u)) withcolor tb; - - label("linejoin" infont "cmtt10" scaled 1.2 rotated 90, (-7/4u, -11/4u)); - label("mitered" infont "cmtt10" rotated 90, (-5/4u,0)) withcolor tr; - label("rounded" infont "cmtt10" rotated 90, (-5/4u,-11/4u)) withcolor tr; - label("beveled" infont "cmtt10" rotated 90, (-5/4u,-11/2u)) withcolor tr; - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/line-caps-and-joins.pdf b/info/drawing-with-metapost/src/line-caps-and-joins.pdf Binary files differdeleted file mode 100644 index c65cacdde4..0000000000 --- a/info/drawing-with-metapost/src/line-caps-and-joins.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/linear-graph.mp b/info/drawing-with-metapost/src/linear-graph.mp deleted file mode 100644 index 396c9ccd4c..0000000000 --- a/info/drawing-with-metapost/src/linear-graph.mp +++ /dev/null @@ -1,52 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - numeric u, m, m', b, b'; - u = 1.44cm; - b = 3.6u; b' = b + 1/2 u; - m = -1; m' = 3/4 m; - - path xx, yy; - xx = (left -- 5 right) scaled u; - yy = xx rotated 90; - - numeric minx, maxx; path ff, gg; - minx = xpart point 1/16 of xx; - maxx = xpart point 15/16 of xx; - ff = (minx, minx * m + b) -- (maxx, maxx * m + b); - gg = (minx, minx * m' + b') -- (maxx, maxx * m' + b'); - - z0 = point 0.4 of ff; - z1 = point 0.54 of ff; - z1 0 = whatever [point 0 of gg, point 1 of gg]; x1 0 = x0; - z1 1 = whatever [point 0 of gg, point 1 of gg]; x1 1 = x1; - - forsuffixes @=0, 1: - draw (x@, 0) -- z@ -- (0, y@) dashed evenly scaled 3/4; - draw z@ -- z1 @ -- (0, y1 @) dashed withdots scaled 1/2; - label.bot("$x_{" & decimal @ & "}$", (x@, 0)); - label.lft("$y_{" & decimal @ & "}$", (0, y@)); - label.lft("$y'_{" & decimal @ & "}$", (0, y1 @)); - endfor - - draw ff withcolor 2/3 red; - draw gg withcolor 3/4 blue; - drawarrow xx; drawarrow yy; - - label.rt("$x$", point 1 of xx); - label.top("$y$", point 1 of yy); - - dotlabel.urt("$b$", (0, b)); - dotlabel.urt("$b'$", (0, b')); - - draw thelabel("slope: $m=" & decimal m & "$", 7 up) - rotated angle (1, m) shifted point 2/3 of ff; - draw thelabel("slope: $m'=" & decimal m' & "$", 7 up) - rotated angle (1, m') shifted point 2/3 of gg; - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/listex.py b/info/drawing-with-metapost/src/listex.py new file mode 100644 index 0000000000..4ef48fd54f --- /dev/null +++ b/info/drawing-with-metapost/src/listex.py @@ -0,0 +1,131 @@ +'''Read a TeX .fls file and produce a consolidated, deduplicated list of the +files involved. Optionally check for MP source files as well''' + +import argparse +import pathlib +import sys + + +def get_files_from_fls(f, want_all): + '''resolve the names in the recorded list of files + and return a deduplicated, sorted list + ''' + pwd = None + files = [] + for line in f.read_text().splitlines(): + key, name = line.split(None, 1) + if key == "PWD": + pwd = pathlib.Path(name) + continue + + if name.startswith("."): + f = pwd / name + elif want_all: + f = pathlib.Path(name) + else: + continue + + f = f.resolve() + + if not f.is_file(): + continue + + if f.suffix in ('.aux', '.toc', '.log', '.maf'): + continue + + if f.suffix.startswith('.mtc'): + continue + + files.append(f) + + return sorted(set(files)) + + +def get_source_files_for_pdfs(files): + '''Heuristically find the MP source for a PDF + ''' + mp_source = [] + for p in files: + # only PDFs... + if p.suffix != '.pdf': + continue + + # but not the main PDF + if p.name == file_record.with_suffix('.pdf').name: + continue + + pdfbytes = p.read_bytes() + + if b'LuaTeX' in pdfbytes: + mp = p.with_suffix('.mp') + tex = p.with_suffix('.tex') + if mp.is_file(): + mp_source.append(mp) + elif tex.is_file(): + mp_source.append(tex) + else: + print(f'No source found for {p} (Luatex)', file=sys.stderr) + + elif b'MetaPost' in pdfbytes: + mp_multi = pathlib.Path(p.stem[:-1]).with_suffix('.mp') + mp_single = p.with_suffix('.mp') + if mp_multi.is_file(): + mp_source.append(mp_multi) + elif mp_single.is_file(): + mp_source.append(mp_single) + else: + print(f'No source found for {p} (Plain MP)', file=sys.stderr) + + else: + print(f'No source found for {p} (??)', file=sys.stderr) + + mp_includes = [] + for f in mp_source: + for line in f.read_text().splitlines(): + if line.startswith("input "): + mp = f.with_stem(line.split()[1]) + if mp.is_file(): + mp_includes.append(mp) + + return sorted(set(mp_source + mp_includes)) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser() + parser.add_argument("file_record", help="TeX .FLS file") + parser.add_argument("--all", action="store_true", + help="Also files from /texmf") + parser.add_argument("--mp", action="store_true", + help="Also MP source files ") + args = parser.parse_args() + + file_record = pathlib.Path(args.file_record).with_suffix(".fls") + # using with_suffix allows you to default to the tex name or no extension + # at all + + if not file_record.is_file(): + print("Cannot see", file_record, file=sys.stderr) + sys.exit(1) + + file_record_mtime = file_record.stat().st_mtime + + files = get_files_from_fls(file_record, args.all) + if args.mp: + files.extend(get_source_files_for_pdfs(files)) + + files = sorted(set(files)) + + need_to_recompile = False + for f in files: + if f.suffix in ('.tex', '.mp'): + if f.stat().st_mtime > file_record_mtime: + print(f, "has been updated since .FLS was created", + file=sys.stderr) + need_to_recompile = True + + if need_to_recompile: + print("Please recompile with -recorder", file=sys.stderr) + sys.exit(1) + + for f in files: + print(f) diff --git a/info/drawing-with-metapost/src/marked-up-photo-with-grid.pdf b/info/drawing-with-metapost/src/marked-up-photo-with-grid.pdf Binary files differdeleted file mode 100644 index ffd5a71b83..0000000000 --- a/info/drawing-with-metapost/src/marked-up-photo-with-grid.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/neo-labels-tte.mp b/info/drawing-with-metapost/src/neo-labels-tte.mp index 1838e838f5..e55d8644b4 100644 --- a/info/drawing-with-metapost/src/neo-labels-tte.mp +++ b/info/drawing-with-metapost/src/neo-labels-tte.mp @@ -5,24 +5,24 @@ \mplibtextextlabel{enable} % <-- added option \begin{document} \begin{mplibcode} - beginfig(1); - for x = 0 upto 1: - draw (80x,16) -- (80x, -68) withcolor 3/4[red, white]; - endfor - for y = 0 upto 3: - draw (0, -20y) -- (160, -20y) withcolor 3/4[red, white]; - endfor +beginfig(1); + for x = 0 upto 1: + draw (80x,16) -- (80x, -68) withcolor 3/4[red, white]; + endfor + for y = 0 upto 3: + draw (0, -20y) -- (160, -20y) withcolor 3/4[red, white]; + endfor - string s; s = "Hand gloves"; - draw s infont defaultfont shifted (0, 0); - draw s infont "phvr8r" shifted (0, -20); - draw TEX(s) shifted (0, -40); - draw btex Hand gloves etex shifted (0, -60); + string s; s = "Hand gloves"; + draw s infont defaultfont shifted (0, 0); + draw s infont "phvr8r" shifted (0, -20); + draw TEX(s) shifted (0, -40); + draw btex Hand gloves etex shifted (0, -60); - dotlabel.urt(s, (80, 0)); - dotlabel.urt(s infont "phvr8r", (80, -20)); - dotlabel.urt(TEX(s), (80, -40)); - dotlabel.urt(btex Hand gloves etex, (80, -60)); - endfig; + dotlabel.urt(s, (80, 0)); + dotlabel.urt(s infont "phvr8r", (80, -20)); + dotlabel.urt(TEX(s), (80, -40)); + dotlabel.urt(btex Hand gloves etex, (80, -60)); +endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/neo-labels.mp b/info/drawing-with-metapost/src/neo-labels.mp index 8b1d60b840..68e78cd8d6 100644 --- a/info/drawing-with-metapost/src/neo-labels.mp +++ b/info/drawing-with-metapost/src/neo-labels.mp @@ -4,24 +4,24 @@ \usepackage{luamplib} \begin{document} \begin{mplibcode} - beginfig(1); - for x = 0 upto 1: - draw (80x,16) -- (80x, -68) withcolor 3/4[red, white]; - endfor - for y = 0 upto 3: - draw (0, -20y) -- (160, -20y) withcolor 3/4[red, white]; - endfor +beginfig(1); + for x = 0 upto 1: + draw (80x,16) -- (80x, -68) withcolor 3/4[red, white]; + endfor + for y = 0 upto 3: + draw (0, -20y) -- (160, -20y) withcolor 3/4[red, white]; + endfor - string s; s = "Hand gloves"; - draw s infont defaultfont shifted (0, 0); - draw s infont "phvr8r" shifted (0, -20); - draw TEX(s) shifted (0, -40); - draw btex Hand gloves etex shifted (0, -60); + string s; s = "Hand gloves"; + draw s infont defaultfont shifted (0, 0); + draw s infont "phvr8r" shifted (0, -20); + draw TEX(s) shifted (0, -40); + draw btex Hand gloves etex shifted (0, -60); - dotlabel.urt(s, (80, 0)); - dotlabel.urt(s infont "phvr8r", (80, -20)); - dotlabel.urt(TEX(s), (80, -40)); - dotlabel.urt(btex Hand gloves etex, (80, -60)); - endfig; + dotlabel.urt(s, (80, 0)); + dotlabel.urt(s infont "phvr8r", (80, -20)); + dotlabel.urt(TEX(s), (80, -40)); + dotlabel.urt(btex Hand gloves etex, (80, -60)); +endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/neo-labels.pdf b/info/drawing-with-metapost/src/neo-labels.pdf Binary files differindex e5a85a74cc..7710a30aa8 100644 --- a/info/drawing-with-metapost/src/neo-labels.pdf +++ b/info/drawing-with-metapost/src/neo-labels.pdf diff --git a/info/drawing-with-metapost/src/penrose-P3.mp b/info/drawing-with-metapost/src/neo-marked-up-photo-grid.mp index 177581a305..5ec111c53a 100644 --- a/info/drawing-with-metapost/src/penrose-P3.mp +++ b/info/drawing-with-metapost/src/neo-marked-up-photo-grid.mp @@ -1,11 +1,11 @@ -\documentclass{standalone} +\documentclass[border=1mm]{standalone} \usepackage{luamplib} \begin{document} -\mplibtextextlabel{enable} \begin{mplibcode} -input penrose beginfig(1); - draw penrose(3); +undraw unitsquare xscaled 360 yscaled 178; +input neo-reference-grid endfig; \end{mplibcode} \end{document} + diff --git a/info/drawing-with-metapost/src/neo-marked-up-photo-grid.pdf b/info/drawing-with-metapost/src/neo-marked-up-photo-grid.pdf Binary files differnew file mode 100644 index 0000000000..c7d056e7ad --- /dev/null +++ b/info/drawing-with-metapost/src/neo-marked-up-photo-grid.pdf diff --git a/info/drawing-with-metapost/src/marked-up-photo.mp b/info/drawing-with-metapost/src/neo-marked-up-photo.mp index c208e79708..3e57bad1dd 100644 --- a/info/drawing-with-metapost/src/marked-up-photo.mp +++ b/info/drawing-with-metapost/src/neo-marked-up-photo.mp @@ -1,4 +1,4 @@ -\documentclass[border=1mm]{standalone} +\documentclass{standalone} \usepackage{luamplib} \usepackage{graphicx} \usepackage{fontspec}\setmainfont[Scale=0.6]{Helvetica} @@ -7,25 +7,20 @@ \begin{mplibcode} beginfig(1); draw btex \includegraphics[width=5in]{glenshiel.jpg} etex; -if false: -for i=1 upto 36: - draw (origin -- 180 up) shifted (10i, 0) withcolor if i mod 10 = 0: red else: 1/2 fi; -endfor -for i=1 upto 18: - draw (origin -- 360 right) shifted (0, 10i) withcolor if i mod 10 = 0: red else: 1/2 fi; -endfor -fi +% input neo-reference-grid vardef callout@#(expr t, p, o) = save T; picture T; T = thelabel.@#(t, p+o); draw T; drawarrow p+o -- p cutbefore bbox T; enddef; -ahangle := 20; ahlength := 2; drawoptions(withpen pencircle scaled 1/4 withcolor 1/2 blue); +ahangle := 20; ahlength := 2; +drawoptions(withpen pencircle scaled 1/4 withcolor 1/2 blue); callout.top("Sgurr na Ciste Dubhe", (80, 96), (-10, 20)); callout.top("Sgurr nan Spainteach", (100, 91), (6, 12)); label.top("\tiny Cuillin Ridge, Isle of Skye", (140, 81)); label.top("Sgurr na Carnach", (190, 90)); label.top("Sgurr Fhuaran", (282, 94)); -label.bot("\itshape View looking west from the summit of Saileag – 19 April 2005", point 5/2 of bbox currentpicture shifted 4 down); +label.bot("\textit{Looking west from the summit of Saileag} – 19 April 2005", + point 5/2 of bbox currentpicture shifted 4 down); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/marked-up-photo.pdf b/info/drawing-with-metapost/src/neo-marked-up-photo.pdf Binary files differindex fc3155d855..b968b0b548 100644 --- a/info/drawing-with-metapost/src/marked-up-photo.pdf +++ b/info/drawing-with-metapost/src/neo-marked-up-photo.pdf diff --git a/info/drawing-with-metapost/src/multi-line-labels.mp b/info/drawing-with-metapost/src/neo-multi-line-labels.mp index 497189ed16..80da860f69 100644 --- a/info/drawing-with-metapost/src/multi-line-labels.mp +++ b/info/drawing-with-metapost/src/neo-multi-line-labels.mp @@ -7,16 +7,14 @@ beginfig(1); label("\vbox{\hsize 4in It is a truth universally acknowledged," & " that a single man in possession of a good fortune," & " must be in want of a wife.\par}", origin); -label(btex \vbox{\hsize 4in - It is a truth universally acknowledged, - that a single man in possession of a good fortune, - must be in want of a wife. - \par} etex, 128 down); -label(btex - \begin{tabular}{c} - A way to get simple\\ - two line labels - \end{tabular} etex, 256 down); +label(btex \vbox{\hsize 4in\noindent + \textsc{It is a truth} universally acknowledged, + that a single man in possession of a good fortune, + must be in want of a wife.\par} etex, 128 down); +label(btex \begin{tabular}{c} + A way to get simple\\ + two line labels + \end{tabular} etex, 270 down); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/multi-line-labels.pdf b/info/drawing-with-metapost/src/neo-multi-line-labels.pdf Binary files differindex ecc0cb7611..84a4de192a 100644 --- a/info/drawing-with-metapost/src/multi-line-labels.pdf +++ b/info/drawing-with-metapost/src/neo-multi-line-labels.pdf diff --git a/info/drawing-with-metapost/src/neo-reference-grid.mp b/info/drawing-with-metapost/src/neo-reference-grid.mp new file mode 100644 index 0000000000..a6262bef52 --- /dev/null +++ b/info/drawing-with-metapost/src/neo-reference-grid.mp @@ -0,0 +1,15 @@ +% Adds a reference grid, sized to the contents of currentpicture +% useful for marking up external images etc +begingroup; + save llx, lly, urx, ury, u; u = 10; + (llx, lly) = llcorner currentpicture; + (urx, ury) = urcorner currentpicture; + drawoptions(withpen pencircle scaled 1/4); + for x = ceiling (llx / u) upto floor (urx / u): + draw (x*u, lly) -- (x*u, ury) withcolor if x mod u = 0: red else: 1/2 fi; + endfor + for y = ceiling (lly / u) upto floor (ury / u): + draw (llx, y*u) -- (urx, y*u) withcolor if y mod u = 0: red else: 1/2 fi; + endfor + drawoptions(); +endgroup; diff --git a/info/drawing-with-metapost/src/neo-simple-circle-labels.mp b/info/drawing-with-metapost/src/neo-simple-circle-labels.mp new file mode 100644 index 0000000000..3050c8673c --- /dev/null +++ b/info/drawing-with-metapost/src/neo-simple-circle-labels.mp @@ -0,0 +1,16 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); +path P; P = for i=0 upto 8: 50 dir 40i -- endfor cycle; +draw P withcolor 2/3 red; +for i=1 upto length P: + draw point i of P withpen pencircle scaled dotlabeldiam; + label("$p_{" & decimal i & "}$", point i of P scaled 1.2); +endfor +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/neo-simple-circle-labels.pdf b/info/drawing-with-metapost/src/neo-simple-circle-labels.pdf Binary files differnew file mode 100644 index 0000000000..07cffe8136 --- /dev/null +++ b/info/drawing-with-metapost/src/neo-simple-circle-labels.pdf diff --git a/info/drawing-with-metapost/src/arch-snub-hexagon.mp b/info/drawing-with-metapost/src/neo-simple-number-line.mp index 09310036f2..a2406b3219 100644 --- a/info/drawing-with-metapost/src/arch-snub-hexagon.mp +++ b/info/drawing-with-metapost/src/neo-simple-number-line.mp @@ -3,11 +3,12 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -input arch-snub-hex-parts beginfig(1); -draw P1 shifted 180 left; -draw P2 shifted 180 right; -currentpicture := currentpicture rotated 90; +labeloffset := 5; +draw (left--right) scaled 2in withcolor 2/3 red; +for i=-4 upto 4: + dotlabel.bot("$" & decimal i & "$", (32i, 0)); +endfor endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/simple-number-line.pdf b/info/drawing-with-metapost/src/neo-simple-number-line.pdf Binary files differindex bb798247c5..a43236dc09 100644 --- a/info/drawing-with-metapost/src/simple-number-line.pdf +++ b/info/drawing-with-metapost/src/neo-simple-number-line.pdf diff --git a/info/drawing-with-metapost/src/unicode.mp b/info/drawing-with-metapost/src/neo-unicode.mp index 629ebe18e2..3f43b097b0 100644 --- a/info/drawing-with-metapost/src/unicode.mp +++ b/info/drawing-with-metapost/src/neo-unicode.mp @@ -5,7 +5,6 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - label("café noir £2.50", origin); label(btex \vbox{\hsize 4in Nous étions à l'Étude, quand le Proviseur entra, suivi d'un diff --git a/info/drawing-with-metapost/src/unicode.pdf b/info/drawing-with-metapost/src/neo-unicode.pdf Binary files differindex 53ca0238c1..53ca0238c1 100644 --- a/info/drawing-with-metapost/src/unicode.pdf +++ b/info/drawing-with-metapost/src/neo-unicode.pdf diff --git a/info/drawing-with-metapost/src/new-fangled-transparency.mp b/info/drawing-with-metapost/src/new-fangled-transparency.mp new file mode 100644 index 0000000000..6aa7d56d59 --- /dev/null +++ b/info/drawing-with-metapost/src/new-fangled-transparency.mp @@ -0,0 +1,35 @@ +\documentclass[border=5mm]{standalone} +\usepackage{dwmpcode} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +def withalpha expr a = + withprescript "tr_alternative=2" + withprescript "tr_transparency=" & decimal a +enddef; +beginfig(1); +path r, g, b; r = fullcircle scaled 48 shifted 12 up; g = r rotated 120; b = g rotated 120; +picture P[]; + +for i=0 upto 7: + numeric a; a = 1/8 + i/8; + P[i] = image( + fill r withcolor 1/2[white, red] withalpha a; + fill g withcolor 1/2[white, green] withalpha a; + fill b withcolor 1/2[white, blue] withalpha a; + draw r withcolor 1/2; + draw g withcolor 1/2; + draw b withcolor 1/2; + label.bot(TEX("\mpl{withalpha " & decimal a & "}") scaled 0.8, point 1/2 of bbox currentpicture); + ); +endfor + +for i=0 upto 7: + draw P[i] shifted 120(i div 4, -(i mod 4)) ; +endfor + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/new-fangled-transparency.pdf b/info/drawing-with-metapost/src/new-fangled-transparency.pdf Binary files differnew file mode 100644 index 0000000000..4967e36bea --- /dev/null +++ b/info/drawing-with-metapost/src/new-fangled-transparency.pdf diff --git a/info/drawing-with-metapost/src/new-fangled-trilobe.mp b/info/drawing-with-metapost/src/new-fangled-trilobe.mp new file mode 100644 index 0000000000..5ffc34f7e4 --- /dev/null +++ b/info/drawing-with-metapost/src/new-fangled-trilobe.mp @@ -0,0 +1,46 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +def withalpha expr a = + withprescript "tr_alternative=2" + withprescript "tr_transparency=" & decimal a +enddef; +beginfig(1); + numeric u; u = 24; color shade[]; string name[]; + shade0 = 1/256(166, 57, 65); name0 = "R"; % rouge + shade1 = 1/256(219, 170, 72); name1 = "J"; % jaune + shade2 = 1/256(36, 54, 84); name2 = "B"; % bleu + path edge[], arc[], ring[]; + for r=1 upto 8: + edge[r] = fullcircle rotated 90 scaled (2r * u) + shifted (0, 7u / sqrt 3) rotated 120; + endfor + for i=2 upto 8: + edge[i] := edge[i] cutbefore edge8 rotated 120 + cutafter edge8 rotated -120; + endfor + arc0 = point 0 of edge1 for i=2 upto 7: .. point 0 of edge[i] endfor; + arc1 = point 0 of edge1 for i=2 upto 7: .. point infinity of edge[i] endfor; + for i=1 upto 7: + ring[i] = edge[i] -- subpath (i-1, i) of arc1 -- + reverse edge[i+1] -- subpath (i, i-1) of arc0 -- cycle; + endfor + for r=0, 1, 2: for i=1 upto 6: % fills first + fill ring[i] rotated 120r withcolor (i/6)[white, shade[r]] withalpha 0.9; + for k=0, 1: + label("$\textsf{" & name[r] & "}" if i<6: & "_" & decimal i fi & "$", + point i-1/2 of arc[k] shifted (-8,-2) rotated 120r); + endfor + endfor endfor + for r=0, 1, 2: % now lines on top + for i=1 upto 7: + draw edge[i] rotated 120r withpen pencircle scaled 1 withcolor 7/8; + endfor + draw arc0 rotated 120r; draw arc1 rotated 120r; + endfor +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/new-fangled-trilobe.pdf b/info/drawing-with-metapost/src/new-fangled-trilobe.pdf Binary files differnew file mode 100644 index 0000000000..be570795c2 --- /dev/null +++ b/info/drawing-with-metapost/src/new-fangled-trilobe.pdf diff --git a/info/drawing-with-metapost/src/nine-point-circle.mp b/info/drawing-with-metapost/src/nine-point-circle.mp deleted file mode 100644 index 8366bb3c1b..0000000000 --- a/info/drawing-with-metapost/src/nine-point-circle.mp +++ /dev/null @@ -1,54 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - pair A, B, C, D, N, M, p, q, r; - A = origin; B = 377 dir 10; C = 233 dir 70; - % pedal points - p = whatever[B, C]; A - p = whatever * (B-C) rotated 90; - q = whatever[C, A]; B - q = whatever * (C-A) rotated 90; - r = whatever[A, B]; C - r = whatever * (A-B) rotated 90; - - D = whatever[A, p] = whatever[B, q]; - N = 1/4(A + B + C + D); - M = D rotatedabout(N, 180); % M is also the circumcentre - - path circumcircle, nine_point_circle; - nine_point_circle = fullcircle scaled 2 abs(N - 1/2[A, B]) shifted N; - circumcircle = fullcircle scaled 2 abs(M - A) shifted M; - - draw nine_point_circle withcolor 3/4 red; - draw circumcircle withcolor 1/2[3/4 blue, white]; - - drawoptions(dashed evenly scaled 1/4 withcolor 1/2); - draw 1/2[A,B] -- M -- 1/2[B, C]; - draw 1/2[C,A] -- M -- D; - draw A -- p; - draw B -- q; - draw C -- r; - - drawoptions(withpen pencircle scaled 1/4); - draw fullcircle scaled 2 shifted 1/2[A, B]; - draw fullcircle scaled 2 shifted 1/2[A, C]; - draw fullcircle scaled 2 shifted 1/2[A, D]; - draw fullcircle scaled 2 shifted 1/2[B, C]; - draw fullcircle scaled 2 shifted 1/2[B, D]; - draw fullcircle scaled 2 shifted 1/2[C, D]; - draw fullcircle scaled 2 shifted p; - draw fullcircle scaled 2 shifted q; - draw fullcircle scaled 2 shifted r; - - drawoptions(); - draw A--B--C--cycle; - dotlabel.llft("$A$", A); - dotlabel.rt("$B$", B); - dotlabel.ulft("$C$", C); - dotlabel.urt("\ $D$", D); - dotlabel.llft("$M$", M); - dotlabel.llft("$N$", N); - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/numbered-axes.mp b/info/drawing-with-metapost/src/numbered-axes.mp deleted file mode 100644 index 47ee8f4ec9..0000000000 --- a/info/drawing-with-metapost/src/numbered-axes.mp +++ /dev/null @@ -1,27 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\usepackage{dwmpcode} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - numeric u, v; u = 40; v = 29; - path xx, yy; - xx = (3/2 left -- 5 right) scaled u; - yy = (3/2 down -- 4 up) scaled v; - for x=-1, 1, 2, 3, 4: - draw yy shifted (x * u, 0) withcolor 7/8; % grid - draw (down--up) shifted (x * u, 0); % ticks - label("$" & decimal x & "$", (x * u, -8)); - endfor - for y=-1, 1, 2, 3: - draw xx shifted (0, y * v) withcolor 7/8; % grid - draw (left--right) shifted (0, y * v); % ticks - label("$" & decimal y & "$", (-10, y * v)); - endfor - drawarrow xx; label.rt("$x$", point 1 of xx); - drawarrow yy; label.top("$y$", point 1 of yy); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/overlaps-missing-filler.mp b/info/drawing-with-metapost/src/overlaps-missing-filler.mp deleted file mode 100644 index edee192c1c..0000000000 --- a/info/drawing-with-metapost/src/overlaps-missing-filler.mp +++ /dev/null @@ -1,16 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(2); - path A, B; - A = fullcircle scaled 2.5cm; - B = fullcircle scaled 1.8cm shifted (1cm,0); - fill buildcycle(A,B) withcolor .8[blue,white]; drawarrow A; drawarrow B; - label.rt(btex Where has the fill colour gone? etex, point 0 of B shifted (1cm,0)); - label.ulft(btex $A$ etex, point 3 of A); - label.urt(btex $B$ etex, point 1 of B); -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/pairs-complex-inverse-and-sqrt.mp b/info/drawing-with-metapost/src/pairs-complex-inverse-and-sqrt.mp new file mode 100644 index 0000000000..f8c9461063 --- /dev/null +++ b/info/drawing-with-metapost/src/pairs-complex-inverse-and-sqrt.mp @@ -0,0 +1,47 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef zinverse(expr z) = 1/abs z * dir - angle z enddef; +vardef zsqrt(expr z) = + if abs z > 0: sqrt(abs z) * dir 1/2 angle fi z +enddef; + +z1 = 0.8 dir 148; z2 = 1.5 dir 60; z3 = 1.0 dir 42; + +input colorbrewer-rgb +numeric u; u = 42; ahangle := 30; +picture axes; axes = image( + path xx, yy; xx = (left--right) scaled 1.2 u; yy = xx rotated 90; + draw fullcircle scaled 2u; + drawarrow xx; label.rt("$\Re$", point 1 of xx); + drawarrow yy; label.top("$\Im$", point 1 of yy); +); +vardef connect(expr a, b, shade) = + save A, B; pair A, B; A = a scaled u; B = b scaled u; + drawarrow A -- origin -- B + cutafter fullcircle scaled 5 shifted B withcolor shade; + draw A withpen pencircle scaled dotlabeldiam; + draw B withpen pencircle scaled dotlabeldiam; + draw B withpen pencircle scaled 2/3 dotlabeldiam withcolor white; +enddef; +picture P[]; +P1 = image(draw axes withcolor 3/4; + label.lrt("\small\texttt{zinverse()}", ulcorner axes shifted 10 left); + connect(z1, zinverse(z1), SetTwo 7 3); + connect(z2, zinverse(z2), SetTwo 7 4); + connect(z3, zinverse(z3), SetTwo 7 5); +); +P2 = image(draw axes withcolor 3/4; + label.lrt("\small\texttt{zsqrt()}", ulcorner axes); + connect(z1, zsqrt(z1), SetTwo 7 3); + connect(z2, zsqrt(z2), SetTwo 7 4); + connect(z3, zsqrt(z3), SetTwo 7 5); +); +beginfig(1); + labeloffset := 12; label.lft(P1, origin); label.rt(P2, origin); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/complex-inverse-and-sqrt.pdf b/info/drawing-with-metapost/src/pairs-complex-inverse-and-sqrt.pdf Binary files differindex b1dae07134..1e4c751540 100644 --- a/info/drawing-with-metapost/src/complex-inverse-and-sqrt.pdf +++ b/info/drawing-with-metapost/src/pairs-complex-inverse-and-sqrt.pdf diff --git a/info/drawing-with-metapost/src/pairs-complex-operators.mp b/info/drawing-with-metapost/src/pairs-complex-operators.mp new file mode 100644 index 0000000000..2a8e760f6e --- /dev/null +++ b/info/drawing-with-metapost/src/pairs-complex-operators.mp @@ -0,0 +1,32 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + numeric u; u = 1cm; + z1 = 2 dir 15; z2 = 1.2 dir 60; + z3 = z1+z2; z4 = z1 zscaled z2; z5 = (x1,-y1); + drawoptions(withcolor 2/3 white); + draw (1/2 left -- 3 right) scaled u ; + draw (1/2 down -- 3 up ) scaled u ; + draw subpath (0,3) of fullcircle scaled 2u rotated -22.5; + drawoptions(); + dotlabel.lrt (btex $\scriptstyle 1$ etex, (u,0)); + dotlabel.ulft(btex $\scriptstyle i$ etex, (0,u)); + interim ahangle := 30; + forsuffixes @=1,2,3,4,5: + x@ := x@ * u; y@ := y@ * u; + drawarrow origin -- z@ + cutafter fullcircle scaled 5 shifted z@ + withcolor 2/3 if @ < 3: blue else: red fi; + endfor + fill fullcircle scaled dotlabeldiam; + dotlabel.rt (btex $A$ etex, z1); + dotlabel.urt(btex $B$ etex, z2); + dotlabel.top(btex $A+B$ etex, z3); + dotlabel.top(btex $A \times B$ etex, z4); + dotlabel.rt (btex $\bar{A}$ etex, z5); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/complex-operators.pdf b/info/drawing-with-metapost/src/pairs-complex-operators.pdf Binary files differindex 11370d7ce7..11370d7ce7 100644 --- a/info/drawing-with-metapost/src/complex-operators.pdf +++ b/info/drawing-with-metapost/src/pairs-complex-operators.pdf diff --git a/info/drawing-with-metapost/src/pairs-double-dragon.mp b/info/drawing-with-metapost/src/pairs-double-dragon.mp new file mode 100644 index 0000000000..b9c5019a12 --- /dev/null +++ b/info/drawing-with-metapost/src/pairs-double-dragon.mp @@ -0,0 +1,44 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\mplibnumbersystem{double} +\begin{mplibcode} +vardef fizz(expr X) = + pair m, n; m = right; n = origin; + numeric x; x = X; + forever: + exitif x = 0; + m := m zscaled (-1/2, -1/2); + if odd x: + n := n + m; + fi + x := x div 2; + endfor + n +enddef; +beginfig(1); + numeric s, t; s = 256; t = 4; + for n=0 upto (s/t*s/t-1): + draw fizz(n) scaled s + withpen pencircle scaled t + withcolor ((7+n mod 8)/16)[1/2 blue, white]; + endfor; + path xx, yy; + xx = (left--right) scaled (s+8); + yy = xx rotated 90; + for i=-1 upto 1: + draw xx shifted (0, s*i) withpen pencircle scaled 1/8; + draw yy shifted (s*i, 0) withpen pencircle scaled 1/8; + if i=0: + dotlabel.lrt("$-i$", (i, -1) scaled s); + dotlabel.lrt("$+i$", (i, +1) scaled s); + else: + dotlabel.lrt("$" & decimal i & "-i$", (i,-1) scaled s); + dotlabel.lrt("$" & decimal i & "$", (i, 0) scaled s); + dotlabel.lrt("$" & decimal i & "+i$", (i, 1) scaled s); + fi + endfor +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pairs-double-dragon.pdf b/info/drawing-with-metapost/src/pairs-double-dragon.pdf Binary files differnew file mode 100644 index 0000000000..211a65dd0e --- /dev/null +++ b/info/drawing-with-metapost/src/pairs-double-dragon.pdf diff --git a/info/drawing-with-metapost/src/random-function.mp b/info/drawing-with-metapost/src/pairs-random-function.mp index d2c13dd10b..d2c13dd10b 100644 --- a/info/drawing-with-metapost/src/random-function.mp +++ b/info/drawing-with-metapost/src/pairs-random-function.mp diff --git a/info/drawing-with-metapost/src/random-function.pdf b/info/drawing-with-metapost/src/pairs-random-function.pdf Binary files differindex 8ec56fba8e..8ec56fba8e 100644 --- a/info/drawing-with-metapost/src/random-function.pdf +++ b/info/drawing-with-metapost/src/pairs-random-function.pdf diff --git a/info/drawing-with-metapost/src/random-selection.mp b/info/drawing-with-metapost/src/pairs-random-selection.mp index d77f7fc141..d77f7fc141 100644 --- a/info/drawing-with-metapost/src/random-selection.mp +++ b/info/drawing-with-metapost/src/pairs-random-selection.mp diff --git a/info/drawing-with-metapost/src/random-selection.pdf b/info/drawing-with-metapost/src/pairs-random-selection.pdf Binary files differindex 54b7a91dc6..54b7a91dc6 100644 --- a/info/drawing-with-metapost/src/random-selection.pdf +++ b/info/drawing-with-metapost/src/pairs-random-selection.pdf diff --git a/info/drawing-with-metapost/src/paths-antireuleaux-set.mp b/info/drawing-with-metapost/src/paths-antireuleaux-set.mp new file mode 100644 index 0000000000..0d0434d2ee --- /dev/null +++ b/info/drawing-with-metapost/src/paths-antireuleaux-set.mp @@ -0,0 +1,24 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +\mplibtextextlabel{enable} +vardef antireuleaux(expr n, r) = + save a; numeric a; a = 90/n; + for t = 0 step 4a until 359: + (0, r) rotated t {left rotated (3a + t)} .. {left rotated (a + t)} + endfor cycle +enddef; +vardef median(expr p) = origin for i=1 upto length p: + point i of p / length p endfor enddef; +input colorbrewer-rgb +beginfig(1); + for n = 3 upto 7: + path p; p = antireuleaux(n, 42) shifted (90n, 0); + pair m; m = point (n+1)/2 of p; + fill p withcolor if odd n: Oranges else: Blues fi 8 2; + draw p; + endfor +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/paths-antireuleaux-set.pdf b/info/drawing-with-metapost/src/paths-antireuleaux-set.pdf Binary files differnew file mode 100644 index 0000000000..a137db48b0 --- /dev/null +++ b/info/drawing-with-metapost/src/paths-antireuleaux-set.pdf diff --git a/info/drawing-with-metapost/src/paths-area-under-graph.mp b/info/drawing-with-metapost/src/paths-area-under-graph.mp new file mode 100644 index 0000000000..5869cf25e2 --- /dev/null +++ b/info/drawing-with-metapost/src/paths-area-under-graph.mp @@ -0,0 +1,38 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb +ahangle := 30; +beginfig(1); + numeric u; + u = 42; + path xx, yy, f; + xx = (1/4 left -- 17/4 right) scaled u; + yy = (1/4 down -- 9/4 up) scaled u; + + f = ((15/32,32/15) for x = 1/2 step 1/8 until 33/8: .. (x,1/x) endfor) scaled u; + + path A; A = % keep next on it's own line.... + buildcycle(yy shifted (u,0), f, yy shifted (2.71828u,0), xx) + ; + fill A withcolor Blues 8 2; + + drawoptions(withcolor 3/4); + for x=1 upto 4: + draw yy shifted (x*u,0) cutafter (xx shifted (0, ypart point 0 of f)); + endfor + for y=1 upto 2: + draw xx shifted (0,y*u) cutafter (yy shifted (xpart point infinity of f,0)); + endfor + + drawoptions(); + draw f withcolor Reds 8 7; + drawarrow xx; + drawarrow yy; + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/paths-area-under-graph.pdf b/info/drawing-with-metapost/src/paths-area-under-graph.pdf Binary files differnew file mode 100644 index 0000000000..4ff0a26be0 --- /dev/null +++ b/info/drawing-with-metapost/src/paths-area-under-graph.pdf diff --git a/info/drawing-with-metapost/src/closed-fixed-polygon.mp b/info/drawing-with-metapost/src/paths-fixed-polygon.mp index 793b4fac8b..793b4fac8b 100644 --- a/info/drawing-with-metapost/src/closed-fixed-polygon.mp +++ b/info/drawing-with-metapost/src/paths-fixed-polygon.mp diff --git a/info/drawing-with-metapost/src/closed-fixed-polygon.pdf b/info/drawing-with-metapost/src/paths-fixed-polygon.pdf Binary files differindex c53cf71886..c53cf71886 100644 --- a/info/drawing-with-metapost/src/closed-fixed-polygon.pdf +++ b/info/drawing-with-metapost/src/paths-fixed-polygon.pdf diff --git a/info/drawing-with-metapost/src/little-hexagon.mp b/info/drawing-with-metapost/src/paths-little-hexagon.mp index 102117cfb0..102117cfb0 100644 --- a/info/drawing-with-metapost/src/little-hexagon.mp +++ b/info/drawing-with-metapost/src/paths-little-hexagon.mp diff --git a/info/drawing-with-metapost/src/little-hexagon.pdf b/info/drawing-with-metapost/src/paths-little-hexagon.pdf Binary files differindex 5a3ea39922..5a3ea39922 100644 --- a/info/drawing-with-metapost/src/little-hexagon.pdf +++ b/info/drawing-with-metapost/src/paths-little-hexagon.pdf diff --git a/info/drawing-with-metapost/src/open-triangle.mp b/info/drawing-with-metapost/src/paths-open-triangle.mp index 5535611558..5535611558 100644 --- a/info/drawing-with-metapost/src/open-triangle.mp +++ b/info/drawing-with-metapost/src/paths-open-triangle.mp diff --git a/info/drawing-with-metapost/src/open-triangle.pdf b/info/drawing-with-metapost/src/paths-open-triangle.pdf Binary files differindex 16986eacca..16986eacca 100644 --- a/info/drawing-with-metapost/src/open-triangle.pdf +++ b/info/drawing-with-metapost/src/paths-open-triangle.pdf diff --git a/info/drawing-with-metapost/src/overlaps-default-fillers.mp b/info/drawing-with-metapost/src/paths-overlaps-default-fillers.mp index 5137cdf984..5137cdf984 100644 --- a/info/drawing-with-metapost/src/overlaps-default-fillers.mp +++ b/info/drawing-with-metapost/src/paths-overlaps-default-fillers.mp diff --git a/info/drawing-with-metapost/src/overlaps-default-fillers.pdf b/info/drawing-with-metapost/src/paths-overlaps-default-fillers.pdf Binary files differindex 51a3e0ef52..51a3e0ef52 100644 --- a/info/drawing-with-metapost/src/overlaps-default-fillers.pdf +++ b/info/drawing-with-metapost/src/paths-overlaps-default-fillers.pdf diff --git a/info/drawing-with-metapost/src/paths-overlaps-missing-filler.mp b/info/drawing-with-metapost/src/paths-overlaps-missing-filler.mp new file mode 100644 index 0000000000..4aaeeb6937 --- /dev/null +++ b/info/drawing-with-metapost/src/paths-overlaps-missing-filler.mp @@ -0,0 +1,18 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); +path A, B; +A = fullcircle scaled 2.5cm; +B = fullcircle scaled 1.8cm shifted (1cm,0); +fill buildcycle(A,B) withcolor .8[blue,white]; +drawarrow A; +drawarrow B; +label.ulft(btex $A$ etex, point 3 of A); +label.urt(btex $B$ etex, point 1 of B); +label.rt(btex Where has the fill colour gone? etex, point 0 of B shifted (1cm,0)); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/overlaps-missing-filler.pdf b/info/drawing-with-metapost/src/paths-overlaps-missing-filler.pdf Binary files differindex 4bf91ed568..4bf91ed568 100644 --- a/info/drawing-with-metapost/src/overlaps-missing-filler.pdf +++ b/info/drawing-with-metapost/src/paths-overlaps-missing-filler.pdf diff --git a/info/drawing-with-metapost/src/overlaps.mp b/info/drawing-with-metapost/src/paths-overlaps.mp index d08b934249..d08b934249 100644 --- a/info/drawing-with-metapost/src/overlaps.mp +++ b/info/drawing-with-metapost/src/paths-overlaps.mp diff --git a/info/drawing-with-metapost/src/overlaps.pdf b/info/drawing-with-metapost/src/paths-overlaps.pdf Binary files differindex f076ef2b7c..f076ef2b7c 100644 --- a/info/drawing-with-metapost/src/overlaps.pdf +++ b/info/drawing-with-metapost/src/paths-overlaps.pdf diff --git a/info/drawing-with-metapost/src/closed-points.mp b/info/drawing-with-metapost/src/paths-points.mp index 9abf287338..9abf287338 100644 --- a/info/drawing-with-metapost/src/closed-points.mp +++ b/info/drawing-with-metapost/src/paths-points.mp diff --git a/info/drawing-with-metapost/src/closed-points.pdf b/info/drawing-with-metapost/src/paths-points.pdf Binary files differindex f99b1bbf2f..f99b1bbf2f 100644 --- a/info/drawing-with-metapost/src/closed-points.pdf +++ b/info/drawing-with-metapost/src/paths-points.pdf diff --git a/info/drawing-with-metapost/src/paths-polygon-chain.mp b/info/drawing-with-metapost/src/paths-polygon-chain.mp new file mode 100644 index 0000000000..163fa652dc --- /dev/null +++ b/info/drawing-with-metapost/src/paths-polygon-chain.mp @@ -0,0 +1,24 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef poly expr n of p = + clearxy; z0 = point 0 of p; z1 = point 1 of p; + for i=2 upto n-1: + z[i] = z[i-2] rotatedabout(z[i-1], 360/n-180); + endfor + for i=0 upto n-1: z[i] -- endfor cycle +enddef; +beginfig(1); + path P[]; P3 = for i=0 upto 2: 6 up rotated 120i -- endfor cycle; + fill P3 withcolor 3/4 red; undraw P3; + for n = 4 upto 23: + numeric m; m = floor(n / 2); + P[n] = poly n of subpath (m, m-1) of P[n-1]; + fill P[n] withcolor (n/48)[3/4 if odd n: red else: blue fi, white]; + undraw P[n]; label(decimal n, center P[n]) withcolor white; + endfor +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/paths-polygon-chain.pdf b/info/drawing-with-metapost/src/paths-polygon-chain.pdf Binary files differnew file mode 100644 index 0000000000..dadf60b9de --- /dev/null +++ b/info/drawing-with-metapost/src/paths-polygon-chain.pdf diff --git a/info/drawing-with-metapost/src/closed-polygon-tops.mp b/info/drawing-with-metapost/src/paths-polygon-tops.mp index 9943092ea8..9943092ea8 100644 --- a/info/drawing-with-metapost/src/closed-polygon-tops.mp +++ b/info/drawing-with-metapost/src/paths-polygon-tops.mp diff --git a/info/drawing-with-metapost/src/closed-polygon-tops.pdf b/info/drawing-with-metapost/src/paths-polygon-tops.pdf Binary files differindex 3c4a736834..3c4a736834 100644 --- a/info/drawing-with-metapost/src/closed-polygon-tops.pdf +++ b/info/drawing-with-metapost/src/paths-polygon-tops.pdf diff --git a/info/drawing-with-metapost/src/closed-polygons.mp b/info/drawing-with-metapost/src/paths-polygons.mp index 22d4e42f97..22d4e42f97 100644 --- a/info/drawing-with-metapost/src/closed-polygons.mp +++ b/info/drawing-with-metapost/src/paths-polygons.mp diff --git a/info/drawing-with-metapost/src/closed-polygons.pdf b/info/drawing-with-metapost/src/paths-polygons.pdf Binary files differindex 4e827ad6d9..4e827ad6d9 100644 --- a/info/drawing-with-metapost/src/closed-polygons.pdf +++ b/info/drawing-with-metapost/src/paths-polygons.pdf diff --git a/info/drawing-with-metapost/src/closed-reuleaux-geometry.mp b/info/drawing-with-metapost/src/paths-reuleaux-geometry.mp index f4e69f3b51..f4e69f3b51 100644 --- a/info/drawing-with-metapost/src/closed-reuleaux-geometry.mp +++ b/info/drawing-with-metapost/src/paths-reuleaux-geometry.mp diff --git a/info/drawing-with-metapost/src/closed-reuleaux-geometry.pdf b/info/drawing-with-metapost/src/paths-reuleaux-geometry.pdf Binary files differindex 190c7b6b22..190c7b6b22 100644 --- a/info/drawing-with-metapost/src/closed-reuleaux-geometry.pdf +++ b/info/drawing-with-metapost/src/paths-reuleaux-geometry.pdf diff --git a/info/drawing-with-metapost/src/closed-reuleaux-set.mp b/info/drawing-with-metapost/src/paths-reuleaux-set.mp index 4088ea8421..4088ea8421 100644 --- a/info/drawing-with-metapost/src/closed-reuleaux-set.mp +++ b/info/drawing-with-metapost/src/paths-reuleaux-set.mp diff --git a/info/drawing-with-metapost/src/closed-reuleaux-set.pdf b/info/drawing-with-metapost/src/paths-reuleaux-set.pdf Binary files differindex 9863d3d1cf..9863d3d1cf 100644 --- a/info/drawing-with-metapost/src/closed-reuleaux-set.pdf +++ b/info/drawing-with-metapost/src/paths-reuleaux-set.pdf diff --git a/info/drawing-with-metapost/src/saturn-code.mp b/info/drawing-with-metapost/src/paths-saturn.mp index 9e80e0a492..1109dee168 100644 --- a/info/drawing-with-metapost/src/saturn-code.mp +++ b/info/drawing-with-metapost/src/paths-saturn.mp @@ -1,3 +1,9 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); path globe, gap, ring[], limb[]; globe = fullcircle scaled 2cm; gap = fullcircle xscaled 3cm yscaled .8cm; @@ -15,3 +21,6 @@ picture saturn; saturn = image( fill limb2 withcolor .2 red + .1 green + .7 white; ); draw saturn rotated 30; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/saturn.pdf b/info/drawing-with-metapost/src/paths-saturn.pdf Binary files differindex 3ba35ab965..3ba35ab965 100644 --- a/info/drawing-with-metapost/src/saturn.pdf +++ b/info/drawing-with-metapost/src/paths-saturn.pdf diff --git a/info/drawing-with-metapost/src/paths-schlafli-polygons.mp b/info/drawing-with-metapost/src/paths-schlafli-polygons.mp new file mode 100644 index 0000000000..e0939c1f19 --- /dev/null +++ b/info/drawing-with-metapost/src/paths-schlafli-polygons.mp @@ -0,0 +1,28 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb + +vardef gcd(expr a, b) = + if b = 0: a else: gcd(b, a mod b) fi +enddef; + +beginfig(1); + for n=2 upto 24: + for s=1 upto floor n/2: + pair p; p = (12n - 24s, -24n); + path gon; gon = for t=0 upto n/gcd(s,n) - 1: + 10 up rotated (360/n * s * t) -- + endfor cycle; + if (n mod s = 0): + fill gon shifted p withcolor PuBuGn[9][1+floor (n/s/6)]; + label("$" & decimal (n/s) & "$", p); + fi + draw gon shifted p withpen pencircle scaled 1/8; + endfor + endfor +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/gons.pdf b/info/drawing-with-metapost/src/paths-schlafli-polygons.pdf Binary files differindex acdbb350d8..545a62a9ef 100644 --- a/info/drawing-with-metapost/src/gons.pdf +++ b/info/drawing-with-metapost/src/paths-schlafli-polygons.pdf diff --git a/info/drawing-with-metapost/src/closed-standards.mp b/info/drawing-with-metapost/src/paths-standards.mp index a3296e6af2..331bb4fb04 100644 --- a/info/drawing-with-metapost/src/closed-standards.mp +++ b/info/drawing-with-metapost/src/paths-standards.mp @@ -5,8 +5,8 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -path unitse; unitse = superellipse(1/2 right, 1/2 up, 1/2 left, 1/2 down,.8); -path xx, yy; xx = (left -- right) scaled 144; yy = (down -- up) scaled 89; +path unitse; unitse = superellipse(1/2 right, 1/2 up, 1/2 left, 1/2 down, 13/16); +path xx, yy; xx = 72 left -- 144 right; yy = 42 down -- 89 up; path u, c, s; u = unitsquare scaled 72; c = fullcircle scaled 72; diff --git a/info/drawing-with-metapost/src/closed-standards.pdf b/info/drawing-with-metapost/src/paths-standards.pdf Binary files differindex 7f3a42a63e..814093509f 100644 --- a/info/drawing-with-metapost/src/closed-standards.pdf +++ b/info/drawing-with-metapost/src/paths-standards.pdf diff --git a/info/drawing-with-metapost/src/paths-superellipses.mp b/info/drawing-with-metapost/src/paths-superellipses.mp new file mode 100644 index 0000000000..88e3c57dc6 --- /dev/null +++ b/info/drawing-with-metapost/src/paths-superellipses.mp @@ -0,0 +1,26 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +def gcd(expr a, b) = if b = 0: a else: gcd(b, a mod b) fi enddef; + +beginfig(1); + + for s = 20 upto 31: + pair z; z = (75s mod 300, if s < 20: 80 elseif s < 24: 0 elseif s < 28: -80 else: -160 fi); + path S; S = superellipse(36 right, 36 up, 36 left, 36 down, 1/32 s); + if (23 < s) and (s < 28): + fill S shifted z withcolor 15/16[blue, white]; + fi + draw S shifted z; + numeric n, d, g; g = gcd(s, 32); n = s/g; d = 32/g; + label("$\frac{" & decimal n & "}{" & decimal d & "}$", z); + endfor + + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/paths-superellipses.pdf b/info/drawing-with-metapost/src/paths-superellipses.pdf Binary files differnew file mode 100644 index 0000000000..32791d6386 --- /dev/null +++ b/info/drawing-with-metapost/src/paths-superellipses.pdf diff --git a/info/drawing-with-metapost/src/closed-triangles.mp b/info/drawing-with-metapost/src/paths-triangles.mp index b39a9bbf92..b39a9bbf92 100644 --- a/info/drawing-with-metapost/src/closed-triangles.mp +++ b/info/drawing-with-metapost/src/paths-triangles.mp diff --git a/info/drawing-with-metapost/src/closed-triangles.pdf b/info/drawing-with-metapost/src/paths-triangles.pdf Binary files differindex e42164b4b7..e42164b4b7 100644 --- a/info/drawing-with-metapost/src/closed-triangles.pdf +++ b/info/drawing-with-metapost/src/paths-triangles.pdf diff --git a/info/drawing-with-metapost/src/penrose-P3.pdf b/info/drawing-with-metapost/src/penrose-P3.pdf Binary files differdeleted file mode 100644 index 71c9c5d98b..0000000000 --- a/info/drawing-with-metapost/src/penrose-P3.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/penrose-stages.mp b/info/drawing-with-metapost/src/penrose-stages.mp deleted file mode 100644 index 94f3800b4c..0000000000 --- a/info/drawing-with-metapost/src/penrose-stages.mp +++ /dev/null @@ -1,39 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input penrose -beginfig(1); - path s, t; phi = 1.61803398875; - s = unitsquare shifted -(1/2, 1/2) rotated 45 xscaled phi yscaled 2 sind(36) scaled 20; - t = unitsquare shifted -(1/2, 1/2) rotated 45 xscaled (1/phi) yscaled 2 sind(72) scaled 20; - picture p[]; - p1 = image( - draw (left--right) scaled 30 dashed evenly; - draw s; - ); - p3 = image( - draw (left--right) scaled 13 dashed evenly; - draw t; - ) rotated 90 shifted 130 right; - p2 = image( - draw subpath (1, 3) of s -- cycle dashed withdots scaled 1/16 withpen pencircle scaled 1/8 withcolor 1/2; - inflate_wide(3, 1, point 1 of s, point 2 of s, point 3 of s); - ) shifted 64 right; - p4 = image( - draw subpath (1, 3) of t -- cycle dashed withdots scaled 1/16 withpen pencircle scaled 1/8 withcolor 1/2; - inflate_tall(3, 1, point 1 of t, point 2 of t, point 3 of t); - ) rotated 90 shifted 200 right; - ahangle := 30; - draw p1; - draw p2; - draw p3; - draw p4; - drawarrow (7 left -- 8 right) shifted point 7/4 of bbox p1 withcolor .67 red; - drawarrow (1 left -- 14 right) shifted point 7/4 of bbox p3 withcolor .67 red; - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/penrose-stages.pdf b/info/drawing-with-metapost/src/penrose-stages.pdf Binary files differdeleted file mode 100644 index ae8b8bc3a6..0000000000 --- a/info/drawing-with-metapost/src/penrose-stages.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/penrose.mp b/info/drawing-with-metapost/src/penrose.mp deleted file mode 100644 index 930a66680c..0000000000 --- a/info/drawing-with-metapost/src/penrose.mp +++ /dev/null @@ -1,84 +0,0 @@ -input colorbrewer-rgb -numeric psi, size; -psi = (sqrt 5 - 1) / 2; -size = 800; -vardef inflate_tall(expr mode, level, a, b, c) = - save d, e; pair d, e; - if level = 0: - drawoptions(withpen pencircle scaled 1/8); - filldraw a--b--c--cycle withcolor (abs(b)/size)[Reds 7 2, Blues 8 2]; - if mode = 2: - draw c--a--b; - else: - % save arc; path arc; - % arc = fullcircle rotated angle (c-a) scaled 1/2 abs(b-a) shifted a - % if turningnumber (a--b--c--cycle) < 0: cutafter else: cutbefore fi (a--b); - % cutdraw arc withpen pencircle scaled 3/2 withcolor Reds 7 4; - % cutdraw arc reflectedabout(b, 1/2[a,c]) withpen pencircle scaled 3/2 withcolor Blues 8 8; - % draw arc reflectedabout(b, 1/2[a,c]) withpen pencircle scaled 1/2 withcolor Blues 8 2; - draw a--b--c; - fi - drawoptions(); - else: - if mode = 3: - d = psi[b,a]; - inflate_tall(mode, level - 1, d, c, a); - inflate_wide(mode, level - 1, c, d, b); - elseif mode = 2: - d = psi[a, b]; - e = psi[b, c]; - inflate_tall(mode, level - 1, c, a, e); - inflate_tall(mode, level - 1, d, a, e); - inflate_wide(mode, level - 1, e, d, b); - fi - fi -enddef; -vardef inflate_wide(expr mode, level, a, b, c) = - save d, e; pair d, e; - if level = 0: - drawoptions(withpen pencircle scaled 1/8); - filldraw a--b--c--cycle withcolor (abs(b)/size)[Reds 7 3, white]; - if mode = 2: - draw c--a--b; - else: - % save arc; path arc; - % arc = fullcircle rotated angle (c-a) scaled 3/2 abs (b-a) shifted a - % if turningnumber (a--b--c--cycle) < 0: cutafter else: cutbefore fi (a--b); - % cutdraw arc withpen pencircle scaled 3/2 withcolor Reds 7 4; - % path arc; - % arc = fullcircle rotated angle (a-c) scaled 1/2 abs (b-a) shifted c - % if turningnumber (a--b--c--cycle) > 0: cutafter else: cutbefore fi (c--b); - % cutdraw arc withpen pencircle scaled 3/2 withcolor Blues 8 8; - % draw arc withpen pencircle scaled 1/2 withcolor Blues 8 2; - draw a--b--c; - - fi - drawoptions(); - else: - if mode = 3: - d = psi[a,b]; e = psi[a,c]; - inflate_tall(mode, level - 1, d, e, b); - inflate_wide(mode, level - 1, e, d, a); - inflate_wide(mode, level - 1, c, e, b); - elseif mode = 2: - d = psi[c, a]; - inflate_tall(mode, level - 1, d, c, b); - inflate_wide(mode, level - 1, b, d, a); - fi - fi -enddef; - -vardef penrose(expr mode) = - save a, b, c, P, R; - pair a, b, c; - b = origin; - c = (sind(18), sind(72)) scaled size; - a = (-xpart c, ypart c); - picture P; P = image(inflate_tall(mode, 7, a, b, c)); - picture R; R = image( - for t = 0 upto 9: - draw P if odd t: reflectedabout(b, c) fi rotatedabout(b, 72t); - endfor); - clip R to (unitsquare shifted -(1/2, 1/2) xscaled 987 yscaled 610); - R -enddef; diff --git a/info/drawing-with-metapost/src/pens-arrow-styles.mp b/info/drawing-with-metapost/src/pens-arrow-styles.mp new file mode 100644 index 0000000000..7e1fa42ef7 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-arrow-styles.mp @@ -0,0 +1,59 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + + +path s, c; + +s = origin -- 80 right; +c = quartercircle scaled 40; + +labeloffset := 20; + +vardef make_arrows(expr t) = image( + picture A, B; + A = image(drawarrow s; drawarrow c;); + B = image(drawdblarrow s; drawdblarrow c;); + label.lft(A, origin); + label.rt(B, origin); + picture T; T = thelabel("\texttt{" & t & "}", 8 down); bboxmargin := 4; path p; p = bbox T; + path S; S = superellipse(point 3/2 of p, point 5/2 of p, point 7/2 of p, point 1/2 of p, 0.78); + string x; x = substring (0, 1) of t; + fill S withcolor if x = "m": 7/8[red, white] elseif x = "c": 7/8[blue, white] else: white fi; + draw S; draw T; +) enddef; + +beginfig(1); + + label("\mpl{drawarrow}", (-60, 28)); + label("\mpl{drawdblarrow}", (60, 28)); + + pair v; v = 40 down; + + draw make_arrows("1"); + + ahangle := 20; ahlength := 6; + draw make_arrows("2") shifted v; + + ahangle := 45; ahlength := 4; +input mparrows +setarrows(open); draw make_arrows("mp1") shifted 2.5v; +setarrows(defaultunfilled); draw make_arrows("mp2") shifted 3.5v; +setarrows(barbed); draw make_arrows("mp3") shifted 4.5v; + + +input cmarrows +setup_cmarrows(macro_name="drawarrow"; arrow_name="texarrow"; parameter_file="cmr10.mf"); +setup_cmarrows(macro_name="drawdblarrow"; arrow_name="twowayarrow"; parameter_file="cmr10.mf"); + draw make_arrows("cm1") shifted 6v; +setup_cmarrows(arrow_name="lefthalfarrow"; parameter_file="cmr10.mf"; macro_name="drawarrow"); +setup_cmarrows(arrow_name="paralleloppositelefthalfarrows"; parameter_file="cmr10.mf"; macro_name="drawdblarrow"); + draw make_arrows("cm2") shifted 7v; + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-arrow-styles.pdf b/info/drawing-with-metapost/src/pens-arrow-styles.pdf Binary files differnew file mode 100644 index 0000000000..8fb68a74d4 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-arrow-styles.pdf diff --git a/info/drawing-with-metapost/src/pens-besides.mp b/info/drawing-with-metapost/src/pens-besides.mp new file mode 100644 index 0000000000..36a930b0d9 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-besides.mp @@ -0,0 +1,63 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +vardef extended(expr p) = + -42 unitvector(direction 0 of p) shifted point 0 of p .. p .. + +42 unitvector(direction 1 of p) shifted point 1 of p +enddef; + +vardef chopper expr t of p = + (up--down) scaled 42 + rotated 1/2(angle direction t-eps of p + angle direction t+eps of p) + shifted point t of p +enddef; + +vardef beside(expr p, d) = + save n, a, b, aa, bb; numeric n; n = length p; + pair a, b, aa, bb; path _part[]; + for i = 1 upto n: + aa := postcontrol i-1 of p - point i-1 of p; + bb := point i of p - precontrol i of p; + a := unitvector(aa) rotated -90 scaled d; + b := unitvector(bb) rotated -90 scaled d; + _part[i] = extended( + point i-1 of p shifted a {aa} .. point i of p shifted b {bb} + ) cutbefore chopper i-1 of p cutafter chopper i of p; + endfor + _part[1] for i=2 upto n: .. _part[i] endfor if cycle p: .. cycle fi +enddef; +beginfig(1); + + path P[]; + + % P1 = origin -- (48,3) -- (96,-3) -- 144 right; + P2 = (22, 13) --- (92, 10) .. (120, 32) .. (138,50) .. (200, 69) .. + (280, 78) .. (300, 84) .. (315, 100) .. (322, 150) .. + (300, 186) --- (200, 187) --- (100, 188) --- (25, 188.75) -- cycle + ; + + % % P1 := P1 shifted (center P2 - center P1) shifted 20 up; + % % P2 = fullcircle scaled 120; + % P3 = (reverse halfcircle -- origin -- down) scaled 64; + % P4 = for i=0 upto 4: 60 up rotated 72i -- endfor cycle; + % P5 = (left {dir 42} .. origin .. right {dir 42}) scaled 64; + % P6 = (left {dir 42} .. right {dir 42}) scaled 64; + % P7 = 40 left {right} .. 20 up .. 40 up {left} .. 20 up .. {right} 40 right; + + for i=1 upto 10: + if known P[i]: + P[i] := P[i] shifted (150i, 0); + draw beside(P[i], 2) withcolor \mpcolor{textblue}; + draw P[i]; + draw beside(P[i], -2) withcolor \mpcolor{textred}; + fi + endfor + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-besides.pdf b/info/drawing-with-metapost/src/pens-besides.pdf Binary files differnew file mode 100644 index 0000000000..a1ae022f33 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-besides.pdf diff --git a/info/drawing-with-metapost/src/pens-crossings.mp b/info/drawing-with-metapost/src/pens-crossings.mp new file mode 100644 index 0000000000..6c4f983839 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-crossings.mp @@ -0,0 +1,57 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + +vardef connect(expr a, b, r, want_erase) = + save p; path p; p = a {b-a rotated r} .. b; + if want_erase: + draw p withpen pencircle scaled 4 withcolor background; + fi + drawarrow p + cutbefore fullcircle scaled 20 shifted a + cutafter fullcircle scaled 20 shifted b; +enddef; + +beginfig(1); + % how many points? + N = 7; + % define the points, from the top, counter-clockwise + for i=0 upto N-1: + z[i] = up scaled 100 rotated (360/N*i); + endfor + interim ahangle := 30; % with slim arrow heads + + picture P[]; + P1 = image( + for i=0 upto N-1: + connect(z[i], z[(i+1) mod N], -30, false); + connect(z[i], z[(i+2) mod N], -20, false); + connect(z[i], z[(i+4) mod N], 30, false); + endfor + % label all the points... + for i=0 upto N-1: + label(decimal (i+1), z[i]) withcolor .67 red; + endfor + ); + P2 = image( + for i=0 upto N-1: + connect(z[i], z[(i+1) mod N], -30, true); + connect(z[i], z[(i+2) mod N], -20, true); + connect(z[i], z[(i+4) mod N], 30, true); + endfor + % label all the points... + for i=0 upto N-1: + label(decimal (i+1), z[i]) withcolor .67 red; + endfor + ); + + label.top(P1, 16 up); + label("Do you think it looks better with crossings?", origin); + label.bot(P2, 10 down); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-crossings.pdf b/info/drawing-with-metapost/src/pens-crossings.pdf Binary files differnew file mode 100644 index 0000000000..5a38f33f3d --- /dev/null +++ b/info/drawing-with-metapost/src/pens-crossings.pdf diff --git a/info/drawing-with-metapost/src/pens-curly.mp b/info/drawing-with-metapost/src/pens-curly.mp new file mode 100644 index 0000000000..a9013455e3 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-curly.mp @@ -0,0 +1,46 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +pair r; r = dir 30; +path S; S = origin {r} .. 300 right {r}; + +numeric head_length, tail_length, amplitude, lambda; +head_length = tail_length = 13; amplitude = 1; lambda = 2; + +vardef zigzag expr p = + save a, b; numeric a, b; a = arctime head_length of p; b = arctime arclength p - tail_length of p; + subpath(0, a) of p + -- _ziggy(subpath(a, b) of p, false) -- + subpath(b, infinity) of p +enddef; +vardef wavy expr p = + save a, b; numeric a, b; a = arctime head_length of p; b = arctime arclength p - tail_length of p; + subpath(0, a) of p + ... _ziggy(subpath(a, b) of p, true) ... + subpath(b, infinity) of p +enddef; + +vardef _ziggy(expr p, soft) = + save t, k, A, s; numeric t, k, A, s; k = 0; A = arclength p; s = A / round(A/lambda); + + point 0 of p + for i=s step s until A: + hide(t := arctime i of p;) + if soft: .. else: -- fi amplitude * if odd incr k: up else: down fi rotated angle direction t of p shifted point t of p + endfor + cutbefore fullcircle scaled 4 lambda shifted point 0 of p + cutafter fullcircle scaled 4 lambda shifted point infinity of p +enddef; + +beginfig(1); + draw S; + drawarrow zigzag S shifted 30 down; + amplitude := 2/3; lambda := 3; + drawarrow wavy S shifted 60 down; +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-curly.pdf b/info/drawing-with-metapost/src/pens-curly.pdf Binary files differnew file mode 100644 index 0000000000..9cdece5534 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-curly.pdf diff --git a/info/drawing-with-metapost/src/pens-feynmp-styles.mp b/info/drawing-with-metapost/src/pens-feynmp-styles.mp new file mode 100644 index 0000000000..d8f014ae06 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-feynmp-styles.mp @@ -0,0 +1,34 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\mplibtextextlabel{enable} +\mplibshowlog{enable} +\begin{mplibcode} +input feynmp; +beginfig(1); + path p[]; + p1 = (left -- right) scaled 50 rotated 40; + p2 = (left {dir 45} .. right {dir 45}) scaled 50 rotated 40; + p3 = fullcircle scaled 72 yscaled 4/5; + p4 = unitsquare shifted -(1/2, 1/2) scaled 50; + + labeloffset := 13; + ahangle := 30; + for i=1, 2, 3, 4: + numeric y; y = 0; + forsuffixes $=curly, zigzag, wiggly: + drawarrow p[i] shifted (96i, 96(incr y)) withcolor 3/4[if i=4: red else: blue fi, white]; + draw $ p[i] shifted (96i, 96y); + if i=1: label.ulft("\mpl{" & str $ & "}", 96(i, y)) fi; + endfor + endfor + + label.bot("The un-morphed paths are drawn faintly in colour behind the morphed paths.", point 1/2 of bbox currentpicture); + label.bot("The macros work on open or closed paths, \red{provided there are no sharp corners}.", point 1/2 of bbox currentpicture shifted 7 up); + + label.ulft("\red{Hmmm...}", point 2 of p4 shifted (4*96, 104)); + +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pens-feynmp-styles.pdf b/info/drawing-with-metapost/src/pens-feynmp-styles.pdf Binary files differnew file mode 100644 index 0000000000..7ae5e05d43 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-feynmp-styles.pdf diff --git a/info/drawing-with-metapost/src/pens-fleuron.mp b/info/drawing-with-metapost/src/pens-fleuron.mp new file mode 100644 index 0000000000..e1de211317 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-fleuron.mp @@ -0,0 +1,17 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); + -z1 = z4 = 7 dir 8; + y2 - y1 = y4 - y3 = 3(y4 - y1); + z2 - z1 = z4 - z3 = whatever * dir 50; + draw z1 .. controls z2 and z3 .. z4 withpen pencircle xscaled 1.2 yscaled 0.2 rotated 50; + undraw z1 .. controls z2 and z3 .. z4 withpen pencircle xscaled 0.4 yscaled 0.03 rotated 50; + for i=1 upto 5: + draw currentpicture shifted ((2**(i-1))*z4); + endfor + currentpicture := currentpicture rotated - angle z4; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pens-fleuron.pdf b/info/drawing-with-metapost/src/pens-fleuron.pdf Binary files differnew file mode 100644 index 0000000000..621e808098 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-fleuron.pdf diff --git a/info/drawing-with-metapost/src/pens-greek-meander.mp b/info/drawing-with-metapost/src/pens-greek-meander.mp new file mode 100644 index 0000000000..663bff3d1a --- /dev/null +++ b/info/drawing-with-metapost/src/pens-greek-meander.mp @@ -0,0 +1,40 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef meander expr p = + save a, u, v, d, dy; numeric a, u, v, d; pair dy; + d = 4 xpart urcorner makepath currentpen; + a = arclength p; v = round(a/8d); u = a if v > 1: / v fi; + if not cycle p: point 0 of p -- fi for t = 0 step u until a-4eps: + hide(dy := d*unitvector(direction arctime t+1/2u of p of p rotated 90)) + subpath(arctime t of p, arctime t+u-2d of p) of p shifted 3dy + -- + subpath(arctime t+u-2d of p, arctime t+1/2 u of p) of p shifted -dy + -- + subpath(arctime t+1/2u of p, arctime t+2d of p) of p shifted dy + -- + subpath(arctime t+2d of p, arctime t+u of p) of p shifted -3dy + -- + endfor if cycle p: cycle else: point infinity of p fi +enddef; + +beginfig(1); + path r; r = (left {right} .. right rotated 10) scaled 100; + linejoin := mitered; + path p[]; + p1 = (left -- right) scaled 50 rotated 40; + p2 = (left {dir 45} .. right {dir 45}) scaled 50 rotated 40; + p3 = fullcircle scaled 72 yscaled 4/5; + p4 = unitsquare shifted -(1/2, 1/2) scaled 50; + interim labeloffset := 13; + interim ahangle := 30; + for i=1, 2, 3, 4: + drawarrow p[i] shifted (96i, 0) withcolor 3/4[if i=4: red else: blue fi, white]; + draw meander p[i] shifted (96i, 0); + endfor + label.ulft("\texttt{meander}", (96, 0)); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pens-greek-meander.pdf b/info/drawing-with-metapost/src/pens-greek-meander.pdf Binary files differnew file mode 100644 index 0000000000..24081c455f --- /dev/null +++ b/info/drawing-with-metapost/src/pens-greek-meander.pdf diff --git a/info/drawing-with-metapost/src/pens-highway.mp b/info/drawing-with-metapost/src/pens-highway.mp new file mode 100644 index 0000000000..dab8aaf397 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-highway.mp @@ -0,0 +1,15 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +path S; S = origin .. 100 right {down} .. origin .. 100 left {down} .. cycle; +beginfig(1); +draw S withpen pencircle scaled 6; +draw S withpen pencircle scaled 5 withcolor 1/2[red, green] * 2; +draw S withpen pencircle scaled 4.5; +draw S dashed evenly scaled 1/2 withcolor white; +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-highway.pdf b/info/drawing-with-metapost/src/pens-highway.pdf Binary files differnew file mode 100644 index 0000000000..9b3e662d5a --- /dev/null +++ b/info/drawing-with-metapost/src/pens-highway.pdf diff --git a/info/drawing-with-metapost/src/pens-line-caps-and-joins.mp b/info/drawing-with-metapost/src/pens-line-caps-and-joins.mp new file mode 100644 index 0000000000..8dd01c2dc7 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-line-caps-and-joins.mp @@ -0,0 +1,57 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\mplibtextextlabel{enable} +\begin{document} +\begin{mplibcode} +beginfig(1); +numeric u; u = 56; +z1 = right scaled u; +z2 = z1 rotated 90; +z3 = z2 rotated 90; +z4 = z3 rotated 90; +z5 = 1/2[z1,z2]; +z6 = 1/2[z2,z3]; +z7 = 1/2[z3,z4]; +z8 = 1/2[z4,z1]; + + +string capnames[], joinnames[]; +capnames[butt] = "\mpl{butt}"; +capnames[rounded] = "\mpl{rounded}"; +capnames[squared] = "\mpl{squared}"; +joinnames[mitered] = "\mpl{mitered}"; +joinnames[rounded] = "\mpl{rounded}"; +joinnames[beveled] = "\mpl{beveled}"; + +picture p; numeric r; r = 2; interim labeloffset := 1; +for i=butt, rounded, squared: + for j = mitered, rounded, beveled: + linecap := i; + linejoin := j; + p := image( + draw fullcircle scaled 8 shifted z5 withpen pencircle scaled 1/8 withcolor \mpcolor{textred}; + drawoptions (withpen pencircle scaled 3); + draw unitsquare shifted -(1/2,1/2) scaled 2u withcolor 7/8; + label.top("\mpl{linecap}", z6); + label.bot(capnames[i], z6); + label.top("\mpl{linejoin}", z8); + label.bot(joinnames[j], z8); + drawarrow z4 -- -(r, r) -- z3; + draw z2-- (r, r) -- z1; + drawdot(z5); + drawarrow halfcircle scaled u rotated 180 shifted z4; + drawoptions(); + ) shifted (5/2u*i, -11/4u*j); + draw p; + if (i=rounded) and (j=rounded): + draw bbox p dashed withdots scaled 1/4 + withcolor \mpcolor{textgreen}; + label.urt("\small \textsf{\textit{default}}", point 3 of bbox p) withcolor \mpcolor{textgreen}; + fi + endfor + endfor +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-line-caps-and-joins.pdf b/info/drawing-with-metapost/src/pens-line-caps-and-joins.pdf Binary files differnew file mode 100644 index 0000000000..19cb8b9036 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-line-caps-and-joins.pdf diff --git a/info/drawing-with-metapost/src/pens-pen-oddity.mp b/info/drawing-with-metapost/src/pens-pen-oddity.mp new file mode 100644 index 0000000000..aa0531e4f3 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-pen-oddity.mp @@ -0,0 +1,71 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\def\t#1{\vbox{\let\\\cr\halign{\texttt{##}\hss\cr#1\cr}}} +\def\ts#1{\vbox{\let\\\cr\openup-4pt\halign{\small\hss\mpl{##}\hss\cr#1\cr}}} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + numeric u; u = 16; + pen P[]; + P1 = makepen(for i=1 upto 90: 1/2 dir 4i -- endfor cycle) scaled u; + P10 = pencircle scaled u; + P100 = pencircle scaled 1/2; + P2 = pensquare scaled u; + P20 = pensquare scaled u; + P200 = pensquare; + P3 = pensquare scaled 0.7071 u rotated 45; + P30 = pensquare scaled 0.7071 u rotated 45; + P300 = pensquare scaled 0.35355 rotated 45; + P4 = penrazor scaled u; + P40 = penrazor scaled u; + P400 = penrazor; + path crook; crook = origin -- (5u, 0) -- 7u * dir 30; + + string cap_name[], join_name[], pen_name[]; + cap_name[butt] = "butt"; + cap_name[rounded] = "rounded"; + cap_name[squared] = "squared"; + join_name[beveled] = "beveled"; + join_name[rounded] = "rounded"; + join_name[mitered] = "mitered"; + pen_name1 = "pencircle"; + pen_name2 = "pensquare"; + pen_name3 = "pensquare\\\quad rotated 45"; + pen_name4 = "penrazor"; + + for i=1, 2: + draw (origin -- 360 right) shifted ((0, 2.25-2.8i) scaled 8u); + label.rt("\t{" & pen_name[i] & "}", (0, 2.15-2.8i) scaled 8u); + for cap = rounded, butt, squared: + interim linecap := cap; + for join = rounded, beveled, mitered: + boolean default; default = (cap=rounded) and (join=rounded); + interim linejoin := join; + pair s; s = (cap, 0.8 join) shifted (0, -2.8i) scaled 8u; + draw crook shifted s withpen P[i] + withcolor + (15/16 if default: - 1/8 fi) + if i=1: [blue, white] fi; + draw (2.5u, 3u) shifted s withpen P[10i] withcolor 3/4; + draw fullcircle scaled 20 shifted (2.5u, 3u) shifted s withcolor 3/4 red; + for k=0, 1, 2: + draw makepath(P[i]) shifted point k of crook shifted s withcolor 1/2[blue, white]; + endfor + draw envelope P[i] of crook shifted s; + draw crook shifted s withpen P[100i] withcolor red; + if default: + label("\ts{linecap\\" & cap_name[cap] & "}", s + (0, 5/4u)); + label("\ts{" & join_name[join] & "\\linejoin}", point 1 of crook shifted s shifted (0, -5/4u)); + else: + label("\ts{" & cap_name[cap] & "}", s + (0, u)); + label("\ts{" & join_name[join] & "}", point 1 of crook shifted s shifted (0, -u)); + fi + endfor + endfor + endfor +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-pen-oddity.pdf b/info/drawing-with-metapost/src/pens-pen-oddity.pdf Binary files differnew file mode 100644 index 0000000000..1d4fa06f0a --- /dev/null +++ b/info/drawing-with-metapost/src/pens-pen-oddity.pdf diff --git a/info/drawing-with-metapost/src/pens-strokes.mp b/info/drawing-with-metapost/src/pens-strokes.mp new file mode 100644 index 0000000000..1c3c68a9c0 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-strokes.mp @@ -0,0 +1,109 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +path S; S = origin .. (48, 10) .. (116, -10) .. (165, 10); + +labeloffset := 14; + +beginfig(1); +picture P[]; +numeric n; n = -1; +P[incr n] = image( + draw S; + label.rt("plain", point 3 of S); +); +show incr n; + +P[incr n] = image( + draw S dashed dashpattern(on 4 off 2 on 1 off 2 on 1 off 2); + label.rt("with a dash pattern", point 3 of S); +); + +P[incr n] = image( + cutdraw S dashed dashpattern(on 4 off 1 on 1 off 1 on 1 off 1); + label.rt("with a sharp dash pattern", point 3 of S); +); + +P[incr n] = image( + cutdraw S withpen pencircle scaled 2; + undraw S withpen pencircle scaled 5/4; + cutdraw S dashed evenly scaled 2 shifted right withpen pencircle scaled 5/4; + label.rt("as a railway line", point 3 of S); +); + +show incr n; + +P[incr n] = image( + draw S; + for a = 2 step 6 until arclength S: + numeric t; t = arctime a of S; + draw (down--up) rotated angle direction t of S shifted point t of S; + endfor + label.rt("as a plainer railway line", point 3 of S); +); + +P[incr n] = image( + numeric A; A = arclength S; + for a = 0 step 1/8 until A: + draw point arctime a of S of S withcolor (a / A); + endfor + label.rt("fading away", point 3 of S); +); + +P[incr n] = image( + for i=0 step 1/512 until length S: + draw point i of S withpen pencircle scaled (4 * (1 - i / length S)) + withcolor (i / length S)[1/2 blue, white]; + endfor + label.rt("fading and diminishing", point 3 of S); +); + +path star; star = for i=0 upto 4: 6 up rotated (144i) -- endfor cycle; +P[incr n] = image( + numeric t, i, a; t = i = a = 0; + for k=0 upto 100: + % show (t, arclength S); + exitif t >= arclength S; + a := arctime t of S; + fill star rotated angle direction a of S shifted point a of S + withcolor if odd incr i: blue else: red fi; + t := t + arclength subpath (2, 3) of star; + star := star scaled 0.94; + endfor + label.rt("with a fancy pattern", point 3 of S); +); + +P[incr n] = image( + numeric u, v; u = 2; v = 1; + picture e; e = image( + draw (-u, v) {right} .. {right} (u, -v) withcolor blue; + cutdraw (-u, -v) {right} .. {right} (u, +v) withpen pencircle scaled 1 withcolor background; + draw (-u, -v) {right} .. {right} (u, +v) withcolor red; + ); + picture f; f = image( + draw (-u, v) {right} .. {right} (u, -v) withcolor red; + cutdraw (-u, -v) {right} .. {right} (u, +v) withpen pencircle scaled 1 withcolor background; + draw (-u, -v) {right} .. {right} (u, +v) withcolor blue; + ); + numeric t, a, T, wd, A; t = a = 0; A = arclength S; wd = xpart (lrcorner e - llcorner e); + for k=0 upto 100: + exitif a > A; + t := arctime a of S; + draw if odd k: f else: e fi rotated angle direction t of S shifted point t of S; + a := a + .8 wd; + endfor + label.rt("as a twisted pair", point 3 of S); +); + +for i=0 upto 28: + if known P[i]: + draw P[i] shifted (0, -34i); + fi +endfor +input show_name +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pens-strokes.pdf b/info/drawing-with-metapost/src/pens-strokes.pdf Binary files differnew file mode 100644 index 0000000000..d19c0c5862 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-strokes.pdf diff --git a/info/drawing-with-metapost/src/pens-tubes.mp b/info/drawing-with-metapost/src/pens-tubes.mp new file mode 100644 index 0000000000..f7526fc70a --- /dev/null +++ b/info/drawing-with-metapost/src/pens-tubes.mp @@ -0,0 +1,32 @@ +\documentclass[border=1mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef tubular@#(expr p) = image( + draw p withpen pencircle scaled 8; + for w = 7.5 step -.5 until 1: + draw p withpen pencircle scaled w withcolor (sqrt(w/8))[white, 1/2 @#]; + endfor +) enddef; +vardef ctubular@#(expr p) = image( + cutdraw p withpen pencircle scaled 8; + for w = 7.5 step -.5 until 1: + cutdraw p withpen pencircle scaled w withcolor (sqrt(w/8))[white, 1/2 @#]; + endfor +) enddef; +beginfig(1); +path half_reef; +d = 1/4; +half_reef = (-7, -d) --- (-2, -d) ... (0, -1) .. (2, 0) .. (0, 1) ... (-2, d) --- (-5, d); +half_reef := half_reef scaled 20; +draw tubular.red(half_reef); +draw tubular.blue(half_reef reflectedabout (up, down)); +draw ctubular.red(subpath(3/2, 5/2) of half_reef); +draw ctubular.red(subpath(7/2, 9/2) of half_reef); +% for i=0 step 1/2 until length half_reef: dotlabel.top(decimal i, point i of half_reef); endfor + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pens-tubes.pdf b/info/drawing-with-metapost/src/pens-tubes.pdf Binary files differnew file mode 100644 index 0000000000..aded171667 --- /dev/null +++ b/info/drawing-with-metapost/src/pens-tubes.pdf diff --git a/info/drawing-with-metapost/src/pics-border-common.mp b/info/drawing-with-metapost/src/pics-border-common.mp new file mode 100644 index 0000000000..e2d8711d2a --- /dev/null +++ b/info/drawing-with-metapost/src/pics-border-common.mp @@ -0,0 +1,30 @@ +input colorbrewer-rgb +picture orthogonals; +orthogonals = image( + interim ahangle := 30; + z0 = 42 left rotated normaldeviate; + z1 = 30 up rotated normaldeviate; + z2 = 31 right rotated normaldeviate; + z3 = 34 down rotated normaldeviate; + path s[]; + for i=0 upto 3: + s[i] = unitsquare zscaled (z[(i+1) mod 4] - z[i]) shifted z[i]; + z[i+4] = 1/2[point 0 of s[i], point 2 of s[i]]; + endfor + z8 = whatever[z4, z6] = whatever[z5, z7]; + + for i=0 upto 3: + fill s[i] withcolor if odd i: Blues else: Oranges fi 8 1; + draw point 3 of s[i] -- subpath (1,4) of s[i] -- point 2 of s[i] withcolor 3/4; + drawarrow subpath (0, 1) of s[i]; + endfor + draw unitsquare scaled 5 rotated angle (z4-z6) shifted z8 withcolor 3/4; + drawarrow z4--z6; + drawarrow z5--z7; +); + +vardef with_rounded_corners expr p = + for i=1 upto length p: + subpath (i-15/16, i-1/16) of p .. + endfor cycle +enddef; diff --git a/info/drawing-with-metapost/src/pics-border-dashed.mp b/info/drawing-with-metapost/src/pics-border-dashed.mp new file mode 100644 index 0000000000..c14e680da4 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-border-dashed.mp @@ -0,0 +1,23 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\begin{mplibcode} +input pics-border-common +beginfig(1); +draw orthogonals; + +bboxmargin := 16; +draw with_rounded_corners bbox currentpicture + dashed evenly scaled 1/2; + +path b; b = bbox currentpicture; +label.urt(btex +\smallmpexternal[firstline=26,lastline=30]{pics-border-common.mp} +etex, point 3/2 of b shifted 10 left); +label.lrt(btex +\smallmpexternal[firstline=10,lastline=12]{pics-border-dashed.mp} +etex, point 3/2 of b shifted 10 left); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pics-border-dashed.pdf b/info/drawing-with-metapost/src/pics-border-dashed.pdf Binary files differnew file mode 100644 index 0000000000..fdd637175b --- /dev/null +++ b/info/drawing-with-metapost/src/pics-border-dashed.pdf diff --git a/info/drawing-with-metapost/src/pics-border-rope.mp b/info/drawing-with-metapost/src/pics-border-rope.mp new file mode 100644 index 0000000000..4ac4baf27d --- /dev/null +++ b/info/drawing-with-metapost/src/pics-border-rope.mp @@ -0,0 +1,13 @@ +\documentclass[border=2mm]{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +input pics-border-common +input rope +beginfig(1); +draw orthogonals; % from the common code... +bboxmargin := 16; +draw rope with_rounded_corners bbox currentpicture; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pics-border-rope.pdf b/info/drawing-with-metapost/src/pics-border-rope.pdf Binary files differnew file mode 100644 index 0000000000..e36ce677ad --- /dev/null +++ b/info/drawing-with-metapost/src/pics-border-rope.pdf diff --git a/info/drawing-with-metapost/src/pics-border-shadow.mp b/info/drawing-with-metapost/src/pics-border-shadow.mp new file mode 100644 index 0000000000..47281ecf63 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-border-shadow.mp @@ -0,0 +1,18 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\begin{mplibcode} +input pics-border-common +beginfig(1); +draw orthogonals; +bboxmargin := 16; +picture P; P = currentpicture; +fill bbox P shifted (3,-3) withcolor 3/4; +unfill bbox P; draw bbox P; draw P; +label.rt(btex +\smallmpexternal[firstline=9, lastline=12]{pics-border-shadow.mp} +etex, point 3/2 of bbox currentpicture shifted 10 left); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pics-border-shadow.pdf b/info/drawing-with-metapost/src/pics-border-shadow.pdf Binary files differnew file mode 100644 index 0000000000..09af23599a --- /dev/null +++ b/info/drawing-with-metapost/src/pics-border-shadow.pdf diff --git a/info/drawing-with-metapost/src/corners.mp b/info/drawing-with-metapost/src/pics-corners.mp index cf4e3ad416..cf4e3ad416 100644 --- a/info/drawing-with-metapost/src/corners.mp +++ b/info/drawing-with-metapost/src/pics-corners.mp diff --git a/info/drawing-with-metapost/src/corners.pdf b/info/drawing-with-metapost/src/pics-corners.pdf Binary files differindex 2588267ec8..2588267ec8 100644 --- a/info/drawing-with-metapost/src/corners.pdf +++ b/info/drawing-with-metapost/src/pics-corners.pdf diff --git a/info/drawing-with-metapost/src/double-angle.mp b/info/drawing-with-metapost/src/pics-double-angle.mp index f09885dfb5..f09885dfb5 100644 --- a/info/drawing-with-metapost/src/double-angle.mp +++ b/info/drawing-with-metapost/src/pics-double-angle.mp diff --git a/info/drawing-with-metapost/src/double-angle.pdf b/info/drawing-with-metapost/src/pics-double-angle.pdf Binary files differindex f0721c8b48..f0721c8b48 100644 --- a/info/drawing-with-metapost/src/double-angle.pdf +++ b/info/drawing-with-metapost/src/pics-double-angle.pdf diff --git a/info/drawing-with-metapost/src/pics-draw-picture.mp b/info/drawing-with-metapost/src/pics-draw-picture.mp new file mode 100644 index 0000000000..84ffc19d37 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-draw-picture.mp @@ -0,0 +1,74 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); +numeric s; s = 21; +path alpha; +alpha = ((-2s, s) {right} +.. halfcircle rotated -90 scaled 2s shifted (2s, 0) +.. {left} (-2s, -s)) shifted (s*left); + +vardef overdraw(expr a, b, r, P, shade) = + linecap := butt; + undraw subpath (a+r, b-r) of P withpen pencircle scaled 2; + draw subpath (a, b) of P withcolor shade; +enddef; + +picture cb; cb = image( + draw alpha withcolor 2/3 red; + undraw alpha rotated 180 withpen pencircle scaled 2; + draw alpha rotated 180 withcolor 2/3 blue; + overdraw(0.21, 0.36, 0.02, alpha, 2/3 red); + overdraw(0.67, 0.86, 0.02, alpha, 2/3 red); + overdraw(3.4, 4.3, 0.1, alpha, 2/3 red); + overdraw(5.4, 5.6, 0.02, alpha, 2/3 red); + overdraw(5.4, 5.6, 0.02, alpha rotated 180, 2/3 blue); +); + + picture P[]; + + P1 = image(draw cb; label.rt("\mpl{draw cb;}", point 3/2 of bbox currentpicture)); + P2 = image(draw cb withpen pencircle scaled 4; label.rt("\mpl{draw cb withpen pencircle scaled 4;}", point 3/2 of bbox currentpicture)); + P3 = image(draw cb withcolor 1/2; label.rt("\mpl{draw cb withcolor 1/2;}", point 3/2 of bbox currentpicture)); + P4 = image(draw cb withpen pencircle scaled 4 withcolor 1/2; label.rt("\mpl{draw cb withpen pencircle scaled 4 withcolor 1/2;}", point 3/2 of bbox currentpicture)); + P5 = image( + color pretzel; pretzel = 1/256(187, 146, 79); + for i=8 step -1/2 until 1/2: + draw cb withpen pencircle scaled i + withcolor (i/8)[white, pretzel]; + endfor + label.rt(btex \vbox{\halign{#\cr + \mpl{for i=8 step -1/2 until 1/2:}\cr + \quad\mpl{draw cb withpen pencircle scaled i}\cr + \qquad\mpl{withcolor sqrt(i/8)[white, pretzel];}\cr + \mpl{endfor}\cr}} etex, point 3/2 of bbox currentpicture); + ); + + P6 = image( + for e within cb: + draw pathpart e withpen penpart e scaled 4 + withcolor 7/8[colorpart e, background]; + endfor + label.rt(btex \vbox{\halign{#\cr + \mpl{for e within cb:}\cr + \quad\mpl{draw pathpart e withpen penpart e scaled 4}\cr + \qquad\mpl{withcolor 7/8[colorpart e, background];}\cr + \mpl{endfor}\cr}} etex, point 3/2 of bbox currentpicture); + ); + + for i=1 upto 6: + if known P[i]: + pair p; p = 60i * down; + label.rt(P[i], p); + fill superellipse(right, up, left, down, 0.8) scaled 6 shifted p + withcolor 2/3; + label("\textsf{" & decimal i & "}", p) withcolor white; + fi; + endfor + + endfig; + \end{mplibcode} + \end{document} diff --git a/info/drawing-with-metapost/src/pics-draw-picture.pdf b/info/drawing-with-metapost/src/pics-draw-picture.pdf Binary files differnew file mode 100644 index 0000000000..ca5b282aeb --- /dev/null +++ b/info/drawing-with-metapost/src/pics-draw-picture.pdf diff --git a/info/drawing-with-metapost/src/fake-transparency.mp b/info/drawing-with-metapost/src/pics-fake-transparency.mp index dfe7086052..e9bf30761d 100644 --- a/info/drawing-with-metapost/src/fake-transparency.mp +++ b/info/drawing-with-metapost/src/pics-fake-transparency.mp @@ -25,33 +25,27 @@ drawarrow xx; drawarrow yy; drawoptions(); +% Large A label.urt("A" infont defaultfont scaled 8, origin) withcolor 1/4 green; - -% draw the "transparent" superellipse box -path se; -%se = unitsquare shifted 1/2 down shifted 1/4 left scaled 3cm; -se = (superellipse(right, up, left, down, 0.81)) -shifted 1/2 right scaled 30 rotated 30; - +% the "transparent" box +path shape; shape = (superellipse(right, up, left, down, 0.81)) + shifted 1/2 right scaled 30 rotated 30; alpha = 5/8; % alpha: 0=invisible, 1=opaque color filler; filler = .95[red,white]; -picture fg, bg; -bg = currentpicture; -fg = image( - for e within bg: +picture bg; bg = currentpicture; % capture the current drawing +picture fg; fg = image( + for e within bg: % redraw everything with blended color draw e withcolor alpha[colorpart e, filler]; - endfor - draw se withpen pencircle scaled 2 withcolor 3/4; - draw subpath (2.718, 3.1415) of se - shifted - center se scaled 7/8 shifted + center se + endfor + draw shape withpen pencircle scaled 2 withcolor 3/4; + draw subpath (2.718, 3.1415) of shape % add decoration + shifted - center shape scaled 7/8 shifted + center shape withpen pencircle scaled 2 withcolor white; - ); -clip fg to se; - -fill se withcolor filler; -draw fg; -draw se withcolor 3/4 blue; +clip fg to shape; % finally clip the fg drawing +fill shape withcolor filler; % fill the shape +draw fg; % and put the fg back on top +draw shape withcolor 3/4 blue; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/fake-transparency.pdf b/info/drawing-with-metapost/src/pics-fake-transparency.pdf Binary files differindex 07f247a29d..671d68a827 100644 --- a/info/drawing-with-metapost/src/fake-transparency.pdf +++ b/info/drawing-with-metapost/src/pics-fake-transparency.pdf diff --git a/info/drawing-with-metapost/src/pics-graph-paper-5mm.mp b/info/drawing-with-metapost/src/pics-graph-paper-5mm.mp new file mode 100644 index 0000000000..679ac1def3 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-graph-paper-5mm.mp @@ -0,0 +1,5 @@ +input automatic-grid +begingroup; save P; picture P; P = currentpicture; clearit; +draw grid(P, 5mm) withpen pencircle scaled 1/4 withcolor (3/4, 3/4, 7/8); +draw grid(P, 10cm) withpen pencircle scaled 1/4 withcolor (1/2, 1/2, 3/4); +draw P; endgroup; diff --git a/info/drawing-with-metapost/src/pics-graph-paper-cm.mp b/info/drawing-with-metapost/src/pics-graph-paper-cm.mp new file mode 100644 index 0000000000..1eb53928b7 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-graph-paper-cm.mp @@ -0,0 +1,5 @@ +input automatic-grid +begingroup; save P; picture P; P = currentpicture; clearit; +draw grid(P, 1mm) withpen pencircle scaled 1/4 withcolor (3/4, 3/4, 7/8); +draw grid(P, 1cm) withpen pencircle scaled 3/8 withcolor (1/2, 1/2, 3/4); +draw P; endgroup; diff --git a/info/drawing-with-metapost/src/pics-graph-paper-example.mp b/info/drawing-with-metapost/src/pics-graph-paper-example.mp new file mode 100644 index 0000000000..22cf5134e6 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-graph-paper-example.mp @@ -0,0 +1,23 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{dwmpcode} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); +path C; C = fullcircle scaled 125 shifted 20 up rotated 16; +for t=0, 1, 4: draw center C -- point t of C withcolor 2/3 blue; endfor +draw C withcolor 3/4 red; dotlabel.urt("Start", point 0 of C); +input pics-graph-paper-inch + +label.ulft(btex \vbox{\hsize 134pt\raggedright +Here is an example that adds graph paper behind a drawing. + +The first three lines make the example drawing, the +final \mpl{input} adds the graph paper. +\par} etex, llcorner currentpicture shifted 10 left); + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/pics-graph-paper-example.pdf b/info/drawing-with-metapost/src/pics-graph-paper-example.pdf Binary files differnew file mode 100644 index 0000000000..e459e8f3d1 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-graph-paper-example.pdf diff --git a/info/drawing-with-metapost/src/pics-graph-paper-inch.mp b/info/drawing-with-metapost/src/pics-graph-paper-inch.mp new file mode 100644 index 0000000000..5ddb765027 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-graph-paper-inch.mp @@ -0,0 +1,6 @@ +input automatic-grid +begingroup; save P; picture P; P = currentpicture; clearit; +draw grid(P, 9) withpen pencircle scaled 4/16 withcolor 1/16(12,12,14); +draw grid(P,36) withpen pencircle scaled 5/16 withcolor 1/16(10,10,13); +draw grid(P,72) withpen pencircle scaled 6/16 withcolor 1/16( 8, 8,12); +draw P; endgroup; diff --git a/info/drawing-with-metapost/src/pics-graph-paper.mp b/info/drawing-with-metapost/src/pics-graph-paper.mp new file mode 100644 index 0000000000..a6a59ced16 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-graph-paper.mp @@ -0,0 +1,16 @@ +vardef grid(expr p, grid_unit) = + save llx, lly, urx, ury; + (llx, lly) = llcorner p - (bboxmargin, bboxmargin); + (urx, ury) = urcorner p + (bboxmargin, bboxmargin); + image( + for x = 1 + floor(llx / grid_unit) upto floor(urx / grid_unit): + draw (x * grid_unit, lly) -- (x * grid_unit, ury); + endfor + for y = 1 + floor(lly / grid_unit) upto floor(ury / grid_unit): + draw (llx, y * grid_unit) -- (urx, y * grid_unit); + endfor + if (llx < 0) and (lly < 0) and (urx > 0) and (ury > 0): + draw fullcircle scaled 3; % show origin if in range + fi + ) +enddef; diff --git a/info/drawing-with-metapost/src/icosahedron.mp b/info/drawing-with-metapost/src/pics-icosahedron.mp index b336628462..7ee50091f8 100644 --- a/info/drawing-with-metapost/src/icosahedron.mp +++ b/info/drawing-with-metapost/src/pics-icosahedron.mp @@ -1,4 +1,4 @@ -\documentclass[border=2mm]{standalone} +\documentclass{standalone} \usepackage{luamplib} \begin{document} \mplibtextextlabel{enable} diff --git a/info/drawing-with-metapost/src/pics-icosahedron.pdf b/info/drawing-with-metapost/src/pics-icosahedron.pdf Binary files differnew file mode 100644 index 0000000000..13372e9cdd --- /dev/null +++ b/info/drawing-with-metapost/src/pics-icosahedron.pdf diff --git a/info/drawing-with-metapost/src/pics-shady-circles.mp b/info/drawing-with-metapost/src/pics-shady-circles.mp new file mode 100644 index 0000000000..eb2caed827 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-shady-circles.mp @@ -0,0 +1,29 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + numeric r; r = 42; z1 = 5/4 r * left; z2 = 2r * right; + path c[]; + c1 = fullcircle scaled 2 abs z1 shifted z1; + c2 = fullcircle scaled 2 abs z2 shifted z2; + c3 = fullcircle scaled abs(z2-z1) shifted 1/2[z1,z2]; + numeric t, u; + (t, whatever) = c2 intersectiontimes c3; + (u, whatever) = c1 intersectiontimes (point t of c2 -- z1); + + path s; + s = subpath (0, u) of c1 -- subpath (t, 4) of c2 -- cycle; + numeric gap; gap = 2; + for i=0 upto 2r / gap: + draw (origin--right) scaled 2r rotated 45t shifted (gap*i,0) + withpen pencircle scaled 1/4 withcolor 2/3 blue; + endfor + clip currentpicture to s; + + draw c1; draw c2; + draw z1 -- z2 -- point t of c2 -- cycle; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pics-shady-circles.pdf b/info/drawing-with-metapost/src/pics-shady-circles.pdf Binary files differnew file mode 100644 index 0000000000..147d0e23b2 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-shady-circles.pdf diff --git a/info/drawing-with-metapost/src/pics-twister.mp b/info/drawing-with-metapost/src/pics-twister.mp new file mode 100644 index 0000000000..bc7ce43551 --- /dev/null +++ b/info/drawing-with-metapost/src/pics-twister.mp @@ -0,0 +1,53 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +vardef compass_rose(expr shade, highlight) = image( + drawoptions(withcolor shade); + draw thelabel("NW" infont defaultfont scaled 3/4, 64 up) rotated +45; + draw thelabel("NE" infont defaultfont scaled 3/4, 64 up) rotated -45; + draw thelabel("SE" infont defaultfont scaled 3/4, 64 down) rotated +45; + draw thelabel("SW" infont defaultfont scaled 3/4, 64 down) rotated -45; + draw fullcircle scaled 144 withpen pencircle scaled 2; + for r = 53, 54, 59, 60, 69: draw fullcircle scaled 2r; endfor + for t=0 step 15 until 350: draw ((53,0) -- (60,0)) rotated t; endfor + for t=0 step 45 until 350: draw ((69,0) -- (80,0)) rotated t; endfor + save s; path s; s = 8 right -- 60 up -- 8 left -- cycle; + for t=0 upto 3: filldraw s rotated (45 + 90t); endfor + s := s scaled 1.414; + for t=0 upto 3: + s := s rotated 90t; + fill s withcolor background; + fill subpath (-1/2, 1) of s -- cycle if t=0: withcolor highlight fi; + draw s; + endfor + unfill fullcircle scaled 28; draw fullcircle scaled 28; + draw origin withpen pencircle scaled dotlabeldiam; + label("N" infont "cmbx12", 92 up); + label("S" infont "cmbx12", 92 down); + label("E" infont "cmbx12", 92 right); + label("W" infont "cmbx12", 92 left); + drawoptions(); +) enddef; +input colorbrewer-rgb +beginfig(1); + picture O; O = compass_rose(Blues 8 8, Reds 8 7) scaled 1/2; + + numeric s; pair p; s = 108; p = origin; + draw O shifted p; + draw bbox O withcolor 3/4[red, white]; + label.urt(TEX("\small\texttt{bbox P}"), point -1 of bbox O) withcolor 3/4[red, white]; + + p := (1s, 0); draw O rotated 30 shifted p; label(TEX("\small\texttt{rotated 30}"), p shifted 54 down); + p := (2s,+15); draw O shifted p; label(TEX("\small\texttt{shifted 15 up}"), p shifted 54 down); + + p := ( 0, -1s); draw O scaled 3/4 shifted p; label(TEX("\small\texttt{scaled 3/4}"), p shifted 54 down); + p := (1s, -1s); draw O xscaled 3/4 shifted p; label(TEX("\small\texttt{xscaled 3/4}"), p shifted 54 down); + p := (2s, -1s); draw O yscaled 3/4 shifted p; label(TEX("\small\texttt{yscaled 3/4}"), p shifted 54 down); + + p := ( 0, -2s); draw O slanted 3/4 shifted p; label(TEX("\small\texttt{slanted 3/4}"), p shifted 54 down); + p := (1s, -2s); draw O zscaled 3/4 dir 21 shifted p; label(TEX("\small\texttt{zscaled 3/4 dir 21}"), p shifted 54 down); + p := (2s, -2s); draw O reflectedabout(up, down) shifted p; label(TEX("\small\texttt{reflectedabout(up, down)}"), p shifted 54 down); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pics-twister.pdf b/info/drawing-with-metapost/src/pics-twister.pdf Binary files differnew file mode 100644 index 0000000000..993733716f --- /dev/null +++ b/info/drawing-with-metapost/src/pics-twister.pdf diff --git a/info/drawing-with-metapost/src/pics-youth.mp b/info/drawing-with-metapost/src/pics-youth.mp new file mode 100644 index 0000000000..3f31bc472f --- /dev/null +++ b/info/drawing-with-metapost/src/pics-youth.mp @@ -0,0 +1,13 @@ +\documentclass{standalone} +\usepackage{graphicx} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +input picture_frame +beginfig(1); + picture F; + F = thelabel(TEX("\includegraphics[width=200pt]{youth.jpg}"), origin); + draw F; draw frame F; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/pics-youth.pdf b/info/drawing-with-metapost/src/pics-youth.pdf Binary files differnew file mode 100644 index 0000000000..08aa6dedbb --- /dev/null +++ b/info/drawing-with-metapost/src/pics-youth.pdf diff --git a/info/drawing-with-metapost/src/picture_frame.mp b/info/drawing-with-metapost/src/picture_frame.mp index d957c54074..f512fd150a 100644 --- a/info/drawing-with-metapost/src/picture_frame.mp +++ b/info/drawing-with-metapost/src/picture_frame.mp @@ -1,5 +1,5 @@ % Toby Thurston -- 16 Apr 2021 -% Draw a kitsch picture frame round a rectangular path +% Draw a kitsch picture frame round a path or picture color gold, dark, grey; gold = 1/256(243, 197, 127); @@ -8,64 +8,57 @@ grey = 1/256(156, 147, 138); picture ball; ball = image(for i=0 upto 16: fill interpath(i/16, - fullcircle scaled 10, - fullcircle scaled 3 shifted (-2, 2) + fullcircle scaled 10, + fullcircle scaled 3 shifted (-2, 2) ) withcolor (i/16)[gold, 15/16 white]; endfor) scaled 1/4; newinternal pf_width; pf_width := 21; vardef frame expr P = - save base, side, f, t, u, xx; - picture base, side; path f; numeric t, u, xx; - - t = arclength subpath (0,1) of bbox P; - u = arclength subpath (1,2) of bbox P; - xx = max(t, u) + 2 pf_width; - f = unitsquare xscaled xx yscaled pf_width; - - % convenience / nonce function - vardef paint_strip(expr y, wd, shade) = - draw subpath (0, 1) of f - shifted (0, if y < 0: pf_width + fi y) - withpen pencircle scaled wd - withcolor shade - enddef; - - base = image( - % background colour - fill f withcolor gold; - % grey strips - paint_strip(2, 3, 5/4 grey); - paint_strip(3.5, 1/4, grey); - paint_strip(5, 1/4, 1/2[gold, dark]); - paint_strip(-6.5, 1/4, 1/2[gold, dark]); - paint_strip(-6, 1/4, 1/2[gold, dark]); - paint_strip(-2, 2, 5/4 grey); - % spatter with random spots - for i=0 upto 4 * arclength(subpath (0,1) of f): - fill fullcircle scaled uniformdeviate 3/4 - shifted (uniformdeviate xx, uniformdeviate pf_width) - withcolor dark; - endfor - % decorative balls - for x = 2 step 3 until xx: - draw ball shifted (x, 2); - endfor - ); - - % make two trapezium shapes - side = base; - clip side to (pf_width, 0) -- (pf_width + u, 0) - -- (2 pf_width + u, pf_width) -- (0, pf_width) -- cycle; - clip base to (pf_width, 0) -- (pf_width + t, 0) - -- (2 pf_width + t, pf_width) -- (0, pf_width) -- cycle; - - % arrange the pieces into a square - image( - draw base rotated 180 shifted point 1 of bbox P shifted (+pf_width, 0); - draw base rotated 0 shifted point 3 of bbox P shifted (-pf_width, 0); - draw side rotated 90 shifted point 0 of bbox P shifted (0, -pf_width); - draw side rotated 270 shifted point 2 of bbox P shifted (0, +pf_width); - ) + save base, side, f, t, u, xx; + picture base, side; path f; numeric t, u, xx; + t = arclength subpath (0,1) of bbox P; + u = arclength subpath (1,2) of bbox P; + xx = max(t, u) + 2 pf_width; + f = unitsquare xscaled xx yscaled pf_width; + % convenience / nonce function + vardef paint_strip(expr y, wd, shade) = + draw subpath (0, 1) of f + shifted (0, if y < 0: pf_width + fi y) + withpen pencircle scaled wd + withcolor shade + enddef; + base = image( + fill f withcolor gold; % background colour + paint_strip(2, 3, 5/4 grey); % grey strips + paint_strip(3.5, 1/4, grey); + paint_strip(5, 1/4, 1/2[gold, dark]); + paint_strip(-6.5, 1/4, 1/2[gold, dark]); + paint_strip(-6, 1/4, 1/2[gold, dark]); + paint_strip(-2, 2, 5/4 grey); + % spatter with random spots + for i=0 upto 4 * arclength(subpath (0,1) of f): + fill fullcircle scaled uniformdeviate 3/4 + shifted (uniformdeviate xx, uniformdeviate pf_width) + withcolor dark; + endfor + % decorative balls + for x = 2 step 3 until xx: + draw ball shifted (x, 2); + endfor + ); + % make two trapezium shapes + side = base; + clip side to (pf_width, 0) -- (pf_width + u, 0) + -- (2 pf_width + u, pf_width) -- (0, pf_width) -- cycle; + clip base to (pf_width, 0) -- (pf_width + t, 0) + -- (2 pf_width + t, pf_width) -- (0, pf_width) -- cycle; + % arrange the pieces into a square + image( + draw base rotated 180 shifted point 1 of bbox P shifted (+pf_width, 0); + draw base rotated 0 shifted point 3 of bbox P shifted (-pf_width, 0); + draw side rotated 90 shifted point 0 of bbox P shifted (0, -pf_width); + draw side rotated 270 shifted point 2 of bbox P shifted (0, +pf_width); + ) enddef; diff --git a/info/drawing-with-metapost/src/pinwheel.mp b/info/drawing-with-metapost/src/pinwheel.mp deleted file mode 100644 index 83a957d415..0000000000 --- a/info/drawing-with-metapost/src/pinwheel.mp +++ /dev/null @@ -1,36 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -vardef pinwheel(expr level, a, b, c, s) = - if level = 0: - fill a--b--c--cycle withcolor s; - draw a--b--c--cycle withpen pencircle scaled 1/16 withcolor Blues 9 1; - % path t; t = a--b--9/10[b,c]--cycle; - % fill t withcolor s; - % draw t withpen pencircle scaled 1/16 withcolor Greens 9 1; - % draw point 5/2 of t withpen pencircle scaled 2 withcolor (1/4 + greenpart s, redpart s, bluepart s); - else: - save d, e, f, g; - pair d, e, f, g; - d = 2/5[b, c]; e = 4/5[b,c]; f = 1/2[e, a]; g = 1/2[a, b]; - pinwheel(level - 1, e, a, c, Blues 9 4); - pinwheel(level - 1, f, g, a, Blues 9 3); - pinwheel(level - 1, f, g, e, Blues 9 2); - pinwheel(level - 1, d, e, g, Blues 9 5); - pinwheel(level - 1, d, b, g, Blues 9 6); - fi -enddef; -beginfig(1); - numeric a, b; b = 6.4in; 2a = b; - pinwheel(5, (0, 0), (b, 0), (0, a), ""); - pinwheel(5, (b, a), (0, a), (b, 0), ""); - currentpicture := currentpicture rotated 90; - % for i=1 upto 1: - % draw currentpicture shifted (lrcorner currentpicture - llcorner currentpicture); - % endfor -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/pinwheel.pdf b/info/drawing-with-metapost/src/pinwheel.pdf Binary files differdeleted file mode 100644 index d0723c21c4..0000000000 --- a/info/drawing-with-metapost/src/pinwheel.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/plain-axes.mp b/info/drawing-with-metapost/src/plain-axes.mp deleted file mode 100644 index e535290d21..0000000000 --- a/info/drawing-with-metapost/src/plain-axes.mp +++ /dev/null @@ -1,17 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - path xx, yy; - xx = (left -- right) scaled 130; - yy = (down -- up) scaled 80; - drawarrow xx; - drawarrow yy; - label.rt("$x$", point 1 of xx); - label.top("$y$", point 1 of yy); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/pole-and-polar.mp b/info/drawing-with-metapost/src/pole-and-polar.mp deleted file mode 100644 index 6673ca6341..0000000000 --- a/info/drawing-with-metapost/src/pole-and-polar.mp +++ /dev/null @@ -1,59 +0,0 @@ -\documentclass[border=3mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - path C, L; - numeric r; - r = 89; - C = fullcircle scaled 2r; - L = (up--down) scaled 138 shifted 180 right rotated 34; - pair a, b, o; - a = point 0 of L; b = point 1 of L; - o = center C; - - pair P, Q, R, P', m; - P = whatever[a, b]; o - P = whatever * (a - b) rotated 90; - Q = C intersectionpoint halfcircle zscaled (P-o) shifted 1/2[P, o]; - R = Q reflectedabout(P, o); - P' = whatever[o, P] = whatever [Q, R]; - - draw fullcircle scaled abs(P' - o) shifted 1/2[o, P'] - dashed withdots scaled 1/4 - withpen pencircle scaled 1/4 - withcolor 1/3 blue; - - draw unitsquare scaled 5 rotated (270 + angle (P-Q)) shifted Q withcolor 3/4 white; - draw unitsquare scaled 5 rotated (90 + angle (P-o)) shifted P withcolor 3/4 white; - draw unitsquare scaled 5 rotated (90 + angle (P-o)) shifted P' withcolor 3/4 white; - - draw P -- Q -- o -- R -- cycle withcolor 1/2 white; - draw Q--R; draw o -- P; - draw L withcolor 2/3 blue; - - draw C dashed evenly scaled 1/2 withcolor 1/2[2/3 blue, white]; - - dotlabel.top("$Q$", Q); - dotlabel.lrt("$R$", R); - dotlabel.urt("$P$", P); - dotlabel.llft("$O$", o); fill fullcircle scaled 3/4 dotlabeldiam shifted o withcolor white; - label.lft("$r$", 1/2[o, Q]); - - drawdot P' withpen pencircle scaled dotlabeldiam; - label("$P'$", P' shifted 10 dir 68) withcolor 2/3 blue; - - drawoptions(withcolor 2/3 blue); - label.bot("\textit{circle of inversion}", point 6 of C); - label.urt("\textit{polar}", point 1/4 of L); - z0 = P' + 20 dir -20; draw z0 -- P' cutafter fullcircle scaled 8 shifted P' - withpen pencircle scaled 1/4; - label.rt("\textit{pole}", z0); - drawoptions(); - - label("$\displaystyle {r\over OP} = {OP' \over r}$", 1/2[point 0 of C, point 1 of L] + 12 down); - label("$\displaystyle r^2 = OP \times OP'$", 1/2[point 0 of C, point 1 of L] + 36 down); - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/qed.mp b/info/drawing-with-metapost/src/qed.mp deleted file mode 100644 index e8ef24e4bd..0000000000 --- a/info/drawing-with-metapost/src/qed.mp +++ /dev/null @@ -1,42 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -def perpendicular expr t of p = - direction t of p rotated 90 shifted point t of p - enddef; - -vardef block(expr r) = - save u, n, s, theta, base, ray; - numeric u, n, s, theta; - u = 5mm; n = 32; s = 8u; theta = -45; - - path base, ray[]; - base = origin for i=1 upto n-1: -- (i/n*s,r*normaldeviate) endfor - -- (s,0) -- (s,-u) -- (0,-u) -- cycle; - - image( - fill base withcolor .8[blue,white]; - draw base withcolor .67 blue; - - for i=2 upto 6: - ray[i] = (left--right) scaled 2/3 s rotated theta shifted (i*u,0); - b := ypart(ray[i] intersectiontimes base); - ray[i] := point 0 of ray[i] - -- point b of base - -- point 0 of ray[i] reflectedabout(point b of base, perpendicular b of base); - drawarrow ray[i]; - endfor - - label("r=" & decimal r, center base); - ) enddef; - -beginfig(0); - - draw block(0); draw block(0.42) shifted 180 right; - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/qed.pdf b/info/drawing-with-metapost/src/qed.pdf Binary files differdeleted file mode 100644 index 361fa0686a..0000000000 --- a/info/drawing-with-metapost/src/qed.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/radical-axis.mp b/info/drawing-with-metapost/src/radical-axis.mp deleted file mode 100644 index ee1c7fd6fe..0000000000 --- a/info/drawing-with-metapost/src/radical-axis.mp +++ /dev/null @@ -1,72 +0,0 @@ -\documentclass[border=1mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} - -vardef radical_axis(expr ca, cb) = - numeric t, d, ra, rb; - ra = abs(center ca - point 0 of ca); - rb = abs(center cb - point 0 of cb); - d = abs(center cb - center ca); - 2t = 1 + (ra+rb) / d * (ra-rb) / d; - (up -- down) scaled 89 - rotated angle (center cb - center ca) - shifted t[center ca, center cb] -enddef; - -vardef tangent_times(expr C, p) = - save m, a, b, G, H; - pair m; numeric a, b; path G, H; - m = 1/2[p, center C]; - H = halfcircle scaled abs (p - center C) - rotated angle (p - center C) shifted m; - G = H rotatedabout(m, 180); - (a, whatever) = C intersectiontimes H; - (b, whatever) = C intersectiontimes G; - (a, b if b < a: + 8 fi) -enddef; - -beginfig(1); - path c[], a[]; - z1 = origin; z2 = 233 right rotated 4; z3 = 209 right rotated -42; - c1 = fullcircle scaled 202 shifted z1; - c2 = fullcircle scaled 106 shifted z2; - c3 = fullcircle scaled 62 shifted z3; - a1 = radical_axis(c1, c2); - a2 = radical_axis(c2, c3); - a3 = radical_axis(c3, c1); - - z0 = whatever [point 0 of a1, point 1 of a1] - = whatever [point 0 of a2, point 1 of a2]; - - numeric t; - (t, whatever) = tangent_times(c1, z0); - - drawoptions(withpen pencircle scaled 1 withcolor 3/4[blue, white]); - draw c1; draw c2; draw c3; - - drawoptions(withcolor 3/4[blue, white]); - draw z1 -- point t of c1 dashed evenly; - - drawoptions(withpen pencircle scaled 1/4); - draw z1 -- z2 -- z3 -- cycle; - drawoptions(); - draw a1; draw a2; draw a3; - - drawoptions(withcolor 2/3 red); - draw fullcircle scaled 2 abs (point t of c1 - z0) shifted z0; - draw z0 -- point t of c1 dashed evenly; - drawdot z0 withpen pencircle scaled dotlabeldiam; - - drawoptions(withcolor 1/4[blue, white]); - drawdot z1 withpen pencircle scaled dotlabeldiam; - drawdot z2 withpen pencircle scaled dotlabeldiam; - drawdot z3 withpen pencircle scaled dotlabeldiam; - label.urt(btex $C_1$ etex, point 1 of c1); - label.urt(btex $C_2$ etex, point 1 of c2); - label.rt (btex $C_3$ etex, point 0 of c3); -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/random-dice.mp b/info/drawing-with-metapost/src/random-dice.mp new file mode 100644 index 0000000000..bd91017dae --- /dev/null +++ b/info/drawing-with-metapost/src/random-dice.mp @@ -0,0 +1,40 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +vardef dice(expr pip_count, pip_color) = + save d,r,p, ul, ur, lr, ll; r = 1/8; + path d; d = for i=0 upto 3: + quartercircle scaled 3 shifted (15,15) rotated 90i -- + endfor cycle; + picture p; p = image( + fill fullcircle scaled 6 withcolor pip_color; + draw fullcircle scaled 6; + ); + pair ul, ur, ll, lr; + ul = 1/5[ulcorner d, lrcorner d]; ur = 1/5[urcorner d, llcorner d]; + ll = 4/5[urcorner d, llcorner d]; lr = 4/5[ulcorner d, lrcorner d]; + image( + fill d withcolor (1, 0.96, 0.8); draw d; + if odd(pip_count): + draw p shifted center d; + fi; + if pip_count > 1: + draw p shifted ul; draw p shifted lr; + fi; + if pip_count > 3: + draw p shifted ur; draw p shifted ll; + fi; + if pip_count = 6: + draw p shifted 1/2[ul,ll]; draw p shifted 1/2[ur,lr]; + fi + ) +enddef; +beginfig(1); +for i=0 upto 4: + draw dice(1+floor uniformdeviate 6, if odd i: red else: blue fi) + rotated (2 normaldeviate) shifted (36i,0); +endfor +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/random-dice.pdf b/info/drawing-with-metapost/src/random-dice.pdf Binary files differnew file mode 100644 index 0000000000..b49e30be4f --- /dev/null +++ b/info/drawing-with-metapost/src/random-dice.pdf diff --git a/info/drawing-with-metapost/src/random-explosions.mp b/info/drawing-with-metapost/src/random-explosions.mp new file mode 100644 index 0000000000..344618d281 --- /dev/null +++ b/info/drawing-with-metapost/src/random-explosions.mp @@ -0,0 +1,32 @@ +\documentclass{standalone} +\usepackage{luamplib} +\usepackage{fontspec} +\setmainfont{PlayfairDisplay-Black}[Scale=2.8] +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb +randomseed:=2128.5073; +beginfig(1); + n = 40; r = 12 ; s = 72; + path explosion; explosion = for i=1 upto n: + (if odd i: - fi r + s + uniformdeviate r) * dir (360/n*i) -- + endfor cycle; + path splash; splash = for i=1 upto n: + (if odd i: - fi r + s + uniformdeviate r) * dir (360/n*i) .. + endfor cycle; + picture P[]; + P1 = image( + fill explosion withcolor Oranges 7 4; + draw explosion withpen pencircle scaled 2 withcolor Reds 7 7; + label("BOOM!", center explosion) withcolor Reds 7 7; + ); + P2 = image( + fill splash withcolor Blues 7 2; + draw splash withpen pencircle scaled 2 withcolor Blues 7 7; + label("SPLAT!", center splash) withcolor Blues 7 7; + ); + label.lft(P1, 10 left); label.rt(P2, 10 right); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/random-explosions.pdf b/info/drawing-with-metapost/src/random-explosions.pdf Binary files differnew file mode 100644 index 0000000000..22e654aa49 --- /dev/null +++ b/info/drawing-with-metapost/src/random-explosions.pdf diff --git a/info/drawing-with-metapost/src/random-exponential-test.mp b/info/drawing-with-metapost/src/random-exponential-test.mp new file mode 100644 index 0000000000..3bb3991c17 --- /dev/null +++ b/info/drawing-with-metapost/src/random-exponential-test.mp @@ -0,0 +1,89 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb +input random-other-distributions + +beginfig(1); + + numeric bucket[]; for i = 1 upto 5: bucket[i] = 0; endfor + numeric scale; scale = 50; + numeric N; N = 80; + numeric stack_height[]; + numeric mu, r, k; mu = 0; + pair w; + + for i=1 upto N: for j=1 upto N: + r := exponentialdeviate scale; + k := floor r; + mu := mu + (r - mu) / (i * N + j); + + if known stack_height[k]: + stack_height[k] := stack_height[k] + 1; + else: + stack_height[k] := 1; + fi + + w := (r, uniformdeviate 1/8 + stack_height[k]); + + + color shade; + if r < scale: bucket[1] := bucket[1] + 1; shade := Greens 8 8; + elseif r < 2 scale: bucket[2] := bucket[2] + 1; shade := Blues 8 8; + elseif r < 3 scale: bucket[3] := bucket[3] + 1; shade := Oranges 8 6; + elseif r < 4 scale: bucket[4] := bucket[4] + 1; shade := Reds 8 6; + else: bucket[5] := bucket[5] + 1; shade := black; + fi + + if r < 7 scale: % trim very high ... + draw w withcolor shade; + fi + endfor endfor + + draw (origin -- 1.44 scale * up) shifted (mu, 0) withcolor 2/3 blue; + label.top("$\mu$", (mu, 1.44 scale)); + + path xx, yy; + xx = origin -- 6 scale * right shifted 12 right; + yy = origin -- 2 N * up; + + ahangle := 30; + for x=1 upto 6: + draw (origin -- 3 down) shifted (scale * x, 0); + label.bot(decimal x, (scale * x, -3)); + endfor + drawarrow xx; + draw yy; + + vardef exponential_pdf(expr x, lambda) = + if x < 0: 0 else: lambda * mexp(-256x * lambda) fi + enddef; + + path E; + E = ((0, exponential_pdf(0, 1)) for x=1 upto 6: .. (x, exponential_pdf(x, 1)) endfor) + xscaled scale yscaled 1.8N; + + draw E withcolor 1/2 red; + + string p; + for i=1 upto 5: + p := decimal (bucket[i] / N / N); + label.bot("\tiny " & p, ((i-1/2) * scale, -10)); + endfor + + pair a, b; + a = point 1/4 of E shifted (2,3); + b = point 1/4 of E shifted (20, 30); + draw a -- b withpen pencircle scaled 1/4; + label.urt("$\lambda e^{-\lambda x}$", b); + + label.llft("\large\textsf{Histogram of exponential deviates}", urcorner currentpicture); + + input show_name + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/random-exponential-test.pdf b/info/drawing-with-metapost/src/random-exponential-test.pdf Binary files differnew file mode 100644 index 0000000000..ce533e3bb2 --- /dev/null +++ b/info/drawing-with-metapost/src/random-exponential-test.pdf diff --git a/info/drawing-with-metapost/src/random-freehand-circumcircle.mp b/info/drawing-with-metapost/src/random-freehand-circumcircle.mp index 290ba81b7e..d668d7c3d0 100644 --- a/info/drawing-with-metapost/src/random-freehand-circumcircle.mp +++ b/info/drawing-with-metapost/src/random-freehand-circumcircle.mp @@ -18,26 +18,27 @@ color sepia; sepia = (0.44, 0.26, 0.08); picture marker; marker = image(for s=-1/2, 1/2: draw (left--right) scaled 2 rotated 60 shifted (s,0); endfor); -def moved_along expr x of p = rotated angle direction x of p - shifted point x of p enddef; - +def moved_along expr x of p = + rotated angle direction x of p + shifted point x of p +enddef; beginfig(1); -pair A, B, C, D; -A = (0,-30); B = (180,0); C = (120,90); D = (1/2 + 1/40 normaldeviate)[A, B]; -path triangle, circumcircle, bisector; -triangle = freehand_path(A--D--B--C--cycle); -bisector = freehand_segment(C--D); -circumcircle = freehand_path(A..B..C..cycle); -draw triangle; -draw bisector; -draw circumcircle withcolor .67 red; -draw marker moved_along 1/2 of triangle withcolor .67 red; -draw marker moved_along 3/2 of triangle withcolor .67 red; -label.lft("A", A); -label.rt ("B", B); -label.top("C", C); -label.bot("D", D); + pair A, B, C, D; + A = (0,-30); B = (180,0); C = (120,90); + D = (1/2 + 1/40 normaldeviate)[A, B]; + path triangle, circumcircle, bisector; + triangle = freehand_path(A--D--B--C--cycle); + bisector = freehand_segment(C--D); + circumcircle = freehand_path(A..B..C..cycle); + draw triangle; + draw bisector; + draw circumcircle withcolor .67 red; + draw marker moved_along 1/2 of triangle withcolor .67 red; + draw marker moved_along 3/2 of triangle withcolor .67 red; + label.lft("A", A); + label.rt ("B", B); + label.top("C", C); + label.bot("D", D); endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/random-freehand-circumcircle.pdf b/info/drawing-with-metapost/src/random-freehand-circumcircle.pdf Binary files differindex d1e3586cd0..a078c71638 100644 --- a/info/drawing-with-metapost/src/random-freehand-circumcircle.pdf +++ b/info/drawing-with-metapost/src/random-freehand-circumcircle.pdf diff --git a/info/drawing-with-metapost/src/random-freehand-through.mp b/info/drawing-with-metapost/src/random-freehand-through.mp index 0bbacf4436..2a07c8b406 100644 --- a/info/drawing-with-metapost/src/random-freehand-through.mp +++ b/info/drawing-with-metapost/src/random-freehand-through.mp @@ -3,40 +3,41 @@ \begin{document} \begin{mplibcode} vardef freehand_through@#(expr a, b) = - save t; pair t; t = @# * unitvector(b - a) rotated (4 + normaldeviate); - a - t .. a {t} .. b {t} .. b + t + save t; pair t; + t = @# * unitvector(b - a) rotated (4 + normaldeviate); + a - t .. a {t} .. b {t} .. b + t enddef; vardef mid_arc@#(expr p, a, b) = - save c; path c; c = fullcircle scaled (2*@#) shifted p cutbefore a cutafter b; - point arctime 1/2 arclength c of c of c + save c; path c; + c = fullcircle scaled (2*@#) shifted p cutbefore a cutafter b; + point arctime 1/2 arclength c of c of c enddef; beginfig(1); -defaultfont := "eurm10"; color sepia; sepia = (0.44, 0.26, 0.08); -pair A, B, C; -A = (0,-30); B = (180,0); C = (120,90); + defaultfont := "eurm10"; color sepia; sepia = (0.44, 0.26, 0.08); + pair A, B, C; + A = (0,-30); B = (180,0); C = (120,90); -path a, b, c; -a = freehand_through 7 (A, B); -b = freehand_through 8 (B, C); -c = freehand_through 6 (C, A); + path a, b, c; + a = freehand_through 7 (A, B); + b = freehand_through 8 (B, C); + c = freehand_through 6 (C, A); -drawoptions(withcolor sepia); -draw a; draw b; draw c; + drawoptions(withcolor sepia); + draw a; draw b; draw c; -drawoptions(withcolor .67 blue); -label.bot ("a", point 3/2 of a); -label.rt ("b", point 3/2 of b); -label.ulft("c", point 3/2 of c); + drawoptions(withcolor .67 blue); + label.bot ("a", point 3/2 of a); + label.rt ("b", point 3/2 of b); + label.ulft("c", point 3/2 of c); -drawoptions(withcolor .5 red); -label(char 11, mid_arc 16 (A, a, c)); -label(char 12, mid_arc 14 (B, b, a)); -label(char 13, mid_arc 14 (C, c, b)); + drawoptions(withcolor .5 red); + label(char 11, mid_arc 16 (A, a, c)); + label(char 12, mid_arc 14 (B, b, a)); + label(char 13, mid_arc 14 (C, c, b)); -drawoptions(); + drawoptions(); endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/random-freehand-through.pdf b/info/drawing-with-metapost/src/random-freehand-through.pdf Binary files differindex 55e5548095..3ae1c66efc 100644 --- a/info/drawing-with-metapost/src/random-freehand-through.pdf +++ b/info/drawing-with-metapost/src/random-freehand-through.pdf diff --git a/info/drawing-with-metapost/src/gaussian.mp b/info/drawing-with-metapost/src/random-gaussian.mp index 540256bddb..540256bddb 100644 --- a/info/drawing-with-metapost/src/gaussian.mp +++ b/info/drawing-with-metapost/src/random-gaussian.mp diff --git a/info/drawing-with-metapost/src/gaussian.pdf b/info/drawing-with-metapost/src/random-gaussian.pdf Binary files differindex 1be302a804..1be302a804 100644 --- a/info/drawing-with-metapost/src/gaussian.pdf +++ b/info/drawing-with-metapost/src/random-gaussian.pdf diff --git a/info/drawing-with-metapost/src/random-other-distributions.mp b/info/drawing-with-metapost/src/random-other-distributions.mp new file mode 100644 index 0000000000..78c96f75ca --- /dev/null +++ b/info/drawing-with-metapost/src/random-other-distributions.mp @@ -0,0 +1,48 @@ + + +vardef normaldeviate = + save u, v, xa; + forever: + u := 1 - uniformdeviate 63/64; + v := sqrt(8/mexp(256)) * (-1/2 + uniformdeviate 1); + xa := v / u; + exitif (xa * xa <= -mlog(u)/64); + endfor + xa +enddef; + +vardef exponentialdeviate expr mu = + save u; + u = 1 - uniformdeviate 1; % hence 0 < u <= 1 and so you avoid + -mu * 1/256 mlog(u) % the danger of calling mlog(0) +enddef; + +vardef tand(expr theta) = + save x, y; + (x, y) = dir theta; + if abs(x) < eps: infinity else: y/x fi +enddef; +vardef exp(expr x) = mexp(256x) enddef; +vardef log(expr x) = 1/256 mlog(x) enddef; + +% this is defined only for a > 1 +vardef gammadeviate(expr a, b) = + save y, x, v, s, accept; boolean accept; + s = sqrt(2a - 1); + forever: + forever: + y := tand(uniformdeviate 180); + exitif abs(y) < 16; + endfor + x := s * y + a - 1; + accept := false; + if x > 0: + v := uniformdeviate 1; + if v <= (1 + y * y) * exp((a - 1) * log(x / (a - 1)) - s * y): + accept := true; + fi + fi + exitif accept; + endfor + x/b +enddef; diff --git a/info/drawing-with-metapost/src/random-qed.mp b/info/drawing-with-metapost/src/random-qed.mp new file mode 100644 index 0000000000..17ec5f9f89 --- /dev/null +++ b/info/drawing-with-metapost/src/random-qed.mp @@ -0,0 +1,39 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +def perpendicular expr t of p = + direction t of p rotated 90 shifted point t of p +enddef; + +vardef block(expr wd, dp, theta, r) = + save base, ray, b; + path base, ray[]; numeric b; + + base = origin for i=1 upto 31: + -- (i/32 * wd, r * normaldeviate) + endfor -- (wd,0) -- (wd,-dp) -- (0,-dp) -- cycle; + + image( + fill base withcolor .8[blue,white]; + draw base withcolor .67 blue; + + for i = 2 upto 6: + ray[i] = (left--right) scaled 2/3 wd rotated -theta + shifted (i/8 * wd,0); + b := ypart (ray[i] intersectiontimes base); + ray[i] := point 0 of ray[i] -- point b of base -- point 0 of ray[i] + reflectedabout(point b of base, perpendicular b of base); + drawarrow ray[i]; + endfor + + label("$r=" & decimal r & "$", center base); + ) +enddef; +beginfig(0); + draw block(108, 16, 45, 0); + draw block(108, 16, 45, 0.42) shifted 180 right; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/random-qed.pdf b/info/drawing-with-metapost/src/random-qed.pdf Binary files differnew file mode 100644 index 0000000000..ecd11c483e --- /dev/null +++ b/info/drawing-with-metapost/src/random-qed.pdf diff --git a/info/drawing-with-metapost/src/random-shapes.mp b/info/drawing-with-metapost/src/random-shapes.mp index de581a58fe..cf9a4aca16 100644 --- a/info/drawing-with-metapost/src/random-shapes.mp +++ b/info/drawing-with-metapost/src/random-shapes.mp @@ -4,21 +4,20 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); -numeric desired_length, n, s; -desired_length = 180; n = 30; s = 80; -for r=0 upto 8: - path shape; - shape = for i=1 upto n: - (s + r * normaldeviate, 0) rotated (360/n*i) .. - endfor cycle; + numeric desired_length, n, s; + desired_length = 180; n = 30; s = 80; + for r=0 upto 8: + path shape; + shape = for i=1 upto n: + (s + r * normaldeviate, 0) rotated (360/n*i) .. + endfor cycle; - shape := shape scaled (desired_length/arclength shape); - - draw shape shifted (r*s, 0) withcolor (r/8)[black,red]; - label(decimal r, (r*s, 0)); + shape := shape scaled (desired_length/arclength shape); -endfor + draw shape shifted (r*s, 0) withcolor (r/8)[black,red]; + label(decimal r, (r*s, 0)); + + endfor endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/random-shapes.pdf b/info/drawing-with-metapost/src/random-shapes.pdf Binary files differindex 540fdb680c..a39edade7e 100644 --- a/info/drawing-with-metapost/src/random-shapes.pdf +++ b/info/drawing-with-metapost/src/random-shapes.pdf diff --git a/info/drawing-with-metapost/src/random-torn-edge-circle.mp b/info/drawing-with-metapost/src/random-torn-edge-circle.mp new file mode 100644 index 0000000000..cc1b05459d --- /dev/null +++ b/info/drawing-with-metapost/src/random-torn-edge-circle.mp @@ -0,0 +1,18 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +input random-torn-edge +beginfig(1); + path c; c = fullcircle scaled 200; + draw c withcolor .8 white; + y=0; n = 600; + path t; t = for i=0 upto n-1: + point i/n*length(c) of c + + (0, walkr y) rotated angle direction i/n*length(c) of c + -- + endfor cycle; + draw t withcolor .67 red; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/random-torn-edge-circle.pdf b/info/drawing-with-metapost/src/random-torn-edge-circle.pdf Binary files differnew file mode 100644 index 0000000000..4d1de0ad6d --- /dev/null +++ b/info/drawing-with-metapost/src/random-torn-edge-circle.pdf diff --git a/info/drawing-with-metapost/src/random-torn-edge.mp b/info/drawing-with-metapost/src/random-torn-edge.mp new file mode 100644 index 0000000000..f92de95c0a --- /dev/null +++ b/info/drawing-with-metapost/src/random-torn-edge.mp @@ -0,0 +1,8 @@ +vardef walkr suffix $ = + save t; boolean t; + t = uniformdeviate 1 < (2 ** - abs($)); + $ := $ if t: + else: - fi signr $; $ +enddef; +vardef signr suffix $ = + if $ < 0: - else: + fi uniformdeviate 1 +enddef; diff --git a/info/drawing-with-metapost/src/random-torn-straight-edge.mp b/info/drawing-with-metapost/src/random-torn-straight-edge.mp new file mode 100644 index 0000000000..73f735f7de --- /dev/null +++ b/info/drawing-with-metapost/src/random-torn-straight-edge.mp @@ -0,0 +1,14 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +input random-torn-edge +beginfig(1); + path t; numeric x, y; + x = 0; y=0; + t = (x, -20) -- (x, y) for i=1 upto 288: + -- (incr x, walkr y) endfor -- (x, -20) -- cycle; + fill t withcolor (1, 1, 31/32); draw t withcolor .67 blue; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/random-torn-straight-edge.pdf b/info/drawing-with-metapost/src/random-torn-straight-edge.pdf Binary files differnew file mode 100644 index 0000000000..ba6d68afba --- /dev/null +++ b/info/drawing-with-metapost/src/random-torn-straight-edge.pdf diff --git a/info/drawing-with-metapost/src/random-two-dimensional-brownian.mp b/info/drawing-with-metapost/src/random-two-dimensional-brownian.mp new file mode 100644 index 0000000000..e1833d96f1 --- /dev/null +++ b/info/drawing-with-metapost/src/random-two-dimensional-brownian.mp @@ -0,0 +1,22 @@ +\documentclass{standalone} +\usepackage{luamplib} +\mplibshowlog{enable} +\begin{document} +\begin{mplibcode} +beginfig(1); +% randomseed := uniformdeviate infinity; +randomseed := 2141.34242; +numeric u, v; u = 5; v = 4; +for n=1 upto 4: + numeric x, y; x = y = 0; + path w; w = (x, y) for i=1 upto 2048: + hide(x := x + normaldeviate * u ; y := y + normaldeviate * v) + .. (x, y) + endfor; + draw w withcolor (2n/10)[white, 2/3 blue]; + draw (x, y) withpen pencircle scaled 3 withcolor 2/3 red; +endfor +draw origin withpen pencircle scaled 3 withcolor 3/4 green; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/random-two-dimensional-brownian.pdf b/info/drawing-with-metapost/src/random-two-dimensional-brownian.pdf Binary files differnew file mode 100644 index 0000000000..8a4cb81690 --- /dev/null +++ b/info/drawing-with-metapost/src/random-two-dimensional-brownian.pdf diff --git a/info/drawing-with-metapost/src/random-walks-normal-bridge.mp b/info/drawing-with-metapost/src/random-walks-normal-bridge.mp new file mode 100644 index 0000000000..61d14e9f07 --- /dev/null +++ b/info/drawing-with-metapost/src/random-walks-normal-bridge.mp @@ -0,0 +1,25 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\mplibshowlog{enable} +\begin{mplibcode} +beginfig(1); + randomseed := 3612.11746; + numeric w, h, n; w = 377; h = 80; n = 500; + draw (origin--right) scaled w; + draw (origin--right) scaled w shifted (0,+h/2) withcolor 3/4; + draw (origin--right) scaled w shifted (0,-h/2) withcolor 3/4; + numeric y; y = 0; + path walk; walk = (0, y) for x=w/n step w/n until w: + hide(y := y + 4 normaldeviate) + -- (x, y) + endfor; + path bridge; bridge = point 0 of walk for i=1 upto n: + -- point i of walk + (0, i/n * -y) endfor; + draw walk withcolor 7/8; % so you can see how it works + undraw bridge withpen pencircle scaled 3/4; + draw bridge withcolor 3/4 blue; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/random-walks-normal-bridge.pdf b/info/drawing-with-metapost/src/random-walks-normal-bridge.pdf Binary files differnew file mode 100644 index 0000000000..64776bb47d --- /dev/null +++ b/info/drawing-with-metapost/src/random-walks-normal-bridge.pdf diff --git a/info/drawing-with-metapost/src/random-walks-normal.mp b/info/drawing-with-metapost/src/random-walks-normal.mp new file mode 100644 index 0000000000..417ace7151 --- /dev/null +++ b/info/drawing-with-metapost/src/random-walks-normal.mp @@ -0,0 +1,27 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\mplibshowlog{enable} +\begin{mplibcode} +beginfig(1); + randomseed := 3612.11746; + numeric w, h, n; w = 377; h = 80; n = 500; + draw (origin--right) scaled w; + draw (origin--right) scaled w shifted (0,+h/2) withcolor 3/4; + draw (origin--right) scaled w shifted (0,-h/2) withcolor 3/4; + for i=1 upto 4: + numeric y; y = 0; + path walk; walk = (0, y) for x=w/n step w/n until w: + hide(y := y + 2 normaldeviate) + -- (x, y) + endfor; + undraw walk withpen pencircle scaled 3/4; + draw walk withcolor (1/2+y/h)[red, blue]; + label.rt("$\scriptstyle" & decimal i & "$", + point infinity of walk); + endfor +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/random-walks-normal.pdf b/info/drawing-with-metapost/src/random-walks-normal.pdf Binary files differnew file mode 100644 index 0000000000..11e69fcd19 --- /dev/null +++ b/info/drawing-with-metapost/src/random-walks-normal.pdf diff --git a/info/drawing-with-metapost/src/random-walks-red-blue.mp b/info/drawing-with-metapost/src/random-walks-red-blue.mp index a11a5f22f3..8ceee94761 100644 --- a/info/drawing-with-metapost/src/random-walks-red-blue.mp +++ b/info/drawing-with-metapost/src/random-walks-red-blue.mp @@ -1,45 +1,33 @@ \documentclass{standalone} \usepackage{luamplib} \begin{document} -\mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); - randomseed := 3.1415; - color tr, tb; tr = 0.84 red; tb = 1.2(.2,.2,.7); - numeric w, h, n; w = 377; h = 80; n = 500; - pair zenith, nadir; zenith = nadir = origin; - path walk[]; + numeric w, h, n; w = 377; h = 80; n = 500; - draw (origin--right) scaled w; - draw (origin--right) scaled w shifted (0,+h/2) withcolor 3/4; - draw (origin--right) scaled w shifted (0,-h/2) withcolor 3/4; - - for i=1 upto 8: - numeric y; y = 0; - walk[i] = origin for x=w/n step w/n until w: - hide( - y := y if uniformdeviate 1 < 1/2: + else: - fi 1; - if y > ypart zenith: zenith := (x,y) ; fi - if y < ypart nadir: nadir := (x,y) ; fi - ) - -- (x,y) - endfor; - undraw walk[i] withpen pencircle scaled 3/4; - draw walk[i] withcolor (1/2+y/h)[tr, tb]; - label.rt("$\scriptstyle" & decimal i & "$", - point infinity of walk[i] - if i=1: shifted (-3, 3) - elseif i=3: shifted (1,3) - elseif i=5: shifted (-3, 3) - elseif i=7: shifted (-1, -4) fi); - endfor - - drawarrow (12 up -- 2 up ) shifted zenith withcolor tb; - drawarrow (12 down -- 2 down) shifted nadir withcolor tr; - - fill fullcircle scaled 2; + draw (origin--right) scaled w; + draw (origin--right) scaled w shifted (0,+h/2) withcolor 3/4; + draw (origin--right) scaled w shifted (0,-h/2) withcolor 3/4; + pair zenith, nadir; zenith = nadir = origin; + color gain, lose; gain = .67 blue; lose = .85 red; + for i=1 upto 8: + path walk; + numeric y; y = 0; + walk = origin for x=w/n step w/n until w: + hide( + y := y if uniformdeviate 1 < 1/2: + else: - fi 1; + if y > ypart zenith: zenith := (x,y) ; fi + if y < ypart nadir: nadir := (x,y) ; fi + ) + -- (x,y) + endfor; + undraw walk withpen pencircle scaled 3/4; + draw walk withcolor (1/2+y/h)[lose, gain]; + endfor + draw origin withpen pencircle scaled 2; + drawarrow (12 up -- 2 up) shifted zenith withcolor gain; + drawarrow (12 down -- 2 down) shifted nadir withcolor lose; endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/random-walks-red-blue.pdf b/info/drawing-with-metapost/src/random-walks-red-blue.pdf Binary files differindex c76047183c..5098669191 100644 --- a/info/drawing-with-metapost/src/random-walks-red-blue.pdf +++ b/info/drawing-with-metapost/src/random-walks-red-blue.pdf diff --git a/info/drawing-with-metapost/src/rec-bush.mp b/info/drawing-with-metapost/src/rec-bush.mp index 594a2eebf5..3d7deb4604 100644 --- a/info/drawing-with-metapost/src/rec-bush.mp +++ b/info/drawing-with-metapost/src/rec-bush.mp @@ -2,25 +2,19 @@ \usepackage{luamplib} \begin{document} \mplibtextextlabel{enable} +\mplibshowlog{enable} \begin{mplibcode} +randomseed:=2321.57867; input colorbrewer-rgb vardef bush(expr start, aim, level, limit) = - save s, target; - numeric s; s = level / limit; - for a = -32, -8, 8, 16: - pair target; - target = aim scaled ((32 + 16 normaldeviate) * s) rotated a shifted start; - draw start -- target - withpen pencircle scaled s - withcolor BrBG[limit][limit-level]; - if level > 1: - bush(target, aim rotated a, level - 1, limit); - fi - endfor + save s, target; pair target; numeric s; s = level / limit; + for a = -32, -8, 8, 16: + target := aim scaled ((64 + 32 normaldeviate) * s) rotated a shifted start; + draw start -- target withpen pencircle scaled s withcolor BrBG[limit][limit-level]; + if level > 1: bush(target, aim rotated a, level - 1, limit); fi + endfor enddef; -beginfig(1); -bush(origin, dir 80, 6, 8); -endfig; +beginfig(1); bush(origin, dir 80, 6, 8); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-bush.pdf b/info/drawing-with-metapost/src/rec-bush.pdf Binary files differindex 415b01c391..179fb57f71 100644 --- a/info/drawing-with-metapost/src/rec-bush.pdf +++ b/info/drawing-with-metapost/src/rec-bush.pdf diff --git a/info/drawing-with-metapost/src/rec-dragon-golden.mp b/info/drawing-with-metapost/src/rec-dragon-golden.mp index df4dc37c48..f6b2879c2d 100644 --- a/info/drawing-with-metapost/src/rec-dragon-golden.mp +++ b/info/drawing-with-metapost/src/rec-dragon-golden.mp @@ -4,19 +4,18 @@ \mplibtextextlabel{enable} \begin{document} \begin{mplibcode} -vardef acosd(expr a) = angle (a, 1 +-+ a) enddef; numeric r, phi, theta; -phi = 0.61803398875; -r = phi**phi; -theta = acosd(1/2(1/r + r - r * r * r)); +phi = 0.61803398875; +r = phi ** phi; +theta = angle (fullcircle scaled 2r intersectionpoint fullcircle scaled (2r*r) shifted right); vardef dragon(expr a, b) = - if abs(a-b) > 1: + if abs(a-b) > 1.618: save p; pair p; p = r[a, b] rotatedabout(a, theta); dragon(a, p) & reverse dragon(b, p) else: - a -- b + a .. b fi enddef; diff --git a/info/drawing-with-metapost/src/rec-dragon-golden.pdf b/info/drawing-with-metapost/src/rec-dragon-golden.pdf Binary files differindex 810ad03560..0796fcedae 100644 --- a/info/drawing-with-metapost/src/rec-dragon-golden.pdf +++ b/info/drawing-with-metapost/src/rec-dragon-golden.pdf diff --git a/info/drawing-with-metapost/src/rec-dragon.mp b/info/drawing-with-metapost/src/rec-dragon.mp index 60b8549cf1..a1ccaf2edc 100644 --- a/info/drawing-with-metapost/src/rec-dragon.mp +++ b/info/drawing-with-metapost/src/rec-dragon.mp @@ -5,35 +5,35 @@ \begin{mplibcode} numeric r, theta; r = sqrt 1/2; theta = 45; vardef dragon(expr level, a, b) = - if level > 0: - save p; pair p; - p = r[a, b] rotatedabout(a, theta); - dragon(level - 1, a, p) & reverse dragon(level - 1, b, p) - else: - a .. b - fi + if level > 0: + save p; pair p; + p = r[a, b] rotatedabout(a, theta); + dragon(level - 1, a, p) & reverse dragon(level - 1, b, p) + else: + a .. b + fi enddef; vardef rounded_corners expr p = - save r, n; numeric r, n; r = 1/3; n = length p; - subpath (0, 1-r) of p - for t=1 upto n-1: - .. subpath (t+r, t+1-r) of p - endfor .. subpath (n-r, n) of p + save r, n; numeric r, n; r = 1/3; n = length p; + subpath (0, 1-r) of p + for t=1 upto n-1: + .. subpath (t+r, t+1-r) of p + endfor .. subpath (n-r, n) of p enddef; beginfig(1); - path d; d = dragon(15, origin, 240 right); - draw d withpen pencircle scaled 1/4 withcolor (.2, .2, .7); - label.top("The dragon curve at level 15", point 1/3 of bbox currentpicture); + path d; d = dragon(15, origin, 240 right); + draw d withpen pencircle scaled 1/4 withcolor (.2, .2, .7); + label.top("The dragon curve at level 15", point 1/3 of bbox currentpicture); - draw rounded_corners dragon(10, origin, 240 right) - shifted 280 down - withcolor .54 red; + draw rounded_corners dragon(10, origin, 240 right) + shifted 280 down + withcolor .54 red; + + label.top("\dots\ and at level 10 with rounded corners", point 1/3 of bbox currentpicture); - label.top("\dots\ and at level 10 with rounded corners", point 1/3 of bbox currentpicture); - endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-dragon.pdf b/info/drawing-with-metapost/src/rec-dragon.pdf Binary files differindex 3338a7adde..457c58035e 100644 --- a/info/drawing-with-metapost/src/rec-dragon.pdf +++ b/info/drawing-with-metapost/src/rec-dragon.pdf diff --git a/info/drawing-with-metapost/src/rec-flowsnake-construction.mp b/info/drawing-with-metapost/src/rec-flowsnake-construction.mp index ec543a7512..b439e318a2 100644 --- a/info/drawing-with-metapost/src/rec-flowsnake-construction.mp +++ b/info/drawing-with-metapost/src/rec-flowsnake-construction.mp @@ -5,48 +5,27 @@ \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); -path h[], snake; -h0 = (for i = 1 upto 6: 40 dir 60i -- endfor cycle) rotated angle (9, -sqrt(3)); -for i = 1 upto 6: - h[i] = h0 shifted (point 0 of h0 - point 2 of h0) rotated 60i; -endfor -snake = point 0 of h3 -- point 1 of h2 -- point 2 of h1 - -- point 1 of h6 -- point 2 of h5 -- point 3 of h0 - -- point 1 of h4 -- point 0 of h5; - -for i=1 upto 6: - draw subpath (4, 9) of h[i] withcolor 3/4; -endfor - -% path usnake; -% usnake = snake -% shifted - point 0 of h3 -% scaled (1/abs(point 0 of h3 - point 0 of h5)); - -% def zx(expr a, b) = zscaled (point b of snake - point a of snake) -% shifted point a of snake enddef; - -% draw usnake zx(1, 0) dashed withdots scaled 1/2 withcolor 2/3 red; -% draw usnake zx(1, 2) dashed withdots scaled 1/2 withcolor 2/3 red; -% draw usnake zx(2, 3) dashed withdots scaled 1/2 withcolor 2/3 red; -% draw usnake zx(3, 4) dashed withdots scaled 1/2 withcolor 2/3 red; -% draw usnake zx(5, 4) dashed withdots scaled 1/2 withcolor 2/3 red; -% draw usnake zx(6, 5) dashed withdots scaled 1/2 withcolor 2/3 red; -% draw usnake zx(6, 7) dashed withdots scaled 1/2 withcolor 2/3 red; - - -draw 2/3[point 0 of h3, point 0 of h5] -- point 0 of h5 withcolor 1/2; -drawarrow point 0 of h3 -- 2/3[point 0 of h3, point 0 of h5] withcolor 1/2; -draw snake withcolor 2/3 red; -for t=1, 5, 6: - drawarrow subpath (t, t-2/3) of snake withcolor \mpcolor{textred}; -endfor -for t=1, 2, 3, 6: - drawarrow subpath (t, t+2/3) of snake withcolor \mpcolor{textred}; -endfor - -dotlabel.llft("$(0, 0)$", point 0 of h3); -dotlabel.lrt ("$(1, 0)$", point 0 of h5); + path h[], snake; + h0 = for i = 1 upto 6: 40 dir 60i -- endfor cycle; + h0 := h0 rotated - angle (9, sqrt(3)); + for i = 1 upto 6: + h[i] = h0 shifted (point 0 of h0 - point 2 of h0) rotated -(120+60i); + draw h[i] withcolor 3/4; + endfor + snake = point 0 of h1 -- point 1 of h2 -- point 2 of h3 + -- point 1 of h4 -- point 2 of h5 -- point 3 of h6 + -- point 4 of h5 -- point 0 of h5; + ahangle := 30; + z0 = point 0 of snake; z1 = point 8 of snake; z23 = 2/3[z0, z1]; + drawoptions(withcolor 1/2); + drawarrow z0 -- z23; draw z23 -- z1; + drawoptions(withcolor \mpcolor{textred}); + draw snake; + for t=1, 5, 6: drawarrow subpath (t, t-2/3) of snake; endfor + for t=1, 2, 3, 6: drawarrow subpath (t, t+2/3) of snake; endfor + drawoptions(); + dotlabel.llft("$(0, 0)$", z0); + dotlabel.lrt ("$(1, 0)$", z1); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-flowsnake-construction.pdf b/info/drawing-with-metapost/src/rec-flowsnake-construction.pdf Binary files differindex 06f111a067..f2ebd6f2ac 100644 --- a/info/drawing-with-metapost/src/rec-flowsnake-construction.pdf +++ b/info/drawing-with-metapost/src/rec-flowsnake-construction.pdf diff --git a/info/drawing-with-metapost/src/rec-flowsnake.mp b/info/drawing-with-metapost/src/rec-flowsnake.mp index be94b53065..18348e5a7b 100644 --- a/info/drawing-with-metapost/src/rec-flowsnake.mp +++ b/info/drawing-with-metapost/src/rec-flowsnake.mp @@ -15,37 +15,6 @@ snake := snake shifted - point 0 of h3; snake := snake rotated - angle (point 0 of h5 - point 0 of h3); snake := snake scaled (1 / length (point 0 of h5 - point 0 of h3)); -vardef hexon(expr a, b) = - pair c, m; - c = b rotatedaround(a, 60); - m = 2/3[c, 1/2[a, b]]; - a -- a rotatedaround(m, 60) -- - b -- b rotatedaround(m, 60) -- - c -- c rotatedaround(m, 60) -- cycle -enddef; - -path w; -w = origin -- right; -w := w -- point 0 of w rotatedabout(point 1 of w, 120); -w := w -- point 1 of w rotatedabout(point 2 of w, -120); -w := w rotated - angle (point 3 of w - point 0 of w); -w := w scaled (1/abs (point 3 of w - point 0 of w)); - -pair a, b; -a = 144 down rotated -60; -b = 144 down rotated +60; -numeric n; n = 4; - -path boundary; -boundary = hexon(a, b); -for i = 1 upto n: - boundary := for t = 1 upto length boundary: - subpath (0, 2) of w - zscaled (point t of boundary - point t-1 of boundary) - shifted point t-1 of boundary -- endfor cycle; -endfor - - vardef rattle(expr level, a, b) = if level > 0: save s; path s; s = snake zscaled (b-a) shifted a; @@ -61,9 +30,11 @@ vardef rattle(expr level, a, b) = fi enddef; beginfig(1); - path s; s = rattle(n, a, b); - fill a + (-40, 0) -- s -- b + (40, 0) -- - b + (40, 224) -- a + (-40, 224) -- cycle withcolor 3/4[1/4 blue, white]; + pair a, b; path s; + a = 124 left; b = 124 right; s = rattle(4, a, b); + fill s -- b + (40, 0) -- b + (40, 224) + -- a - (40, -224) -- a - (40,0) -- cycle + withcolor 3/4[1/4 blue, white]; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-flowsnake.pdf b/info/drawing-with-metapost/src/rec-flowsnake.pdf Binary files differindex 3bcc884ad1..6cf1442af2 100644 --- a/info/drawing-with-metapost/src/rec-flowsnake.pdf +++ b/info/drawing-with-metapost/src/rec-flowsnake.pdf diff --git a/info/drawing-with-metapost/src/rec-gcd-comparison.mp b/info/drawing-with-metapost/src/rec-gcd-comparison.mp new file mode 100644 index 0000000000..0bf5c3b235 --- /dev/null +++ b/info/drawing-with-metapost/src/rec-gcd-comparison.mp @@ -0,0 +1,34 @@ +vardef gcd(expr a, b) = if b = 0: a else: gcd(b, a mod b) fi enddef; + +show + (gcd(560,257) = 1) and + (gcd(12,3384) = 12) and + (gcd(2454,541) = 1) and + (gcd(2824,494) = 2) and + (gcd(3633,2930) = 1) and + (gcd(3555,3738) = 3) and + (gcd(2743,3484) = 13) and + (gcd(1267,1330) = 7) and + (gcd(2718,1672) = 2) and + (gcd(2515,3980) = 5); + +vardef gcd(expr A, B) = save r, a, b; numeric a, b, r; a := A; b := B; + forever: + r := a mod b; exitif r = 0; + a := b; b := r; + endfor b +enddef; + +show + (gcd(560,257) = 1) and + (gcd(12,3384) = 12) and + (gcd(2454,541) = 1) and + (gcd(2824,494) = 2) and + (gcd(3633,2930) = 1) and + (gcd(3555,3738) = 3) and + (gcd(2743,3484) = 13) and + (gcd(1267,1330) = 7) and + (gcd(2718,1672) = 2) and + (gcd(2515,3980) = 5); + +end. diff --git a/info/drawing-with-metapost/src/rec-general-tree-deviate.mp b/info/drawing-with-metapost/src/rec-general-tree-deviate.mp index f6e1ac1e7b..5b0bc6c4db 100644 --- a/info/drawing-with-metapost/src/rec-general-tree-deviate.mp +++ b/info/drawing-with-metapost/src/rec-general-tree-deviate.mp @@ -2,32 +2,33 @@ \usepackage{luamplib} \begin{document} \mplibtextextlabel{enable} +\mplibshowlog{enable} \begin{mplibcode} -input colorbrewer-rgb +% randomseed := uniformdeviate infinity; +randomseed := 134.7384; r = 0.75; theta = 17; vardef make_tree(expr bar) = - save a; numeric a; a = abs(point 1 of bar - point 0 of bar); - cutdraw bar withpen pencircle scaled (a/8); - if a > 5: - save s; pair s; s = 1/32 a * r * unitvector(direction 1 of bar) rotated 90; - make_tree( - bar shifted - point 0 of bar shifted s - scaled (r + 1/16 normaldeviate) - rotated (theta + 8 normaldeviate) - shifted point 1 of bar - ); - make_tree( - bar shifted - point 0 of bar shifted -s - scaled (r + 1/16 normaldeviate) - rotated -(theta + 8 normaldeviate) - shifted point 1 of bar - ); - fi + save a; numeric a; a = abs(point 1 of bar - point 0 of bar); + cutdraw bar withpen pencircle scaled (a/8); + if a > 5: + save s; pair s; s = 1/32 a * r * unitvector(direction 1 of bar) rotated 90; + make_tree( + bar shifted - point 0 of bar shifted s + scaled (r + 1/16 normaldeviate) rotated (theta + 8 normaldeviate) + shifted point 1 of bar + ); + make_tree( + bar shifted - point 0 of bar shifted -s + scaled (r + 1/16 normaldeviate) rotated -(theta + 8 normaldeviate) + shifted point 1 of bar + ); + fi enddef; beginfig(1); -for i=1 upto 4: + for i=1 upto 4: picture T; T = image(make_tree(origin -- 40 up)); draw T shifted (170i, 0); -endfor + endfor + input show_name; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-general-tree-deviate.pdf b/info/drawing-with-metapost/src/rec-general-tree-deviate.pdf Binary files differindex 3803c073ca..6d127bd61b 100644 --- a/info/drawing-with-metapost/src/rec-general-tree-deviate.pdf +++ b/info/drawing-with-metapost/src/rec-general-tree-deviate.pdf diff --git a/info/drawing-with-metapost/src/rec-general-tree.mp b/info/drawing-with-metapost/src/rec-general-tree.mp index c4e31178af..7d9e857ce1 100644 --- a/info/drawing-with-metapost/src/rec-general-tree.mp +++ b/info/drawing-with-metapost/src/rec-general-tree.mp @@ -6,9 +6,10 @@ vardef make_tree(expr bar) = save a; numeric a; a = abs(point 1 of bar - point 0 of bar); cutdraw bar withpen pencircle scaled 1.2(1/8 a) withcolor background; - cutdraw bar withpen pencircle scaled (1/8 a) withcolor 1/256(57, 35, 32); + cutdraw bar withpen pencircle scaled (1/8 a) withcolor 1/256(148,98,58); if a > leaf: - save s; pair s; s = 1/32 a * r * unitvector(direction 1 of bar) rotated 90; + save s; pair s; + s = 1/32 a * r * unitvector(direction 1 of bar) rotated 90; make_tree( bar shifted - point 0 of bar shifted s scaled r rotated theta @@ -20,14 +21,13 @@ vardef make_tree(expr bar) = shifted point 1 of bar ); else: - draw point 1 of bar withpen pencircle scaled 1 withcolor 2/3 green; + draw point 1 of bar withpen pencircle scaled 2 withcolor 2/3 green; fi enddef; beginfig(1); -numeric stem, leaf, r, theta; -r = 0.75; theta = 14; -stem = 100; leaf = 3; % max(1, round(stem * (r ** 12))); -make_tree(origin -- stem * up); + numeric leaf, r, theta; + leaf = 3; r = 0.71; theta = 14; + make_tree(origin -- 100 up); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-general-tree.pdf b/info/drawing-with-metapost/src/rec-general-tree.pdf Binary files differindex 8db8f8a29e..384e3c9dad 100644 --- a/info/drawing-with-metapost/src/rec-general-tree.pdf +++ b/info/drawing-with-metapost/src/rec-general-tree.pdf diff --git a/info/drawing-with-metapost/src/rec-h-tree.mp b/info/drawing-with-metapost/src/rec-h-tree.mp index a131038491..3790ddfec8 100644 --- a/info/drawing-with-metapost/src/rec-h-tree.mp +++ b/info/drawing-with-metapost/src/rec-h-tree.mp @@ -5,25 +5,41 @@ \begin{mplibcode} input colorbrewer-rgb r = 0; -vardef make_H(expr level, bar, thickness) = + +vardef decorate(expr a, b, s, z) = + save F, w; picture F; pair w; w = (mlog(a/b), 400 + normaldeviate); + F = thelabel(TEX("$\frac{" & decimal a & "}{" & decimal b & "}$") scaled s, z); + + + fill bbox F withcolor 1/4[white, if a/b < 1: red else: blue fi]; draw F; + + draw w withpen pencircle scaled 1; +enddef; + +vardef make_H(expr level, scale, bar, thickness, n, d) = cutdraw bar withpen pencircle scaled thickness - withcolor Blues[9][9 - floor(level/2)]; + withcolor Blues[8][level]; + + decorate(n, d, scale, point 1/2 of bar); % save spike, m; path spike; pair m; m = unitvector(direction 1/2 of bar rotated 90); % spike = point 0 of bar .. m scaled +thickness shifted point 1/2 of bar .. point 1 of bar & % point 1 of bar .. m scaled -thickness shifted point 1/2 of bar .. point 0 of bar & cycle; % fill spike withcolor Reds 9 7; - if level > 0: + if level > 1: save foo, fo; path foo, fo; foo = bar shifted - point 1/2 of bar scaled 0.7071067811865475; - make_H(level - 1, foo rotated 90 shifted point r of bar, thickness); - make_H(level - 1, foo rotated 90 shifted point 1-r of bar, thickness); + make_H(level - 1, scale * .8, foo rotated (90+1/4normaldeviate) shifted point r of bar, thickness, n, n+d); + make_H(level - 1, scale * .8, foo rotated (90+1/4normaldeviate) shifted point 1-r of bar, thickness, n+d, d); + else: + decorate(n, n+d, scale, point 0 of bar); + decorate(n+d, d, scale, point 1 of bar); fi enddef; beginfig(1); -make_H(8, (left -- right) scaled 200, 1/2); +make_H(9, 1.4, (left -- right) scaled 256, 1/2, 1, 1); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-h-tree.pdf b/info/drawing-with-metapost/src/rec-h-tree.pdf Binary files differindex 5efa7ed845..37da0af380 100644 --- a/info/drawing-with-metapost/src/rec-h-tree.pdf +++ b/info/drawing-with-metapost/src/rec-h-tree.pdf diff --git a/info/drawing-with-metapost/src/rec-koch-steps.mp b/info/drawing-with-metapost/src/rec-koch-steps.mp index e696eac4f8..623798d397 100644 --- a/info/drawing-with-metapost/src/rec-koch-steps.mp +++ b/info/drawing-with-metapost/src/rec-koch-steps.mp @@ -5,27 +5,27 @@ \begin{mplibcode} vardef koch(expr level, a, b) = - if level = 0: - a -- b - else: - save p, q, r; pair p, q, r; - p = 1/3[a,b]; r = 2/3[a,b]; q = r rotatedabout(p, 60); - koch(level-1, a, p) & - koch(level-1, p, q) & - koch(level-1, q, r) & - koch(level-1, r, b) - fi + if level = 0: + a -- b + else: + save p, q, r; pair p, q, r; + p = 1/3[a,b]; r = 2/3[a,b]; q = r rotatedabout(p, 60); + koch(level-1, a, p) & + koch(level-1, p, q) & + koch(level-1, q, r) & + koch(level-1, r, b) + fi enddef; beginfig(1); - wd = 300; - for n=0 upto 4: - numeric y; y = -1/3 wd * n; - path k; k = koch(n, origin, (wd, 0)) shifted (0, y); - draw k withcolor 2/3 blue; - label.urt("\small\textsf{Level " & decimal n & "}", point infinity of k); - label.top("$\scriptstyle " & decimal length k & "/" & decimal arclength k & "$", (wd/2, y)); - endfor - + wd = 300; + for n=0 upto 4: + numeric y; y = -1/3 wd * n; + path k; k = koch(n, origin, (wd, 0)) shifted (0, y); + draw k withcolor 2/3 blue; + label.urt("\small\textsf{Level " & decimal n & "}", point infinity of k); + label.top("$\scriptstyle " & decimal length k & "/" & decimal arclength k & "$", (wd/2, y)); + endfor + input show_name endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-koch-steps.pdf b/info/drawing-with-metapost/src/rec-koch-steps.pdf Binary files differindex d0be311ae6..556afcc1a9 100644 --- a/info/drawing-with-metapost/src/rec-koch-steps.pdf +++ b/info/drawing-with-metapost/src/rec-koch-steps.pdf diff --git a/info/drawing-with-metapost/src/rec-sierpinski-garlands.mp b/info/drawing-with-metapost/src/rec-sierpinski-garlands.mp new file mode 100644 index 0000000000..0929fcfe08 --- /dev/null +++ b/info/drawing-with-metapost/src/rec-sierpinski-garlands.mp @@ -0,0 +1,36 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb + +vardef garland(expr level, shape) = + if level = 0: + fill shape withcolor filler; draw shape withpen pencircle scaled 1/8; + else: + save little_shape; path little_shape; + little_shape = shape scaled factor; + for i=1 upto length shape: + garland(level - 1, little_shape shifted (point i of shape - point i of little_shape)); + endfor + fi +enddef; +vardef sf(expr n) = + numeric s; s = 0; + for k=1 upto floor (n/4): + s := s + cosd(360 / n * k); + endfor + 1 / (2 * (1 + s)) +enddef; +beginfig(1); + color filler; numeric factor; path poly; + for n=5 upto 9: + filler := Reds[7][n-3]; factor := sf(n); + poly := for i=1 upto n: 64 up rotated (360/n*i) -- endfor cycle; + draw image(garland(3, poly)) shifted (144n, 0); + endfor + input show_name +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/rec-sierpinski-garlands.pdf b/info/drawing-with-metapost/src/rec-sierpinski-garlands.pdf Binary files differnew file mode 100644 index 0000000000..59723908cf --- /dev/null +++ b/info/drawing-with-metapost/src/rec-sierpinski-garlands.pdf diff --git a/info/drawing-with-metapost/src/rec-sierpinski-pentagon.mp b/info/drawing-with-metapost/src/rec-sierpinski-pentagon.mp deleted file mode 100644 index 1829c8003c..0000000000 --- a/info/drawing-with-metapost/src/rec-sierpinski-pentagon.mp +++ /dev/null @@ -1,33 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input colorbrewer-rgb -vardef make_gasket(expr t, s, level, c) = - if level = 0: - fill t withcolor Reds[7][7-c]; - draw t; - else: - save little_t; path little_t; little_t = t scaled s; - for i=1 upto length t: - make_gasket(little_t shifted (point i of t - point i of little_t), s, level-1, c); - endfor - fi -enddef; -vardef sf(expr n) = - numeric s; s = 0; - for k=1 upto floor (n/4): - s := s + cosd(360 / n * k); - endfor - 1 / (2 * (1 + s)) -enddef; -beginfig(1); - for n=5 upto 9: - draw image(make_gasket(for i=1 upto n: 64 up rotated (360/n*i) -- endfor cycle, sf(n), 3, n-4)) - shifted (144n, 0); - endfor - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/rec-sierpinski-pentagon.pdf b/info/drawing-with-metapost/src/rec-sierpinski-pentagon.pdf Binary files differdeleted file mode 100644 index 718d201949..0000000000 --- a/info/drawing-with-metapost/src/rec-sierpinski-pentagon.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/rec-sierpinski-triangle.mp b/info/drawing-with-metapost/src/rec-sierpinski-triangle.mp index c0bbc2ec1a..3632a77a85 100644 --- a/info/drawing-with-metapost/src/rec-sierpinski-triangle.mp +++ b/info/drawing-with-metapost/src/rec-sierpinski-triangle.mp @@ -3,19 +3,19 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} -vardef make_gasket(expr t, s, limit) = - if length (point 1 of t - point 0 of t) < limit: - fill t; - else: - save little_t; path little_t; little_t = t scaled s; - for i=1 upto length t: - make_gasket(little_t shifted (point i of t - point i of little_t), s, limit); - endfor - fi +vardef gasket(expr t, s, limit) = + if length (point 1 of t - point 0 of t) < limit: + fill t; + else: + save little_t; path little_t; little_t = t scaled s; + for i=1 upto length t: + gasket(little_t shifted (point i of t - point i of little_t), s, limit); + endfor + fi enddef; beginfig(1); - path T; T = for i = 1 upto 3: 220 up rotated (120i) -- endfor cycle; - make_gasket(T, 1/2, 20); + path T; T = for i = 1 upto 3: 220 up rotated (120i) -- endfor cycle; + gasket(T, 1/2, 20); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-sierpinski-triangle.pdf b/info/drawing-with-metapost/src/rec-sierpinski-triangle.pdf Binary files differindex 7a2c122f2c..1174f355e7 100644 --- a/info/drawing-with-metapost/src/rec-sierpinski-triangle.pdf +++ b/info/drawing-with-metapost/src/rec-sierpinski-triangle.pdf diff --git a/info/drawing-with-metapost/src/rec-simple-tree.mp b/info/drawing-with-metapost/src/rec-simple-tree.mp index 59657cb1b8..6721d7bd24 100644 --- a/info/drawing-with-metapost/src/rec-simple-tree.mp +++ b/info/drawing-with-metapost/src/rec-simple-tree.mp @@ -15,18 +15,22 @@ vardef make_tree(expr level, bar) = fi enddef; beginfig(1); -picture T[]; -numeric r, theta; -r = 0.58; theta = 60; T1 = image( - make_tree(3, origin -- 100 up); - label.urt("\ $r=" & decimal r & "$, $\theta=" & decimal theta & "$", origin) withcolor \mpcolor{textred}; +picture T[]; numeric r, theta; +r := 0.58; theta := 60; T1 = image( + make_tree(3, origin -- 100 up); ); r := 0.75; theta := 14; T2 = image( - make_tree(10, origin -- 100 up); - label.urt("\ $r=" & decimal r & "$, $\theta=" & decimal theta & "$", origin) withcolor \mpcolor{textred}; + make_tree(10, origin -- 100 up); ); draw T1 shifted 32 up; draw T2 shifted 128 right; + +drawoptions(withcolor \mpcolor{textred}); +r := 0.58; theta := 60; +label.urt("\ $r=" & decimal r & "$, $\theta=" & decimal theta & "$", 32 up); + +r := 0.75; theta := 14; +label.urt("\ $r=" & decimal r & "$, $\theta=" & decimal theta & "$", 128 right); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/rec-simple-tree.pdf b/info/drawing-with-metapost/src/rec-simple-tree.pdf Binary files differindex 1c3c848604..5f27bb80bf 100644 --- a/info/drawing-with-metapost/src/rec-simple-tree.pdf +++ b/info/drawing-with-metapost/src/rec-simple-tree.pdf diff --git a/info/drawing-with-metapost/src/rope.mp b/info/drawing-with-metapost/src/rope.mp index 09bf92a56a..1a0eb6b141 100644 --- a/info/drawing-with-metapost/src/rope.mp +++ b/info/drawing-with-metapost/src/rope.mp @@ -1,21 +1,20 @@ +def twisted expr t of p = + rotated angle direction arctime t of p of p + shifted point arctime t of p of p +enddef; vardef rope expr c = - save s, w, hemp, n, a, b, A; - color hemp; hemp = 1/256 (192, 149, 82); - numeric s, w, n, A; - w = -1; n = -1; A = arclength c; s = A/floor(A/2); - path a[]; - for t=0 step s until A + 1: - a[incr n] = (0,+w) rotated angle direction arctime t-3/2s of c of c shifted point arctime t-3/2s of c of c - .. (0,+w) rotated angle direction arctime t-1/2s of c of c shifted point arctime t-1/2s of c of c - .. (0,-w) rotated angle direction arctime t+1/2s of c of c shifted point arctime t+1/2s of c of c - .. (0,-w) rotated angle direction arctime t+3/2s of c of c shifted point arctime t+3/2s of c of c; - endfor - image( - for i=1 upto n: - path b; b = buildcycle(a[i-1], reverse a[i]); - fill b withcolor 1/2[white, hemp]; - draw b withpen pencircle scaled 1/8; - endfor - ) - enddef; + save s, w, hemp, n, a, b, A; + color hemp; hemp = 1/256 (192, 149, 82); + w = -1; n = -1; A = arclength c; s = A/floor(A/2); + path a[]; + for t=0 step s until A + 1: a[incr n] = + (0,+w) twisted t-3/2s of c .. (0,+w) twisted t-1/2s of c .. + (0,-w) twisted t+1/2s of c .. (0,-w) twisted t+3/2s of c; + endfor + image(for i=1 upto n: + path b; b = buildcycle(a[i-1], reverse a[i]); + fill b withcolor 1/2[white, hemp]; + draw b withpen pencircle scaled 1/8; + endfor) +enddef; diff --git a/info/drawing-with-metapost/src/ruler-cm.mp b/info/drawing-with-metapost/src/ruler-cm.mp index bdbaad10b5..8074f1bc94 100644 --- a/info/drawing-with-metapost/src/ruler-cm.mp +++ b/info/drawing-with-metapost/src/ruler-cm.mp @@ -1,6 +1,3 @@ -numeric u[]; -u0 = 1 cm; -u1 = 1 mm; +numeric u[]; u0 = 1 cm; u1 = 5 mm; u2 = 1 mm; drawoptions(withcolor 0.54 red); input ruler -drawoptions(); diff --git a/info/drawing-with-metapost/src/ruler-inch.mp b/info/drawing-with-metapost/src/ruler-inch.mp index 54fb5a654d..1090abf7d1 100644 --- a/info/drawing-with-metapost/src/ruler-inch.mp +++ b/info/drawing-with-metapost/src/ruler-inch.mp @@ -1,6 +1,3 @@ -numeric u[]; -u0 = 1 in; -u1 = 6 bp; -drawoptions(withcolor 0.54 red); +numeric u[]; u0 = 72; u1 = 18; u2 = 6; +drawoptions(withcolor 0.67 blue); input ruler -drawoptions(); diff --git a/info/drawing-with-metapost/src/ruler-pt.mp b/info/drawing-with-metapost/src/ruler-pt.mp deleted file mode 100644 index 0b0992bae4..0000000000 --- a/info/drawing-with-metapost/src/ruler-pt.mp +++ /dev/null @@ -1,6 +0,0 @@ -numeric u[]; -u0 = 12 bp; -u1 = 1 bp; -drawoptions(withcolor 0.54 red); -input ruler -drawoptions(); diff --git a/info/drawing-with-metapost/src/ruler.mp b/info/drawing-with-metapost/src/ruler.mp index 9d11af25d3..0736abf47e 100644 --- a/info/drawing-with-metapost/src/ruler.mp +++ b/info/drawing-with-metapost/src/ruler.mp @@ -1,19 +1,17 @@ % add a ruler along the left hand and lower edges % of the bounding box of the currentpicture -% ** meant to be embedded by something that sets u[] appropriately ** -path B; B = bbox currentpicture; -for s=0, 1: - path p; numeric a; pair o; - p = subpath (0, 1) of if s=0: reverse fi B; - a = arclength p; - o = if s=0: left else: down fi; - for i=0 upto 3: - exitif not known u[i]; - for j=0 upto floor(a/u[i]): - pair t; t = point arctime j*u[i] of p of p; - draw (origin -- (6 - 2i) * o) shifted t; - if i=0: label(decimal j, t shifted 12 o); fi - endfor +path B, p; pair o; B = bbox currentpicture; +for s=-1, 1: + p := subpath (0, s) of B; + a := arclength p; + o := if s < 0: left else: down fi; + for i=0 upto 3: + exitif not known u[i]; + for j=0 upto floor(a/u[i]): + pair t; t = point arctime j*u[i] of p of p; + draw (origin -- (7 - 2i) * o) shifted t; + if i=0: label(decimal j, t shifted 12 o); fi endfor - draw p; -endfor + endfor + draw p; +endfor diff --git a/info/drawing-with-metapost/src/saturn.mp b/info/drawing-with-metapost/src/saturn.mp deleted file mode 100644 index 08825c4f94..0000000000 --- a/info/drawing-with-metapost/src/saturn.mp +++ /dev/null @@ -1,10 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); -input saturn-code -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/shadows.mp b/info/drawing-with-metapost/src/shadows.mp deleted file mode 100644 index 9134946b15..0000000000 --- a/info/drawing-with-metapost/src/shadows.mp +++ /dev/null @@ -1,37 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - -path b, w; -b = ((-3,-4)--(3,-2)--(3,+2)--(-3,4)--cycle) scaled 5; -w = b reflectedabout(up, down); - -numeric n; -n = 128; - -picture B, W; -B = image(for i=0 step 1/n until 1: - draw point 4-i of b -- point 1+i**2 of b - withcolor 1-i**8; - endfor); - - W = image(for i=0 step 1/n until 1: - draw point 4-i of w -- point 1+i**2 of w - withcolor 3/4-i**8; - endfor); - -for i=-9 upto 9: - for j=-4 upto 4: - draw if odd (i+j): W else: B fi shifted (i*30,j*30); - endfor -endfor - -clip currentpicture to bbox currentpicture yscaled 7/8; - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/shadows.pdf b/info/drawing-with-metapost/src/shadows.pdf Binary files differdeleted file mode 100644 index ea0b67ef2b..0000000000 --- a/info/drawing-with-metapost/src/shadows.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/shady-circles.mp b/info/drawing-with-metapost/src/shady-circles.mp deleted file mode 100644 index 62737f38fe..0000000000 --- a/info/drawing-with-metapost/src/shady-circles.mp +++ /dev/null @@ -1,24 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); -path c, C; numeric r; r = 60; -c = fullcircle scaled 2r shifted (-r, 0); -C = fullcircle scaled 4r shifted (2r, 0); -numeric t, u; -(t, whatever) = C intersectiontimes C shifted (center c - center C); -(u, whatever) = c intersectiontimes (point t of C -- center c); -path s; -s = subpath (0, u) of c -- subpath (t, 4) of C -- cycle; -for i=0 upto r: - draw (left--right) scaled 2r rotated -42 shifted (3i, 0) - withpen pencircle scaled 1/4 withcolor 2/3 blue; -endfor -clip currentpicture to s; -draw c; draw C; -draw center c -- center C -- point t of C -- cycle; -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/shady-circles.pdf b/info/drawing-with-metapost/src/shady-circles.pdf Binary files differdeleted file mode 100644 index df8eef9b56..0000000000 --- a/info/drawing-with-metapost/src/shady-circles.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/show_name.mp b/info/drawing-with-metapost/src/show_name.mp new file mode 100644 index 0000000000..8dda691159 --- /dev/null +++ b/info/drawing-with-metapost/src/show_name.mp @@ -0,0 +1 @@ +label.llft("\tiny\texttt{" & jobname & ".mp}", lrcorner bbox currentpicture); diff --git a/info/drawing-with-metapost/src/simple-circle-labels.mp b/info/drawing-with-metapost/src/simple-circle-labels.mp deleted file mode 100644 index 77aa5e450b..0000000000 --- a/info/drawing-with-metapost/src/simple-circle-labels.mp +++ /dev/null @@ -1,15 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); -path C; C = fullcircle scaled 100; draw C withcolor 2/3 red; -for i=0 upto 11: - drawdot point 2/3 i of C withpen pencircle scaled dotlabeldiam; - label("$p_{" & decimal i & "}$", point 2/3 i of C scaled 1.2); -endfor -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/simple-circle-labels.pdf b/info/drawing-with-metapost/src/simple-circle-labels.pdf Binary files differdeleted file mode 100644 index 209463a97a..0000000000 --- a/info/drawing-with-metapost/src/simple-circle-labels.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/simple-number-line.mp b/info/drawing-with-metapost/src/simple-number-line.mp deleted file mode 100644 index 83ef3d2833..0000000000 --- a/info/drawing-with-metapost/src/simple-number-line.mp +++ /dev/null @@ -1,14 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - draw (left--right) scaled 2in withcolor 2/3 red; - for i=-4 upto 4: - dotlabel.top("$" & decimal i & "$", (32i, 0)); - endfor -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/tangent-times.mp b/info/drawing-with-metapost/src/tangent-times.mp deleted file mode 100644 index ecbb62bb97..0000000000 --- a/info/drawing-with-metapost/src/tangent-times.mp +++ /dev/null @@ -1,11 +0,0 @@ -vardef tangent_times(expr C, p) = - save m, a, b, G, H; - pair m; numeric a, b; path G, H; - m = 1/2[p, center C]; - H = halfcircle scaled abs (p - center C) - rotated angle (p - center C) shifted m; - G = H rotatedabout(m, 180); - (a, whatever) = C intersectiontimes H; - (b, whatever) = C intersectiontimes G; - (a, b if b < a: + 8 fi) -enddef; diff --git a/info/drawing-with-metapost/src/tangents-two-circles-exterior.pdf b/info/drawing-with-metapost/src/tangents-two-circles-exterior.pdf Binary files differdeleted file mode 100644 index db6464e4a4..0000000000 --- a/info/drawing-with-metapost/src/tangents-two-circles-exterior.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/tikzcd-example.mp b/info/drawing-with-metapost/src/tikzcd-example.mp deleted file mode 100644 index 3796618baf..0000000000 --- a/info/drawing-with-metapost/src/tikzcd-example.mp +++ /dev/null @@ -1,58 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -vardef sbox primary P = - superellipse(1/2[point 1 of bbox P, point 2 of bbox P], - 1/2[point 2 of bbox P, point 3 of bbox P], - 1/2[point 3 of bbox P, point 0 of bbox P], - 1/2[point 0 of bbox P, point 1 of bbox P], 0.75) - enddef; - -beginfig(1); - r = 0.9; - z0 = (0, 0); - z1 = r*(89, -55); - z2 = r*(42, 30); - z3 = z1 + z2; - - picture FE, FEV, E, EV, M, N, U, V; - FE = thelabel("$f^*E$", (x0, y0)); - M = thelabel("$M$", (x0, y1)); - E = thelabel("$E$", (x1, y0)); - N = thelabel("$N$", (x1, y1)); - FEV = thelabel("$f^*E_V$", (x2, y2)); - U = thelabel("$U$", (x2, y3)); - EV = thelabel("$E_V$", (x3, y2)); - V = thelabel("$V$", (x3, y3)); - - forsuffixes @=E, M, N, U, V, EV, FE, FEV: draw @; endfor - - ahangle := 20; - vardef connect(expr a, b) = - save line; path line; - interim bboxmargin := 3; - line = center a .. center b - cutbefore sbox a cutafter sbox b; - cutdraw line withpen pencircle scaled 4 withcolor background; - drawarrow line - enddef; - - connect(FEV, EV); - connect(FEV, U); - connect(EV, V); - connect(U, V); - - connect(FEV, FE); - connect(EV, E); - connect(U, M); - connect(V, N); - - connect(FE, E); - connect(FE, M); - connect(E, N); - connect(M, N); -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/tiling-ammann-bounded.mp b/info/drawing-with-metapost/src/tiling-ammann-bounded.mp new file mode 100644 index 0000000000..7ff7c4b16b --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann-bounded.mp @@ -0,0 +1,20 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input tiling-ammann-procedures + +beginfig(1); + + pickup pencircle scaled 1/8; + path shape; shape = r scaled 360; + + bounded_rhomb(4, point 0 of shape, point 2 of shape); + draw shape withpen pencircle scaled 1/2; + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-ammann-bounded.pdf b/info/drawing-with-metapost/src/tiling-ammann-bounded.pdf Binary files differnew file mode 100644 index 0000000000..ae0bb78c06 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann-bounded.pdf diff --git a/info/drawing-with-metapost/src/tiling-ammann-procedures.mp b/info/drawing-with-metapost/src/tiling-ammann-procedures.mp new file mode 100644 index 0000000000..9d76c33e35 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann-procedures.mp @@ -0,0 +1,81 @@ +% procedures for tiling-ammann-* drawings + +input colorbrewer-rgb + +def withalpha expr a = + withprescript "tr_alternative=2" + withprescript "tr_transparency=" & decimal a +enddef; + +path r, s; +r = origin -- (1/2, 1/2-sqrt(1/2)) -- right -- (1/2, sqrt(1/2)-1/2) -- cycle; +s = origin -- (1/2, -1/2) -- right -- (1/2, 1/2) -- cycle; +numeric p, q; +p = sqrt(2) - 1; q = 1 - sqrt(1/2); +vardef rhomb(expr level, a, b) = + save R; path R; R = r zscaled (b-a) shifted a; + if level = 0: + fill subpath (0, 2) of R -- cycle withalpha 0.9 withcolor Blues 9 3; + fill subpath (2, 4) of R -- cycle withalpha 0.9 withcolor Blues 9 4; + draw R withcolor 1/2; + else: + rhomb(level-1, a, p[a,b]); + rhomb(level-1, b, p[b,a]); + rhomb(level-1, point 1 of R, point 3 of R); + square(level-1, point 1 of R, point +p of R); + square(level-1, point 3 of R, point -p of R); + square(level-1, point 1 of R, point 2-p of R); + square(level-1, point 3 of R, point 2+p of R); + fi +enddef; +vardef square(expr level, a, b) = + save S; path S; S = s zscaled (b-a) shifted a; + if level = 0: + fill subpath (0, 2) of S -- cycle withalpha 0.9 withcolor Oranges 8 3; + fill subpath (2, 4) of S -- cycle withalpha 0.9 withcolor Oranges 8 2; + draw S withcolor 1/2; + else: + rhomb(level-1, a, q[point 1 of S, point 3 of S]); + rhomb(level-1, a, q[point 3 of S, point 1 of S]); + rhomb(level-1, point 1 of S, q[b,a]); + rhomb(level-1, point 3 of S, q[b,a]); + square(level-1, q[b,a], q[a,b]); + square(level-1, point 1 of S, point +p of S); + square(level-1, point 3 of S, point -p of S); + square(level-1, b, point +1+p of S); + square(level-1, b, point -1-p of S); + fi +enddef; + +path t[]; +t0 = origin -- right -- point 3 of s -- cycle; +t1 = origin -- right -- point 1 of s -- cycle; +vardef bounded_rhomb(expr level, a, b) = + save R; path R; R = r zscaled (b-a) shifted a; + if level = 0: + fill subpath (0, 2) of R -- cycle withcolor Blues 9 4; + fill subpath (2, 4) of R -- cycle withcolor Blues 9 5; + draw R withcolor 1/2; + else: + bounded_rhomb(level-1, a, p[a,b]); + bounded_rhomb(level-1, b, p[b,a]); + bounded_rhomb(level-1, point 1 of R, point 3 of R); + half_square(level-1, point 1 of R, point +p of R, 1); + half_square(level-1, point 3 of R, point -p of R, 0); + half_square(level-1, point 3 of R, point 2+p of R, 1); + half_square(level-1, point 1 of R, point 2-p of R, 0); + fi +enddef; +vardef half_square(expr level, a, b, side) = + save T; path T; T = t[side] zscaled (b-a) shifted a; + if level = 0: + fill T withalpha 0.9 withcolor Oranges[8][3+side]; + draw subpath (1, 3) of T withcolor 1/2; + else: + bounded_rhomb(level-1, point 0 of T, p[point 1/2 of T, point 2 of T]); + bounded_rhomb(level-1, point 2 of T, point sqrt(1/2) of T); + half_square(level-1, point 1 of T, point 2-p of T, side); + half_square(level-1, point 2 of T, point 3-p of T, side); + half_square(level-1, point 1-q of T, point q of T, 1-side); + fi +enddef; diff --git a/info/drawing-with-metapost/src/tiling-ammann-substitutions-bounded.mp b/info/drawing-with-metapost/src/tiling-ammann-substitutions-bounded.mp new file mode 100644 index 0000000000..81e933dea4 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann-substitutions-bounded.mp @@ -0,0 +1,65 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input tiling-ammann-procedures + +path rr, ss, tt; +rr = r scaled 48; +ss = t0 scaled 36; +tt = t1 scaled 36; + +dotlabeldiam := 2; + +picture P[]; +P1 = image( + bounded_rhomb(0, point 0 of rr, point 2 of rr); + dotlabel.ulft("$a$", point 0 of rr); + dotlabel.urt("$b$", point 2 of rr); +); +P2 = image( + draw rr dashed withdots scaled 1/4; + bounded_rhomb(1, point 0 of rr, point 2 of rr); +); +P3 = image( + drawarrow 16 left -- 20 right; + label(P1, 50 left); + label(P2, 50 right); +); + +P4 = image( + half_square(0, point 0 of ss, point 1 of ss, 0); + dotlabel.ulft("$a$", point 0 of ss); + dotlabel.urt ("$b$", point 1 of ss); +); +P5 = image( + half_square(0, point 0 of tt, point 1 of tt, 1); +); +P6 = image( + half_square(1, point 0 of ss, point 1 of ss, 0); + draw ss dashed withdots scaled 1/4; +); +P7 = image( + half_square(1, point 0 of tt, point 1 of tt, 1); + draw tt dashed withdots scaled 1/4; +); + +P8 = image( + label.top(P4, 50 left); + label.bot(P5, 50 left); + label.top(P6, 50 right + 8 up); + label.bot(P7, 50 right + 8 down); + path a; a = 18 left -- 24 right; + drawarrow a rotated 4 shifted 12 up; + drawarrow a rotated -4 shifted 12 down; +); + +beginfig(1); + label.lft(P3, 13 left); + label.rt (P8, 13 right); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-ammann-substitutions-bounded.pdf b/info/drawing-with-metapost/src/tiling-ammann-substitutions-bounded.pdf Binary files differnew file mode 100644 index 0000000000..e9ff77bf37 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann-substitutions-bounded.pdf diff --git a/info/drawing-with-metapost/src/tiling-ammann-substitutions-overlapping.mp b/info/drawing-with-metapost/src/tiling-ammann-substitutions-overlapping.mp new file mode 100644 index 0000000000..2a20f18e5d --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann-substitutions-overlapping.mp @@ -0,0 +1,59 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input tiling-ammann-procedures + +picture P[]; + +path ss, rr; + +ss = s scaled 36; +rr = r scaled 48; + +dotlabeldiam := 2; + +P1 = image( + square(0, point 0 of ss, point 2 of ss); + dotlabel.ulft("$a$", point 0 of ss); + dotlabel.urt ("$b$", point 2 of ss); +); +P2 = image( + draw ss dashed withdots scaled 1/4; + square(1, point 0 of ss, point 2 of ss); +); + +P3 = image( + drawarrow 20 left -- 20 right; + label(P1, 50 left); + label(P2, 50 right); +); + +P4 = image( + rhomb(0, point 0 of rr, point 2 of rr); + dotlabel.ulft("$a$", point 0 of rr); + dotlabel.urt("$b$", point 2 of rr); +); + +P5 = image( + draw rr dashed withdots scaled 1/4; + rhomb(1, point 0 of rr, point 2 of rr); + +); + +P6 = image( + drawarrow 16 left -- 20 right; + label(P4, 50 left); + label(P5, 50 right); + +); + +beginfig(1); + label.lft(P6, 13 left); + label.rt(P3, 13 right); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-ammann-substitutions-overlapping.pdf b/info/drawing-with-metapost/src/tiling-ammann-substitutions-overlapping.pdf Binary files differnew file mode 100644 index 0000000000..53410fadfe --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann-substitutions-overlapping.pdf diff --git a/info/drawing-with-metapost/src/tiling-ammann.mp b/info/drawing-with-metapost/src/tiling-ammann.mp new file mode 100644 index 0000000000..9da148243d --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann.mp @@ -0,0 +1,20 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input tiling-ammann-procedures + +beginfig(1); + + pickup pencircle scaled 1/8; + path shape; shape = r scaled 360; + + rhomb(4, point 0 of shape, point 2 of shape); + draw shape withpen pencircle scaled 1/2; + +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-ammann.pdf b/info/drawing-with-metapost/src/tiling-ammann.pdf Binary files differnew file mode 100644 index 0000000000..e89fe63618 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-ammann.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-3-4-3-4.mp b/info/drawing-with-metapost/src/tiling-arch-3-4-3-4.mp new file mode 100644 index 0000000000..60dd7f7be2 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-3-4-3-4.mp @@ -0,0 +1,51 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +beginfig(1); + input colorbrewer-rgb + path s[], t[]; + s1 = unitsquare scaled 21 rotated 15; s2 = s1 rotated 150; + t1 = subpath (4, 3) of s1 -- point 1 of s2 -- cycle; + t2 = t1 reflectedabout(point 1 of t1, point 2 of t1); + t3 = t1 rotated 150; t4 = t1 rotated 210; + picture color_unit, grid_unit; + color_unit = image( + fill s1 withcolor Oranges 8 1; + fill s2 withcolor Oranges 8 2; + fill t1 withcolor Blues 8 1; + fill t2 withcolor Blues 8 2; + fill t3 withcolor Blues 8 3; + fill t4 withcolor Blues 8 4; + ); + grid_unit = image( + draw s1; draw s2; + draw t2; draw t3; draw t4; + ); + pair u, v; + u = point 1 of s1 - point 1 of s2; + v = u rotated 90; + numeric n; n = 3; + forsuffixes $=color_unit, grid_unit: + for i=-n upto n: + for j=-n upto n: + draw $ shifted (i * u + j * v); + endfor + endfor + endfor + + label.bot("The arrangement of polygons in the units was carefully", + point 1/2 of bbox currentpicture shifted 21 down); + label.bot("chosen to give the tiling neat edges.", + point 1/2 of bbox currentpicture); + path b; b = bbox currentpicture shifted 34 down; + draw color_unit shifted point 1/4 of b; + draw grid_unit shifted point 3/4 of b; + path b; b = bbox currentpicture shifted 13 down; + label("\texttt{color\_unit}", point 1/4 of b); + label("\texttt{grid\_unit}", point 3/4 of b); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-arch-3-4-3-4.pdf b/info/drawing-with-metapost/src/tiling-arch-3-4-3-4.pdf Binary files differnew file mode 100644 index 0000000000..5df58f70c8 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-3-4-3-4.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-3-4-6-4.mp b/info/drawing-with-metapost/src/tiling-arch-3-4-6-4.mp new file mode 100644 index 0000000000..c1a6844c65 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-3-4-6-4.mp @@ -0,0 +1,50 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); +def withalpha expr a = % <-- this requires "luamplib" + withprescript "tr_alternative=2" + withprescript "tr_transparency=" & decimal a +enddef; +input colorbrewer-rgb +path d; d = for i=1 upto 12: 18 dir (15+30i) -- endfor cycle; + +color shade[]; +shade0 = Oranges 8 4; shade1 = Blues 8 4; +shade2 = Greens 8 4; shade3 = Reds 8 4; + +vardef unit(expr n) = image( + fill d withalpha 0.9 withcolor shade[n mod 4]; + draw d; +) enddef; +pair u, v; +u = point 0 of d - point 3 of d; +v = u rotated 60; +numeric n; n = 6; +for i=-n upto n: + for j=-n upto n: + draw unit(3i-7j) shifted ((i-floor(j/2)) * u + j * v); + endfor +endfor +clip currentpicture to unitsquare shifted -(1/2, 1/2) scaled 42n; + +picture p; p = image( + draw d; draw point 0 of d withpen pencircle scaled 2; + drawoptions(withcolor 3/4[red, white]); + draw d shifted u; draw point 0 of d shifted u withpen pencircle scaled 2; + drawoptions(withcolor 3/4[blue, white]); + draw d shifted v; draw point 0 of d shifted v withpen pencircle scaled 2; + drawoptions(); + drawarrow origin -- u withcolor red; + drawarrow origin -- v withcolor blue; +); +label.bot(p, point 1/2 of bbox currentpicture shifted 13 down); +label.bot(btex \vbox{\hsize 3.4in\noindent +The vectors are chosen so that the dodecagons overlap to make +the required triangles, squares, and hexagons.} etex, +point 1/2 of bbox currentpicture shifted 13 down); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-arch-3-4-6-4.pdf b/info/drawing-with-metapost/src/tiling-arch-3-4-6-4.pdf Binary files differnew file mode 100644 index 0000000000..089e31ea5a --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-3-4-6-4.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-4-6-12.mp b/info/drawing-with-metapost/src/tiling-arch-4-6-12.mp new file mode 100644 index 0000000000..fbf10256e8 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-4-6-12.mp @@ -0,0 +1,63 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb + +path unithex; +unithex = for i = 0 upto 5: dir 60i -- endfor cycle; +unithex := unithex shifted - point 4 of unithex; + +def fixed_at_point expr n of p = + zscaled (point n of p - point n+1 of p) shifted point n+1 of p +enddef; + +beginfig(1); + path dodo, h[], s[]; + dodo = for i = 1 upto 12: 21 dir (15 + 30i) -- endfor cycle; + h1 = unithex fixed_at_point 1 of dodo; + h2 = unithex fixed_at_point 3 of dodo; + s1 = unitsquare fixed_at_point 0 of dodo; + s2 = unitsquare fixed_at_point 2 of dodo; + s3 = unitsquare fixed_at_point 4 of dodo; + + picture colour_unit, line_unit; + colour_unit = image( + fill dodo withcolor Greens 9 2; + fill h1 withcolor Greens 9 3; + fill h2 withcolor Greens 9 3; + fill s1 withcolor Greens 9 4; + fill s2 withcolor Greens 9 4; + fill s3 withcolor Greens 9 4; + ); + line_unit = image( + forsuffixes $=dodo, s1, s2, s3, h1, h2: + draw $ withpen pencircle scaled 1/4; + pair m; m = center $; % all shapes have even number of sides + for i=1 upto length $: + cutdraw m -- point i - 1/2 of $ + if odd i: cutbefore fullcircle scaled (length $ / 4) shifted m fi + withpen pencircle scaled 1/4 + withcolor Reds 4 3; + endfor + endfor + ); + + pair u, v; + u = point 3 of s2 - point 8 of dodo; + v = u rotated 60; + + numeric n; n = 4; + forsuffixes @ = colour_unit, line_unit: + for i=-n upto n: + for j=-n upto n: + draw @ shifted (i*u + j*v - floor(i/2) * v); + endfor + endfor + endfor + + clip currentpicture to bbox dodo scaled 2n yscaled sqrt(3/4); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tiling-arch-4-6-12.pdf b/info/drawing-with-metapost/src/tiling-arch-4-6-12.pdf Binary files differnew file mode 100644 index 0000000000..dda414c738 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-4-6-12.pdf diff --git a/info/drawing-with-metapost/src/arch-4-8-8-parts.mp b/info/drawing-with-metapost/src/tiling-arch-4-8-8-parts.mp index 53aec91d14..53aec91d14 100644 --- a/info/drawing-with-metapost/src/arch-4-8-8-parts.mp +++ b/info/drawing-with-metapost/src/tiling-arch-4-8-8-parts.mp diff --git a/info/drawing-with-metapost/src/arch-4-8-8-parts.pdf b/info/drawing-with-metapost/src/tiling-arch-4-8-8-parts.pdf Binary files differindex 6466e01641..6466e01641 100644 --- a/info/drawing-with-metapost/src/arch-4-8-8-parts.pdf +++ b/info/drawing-with-metapost/src/tiling-arch-4-8-8-parts.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-4-8-8.mp b/info/drawing-with-metapost/src/tiling-arch-4-8-8.mp new file mode 100644 index 0000000000..7c5b159387 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-4-8-8.mp @@ -0,0 +1,33 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +input colorbrewer-rgb +path o, r[]; +o = (for i=0 upto 7: 21 dir 45i -- endfor cycle) rotated -90/4; +pair t; t = whatever[point 0 of o, point 1 of o] += whatever[point 2 of o, point 3 of o]; +r1 = subpath (1,2) of o -- t -- cycle; +r2 = r1 rotated 90; +r3 = r2 rotated 90; +r4 = r3 rotated 90; +picture filler; filler = image( + filldraw r1 withcolor Reds 8 3; + filldraw r2 withcolor Blues 8 3; + filldraw r3 withcolor Reds 8 3; + filldraw r4 withcolor Blues 8 3; + filldraw o withcolor Purples 8 2; +); +pair u, v; +u = point 0 of o - point 5 of o; v = u rotated 90; +beginfig(1); + numeric n; n = 5; + for i=-n upto n: for j=-n upto n: + draw filler rotated ((i+j) mod 2 * 90) shifted (i*u + j*v); + endfor endfor + for i=-n upto n: for j=-n upto n: + draw o shifted (i*u + j*v); + endfor endfor +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tiling-arch-4-8-8.pdf b/info/drawing-with-metapost/src/tiling-arch-4-8-8.pdf Binary files differnew file mode 100644 index 0000000000..8c89bb5eca --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-4-8-8.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-hexagon.mp b/info/drawing-with-metapost/src/tiling-arch-hexagon.mp new file mode 100644 index 0000000000..683d2c1a4f --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-hexagon.mp @@ -0,0 +1,47 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb +beginfig(1); + + path h[]; pair m[]; + for i=0 upto 2: + h[i] = (for j=0 upto 5: 30 dir 60j -- endfor cycle); + h[i] := h[i] shifted - point 0 of h[i] rotated (30+120i); + m[i] = 1/2[point 0 of h[i], point 3 of h[i]]; + endfor + + picture unit; + unit = image( + numeric i; i = -1; + forsuffixes $ = Purples, Oranges, Blues: + pair m; m = m[incr i]; + for j=1 upto 3: + fill subpath (-2i+2j, 2-2i+2j) of h[i] -- m -- cycle withcolor $[8][1+j]; + endfor + for j=1 upto 3: + draw m -- point 2j of h[i] withcolor $[8][1]; + endfor + endfor + + ); + + pair u, v; + u = point 3 of h1 - point 1 of h0; + v = u rotated 60; + + numeric n; n = 4; + for i=-n upto n: + for j=-n upto n: + draw unit shifted (i*u + j*v); + endfor + endfor + + path se; se = superellipse(right, up, left, down, 0.86); + clip currentpicture to se scaled 168; + +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tiling-arch-hexagon.pdf b/info/drawing-with-metapost/src/tiling-arch-hexagon.pdf Binary files differnew file mode 100644 index 0000000000..87d9c63d05 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-hexagon.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-hst.mp b/info/drawing-with-metapost/src/tiling-arch-hst.mp new file mode 100644 index 0000000000..9a1a964dec --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-hst.mp @@ -0,0 +1,54 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb + +beginfig(1); + path t[], s[], h; + h = for i=0 upto 5: 42 dir 60i -- endfor cycle; + for i = 1 upto 3: + s[i] = unitsquare zscaled (point i-1 of h - point i of h) shifted point i of h; + endfor + t1 = point 1 of h -- point 3 of s1 -- point 2 of s2 -- cycle; + t2 = point 2 of h -- point 3 of s2 -- point 2 of s3 -- cycle; + + picture unit; + unit = image( + for i=1 upto 2: + fill t[i] withcolor Blues 8 4; + endfor + for i=1 upto 3: + fill s[i] withcolor Greens 8 1; + endfor + fill h withcolor Oranges 9 4; + forsuffixes $=t1, t2: + pair m; m = 2/3[point 0 of $, point 3/2 of $]; + for i=1 upto 3: + draw m -- point i+1/2 of $ withcolor Blues 8 8; + endfor + endfor + forsuffixes $=s1, s2, s3: + draw point 1/2 of $ -- point 5/2 of $ withcolor Oranges 8 8; + draw point 3/2 of $ -- point 7/2 of $ withcolor Blues 8 8; + endfor + for i=1 upto 3: + draw point i-1/2 of h -- point i+5/2 of h withcolor Oranges 8 8; + endfor + ); + + pair u, v; + u = point 3 of s2 - point 4 of h; + v = u rotated 60; + + numeric n; n=4; + for i=-n upto n: + for j=-n upto n: + draw unit shifted (i*u + j*v - floor (j/2) * u); + endfor + endfor + clip currentpicture to fullcircle scaled (7/4n * abs(u)); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tiling-arch-hst.pdf b/info/drawing-with-metapost/src/tiling-arch-hst.pdf Binary files differnew file mode 100644 index 0000000000..fa224b2733 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-hst.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-snub-hex-parts.mp b/info/drawing-with-metapost/src/tiling-arch-snub-hex-parts.mp new file mode 100644 index 0000000000..a1e8c7a6d9 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-snub-hex-parts.mp @@ -0,0 +1,48 @@ +input colorbrewer-rgb +% a polygon of n sides on a given path +vardef poly expr n of p = + clearxy; z0 = point 0 of p; z1 = point 1 of p; + for i=2 upto n-1: + z[i] = z[i-2] rotatedabout(z[i-1], 360/n-180); + endfor + for i=0 upto n-1: z[i] -- endfor cycle +enddef; +vardef centroid(expr p) = save n; n = length p; origin for i=1 upto n: + point i of p / n endfor enddef; +path t[], h; +h = poly 6 of (origin -- 21 dir 60); +for i=1 upto 6: + t[i] = poly 3 of subpath (i, i-1) of h; +endfor +picture P[], unit[]; +for k=0, 2: + t7 := poly 3 of subpath (k, k-1) of t6; + t8 := poly 3 of subpath (k, k-1) of t3; + pair u, v; + u = point 2+k/2 of h - point 2 of t6; + v = u rotated -60; + unit[k] = image( + for i=1 upto 6: + fill t[i] withcolor Blues 8 if odd i: 2 else: 3 fi; + endfor + for i=7 upto 8: + fill t[i] withcolor Oranges 8 if odd i: 3 else: 2 fi; + endfor + fill h withcolor Oranges 8 1; + forsuffixes $=h, t1, t2, t3, t4, t5, t6, t7, t8: + draw $ withpen pencircle scaled 1/4 withcolor 1/2; + for i=1 upto length $: + draw centroid($) -- point i - 1/2 of $ withcolor Reds 7 6; + endfor + endfor + ); + + numeric n; n=4; + P[k] = image( + for i=-n upto n: + for j=-n upto n: + draw unit[k] shifted (i*u + j*v - floor (j/2) * u); + endfor + endfor + clip currentpicture to superellipse(168 right, 168 up, 168 left, 168 down, 0.78); + ); +endfor diff --git a/info/drawing-with-metapost/src/projections.mp b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon-unit.mp index 42d683c89d..e724070668 100644 --- a/info/drawing-with-metapost/src/projections.mp +++ b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon-unit.mp @@ -3,8 +3,10 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} +input tiling-arch-snub-hex-parts beginfig(1); -input projections-code + draw unit0 shifted 50 left; + draw unit2 shifted 50 right; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/tiling-arch-snub-hexagon-unit.pdf b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon-unit.pdf Binary files differnew file mode 100644 index 0000000000..fc4171e407 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon-unit.pdf diff --git a/info/drawing-with-metapost/src/tiling-arch-snub-hexagon.mp b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon.mp new file mode 100644 index 0000000000..df93be60f4 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon.mp @@ -0,0 +1,14 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input tiling-arch-snub-hex-parts +beginfig(1); +draw P0 shifted 180 up; +draw P2 shifted 180 down; +numeric wd; wd = xpart (urcorner P0 - llcorner P0); +currentpicture := currentpicture scaled (250/wd); +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tiling-arch-snub-hexagon.pdf b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon.pdf Binary files differnew file mode 100644 index 0000000000..75e56c3a74 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-snub-hexagon.pdf diff --git a/info/drawing-with-metapost/src/arch-snub-square.mp b/info/drawing-with-metapost/src/tiling-arch-snub-square.mp index c607b4e5c4..bc8f3ec85e 100644 --- a/info/drawing-with-metapost/src/arch-snub-square.mp +++ b/info/drawing-with-metapost/src/tiling-arch-snub-square.mp @@ -14,7 +14,7 @@ vardef poly expr n of p = endfor for i=0 upto n-1: z[i] -- endfor cycle enddef; -vardef median(expr P) = +vardef centroid(expr P) = (origin for i=1 upto length P: + point i of P endfor) / length P enddef; beginfig(1); @@ -35,7 +35,7 @@ beginfig(1); fill t2 withcolor Greens 8 3; fill s2 withcolor Reds 8 5; forsuffixes $=s1, t1, s2, t2, t3, t4: - pair m; m = median($); + pair m; m = centroid($); for i=1 upto length $: draw point i - 1/2 of $ -- m withpen pencircle scaled 3/2 withcolor Spectral 3 2; @@ -53,20 +53,6 @@ beginfig(1); endfor endfor - % picture p; p = currentpicture; - % (wd, ht) = (urcorner p - llcorner p); - % currentpicture := nullpicture; - % p := p scaled (145mm / wd); - % undraw unitsquare xscaled 148mm yscaled 210mm shifted llcorner p shifted -(1.5mm, 1.5mm) - % withpen pencircle scaled 1/8; - % z0 = 1/2[llcorner currentpicture, ulcorner currentpicture]; - % draw z0 -- z0 shifted 3 right withpen pencircle scaled 1/8; - % z1 = 1/2[lrcorner currentpicture, urcorner currentpicture]; - % draw z1 -- z1 shifted 3 left withpen pencircle scaled 1/8; - % draw p; - % picture r; r = currentpicture rotated 90; - % currentpicture := nullpicture; - % draw r; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/tiling-arch-snub-square.pdf b/info/drawing-with-metapost/src/tiling-arch-snub-square.pdf Binary files differnew file mode 100644 index 0000000000..ed171de376 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-arch-snub-square.pdf diff --git a/info/drawing-with-metapost/src/archimedes.mp b/info/drawing-with-metapost/src/tiling-archimedes.mp index 81608868a8..0eba803624 100644 --- a/info/drawing-with-metapost/src/archimedes.mp +++ b/info/drawing-with-metapost/src/tiling-archimedes.mp @@ -9,48 +9,48 @@ picture P[]; % (4,6,12) numeric dx; dx = u*(1+ cosd(15)/sind(15)); picture unit; unit = image( - path s; s = unitsquare shifted -(1/2,1/2) scaled u shifted (dx/2,0); - for t=0 upto 2: - draw s rotated 120t; - for tt=1 upto 3: - draw subpath(3,4) of s rotated (120t+30tt); - endfor - endfor + path s; s = unitsquare shifted -(1/2,1/2) scaled u shifted (dx/2,0); + for t=0 upto 2: + draw s rotated 120t; + for tt=1 upto 3: + draw subpath(3,4) of s rotated (120t+30tt); + endfor + endfor ); P1 = image( - draw unit withpen pencircle scaled 4 withcolor .8[red,white]; - for x=-5dx step dx until 5dx: - for y=-5dx step dx until 5dx: - draw unit shifted (x,0) shifted ((y,0) rotated 60); - endfor + draw unit withpen pencircle scaled 4 withcolor .8[red,white]; + for x=-5dx step dx until 5dx: + for y=-5dx step dx until 5dx: + draw unit shifted (x,0) shifted ((y,0) rotated 60); endfor - clip currentpicture to box; draw box dashed withdots scaled 1/4; - label.bot("$(4, 6, 12)$", point 1/2 of bbox currentpicture); + endfor + clip currentpicture to box; draw box dashed withdots scaled 1/4; + label.bot("$(4, 6, 12)$", point 1/2 of bbox currentpicture); ); numeric dx; dx = u*(cosd(180/8)/sind(180/8)); path octagon; octagon = for t = 0 upto 7: 1/2(dx,u) rotated 45t -- endfor cycle; P2 = image( - draw octagon withpen pencircle scaled 4 withcolor .8[red,white]; - for x=-5dx step dx until 5dx: - for y=-5dx step dx until 5dx: - draw octagon shifted (x,y); - endfor + draw octagon withpen pencircle scaled 4 withcolor .8[red,white]; + for x=-5dx step dx until 5dx: + for y=-5dx step dx until 5dx: + draw octagon shifted (x,y); endfor - clip currentpicture to box; draw box dashed withdots scaled 1/4; - label.bot("$(4, 8^2)$", point 1/2 of bbox currentpicture); + endfor + clip currentpicture to box; draw box dashed withdots scaled 1/4; + label.bot("$(4, 8^2)$", point 1/2 of bbox currentpicture); ); numeric dx; dx = u*(cosd(180/12)/sind(180/12)); path unit; unit = for t=0 upto 11: 1/2(dx,u) rotated 30t -- endfor cycle; P3 = image( - draw unit withpen pencircle scaled 4 withcolor .8[red,white]; - for x=-5dx step dx until 5dx: - for y=-5dx step dx until 5dx: - draw unit shifted (x,0) shifted ((y,0) rotated 60); - endfor + draw unit withpen pencircle scaled 4 withcolor .8[red,white]; + for x=-5dx step dx until 5dx: + for y=-5dx step dx until 5dx: + draw unit shifted (x,0) shifted ((y,0) rotated 60); endfor - clip currentpicture to box; draw box dashed withdots scaled 1/4; - label.bot("$(3, 12^2)$", point 1/2 of bbox currentpicture); + endfor + clip currentpicture to box; draw box dashed withdots scaled 1/4; + label.bot("$(3, 12^2)$", point 1/2 of bbox currentpicture); ); % path box; box = unitsquare shifted -(1/2,1/2) scaled 12u; @@ -83,20 +83,20 @@ P3 = image( % (3,4,6,4) numeric dx; dx = u*(1+cosd(30)/sind(30)); picture unit; unit = image( - path s; s = unitsquare shifted -(1/2,1/2) scaled u shifted (dx/2,0); - for t=0 upto 2: - draw s rotated 120t; - endfor + path s; s = unitsquare shifted -(1/2,1/2) scaled u shifted (dx/2,0); + for t=0 upto 2: + draw s rotated 120t; + endfor ); P4 = image( - draw unit withpen pencircle scaled 4 withcolor .8[red,white]; - for x=-5dx step dx until 5dx: - for y=-5dx step dx until 5dx: - draw unit shifted (x,0) shifted ((y,0) rotated 60); - endfor + draw unit withpen pencircle scaled 4 withcolor .8[red,white]; + for x=-5dx step dx until 5dx: + for y=-5dx step dx until 5dx: + draw unit shifted (x,0) shifted ((y,0) rotated 60); endfor - clip currentpicture to box; draw box dashed withdots scaled 1/4; - label.bot("$(3, 4, 6, 4)$", point 1/2 of bbox currentpicture); + endfor + clip currentpicture to box; draw box dashed withdots scaled 1/4; + label.bot("$(3, 4, 6, 4)$", point 1/2 of bbox currentpicture); ); % beginfig(6); @@ -179,10 +179,10 @@ P4 = image( % endfig; beginfig(1); -draw P1; -draw P2 shifted (12.5u, 0); -draw P3 shifted (0, -14.4u); -draw P4 shifted (12.5u, -14.4u); + draw P1; + draw P2 shifted (12.5u, 0); + draw P3 shifted (0, -14.4u); + draw P4 shifted (12.5u, -14.4u); endfig; \end{mplibcode} diff --git a/info/drawing-with-metapost/src/tiling-archimedes.pdf b/info/drawing-with-metapost/src/tiling-archimedes.pdf Binary files differnew file mode 100644 index 0000000000..668ae84423 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-archimedes.pdf diff --git a/info/drawing-with-metapost/src/conway.mp b/info/drawing-with-metapost/src/tiling-conway.mp index 41d94bae34..1ecbcbe229 100644 --- a/info/drawing-with-metapost/src/conway.mp +++ b/info/drawing-with-metapost/src/tiling-conway.mp @@ -3,20 +3,21 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} +input colorbrewer-rgb +input tiling-pinwheel-macro beginfig(1); pair a, b, c, d, e, f, g; -a = origin; b = 180 right; c = 90 up; -d = 2/5[b, c]; e = 4/5[b,c]; f = 1/2[e, a]; g = 1/2[a, b]; +a = origin; b = 180 right; c = 1/2 b rotated 90; +d = 1/2[a,b]; e = 1/5[c,b]; f = 1/2[a,e]; g = 1/2[b,e]; +pinwheel(1,a,b,c,""); -fill a--b--c--cycle withcolor 15/16[blue, white]; -draw a--b--c--a--e--g--f; draw g--d; dotlabel.llft("$a$", a); dotlabel.lrt ("$b$", b); dotlabel.ulft("$c$", c); -dotlabel.urt ("$d$", d); +dotlabel.bot ("$d$", d); dotlabel.urt ("$e$", e); dotlabel.ulft("$f$", f); -dotlabel.bot ("$g$", g); +dotlabel.urt ("$g$", g); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/conway.pdf b/info/drawing-with-metapost/src/tiling-conway.pdf Binary files differindex 4ca336f367..173944e606 100644 --- a/info/drawing-with-metapost/src/conway.pdf +++ b/info/drawing-with-metapost/src/tiling-conway.pdf diff --git a/info/drawing-with-metapost/src/tiling-hex-trig.mp b/info/drawing-with-metapost/src/tiling-hex-trig.mp index ce9d1565e6..aa4089fe99 100644 --- a/info/drawing-with-metapost/src/tiling-hex-trig.mp +++ b/info/drawing-with-metapost/src/tiling-hex-trig.mp @@ -24,49 +24,49 @@ vardef make_image(expr P, n, u, v, s, arrows) = currentpicture enddef; beginfig(1); - path hexagon, triangle; pair u, v; numeric n; - hexagon = for i=0 upto 5: (0, 16) rotated 60i -- endfor cycle; - triangle = for i=0 upto 2: (0, 16) rotated 120i -- endfor cycle; + path hexagon, triangle; pair u, v; numeric n; + triangle = for i=0 upto 2: (0, 16) rotated 120i -- endfor cycle; + hexagon = for i=0 upto 5: (0, 16) rotated 60i -- endfor cycle; - u = point 0 of triangle - point 1 of triangle; - v = u rotated -60; + u = point 0 of triangle - point 1 of triangle; + v = u rotated -60; - path s; s = superellipse(89 right, 89 up, 89 left, 89 down, 0.78); - n = 8; - picture P[]; - P3 = make_image(triangle, n, u, v, s, true); - P6 = make_image(hexagon, n, u, v, s, true); + path s; s = superellipse(89 right, 89 up, 89 left, 89 down, 0.78); + n = 8; + picture P[]; + P3 = make_image(triangle, n, u, v, s, true); + P6 = make_image(hexagon, n, u, v, s, true); - picture T; T = image( - path t'; t' = triangle reflectedabout(point 0 of triangle, point 1 of triangle); - fill triangle withcolor Reds 8 2; - fill t' withcolor Blues 8 2; - draw triangle; - draw t'; - ); - P4 = make_image(T, n, u, v, s, true); - picture H; H = image( - path ha, hb; - ha = hexagon reflectedabout(point 0 of hexagon, point 1 of hexagon); - hb = hexagon reflectedabout(point 0 of hexagon, point 5 of hexagon); - fill hexagon withcolor Oranges 8 2; - fill ha withcolor Blues 8 2; - fill hb withcolor Greens 8 2; - draw hexagon; draw ha; draw hb; - ); - P7 = make_image(H, n, u zscaled 1.732 dir 30, v zscaled 1.732 dir 30, s, true); + picture T; T = image( + path t'; t' = triangle reflectedabout(point 0 of triangle, point 1 of triangle); + fill triangle withcolor Reds 8 2; + fill t' withcolor Blues 8 2; + draw triangle; + draw t'; + ); + P4 = make_image(T, n, u, v, s, true); + picture H; H = image( + path ha, hb; + ha = hexagon reflectedabout(point 0 of hexagon, point 1 of hexagon); + hb = hexagon reflectedabout(point 0 of hexagon, point 5 of hexagon); + fill hexagon withcolor Oranges 8 2; + fill ha withcolor Blues 8 2; + fill hb withcolor Greens 8 2; + draw hexagon; draw ha; draw hb; + ); + P7 = make_image(H, n, u zscaled 1.732 dir 30, v zscaled 1.732 dir 30, s, true); - picture dualt, dualh; - dualt = image( - draw triangle withcolor 1/2; - for i=0 upto 2: draw origin -- point i+1/2 of triangle withcolor Reds 7 6; endfor - draw currentpicture reflectedabout(point 0 of triangle, point 1 of triangle); + picture dualt, dualh; + dualt = image( + draw triangle withcolor 1/2; + for i=0 upto 2: draw origin -- point i+1/2 of triangle withcolor Reds 7 6; endfor + draw currentpicture reflectedabout(point 0 of triangle, point 1 of triangle); ); dualh = image( - draw hexagon withcolor 1/2; - for i=0 upto 5: - draw origin -- point i+1/2 of hexagon withcolor Reds 7 6; - endfor + draw hexagon withcolor 1/2; + for i=0 upto 5: + draw origin -- point i+1/2 of hexagon withcolor Reds 7 6; + endfor ); P5 = make_image(dualt, n, u, v, s, false); P8 = make_image(dualh, n, u, v, s, false); @@ -77,7 +77,7 @@ beginfig(1); draw P6 shifted (+100, +100); draw P7 shifted (+100, -100); draw P8 shifted (+100, -300); -endfig; -\end{mplibcode} -\end{document} + endfig; + \end{mplibcode} + \end{document} diff --git a/info/drawing-with-metapost/src/tiling-hex-trig.pdf b/info/drawing-with-metapost/src/tiling-hex-trig.pdf Binary files differindex a4a9313e42..17cccd5893 100644 --- a/info/drawing-with-metapost/src/tiling-hex-trig.pdf +++ b/info/drawing-with-metapost/src/tiling-hex-trig.pdf diff --git a/info/drawing-with-metapost/src/tiling-kepler-k.mp b/info/drawing-with-metapost/src/tiling-kepler-k.mp index 81ea654def..499c283f47 100644 --- a/info/drawing-with-metapost/src/tiling-kepler-k.mp +++ b/info/drawing-with-metapost/src/tiling-kepler-k.mp @@ -11,7 +11,7 @@ beginfig(1); ahangle := 10; unit = image( for i=-1 upto 1: - fill s rotated 60i withcolor Spectral[9][3+2i]; + fill s rotated 60i withcolor Oranges 8 3; draw s rotated 60i; endfor ); @@ -24,7 +24,11 @@ beginfig(1); draw unit shifted (i * u + j * v); endfor endfor - clip currentpicture to fullcircle scaled 400; + + picture P; P = currentpicture; currentpicture := nullpicture; + fill fullcircle scaled 400 withcolor Blues 5 4; + clip P to fullcircle scaled 400; + draw P; endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/tiling-kepler-k.pdf b/info/drawing-with-metapost/src/tiling-kepler-k.pdf Binary files differindex c2b4272c60..6c457f3fbb 100644 --- a/info/drawing-with-metapost/src/tiling-kepler-k.pdf +++ b/info/drawing-with-metapost/src/tiling-kepler-k.pdf diff --git a/info/drawing-with-metapost/src/tiling-kepler-y.mp b/info/drawing-with-metapost/src/tiling-kepler-y.mp new file mode 100644 index 0000000000..1ce6159f60 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-kepler-y.mp @@ -0,0 +1,50 @@ +\documentclass[border=0mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +path o; +o = for i=0 upto 7: 8 right rotated (45/2 + 45i) -- endfor cycle; +numeric a, b; +a = abs(point 1/2 of o - point 9/2 of o); +b = abs(point 0 of o - point 1 of o); +o := o shifted 1/2(2a + b, a); +path s, t, x; +s = unitsquare zscaled (point 4 of o - point 5 of o) shifted point 5 of o; +t = unitsquare zscaled (point 6 of o - point 7 of o) shifted point 7 of o; +x = unitsquare zscaled (point 7 of o - point 8 of o) shifted point 8 of o; + +input colorbrewer-rgb + +picture unit; +unit = image( + for i=0 upto 7: + fill o rotated 45i withcolor Oranges 8 3; + draw o rotated 45i; + fill s rotated 45i withcolor Blues 8 2; + draw s rotated 45i; + endfor + for i = 0, 1, 2, 3, 5, 7: + fill t rotated 45i withcolor Blues 8 4; + draw t rotated 45i; + endfor + for i = 1, 3, 5, 7: + fill x rotated 45i withcolor Blues 8 4; + draw x rotated 45i; + endfor +); + +beginfig(1); + pair u, v; u = 2 center t; v = u rotated 90; + n = 4; + for i=-n upto n: + for j = -n upto n: + draw unit shifted (i * u + j * v); + endfor + endfor + + clip currentpicture to unitsquare shifted -(1/2, 1/2) yscaled sqrt(2) scaled 105mm; + +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tiling-kepler-y.pdf b/info/drawing-with-metapost/src/tiling-kepler-y.pdf Binary files differnew file mode 100644 index 0000000000..9c238159e3 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-kepler-y.pdf diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart-construction.mp b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart-construction.mp new file mode 100644 index 0000000000..a1caf2336f --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart-construction.mp @@ -0,0 +1,96 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input colorbrewer-rgb + +numeric phi; phi = 0.61803398875; + +path wide[], tall[]; +wide0 = origin -- right -- phi * dir 36 -- cycle; +wide1 = origin -- right -- phi * dir -36 -- cycle; +tall0 = origin -- right -- (1+phi) * dir 72 -- cycle; +tall1 = origin -- right -- (1+phi) * dir -72 -- cycle; + +vardef half_dart(expr level, a, b, side) = + save T; path T; T = wide[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Purples[9][3+side]; + draw subpath (0, 2) of T; + else: + half_dart(level - 1, point 1 of T, point 2 of T, side); + half_kite(level - 1, point 2 of T, point phi of T, 1-side); + fi +enddef; + +vardef half_kite(expr level, a, b, side) = + save T; path T; T = tall[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Blues[9][2+side]; + draw subpath (0, 2) of T; + else: + half_dart(level - 1, point 2 of T, point 2+phi of T, side); + half_kite(level - 1, point 2+phi of T, point 0 of T, side); + half_kite(level - 1, point 2+phi of T, point 1+phi of T, 1-side); + fi +enddef; + +beginfig(1); + + picture kite, dart, P[]; + + kite = image( + half_kite(0, origin, 34 dir 198, 0); + half_kite(0, origin, 34 dir -18, 1); + label.bot("Kite", 55 down); + ); + + dart = image( + half_dart(0, origin, 55 dir 234, 0); + half_dart(0, origin, 55 dir 306, 1); + currentpicture := currentpicture shifted 4 down; + undraw origin; + label.bot("Dart", 55 down); + ); + + + pickup pencircle scaled 1/4; + + pair a, b; a = origin; b = 21 dir 198; + P1 = image(half_kite(0, a, b, 0); dotlabel.ulft("$a$", a); dotlabel.ulft("$b$", b)); + P2 = image(half_kite(1, a, b, 0)); + + b := b reflectedabout(up, down); + P3 = image(half_kite(0, a, b, 1); dotlabel.urt("$a$", a); dotlabel.urt("$b$", b)); + P4 = image(half_kite(1, a, b, 1)); + P5 = image(begingroup; save arr; path arr; arr = (up--down) scaled 12; + drawarrow arr; + interim labeloffset := 8; + label.ulft(P1, point 0 of arr); label.urt(P3, point 0 of arr); + label.llft(P2, point 1 of arr); label.lrt(P4, point 1 of arr); + endgroup); + + b := 34 dir 234; + P6 = image(half_dart(0, a, b, 0); dotlabel.ulft("$a$", a); dotlabel.ulft("$b$", b)); + P7 = image(half_dart(1, a, b, 0)); + + b := b reflectedabout(up, down); + P8 = image(half_dart(0, a, b, 1); dotlabel.urt("$a$", a); dotlabel.urt("$b$", b)); + P9 = image(half_dart(1, a, b, 1)); + P10 = image(begingroup; save arr; path arr; arr = (up--down) scaled 12; + drawarrow arr; + interim labeloffset := 8; + label.ulft(P6, point 0 of arr); label.urt(P8, point 0 of arr); + label.llft(P7, point 1 of arr); label.lrt(P9, point 1 of arr); + endgroup); + + label(kite, 42 left); + label(dart, 42 right); + label(P5, 134 left); + label(P10, 134 right); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart-construction.pdf b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart-construction.pdf Binary files differnew file mode 100644 index 0000000000..576713a5f7 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart-construction.pdf diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart.mp b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart.mp new file mode 100644 index 0000000000..5f8853f1d6 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart.mp @@ -0,0 +1,49 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input colorbrewer-rgb + +numeric phi; phi = 0.61803398875; + +path wide[], tall[]; +wide0 = origin -- right -- phi * dir 36 -- cycle; +wide1 = origin -- right -- phi * dir -36 -- cycle; +tall0 = origin -- right -- (1+phi) * dir 72 -- cycle; +tall1 = origin -- right -- (1+phi) * dir -72 -- cycle; + +vardef half_dart(expr level, a, b, side) = + save T; path T; T = wide[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Purples[9][3+side]; + draw subpath (0, 2) of T; + else: + half_dart(level - 1, point 1 of T, point 2 of T, side); + half_kite(level - 1, point 2 of T, point phi of T, 1-side); + fi +enddef; + +vardef half_kite(expr level, a, b, side) = + save T; path T; T = tall[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Blues[9][2+side]; + draw subpath (0, 2) of T; + else: + half_dart(level - 1, point 2 of T, point 2+phi of T, side); + half_kite(level - 1, point 2+phi of T, point 0 of T, side); + half_kite(level - 1, point 2+phi of T, point 1+phi of T, 1-side); + fi +enddef; + +beginfig(1); + numeric wd; wd = 5in; + drawoptions(withpen pencircle scaled 1/8); + half_dart(9, 1.375 wd * left, 1.375 wd * right, 0); + drawoptions(); + clip currentpicture to unitsquare shifted 1/2 left scaled wd yscaled phi; +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart.pdf b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart.pdf Binary files differnew file mode 100644 index 0000000000..00366a9681 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p2-kite-dart.pdf diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs-construction.mp b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs-construction.mp new file mode 100644 index 0000000000..ac1bf4d0d2 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs-construction.mp @@ -0,0 +1,98 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input colorbrewer-rgb + +numeric phi; phi = 0.61803398875; + +path wide[], tall[]; +wide0 = origin -- right -- phi * dir 36 -- cycle; +wide1 = origin -- right -- phi * dir -36 -- cycle; +tall0 = origin -- right -- (1+phi) * dir 72 -- cycle; +tall1 = origin -- right -- (1+phi) * dir -72 -- cycle; + +vardef half_thick(expr level, a, b, side) = + save T; path T; T = wide[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Purples[9][2+2side]; + draw subpath (1, 3) of T; + else: + half_thick(level - 1, point phi of T, point 0 of T, 1-side); + half_thick(level - 1, point 1 of T, point 2 of T, side); + half_thin(level - 1, point 2 of T, point -phi of T, side); + fi +enddef; + +vardef half_thin(expr level, a, b, side) = + save T; path T; T = tall[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Blues[9][2+2side]; + draw subpath (1, 3) of T; + else: + half_thick(level - 1, point 0 of T, point 2 of T, 1-side); + half_thin(level - 1, point 1 of T, point 2-phi of T, side); + fi +enddef; + +picture thin, thick, P[]; + +pair a, b; a = -b = 13 down; +thin = image( + half_thin(0, a, b, 0); + half_thin(0, a, b, 1); + label.bot("Thin", 42 down); undraw 28 up; +); + +for s=0, 1: + P[1+s] = image( + half_thin(0, a, b, s); + dotlabel.bot("$a$", a); + dotlabel.top("$b$", b); + label("$" & decimal s & "$", (17 * (2s-1), 0)); + ); + P[3+s] = image(half_thin(1, a, b, s)); +endfor + +P5 = image( + begingroup; interim labeloffset := 8; save arr; + path arr; arr = 21 up -- 21 down; drawarrow arr; + label.ulft(P1, point 0 of arr); label.urt(P2, point 0 of arr); + label.llft(P3, point 1 of arr); label.lrt(P4, point 1 of arr); + endgroup; +); + +pair a, b; a = -b = 28 down; +thick = image( + half_thick(0, a, b, 0); + half_thick(0, a, b, 1); + label.bot("Thick", 42 down); +); + +for s=0, 1: + P[6+s] = image( + half_thick(0, a, b, s); + dotlabel.bot("$a$", a); + dotlabel.top("$b$", b); + label("$" & decimal s & "$", (11 * (2s-1), 0)); + ); + P[8+s] = image(half_thick(1, a, b, s)); +endfor + +P10 = image( + begingroup; interim labeloffset := 8; save arr; + path arr; arr = 8 up -- 8 down; drawarrow arr; + label.ulft(P6, point 0 of arr); label.urt(P7, point 0 of arr); + label.llft(P8, point 1 of arr); label.lrt(P9, point 1 of arr); + endgroup; +); + +beginfig(1); + label(thin, 53 left); label(P5, 132 left); + label(thick, 53 right); label(P10, 132 right); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs-construction.pdf b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs-construction.pdf Binary files differnew file mode 100644 index 0000000000..d297aca4ac --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs-construction.pdf diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs.mp b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs.mp new file mode 100644 index 0000000000..8b947d9361 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs.mp @@ -0,0 +1,49 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +input colorbrewer-rgb + +numeric phi; phi = 0.61803398875; + +path wide[], tall[]; +wide0 = origin -- right -- phi * dir 36 -- cycle; +wide1 = origin -- right -- phi * dir -36 -- cycle; +tall0 = origin -- right -- (1+phi) * dir 72 -- cycle; +tall1 = origin -- right -- (1+phi) * dir -72 -- cycle; + +vardef half_thick(expr level, a, b, side) = + save T; path T; T = wide[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Purples[9][1+side]; + draw subpath (1, 3) of T; + else: + half_thick(level - 1, point phi of T, point 0 of T, 1-side); + half_thick(level - 1, point 1 of T, point 2 of T, side); + half_thin(level - 1, point 2 of T, point -phi of T, side); + fi +enddef; + +vardef half_thin(expr level, a, b, side) = + save T; path T; T = tall[side] zscaled (b-a) shifted a; + if level = 0: + fill T withcolor Blues[9][2+side]; + draw subpath (1, 3) of T; + else: + half_thick(level - 1, point 0 of T, point 2 of T, 1-side); + half_thin(level - 1, point 1 of T, point 2-phi of T, side); + fi +enddef; + +beginfig(1); + numeric wd; wd = 5in; + drawoptions(withpen pencircle scaled 1/8); + half_thick(8, 1.375 wd * left, 1.375 wd * right, 0); + drawoptions(); + clip currentpicture to unitsquare shifted 1/2 left scaled wd yscaled phi; +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs.pdf b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs.pdf Binary files differnew file mode 100644 index 0000000000..834faf7246 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-penrose-tatham-p3-rhombs.pdf diff --git a/info/drawing-with-metapost/src/tiling-pinwheel-macro.mp b/info/drawing-with-metapost/src/tiling-pinwheel-macro.mp new file mode 100644 index 0000000000..512bdebc8f --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-pinwheel-macro.mp @@ -0,0 +1,15 @@ +input colorbrewer-rgb +vardef pinwheel(expr level, a, b, c, s) = + if level = 0: + fill a--b--c--cycle withcolor s; + draw a--b--c--cycle; + else: + save d, e, f, g; pair d, e, f, g; + d = 1/2[a,b]; e = 1/5[c,b]; f = 1/2[a,e]; g = 1/2[b,e]; + pinwheel(level - 1, f, d, e, Blues 9 2); + pinwheel(level - 1, f, d, a, Blues 9 3); + pinwheel(level - 1, e, a, c, Blues 9 4); + pinwheel(level - 1, g, e, d, Blues 9 5); + pinwheel(level - 1, g, b, d, Blues 9 6); + fi +enddef; diff --git a/info/drawing-with-metapost/src/tiling-pp48a.mp b/info/drawing-with-metapost/src/tiling-pp48a.mp new file mode 100644 index 0000000000..0b0333c960 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-pp48a.mp @@ -0,0 +1,29 @@ +% inspired by Grünbaum & Shephard - fig 8.0.1 +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input colorbrewer-rgb +beginfig(1); + numeric r, s; s = 9; r = 2s * (sind(75)-sind(45)); + path a; a = unitsquare rotated -45 scaled s shifted (r, 0); + picture unit; unit = image( + for t=0 upto 5: + fill a rotated 60t withcolor Spectral[6][t mod 3 + 3]; + draw a rotated 60t; + endfor + ); + pair u, v; + u = (2s * sind(75), 0); u := u + u rotated 60; u := u rotated 60; + v = u rotated 60; + numeric n; n = 5; + for i = -n upto n: + for j = -n upto n: + draw unit shifted (i*u + j*v - floor(j/2)*u); + endfor + endfor +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-pp48a.pdf b/info/drawing-with-metapost/src/tiling-pp48a.pdf Binary files differnew file mode 100644 index 0000000000..59b61ee6b6 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-pp48a.pdf diff --git a/info/drawing-with-metapost/src/tiling-simple.mp b/info/drawing-with-metapost/src/tiling-simple.mp index 6b0fdf540a..1bb41d059d 100644 --- a/info/drawing-with-metapost/src/tiling-simple.mp +++ b/info/drawing-with-metapost/src/tiling-simple.mp @@ -5,34 +5,29 @@ beginfig(1); picture P[]; P1 = image( -for i = -10 upto 10: + for i = -10 upto 10: draw (left--right) scaled 200 shifted (0, 20i); draw (down--up) scaled 200 shifted (20i, 0); -endfor -clip currentpicture to fullcircle scaled 180; -draw fullcircle scaled 180; + endfor + path c; c = fullcircle scaled 180; clip currentpicture to c; draw c; ); P2 = image( -path unit; pair u, v; color a, b; -unit = unitsquare scaled 24; -u = point 1 of unit - point 0 of unit; -v = point 3 of unit - point 0 of unit; -a = 3/4[red, white]; b = 3/4[blue, white]; -for i=-5 upto 5: - for j=-5 upto 5: - fill unit shifted (i*u + j*v) - withcolor if odd (i+j): a else: b fi; - endfor -endfor -for i=-5 upto 5: - for j=-5 upto 5: - draw subpath (0,2) of unit shifted (i*u + j*v); + path unit; pair u, v; color a, b; + unit = unitsquare scaled 24; + u = point 1 of unit - point 0 of unit; + v = point 3 of unit - point 0 of unit; + a = 3/4[red, white]; b = 3/4[blue, white]; + for i=-5 upto 5: + for j=-5 upto 5: + fill unit shifted (i*u + j*v) + withcolor if odd (i+j): a else: b fi; + draw subpath (-1,1) of unit shifted (i*u + j*v); + endfor endfor -endfor -clip currentpicture to fullcircle scaled 180; -draw fullcircle scaled 180; + path c; c = fullcircle scaled 180; clip currentpicture to c; draw c; ); +undraw (left--right) scaled 2in; draw P1; draw P2 shifted 200 down; endfig; diff --git a/info/drawing-with-metapost/src/tiling-simple.pdf b/info/drawing-with-metapost/src/tiling-simple.pdf Binary files differindex ef086a2e0a..4a40647842 100644 --- a/info/drawing-with-metapost/src/tiling-simple.pdf +++ b/info/drawing-with-metapost/src/tiling-simple.pdf diff --git a/info/drawing-with-metapost/src/tiling-subs-pinwheel.mp b/info/drawing-with-metapost/src/tiling-subs-pinwheel.mp new file mode 100644 index 0000000000..e13e71cba4 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-subs-pinwheel.mp @@ -0,0 +1,16 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input tiling-pinwheel-macro +beginfig(1); + pair a, b, c; a = origin; b = 460 right; c = 1/2 b rotated 90; + drawoptions(withpen pencircle scaled 1/8 withcolor white); + pinwheel(5, a, b, c, ""); + drawoptions(); + draw currentpicture rotatedabout(1/2[b,c], 180); + currentpicture := currentpicture rotated 90; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/tiling-subs-pinwheel.pdf b/info/drawing-with-metapost/src/tiling-subs-pinwheel.pdf Binary files differnew file mode 100644 index 0000000000..6d9d625007 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-subs-pinwheel.pdf diff --git a/info/drawing-with-metapost/src/tiling-subs-triangle.mp b/info/drawing-with-metapost/src/tiling-subs-triangle.mp new file mode 100644 index 0000000000..aaf5e0eb06 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-subs-triangle.mp @@ -0,0 +1,82 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\mplibtextextlabel{enable} +\begin{document} +\begin{mplibcode} + +vardef tall(expr level, a, b, c) = + if level = 0: + fill a--b--c--cycle withcolor 3/4[blue, white]; + draw a--c--b; + else: + save m; pair m; m = 1/3 (a + b + c); % the centroid + wide(level - 1, a, b, m); + wide(level - 1, b, c, m); + wide(level - 1, c, a, m); + fi +enddef; +vardef wide(expr level, a, b, c) = + if level = 0: + fill a--b--c--cycle withcolor 7/8[blue, white]; + draw a--c--b; + else: + save p, q; pair p, q; p = 1/3[a,b]; q = 1/3[b,a]; + wide(level - 1, c, a, p); + tall(level - 1, p, q, c); + wide(level - 1, b, c, q); + fi +enddef; + +beginfig(1); + + picture P[]; + for i=0,1,2: z[1+i] = 173.2 up rotated 120i; endfor + for i=0,1,2: z[4+i] = 17.32 up rotated 120i; endfor + + P1 = image( + pickup pencircle scaled 1/8; + tall(6, z1, z2, z3); + ); + + P2 = image( + tall(0, z4, z5, z6) + ); + P3 = image( + tall(1, z4, z5, z6) + ); + P4 = image( + drawarrow 10 left -- 10 right; + label.lft(P2, 12 left); + label.rt(P3, 12 right); + label.top("The \textit{tall} macro dissects a tall triangle into 3 wide ones", + point 5/2 of bbox currentpicture shifted 6 up); + ); + + P5 = image( + wide(0, z5, z6, origin) + ); + + P6 = image( + wide(1, z5, z6, origin) + ); + + P7 = image( + drawarrow 10 left -- 10 right; + label.lft(P5, 12 left); + label.rt(P6, 12 right); + label.top("The \textit{wide} macro dissects a wide triangle into 2 wides, and 1 tall.", + point 5/2 of bbox currentpicture shifted 6 up); + ); + + draw P1; + label.top(P7, point 5/2 of bbox currentpicture shifted 12 up); + label.top(P4, point 5/2 of bbox currentpicture shifted 12 up); + + label.bot(btex \vbox{\hsize 4.2in\raggedright\noindent + Note that only part of the perimeter of each triangle is drawn, to give + the illusion that the completed tiling is made up of identical rhombs.} etex, + point 1/2 of bbox currentpicture shifted 12 down); +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tiling-subs-triangle.pdf b/info/drawing-with-metapost/src/tiling-subs-triangle.pdf Binary files differnew file mode 100644 index 0000000000..3794c49561 --- /dev/null +++ b/info/drawing-with-metapost/src/tiling-subs-triangle.pdf diff --git a/info/drawing-with-metapost/src/tiling.mp b/info/drawing-with-metapost/src/tiling.mp deleted file mode 100644 index 9a82b1fd39..0000000000 --- a/info/drawing-with-metapost/src/tiling.mp +++ /dev/null @@ -1,56 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - -prologues := 3; -outputtemplate := "%j%c.eps"; -vardef poly_on(expr a,b,n) = - save s,t,c; pair c; - s = 360/n; - t = 90-180/n; - c = whatever[a,b rotatedabout(a,+t)] - = whatever[b,a rotatedabout(b,-t)]; - for i=0 upto n-1: a rotatedabout(c,i*s) -- endfor cycle -enddef; - -vardef make_uniform_tiling_shd(expr u, reps, scolor, hcolor, dcolor) = - save x,y,s, h, d, t; path s[], h[], d; picture t; - (x,y) = dir 15; - d = for i=0 upto 11: (x/2y, 1/2) scaled u rotated 30i -- endfor cycle; - for i=0 upto 2: s[i] = unitsquare scaled u shifted point -1 of d rotated (60+60i); endfor - for i=0 upto 1: h[i] = poly_on(point 9+2i of d, point 8+2i of d, 6); endfor - t = image( - fill d withcolor dcolor; - for i=0 upto 2: fill s[i] withcolor scolor; endfor - for i=0 upto 1: fill h[i] withcolor hcolor; endfor - - draw d; - for i=0 upto 2: draw s[i]; endfor - for i=0 upto 1: draw h[i]; endfor - ); - save dx, dy; pair dx, dy; - dx = (u,0) + point -1/2 of d - point 11/2 of d; - dy = dx rotated 60; - for i=-reps upto reps: - for j=-reps upto reps: - draw t shifted (i*dx) shifted (j*dy); - endfor - endfor -enddef; - -def rgb(expr r,g,b) = (r/255, g/255, b/255) enddef; -color b[]; -b1 = rgb(255,255,217); -b2 = rgb(237,248,177); -b3 = rgb(199,233,180); - -beginfig(2); -picture tt; tt = image(make_uniform_tiling_shd(4mm, 7, b1, b2, b3); fill fullcircle scaled 3 withcolor red;); -clip tt to fullcircle scaled 12cm; draw tt; -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/tiling.pdf b/info/drawing-with-metapost/src/tiling.pdf Binary files differdeleted file mode 100644 index b37895e16c..0000000000 --- a/info/drawing-with-metapost/src/tiling.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/torn-edge-circle.mp b/info/drawing-with-metapost/src/torn-edge-circle.mp deleted file mode 100644 index 9a461eb737..0000000000 --- a/info/drawing-with-metapost/src/torn-edge-circle.mp +++ /dev/null @@ -1,18 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -input torn-edge -beginfig(1); -path c; c = fullcircle scaled 200; -draw c withcolor .8 white; -y=0; n = 600; -path t; t = for i=0 upto n-1: - point i/n*length(c) of c - + (0, walkr y) rotated angle direction i/n*length(c) of c - -- -endfor cycle; -draw t withcolor .67 red; -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/torn-edge-circle.pdf b/info/drawing-with-metapost/src/torn-edge-circle.pdf Binary files differdeleted file mode 100644 index 2142838a3d..0000000000 --- a/info/drawing-with-metapost/src/torn-edge-circle.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/torn-edge-straight.mp b/info/drawing-with-metapost/src/torn-edge-straight.mp deleted file mode 100644 index 18a365c4c2..0000000000 --- a/info/drawing-with-metapost/src/torn-edge-straight.mp +++ /dev/null @@ -1,14 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -input torn-edge -beginfig(2); -path t; numeric x, y; -x = 0; y=0; -t = (x, -20) -- (x, y) for i=1 upto 288: -- (incr x, walkr y) endfor -- (x, -20) -- cycle; -fill t withcolor 1/32(32,32,31); -draw t withcolor .67 blue; -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/torn-edge-straight.pdf b/info/drawing-with-metapost/src/torn-edge-straight.pdf Binary files differdeleted file mode 100644 index c0afc7349f..0000000000 --- a/info/drawing-with-metapost/src/torn-edge-straight.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/torn-edge.mp b/info/drawing-with-metapost/src/torn-edge.mp deleted file mode 100644 index 5d0afface0..0000000000 --- a/info/drawing-with-metapost/src/torn-edge.mp +++ /dev/null @@ -1,7 +0,0 @@ -vardef signr suffix $ = - if $<0: - else: + fi uniformdeviate 1 - enddef; -vardef walkr suffix $ = - $ := $ if uniformdeviate 1 < (2**-abs($)): + else: - fi signr $; - $ - enddef; diff --git a/info/drawing-with-metapost/src/trad-braces.mp b/info/drawing-with-metapost/src/trad-braces.mp new file mode 100644 index 0000000000..595248ceba --- /dev/null +++ b/info/drawing-with-metapost/src/trad-braces.mp @@ -0,0 +1,37 @@ +\documentclass[border=5mm]{standalone} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +vardef do_brace(expr a, b, offset, r) = + save d, e, m, n, brace, hook; pair e; path brace, hook[]; + d = angle(b-a); + e = up scaled offset rotated d shifted r[a,b]; + n = 1/2 offset; m = abs(n); + hook1 = origin {0, n} .. (m, n) {1,0}; + hook2 = (-m,-n) {1,0} .. {0, n} origin {0,-n} .. (m,-n) {1,0}; + hook3 = (-m, n) {1,0} .. {0,-n} origin; + brace = (hook1 rotated d shifted a -- + hook2 rotated d shifted e -- + hook3 rotated d shifted b) shifted (up scaled n rotated d); + draw brace withpen pencircle yscaled .6 xscaled .1666 rotated d; + point 3 of brace +enddef; + +beginfig(1); +z1 = origin; +z2 = 180 right rotated 13; +draw z1--z2 withcolor .7 white; +dotlabel.llft("$z_1$",z1); +dotlabel.urt("$z_2$",z2); +drawoptions(withcolor 2/3 red); +label.lrt("Here", do_brace(z1, z2, -12, 3/4)); +drawoptions(); +begingroup; interim ahangle := 180; interim ahlength := 3; +drawdblarrow (z1--z2) shifted (12 up rotated angle (z2-z1)) withcolor 2/3 blue; +endgroup; + + +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/braces.pdf b/info/drawing-with-metapost/src/trad-braces.pdf Binary files differindex 28064cabad..d3ebc86b0b 100644 --- a/info/drawing-with-metapost/src/braces.pdf +++ b/info/drawing-with-metapost/src/trad-braces.pdf diff --git a/info/drawing-with-metapost/src/callout.mp b/info/drawing-with-metapost/src/trad-callout.mp index be171d03e5..f450baef4c 100644 --- a/info/drawing-with-metapost/src/callout.mp +++ b/info/drawing-with-metapost/src/trad-callout.mp @@ -1,19 +1,18 @@ \documentclass[border=5mm]{standalone} \usepackage{luamplib} \begin{document} -\mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); path a; a = (left .. right) scaled 42; pair P; P = origin; r = 31; draw a rotated r withcolor 2/3 red; draw a rotated (90+r) withcolor 2/3 red; -drawdot P withpen pencircle scaled dotlabeldiam; -label("$P$", P shifted 10 dir 68); - z0 = P + 20 dir -20; - draw z0 -- P - cutafter fullcircle scaled 8 shifted P - withpen pencircle scaled 1/4; - label.rt("\textit{pole}", z0); +draw P withpen pencircle scaled dotlabeldiam; +label(btex $P$ etex, P shifted 10 dir 68); +z0 = P + 20 dir -20; +draw z0 -- P + cutafter fullcircle scaled 8 shifted P + withpen pencircle scaled 1/4; +label.rt(btex \textit{pole} etex, z0); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/callout.pdf b/info/drawing-with-metapost/src/trad-callout.pdf Binary files differindex 07f6e21964..27ee0c69ff 100644 --- a/info/drawing-with-metapost/src/callout.pdf +++ b/info/drawing-with-metapost/src/trad-callout.pdf diff --git a/info/drawing-with-metapost/src/dynamic-labels.mp b/info/drawing-with-metapost/src/trad-dynamic-labels.mp index d831d99a4b..d831d99a4b 100644 --- a/info/drawing-with-metapost/src/dynamic-labels.mp +++ b/info/drawing-with-metapost/src/trad-dynamic-labels.mp diff --git a/info/drawing-with-metapost/src/dynamic-labels.pdf b/info/drawing-with-metapost/src/trad-dynamic-labels.pdf Binary files differindex 94ed338990..94ed338990 100644 --- a/info/drawing-with-metapost/src/dynamic-labels.pdf +++ b/info/drawing-with-metapost/src/trad-dynamic-labels.pdf diff --git a/info/drawing-with-metapost/src/euler-sampler.mp b/info/drawing-with-metapost/src/trad-euler-sampler.mp index 72101fb1da..72101fb1da 100644 --- a/info/drawing-with-metapost/src/euler-sampler.mp +++ b/info/drawing-with-metapost/src/trad-euler-sampler.mp diff --git a/info/drawing-with-metapost/src/euler-sampler.pdf b/info/drawing-with-metapost/src/trad-euler-sampler.pdf Binary files differindex 1da31b1984..1da31b1984 100644 --- a/info/drawing-with-metapost/src/euler-sampler.pdf +++ b/info/drawing-with-metapost/src/trad-euler-sampler.pdf diff --git a/info/drawing-with-metapost/src/trad-greek-default-encoding.mp b/info/drawing-with-metapost/src/trad-greek-default-encoding.mp new file mode 100644 index 0000000000..be5ebafe0b --- /dev/null +++ b/info/drawing-with-metapost/src/trad-greek-default-encoding.mp @@ -0,0 +1,20 @@ +\documentclass[border=3mm]{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); + string ab, AB; + ab = ("" for i=11 upto 23: & char i endfor + & "o" for i=24 upto 33: & char i endfor); + AB = ("AB" & char 0 & char 1 & "EZH" & char 2 & "IK" + & char 3 & "MNO" & char 4 & char 5 & "P" + & char 6 & "T" & char 7 & char 8 & "X" + & char 9 & char 10); + + draw ab infont "cmmi10"; + draw AB infont "cmmi10" shifted 12 down; + draw ab infont "eurm10" shifted 32 down; + draw AB infont "eurm10" shifted 44 down; +endfig; +\end{mplibcode} +\end{document} diff --git a/info/drawing-with-metapost/src/trad-greek-default-encoding.pdf b/info/drawing-with-metapost/src/trad-greek-default-encoding.pdf Binary files differnew file mode 100644 index 0000000000..ba18279766 --- /dev/null +++ b/info/drawing-with-metapost/src/trad-greek-default-encoding.pdf diff --git a/info/drawing-with-metapost/src/greek-gfs-encoding.mp b/info/drawing-with-metapost/src/trad-greek-gfs-encoding.mp index fbdcdcc513..30f4a97636 100644 --- a/info/drawing-with-metapost/src/greek-gfs-encoding.mp +++ b/info/drawing-with-metapost/src/trad-greek-gfs-encoding.mp @@ -1,14 +1,14 @@ -\documentclass{standalone} +\documentclass[border=3mm]{standalone} \usepackage{luamplib} \begin{document} \begin{mplibcode} -beginfig(2); +beginfig(1); string ab, AB; ab = "abgdezhjiklmnoxprstufqyw"; AB = "ABGDEZHJIKLMNOXPRSTUFQYW"; y := 0; for $="grmn1000", "gporsonrg6r", "gneohellenicrg6r": - draw $ infont "cmss10" scaled 0.8 shifted (0,y) withcolor .67 red; + draw ("draw ab infont " & ditto & $ & ditto) infont "texnansi-lmtt10" scaled 0.8 shifted (0,y) withcolor .67 red; draw ab infont $ shifted (0,y-10); draw AB infont $ shifted (0,y-22); y := y - 40; diff --git a/info/drawing-with-metapost/src/greek-gfs-encoding.pdf b/info/drawing-with-metapost/src/trad-greek-gfs-encoding.pdf Binary files differindex 383e3a63df..0f6f69488e 100644 --- a/info/drawing-with-metapost/src/greek-gfs-encoding.pdf +++ b/info/drawing-with-metapost/src/trad-greek-gfs-encoding.pdf diff --git a/info/drawing-with-metapost/src/greek-homer.mp b/info/drawing-with-metapost/src/trad-greek-homer.mp index 0a872fe16e..0a872fe16e 100644 --- a/info/drawing-with-metapost/src/greek-homer.mp +++ b/info/drawing-with-metapost/src/trad-greek-homer.mp diff --git a/info/drawing-with-metapost/src/greek-homer.pdf b/info/drawing-with-metapost/src/trad-greek-homer.pdf Binary files differindex f455cf1a21..f455cf1a21 100644 --- a/info/drawing-with-metapost/src/greek-homer.pdf +++ b/info/drawing-with-metapost/src/trad-greek-homer.pdf diff --git a/info/drawing-with-metapost/src/infont-annotated.mp b/info/drawing-with-metapost/src/trad-infont-annotated.mp index 670c1f12b5..670c1f12b5 100644 --- a/info/drawing-with-metapost/src/infont-annotated.mp +++ b/info/drawing-with-metapost/src/trad-infont-annotated.mp diff --git a/info/drawing-with-metapost/src/infont-annotated.pdf b/info/drawing-with-metapost/src/trad-infont-annotated.pdf Binary files differindex acc76a9f1d..c54d20cf9b 100644 --- a/info/drawing-with-metapost/src/infont-annotated.pdf +++ b/info/drawing-with-metapost/src/trad-infont-annotated.pdf diff --git a/info/drawing-with-metapost/src/infont-example.mp b/info/drawing-with-metapost/src/trad-infont-example.mp index 0b2a4d965b..0b2a4d965b 100644 --- a/info/drawing-with-metapost/src/infont-example.mp +++ b/info/drawing-with-metapost/src/trad-infont-example.mp diff --git a/info/drawing-with-metapost/src/infont-example.pdf b/info/drawing-with-metapost/src/trad-infont-example.pdf Binary files differindex 1e772668cc..1e772668cc 100644 --- a/info/drawing-with-metapost/src/infont-example.pdf +++ b/info/drawing-with-metapost/src/trad-infont-example.pdf diff --git a/info/drawing-with-metapost/src/minus.mp b/info/drawing-with-metapost/src/trad-minus.mp index ebf8f8cb04..e7a4584d45 100644 --- a/info/drawing-with-metapost/src/minus.mp +++ b/info/drawing-with-metapost/src/trad-minus.mp @@ -1,4 +1,4 @@ -\documentclass[border=2mm]{standalone} +\documentclass{standalone} \usepackage{luamplib} \begin{document} \begin{mplibcode} diff --git a/info/drawing-with-metapost/src/minus.pdf b/info/drawing-with-metapost/src/trad-minus.pdf Binary files differindex 05d57963b4..05d57963b4 100644 --- a/info/drawing-with-metapost/src/minus.pdf +++ b/info/drawing-with-metapost/src/trad-minus.pdf diff --git a/info/drawing-with-metapost/src/porson.mp b/info/drawing-with-metapost/src/trad-porson.mp index 59ac82181b..59ac82181b 100644 --- a/info/drawing-with-metapost/src/porson.mp +++ b/info/drawing-with-metapost/src/trad-porson.mp diff --git a/info/drawing-with-metapost/src/porson.pdf b/info/drawing-with-metapost/src/trad-porson.pdf Binary files differindex 7a26026f46..7a26026f46 100644 --- a/info/drawing-with-metapost/src/porson.pdf +++ b/info/drawing-with-metapost/src/trad-porson.pdf diff --git a/info/drawing-with-metapost/src/split-labels.mp b/info/drawing-with-metapost/src/trad-split-labels.mp index ca298e5e99..78006abd2a 100644 --- a/info/drawing-with-metapost/src/split-labels.mp +++ b/info/drawing-with-metapost/src/trad-split-labels.mp @@ -1,8 +1,7 @@ -\documentclass[border=0mm]{standalone} +\documentclass{standalone} \usepackage{luamplib} \def\s#1{\let\\\cr\vbox{\halign{\hfil\strut ##\hfil\cr#1\crcr}}} \begin{document} -\mplibtextextlabel{enable} \begin{mplibcode} input colorbrewer-rgb beginfig(1); diff --git a/info/drawing-with-metapost/src/split-labels.pdf b/info/drawing-with-metapost/src/trad-split-labels.pdf Binary files differindex d1a1ba6fd5..c2029e350b 100644 --- a/info/drawing-with-metapost/src/split-labels.pdf +++ b/info/drawing-with-metapost/src/trad-split-labels.pdf diff --git a/info/drawing-with-metapost/src/utf8.mp b/info/drawing-with-metapost/src/trad-utf8.mp index 5606860388..abccfd5a07 100644 --- a/info/drawing-with-metapost/src/utf8.mp +++ b/info/drawing-with-metapost/src/trad-utf8.mp @@ -2,10 +2,7 @@ \usepackage{luamplib} \begin{document} \begin{mplibcode} -beginfig(1); - def U primary s = if string s: decode(s) fi enddef; - vardef decode(expr given) = save a,b,i,s,out; string s, out; numeric a, b, i; out = ""; i=0; @@ -25,11 +22,11 @@ vardef decode(expr given) = out enddef; beginfig(2); - draw "café noir £2.50" infont "pncr8r"; - draw U"café noir £2.50" infont "pncr8r" shifted 12 down; - defaultfont := "pncr8r"; - label.rt("café noir £2.50", 24 down); - label.rt(U"café noir £2.50", 36 down); +draw "café noir £2.50" infont "ptmr8r"; +draw decode("café noir £2.50") infont "ptmr8r" shifted 12 down; +defaultfont := "pncr8r"; +label.rt("café noir £2.50", 24 down); +label.rt(decode("café noir £2.50"), 36 down); endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/trad-utf8.pdf b/info/drawing-with-metapost/src/trad-utf8.pdf Binary files differnew file mode 100644 index 0000000000..9b8e6ab907 --- /dev/null +++ b/info/drawing-with-metapost/src/trad-utf8.pdf diff --git a/info/drawing-with-metapost/src/verbatim-listing.mp b/info/drawing-with-metapost/src/trad-verbatim-listing.mp index 448246aac3..5c4102b7a8 100644 --- a/info/drawing-with-metapost/src/verbatim-listing.mp +++ b/info/drawing-with-metapost/src/trad-verbatim-listing.mp @@ -1,30 +1,26 @@ -prologues := 3; -outputtemplate := "%j.eps"; +prologues := 3; outputtemplate := "%j.eps"; verbatimtex \documentclass{article} \usepackage{listings} -\newcommand\mpstyle{\lstset{ -language=Metapost, basicstyle=\ttfamily, -frame=none, columns=fullflexible, -keepspaces=true, showstringspaces=false}} +\usepackage{xcolor} +\newcommand\mpstyle{\lstset{language=Metapost, +basicstyle=\ttfamily,columns=fullflexible,commentstyle=\color{red}, +frame=none,keepspaces=true,showstringspaces=false}} \lstnewenvironment{code}[1][]{\mpstyle\lstset{#1}}{} \begin{document} etex beginfig(1); -picture P; -P = thelabel(btex \vbox{\begin{code} +picture P; P = thelabel(btex \vbox{\begin{code} % special operators vardef incr suffix $ = $:=$+1; $ enddef; vardef decr suffix $ = $:=$-1; $ enddef; - def reflectedabout(expr w,z) = % reflects about the line w..z transformed begingroup transform T_; w transformed T_ = w; z transformed T_ = z; xxpart T_ = -yypart T_; xypart T_ = yxpart T_; % T_ is a reflection - T_ endgroup enddef; + T_ endgroup enddef; \end{code}} etex, origin); fill bbox P withcolor (1,1,31/32); draw P; draw bbox P; -endfig; -end. +endfig; end. diff --git a/info/drawing-with-metapost/src/trad-verbatim-listing.pdf b/info/drawing-with-metapost/src/trad-verbatim-listing.pdf Binary files differnew file mode 100644 index 0000000000..7b5286ce22 --- /dev/null +++ b/info/drawing-with-metapost/src/trad-verbatim-listing.pdf diff --git a/info/drawing-with-metapost/src/trad-verbatim-with-infont.mp b/info/drawing-with-metapost/src/trad-verbatim-with-infont.mp new file mode 100644 index 0000000000..d912277b50 --- /dev/null +++ b/info/drawing-with-metapost/src/trad-verbatim-with-infont.mp @@ -0,0 +1,18 @@ +\documentclass{standalone} +\usepackage{luamplib} +\begin{document} +\begin{mplibcode} +beginfig(1); + string s; s = "\TeX\ sets maths like this $e=mc^2$"; + draw ("1. " & s) infont defaultfont; + draw ("2. " & s) infont "texnansi-lmr10" shifted 20 down; + draw ("3. " & s) infont "cmtt10" shifted 40 down; + draw ("4. " & s) infont "texnansi-lmtt10" shifted 60 down; + bboxmargin := 14; + picture p; p = currentpicture; + fill bbox currentpicture withcolor (1,1,31/32); + draw p; draw bbox p; +endfig; +\end{mplibcode} +\end{document} +end. diff --git a/info/drawing-with-metapost/src/trad-verbatim-with-infont.pdf b/info/drawing-with-metapost/src/trad-verbatim-with-infont.pdf Binary files differnew file mode 100644 index 0000000000..0c7cfc5929 --- /dev/null +++ b/info/drawing-with-metapost/src/trad-verbatim-with-infont.pdf diff --git a/info/drawing-with-metapost/src/trigonometry-functions.mp b/info/drawing-with-metapost/src/trigonometry-functions.mp new file mode 100644 index 0000000000..5883390aa5 --- /dev/null +++ b/info/drawing-with-metapost/src/trigonometry-functions.mp @@ -0,0 +1,49 @@ +numeric pi; +% approximate value +pi := 3.14159; +% measure round a circular arc... +pi := 1/4 arclength (quartercircle scaled 16); +% up to 32 digits of precision +pi := 3.1415926535897932384626433832795; +% as many digits as are needed... +vardef getpi = + save lasts, t, s, n, na, d, da; + lasts=0; s=t=3; n=1; na=0; d=0; da=24; + forever: + exitif lasts=s; + lasts := s; + n := n+na; na := na+8; + d := d+da; da := da+32; + t := t*n/d; + s := s+t; + endfor + s +enddef; +pi := getpi; + +% conversions +def degrees(expr theta) = theta / pi * 180 enddef; +def radians(expr theta) = theta / 180 * pi enddef; +% trig functions that expect radians +def sin(expr theta) = sind(degrees(theta)) enddef; +def cos(expr theta) = cosd(degrees(theta)) enddef; +% inverse trig functions +def acosd(expr a) = angle (a,1+-+a) enddef; +def asind(expr a) = angle (1+-+a,a) enddef; +def acos(expr a) = radians(acosd(a)) enddef; +def asin(expr a) = radians(asind(a)) enddef; +% tangents +vardef tand(expr theta) = save x,y; (x,y)=dir theta; y/x enddef; +def atand(expr a) = angle (1,a) enddef; + + +% tests - run with plain `mpost` and scaled numebr system +show pi = 3.14159; +show abs(degrees(1) - 57.29577951308232) < 2 eps; +show radians(90) = 1/2 pi; +show sin(1)**2 + cos(1)**2 = 1; +show abs(acosd(1/2) - 60) < eps; +show abs(asind(1/2) - 30) < eps; +show tand(45) = 1; +show atand(1) = 45; +end diff --git a/info/drawing-with-metapost/src/trisection-simple.mp b/info/drawing-with-metapost/src/trisection-simple.mp deleted file mode 100644 index 8f55281efb..0000000000 --- a/info/drawing-with-metapost/src/trisection-simple.mp +++ /dev/null @@ -1,22 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - path ray; - numeric theta; - ray = origin -- 200 right; - theta = 42; - draw ray; - draw ray rotated 1/3 theta withcolor 2/3 red; - draw ray rotated 2/3 theta withcolor 2/3 red; - draw ray rotated theta; - dotlabel.llft("$0$", origin); - label("$\theta/3$", 72 right rotated 1/6 theta) withcolor 2/3 blue; - label("$\theta/3$", 72 right rotated 3/6 theta) withcolor 2/3 blue; - label("$\theta/3$", 72 right rotated 5/6 theta) withcolor 2/3 blue; -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/tufte-budget.mp b/info/drawing-with-metapost/src/tufte-budget.mp index 6fd4c3ead1..f514dcf1a9 100644 --- a/info/drawing-with-metapost/src/tufte-budget.mp +++ b/info/drawing-with-metapost/src/tufte-budget.mp @@ -6,60 +6,41 @@ \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} +input tufte-manila-paper beginfig(1); -path data, p; -data = (1967, 311) - -- (1968, 332) - -- (1969, 372) - -- (1970, 385) - -- (1971, 385) - -- (1972, 393) - -- (1973, 387) - -- (1974, 381) - -- (1975, 387) - -- (1976, 400) - -- (1977, 380); - -numeric u, v; -u = xpart urcorner textext("1980\kern 0.75em"); -v = 1.414; -p = data shifted -(xpart point 0 of data, 300) xscaled u yscaled v; -draw p; - -for d = 300 step 20 until 400: - numeric y; y = (d - 300) * v; + path data; numeric n; + data = (1967, 311) -- (1968, 332) -- (1969, 372) -- (1970, 385) + -- (1971, 385) -- (1972, 393) -- (1973, 387) -- (1974, 381) + -- (1975, 387) -- (1976, 400) -- (1977, 380); + n = length data; + numeric u, v; path p; % make data --> p + u = xpart urcorner textext("1980\kern 0.75em"); v = 1.414; + p = data shifted -(xpart point 0 of data, 300) xscaled u yscaled v; + for i=0 upto n: z[i] = point i of p; endfor + for d = 300 step 20 until 400: % y-axis + numeric y; y = (d - 300) * v; draw (-8, y) -- (-12, y); label.lft("\strut\scriptsize\$\,\small" & decimal d, (-12, y)); - draw (-8, y) -- (-12, y); - if d > 370: - draw (xpart point 3 of p, y) -- (xpart point infinity of p + 8, y) - dashed evenly scaled 1/4 withpen pencircle scaled 1/4; - fi -endfor -path a; a = (xpart point infinity of p + 21, (380 - 300) * v) - -- (xpart point infinity of p + 21, (400 - 300) * v); -interim ahangle := 180; -interim ahlength := 2; -drawdblarrow a withpen pencircle scaled 1/4; -label("\small 5\%", point 1/2 of a shifted 12 right); - -for t=0 upto length p: - numeric x, y; (x, y) = point t of p; - undraw (x, y) withpen pencircle scaled 2 dotlabeldiam; - draw (x, y) withpen pencircle scaled dotlabeldiam; - draw (x, -8) -- (x, -12); - label("\strut\small" & decimal xpart point t of data, (x, -20)); -endfor - -label.urt(btex \vbox{\halign{\small #\hfill\cr -Per capita\cr budget expenditure\cr in constant dollars\cr}} etex, -(0, (410 - 300) * v)); - -picture p; p = currentpicture; currentpicture := nullpicture; -bboxmargin := 12; -fill bbox p withcolor 1/32(32, 32, 31); -draw p; - + endfor + path a, b, c; % annotating lines + a = (x3, y[n-1]) -- (x[n] + 8, y[n-1]); + b = (x3, y[n]) -- (x[n] + 8, y[n]); + c = (x[n] + 21, y[n]) -- (x[n] + 21, y[n-1]); + drawoptions(withpen pencircle scaled 1/4); + draw a dashed evenly scaled 1/4; + draw b dashed evenly scaled 1/4; + draw c; + for i=0,1: draw (left--right) scaled 2 shifted point i of c; endfor + label("\small 5\%", point 1/2 of c shifted 12 right); + drawoptions(); + draw p; % the data points + for i = 0 upto n: + undraw z[i] withpen pencircle scaled 2 dotlabeldiam; + draw z[i] withpen pencircle scaled dotlabeldiam; + draw (x[i], -8) -- (x[i], -12); + label("\strut\small" & decimal xpart point i of data, (x[i], -20)); + endfor + label.urt(btex \vbox{\halign{\small #\hfill\cr Per capita\cr + budget expenditure\cr in constant dollars\cr}} etex, (x0,y[n-1]+10v)); endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/tufte-budget.pdf b/info/drawing-with-metapost/src/tufte-budget.pdf Binary files differindex 9a369d27d1..9527862699 100644 --- a/info/drawing-with-metapost/src/tufte-budget.pdf +++ b/info/drawing-with-metapost/src/tufte-budget.pdf diff --git a/info/drawing-with-metapost/src/tufte-currency.mp b/info/drawing-with-metapost/src/tufte-currency.mp index 708f229696..bd469af94d 100644 --- a/info/drawing-with-metapost/src/tufte-currency.mp +++ b/info/drawing-with-metapost/src/tufte-currency.mp @@ -3,7 +3,7 @@ \usepackage{unicode-math} \setmainfont[Numbers=OldStyle]{TeX Gyre Pagella} \setmathfont{TeX Gyre Pagella Math} -\def\tl#1{\vbox{\tiny\let\\\cr\halign{\hss ##\hss\cr#1\crcr}}} +\def\tl#1{\vbox{\small\let\\\cr\halign{\hss ##\hss\cr#1\crcr}}} \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} @@ -290,28 +290,66 @@ euro = -- (base(2022, 02, 28), 83.827900) -- (base(2022, 03, 31), 83.615400) -- (base(2022, 04, 30), 83.557800) - -- (base(2022, 05, 22), 84.892600) + -- (base(2022, 05, 31), 84.954600) + -- (base(2022, 06, 30), 85.784300) + -- (base(2022, 07, 31), 84.922300) + -- (base(2022, 08, 31), 84.566100) + -- (base(2022, 09, 30), 87.545600) + -- (base(2022, 10, 31), 87.084200) + -- (base(2022, 11, 30), 86.959400) + -- (base(2022, 12, 31), 86.945600) + -- (base(2023, 01, 31), 88.136600) + -- (base(2023, 02, 28), 88.710800) + -- (base(2023, 03, 31), 88.288100) + -- (base(2023, 04, 30), 88.306300) + -- (base(2023, 05, 31), 87.190600) + -- (base(2023, 06, 30), 85.824200) + -- (base(2023, 07, 31), 85.8333) + -- (base(2023, 08, 31), 85.9054) + -- (base(2023, 09, 30), 86.2139) + -- (base(2023, 10, 31), 86.8168) + -- (base(2023, 11, 30), 87.0744) + -- (base(2023, 12, 31), 86.2330) + -- (base(2024, 01, 31), 85.8814) + -- (base(2024, 02, 29), 85.4670) + -- (base(2024, 03, 31), 85.5549) + -- (base(2024, 04, 30), 85.6500) + -- (base(2024, 05, 31), 85.6277) + -- (base(2024, 06, 30), 84.7218) + -- (base(2024, 07, 31), 84.4672) + -- (base(2024, 08, 31), 85.1493) + -- (base(2024, 09, 30), 84.0409) + -- (base(2024, 10, 26), 83.5291) ; -years = (base(1999, 01, 01), 1999) for y=2000 upto 2022: -- (base(y, 1, 1), y) endfor; +years = (base(1999, 01, 01), 1999) for y=2000 upto 2025: -- (base(y, 1, 1), y) endfor; +numeric u, v; u = 67; v = 5; numeric offset; offset = base(1999, 1, 1); -euro := euro shifted -(offset, 0) xscaled 42 yscaled 3; -years := years shifted -(offset, 0) xscaled 42; +euro := euro shifted -(offset, 0) xscaled u yscaled v; +years := years shifted -(offset, 0) xscaled u; +input tufte-manila-paper beginfig(1); -draw euro withcolor 3/4 blue; -numeric baseline; baseline = 54*3; -draw (xpart point 0 of euro, baseline) -- (xpart point infinity of euro, baseline); + +draw euro + withpen pencircle scaled 1/4 withcolor 3/4; +for t=0 upto length euro: draw point t of euro + withpen pencircle scaled if t mod 12 = 0: 3/2 else: 1 fi + withcolor 3/4 blue; endfor +numeric baseline_height; baseline_height = 54v; +draw (xpart point 0 of euro, baseline_height) -- (xpart point infinity of euro, baseline_height); for t = 1 upto length years: - numeric x, y, q; (x, y) = point t of years; 4q = xpart (point t-1 of years - point t of years); - draw (x, baseline) -- (x, baseline + 4); + numeric x, y, q; + (x, y) = point t of years; + 4q = xpart (point t-1 of years - point t of years); + draw (x, baseline_height) -- (x, baseline_height + 4); for i=1 upto 3: - draw (x + i*q, baseline) -- (x + i*q, baseline + 2); + draw (x + i*q, baseline_height) -- (x + i*q, baseline_height + 2); endfor if not odd y: - label.bot("\small\strut " & decimal y, (x, baseline)); + label.bot("\small\strut " & decimal y, (x, baseline_height)); fi endfor numeric minx, miny, maxx, maxy; @@ -322,42 +360,45 @@ for i=0 upto length euro: if y > maxy: maxy := y; maxx := x; fi if y < miny: miny := y; minx := x; fi endfor -draw (2 up -- up) scaled 2 shifted (maxx, maxy) withcolor red; -draw (2 down -- down) scaled 2 shifted (minx, miny) withcolor red; +fill ((0,1)--(1,4)--(-1,4)--cycle) scaled 2 shifted (maxx, maxy) withcolor 1/2 green; +fill ((0,-1)--(1,-4)--(-1,-4)--cycle) scaled 2 shifted (minx, miny) withcolor 3/4 red; -numeric left_axis, right_axis; left_axis = -16; right_axis = 368; +numeric left_axis_x, right_axis_x; +left_axis_x = xpart point 0 of euro - 24; +right_axis_x = xpart point infinity of euro + 24; -draw (left_axis, miny) -- (left_axis, maxy); +draw (left_axis_x, miny) -- (left_axis_x, maxy); for y = 60 step 10 until 100: - draw (left_axis, 3y) -- (left_axis + 2, 3y); - label.lft("\small\strut " & if y < 100: "0." & decimal y else: "1.00" fi, (left_axis, 3y)); + draw (left_axis_x, y * v) -- (left_axis_x + 2, y * v); + label.lft("\small\strut " & if y < 100: "0." & decimal y else: "1.00" fi, (left_axis_x, y * v)); endfor -draw (right_axis, miny) -- (right_axis, maxy); +draw (right_axis_x, miny) -- (right_axis_x, maxy); for eur = 100 step 10 until 170: numeric y; y = 100/eur * 100; - draw (right_axis, 3y) -- (right_axis - 2, 3y); - label.rt("\small\strut " & if eur=100: "1.00" else: "1." & decimal (eur mod 100) fi, (right_axis, 3y)); + draw (right_axis_x, y * v) -- (right_axis_x - 2, y * v); + label.rt("\small\strut " & if eur=100: "1.00" else: "1." & decimal (eur mod 100) fi, (right_axis_x, y * v)); endfor -label.top("\small £/€", (left_axis - 10, 310)); -label.top("\small €/£", (right_axis + 10, 310)); - -interim dotlabeldiam := 3/2; -dotlabel.top("\tiny Creation", (base(1999, 1, 1) - offset, 71) xscaled 42 yscaled 3); -dotlabel.top("\tiny 9/11", (base(2001, 9, 11) - offset, 64) xscaled 42 yscaled 3); -dotlabel.lrt("\tl{Lehmans\\collapse}", (base(2008, 9, 15) - offset, 77) xscaled 42 yscaled 3); -dotlabel.lrt("\tl{Brexit\\vote}", (base(2016, 6, 24) - offset, 77) xscaled 42 yscaled 3); -dotlabel.bot("\tl{UK leaves\\EU}", (base(2020, 1, 31) - offset, 83) xscaled 42 yscaled 3); -dotlabel.top("\tl{WHO declares\\pandemic}", (base(2020, 3, 11) - offset, 91) xscaled 42 yscaled 3); -dotlabel.bot("\tl{Ukraine\\invaded}", (base(2022, 2, 24) - offset, 82.5) xscaled 42 yscaled 3); +label.ulft("\small £/€", (left_axis_x, 103v)); +label.urt ("\small €/£", (right_axis_x, 103v)); +label.top("Monthly average exchange rates Euro v.\@ Sterling", (1/2 left_axis_x + 1/2 right_axis_x, 103v)); +vardef event_label@#(expr t, z) = + fill unitsquare shifted -(1/2,1/2) rotated 45 scaled 2 shifted z; + label@#(t, z); +enddef; -picture p; p = currentpicture; currentpicture := nullpicture; -bboxmargin := 12; -fill bbox p withcolor 1/32(32, 32, 31); -draw p; +event_label.top("\small Creation", (base(1999, 1, 1) - offset, 71) xscaled u yscaled v); +event_label.top("\small 9/11", (base(2001, 9, 11) - offset, 64) xscaled u yscaled v); +event_label.lrt("\tl{US / UK\\invade Iraq}", (base(2003, 3, 20) - offset, 64) xscaled u yscaled v); +event_label.lrt("\tl{Lehmans\\collapse}", (base(2008, 9, 15) - offset, 77) xscaled u yscaled v); +event_label.lrt("\tl{Brexit\\vote}", (base(2016, 6, 24) - offset, 77) xscaled u yscaled v); +event_label.bot("\tl{UK leaves\\EU}", (base(2020, 1, 31) - offset, 83) xscaled u yscaled v); +event_label.top("\tl{WHO declares\\pandemic}", (base(2020, 3, 11) - offset, 91) xscaled u yscaled v); +event_label.bot("\tl{Ukraine\\invaded}", (base(2022, 2, 24) - offset, 82.5) xscaled u yscaled v); +input show_name endfig; \end{mplibcode} \end{document} diff --git a/info/drawing-with-metapost/src/tufte-currency.pdf b/info/drawing-with-metapost/src/tufte-currency.pdf Binary files differindex 18bb4f461b..43b69eac68 100644 --- a/info/drawing-with-metapost/src/tufte-currency.pdf +++ b/info/drawing-with-metapost/src/tufte-currency.pdf diff --git a/info/drawing-with-metapost/src/tufte-manila-paper.mp b/info/drawing-with-metapost/src/tufte-manila-paper.mp new file mode 100644 index 0000000000..97805eefbe --- /dev/null +++ b/info/drawing-with-metapost/src/tufte-manila-paper.mp @@ -0,0 +1,3 @@ +extra_beginfig := "background := (1,1,31/32);"; +extra_endfig := "picture p; p = currentpicture; clearit;" + & "bboxmargin := 12; unfill bbox p; draw p;"; diff --git a/info/drawing-with-metapost/src/tufte-mpg.mp b/info/drawing-with-metapost/src/tufte-mpg.mp index ab52f8336f..6d33009c13 100644 --- a/info/drawing-with-metapost/src/tufte-mpg.mp +++ b/info/drawing-with-metapost/src/tufte-mpg.mp @@ -1,55 +1,38 @@ \documentclass{standalone} \usepackage{luamplib} -\usepackage{unicode-math} +\mplibtextextlabel{enable} +\usepackage{fontspec} \setmainfont[Numbers=OldStyle]{TeX Gyre Pagella} -\setmathfont{TeX Gyre Pagella Math} \begin{document} -\mplibtextextlabel{enable} \begin{mplibcode} +input tufte-manila-paper beginfig(1); -path data, p; -data = (1978, 18) - -- (1979, 19) - -- (1980, 20) - -- (1981, 22) - -- (1982, 24) - -- (1983, 26) - -- (1984, 27) - -- (1985, 27.5); -numeric u, v; -u = xpart urcorner textext("1980\kern 0.75em"); -v = 8; -p = data shifted -(xpart point 0 of data, 0) xscaled u yscaled v; -draw (xpart point 0 of p, 20) -- p -- (xpart point infinity of p, 20); -draw (xpart point 0 of p, 0) -- (xpart point infinity of p, 0); +path data, p; numeric n, u, v; +data = (1978, 18) -- (1979, 19) -- (1980, 20) -- (1981, 22) -- + (1982, 24) -- (1983, 26) -- (1984, 27) -- (1985, 27.5); +u = xpart urcorner textext("1980\quad"); v = 7; +p = data shifted -(1978, 0) xscaled u yscaled v; -for t=0 upto length p: - numeric x, y; (x, y) = point t of p; - undraw (x, y) withpen pencircle scaled 2 dotlabeldiam; - draw (x, y) withpen pencircle scaled dotlabeldiam; - label("\strut" & decimal ypart point t of data, (x, y + 8)); - draw (x, 0) -- (x, 4); - label("\strut" & decimal xpart point t of data, (x, 12)); +draw p; +for i=0 upto length p: + z[i] = point i of p; + undraw z[i] withpen pencircle scaled 2 dotlabeldiam; + dotlabel.top("\strut" & decimal ypart point i of data, z[i]); + label("\strut" & decimal xpart point i of data, (x[i], 12)); + draw (x[i], 0) -- (x[i], 4); endfor +draw (x0, 20) -- z0; draw (x7, 20) -- z7; draw (x0, 0) -- (x7, 0); dotlabel.rt(btex \vbox to 6pt{\halign{\small #\hss\cr -13.7 mpg, average\cr for all cars on\cr road, 1978\cr}\vss} etex, -(xpart point 0 of p, 13.7v)); + 13.7 mpg, average\cr for all cars on\cr road, 1978\cr + }\vss} etex, (x0, 13.7v)); dotlabel.lft(btex \vbox to 6pt{\halign{\small #\hss\cr -19.5 mpg, expected\cr average for all cars\cr on road, 1985\cr}\vss} etex, -(xpart point infinity of p, 19.5v)); - + 19.5 mpg, expected\cr average for all cars\cr on road, 1985\cr + }\vss} etex, (x7, 19.5v)); label.top(btex \vbox{\halign{\hss\textsc{#}\hss\cr -required fuel economy standards:\cr -new cars built from 1978 to 1985\cr}} etex, -point 5/2 of bbox currentpicture shifted 21 up); - -picture p; p = currentpicture; currentpicture := nullpicture; -bboxmargin := 12; -fill bbox p withcolor 1/32(32, 32, 31); -draw p; - + required fuel economy standards:\cr + new cars built from 1978 to 1985\cr}} etex, + point 5/2 of bbox currentpicture shifted 13 up); endfig; \end{mplibcode} \end{document} - diff --git a/info/drawing-with-metapost/src/tufte-mpg.pdf b/info/drawing-with-metapost/src/tufte-mpg.pdf Binary files differindex 7eac49d2b4..e47d26d17c 100644 --- a/info/drawing-with-metapost/src/tufte-mpg.pdf +++ b/info/drawing-with-metapost/src/tufte-mpg.pdf diff --git a/info/drawing-with-metapost/src/tufte-snow.mp b/info/drawing-with-metapost/src/tufte-snow.mp new file mode 100644 index 0000000000..43df7b435e --- /dev/null +++ b/info/drawing-with-metapost/src/tufte-snow.mp @@ -0,0 +1,67 @@ +\documentclass{standalone} +\usepackage{fontspec} +\setmainfont[Numbers=OldStyle]{TeX Gyre Pagella} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} +input tufte-manila-paper +beginfig(1); + +numeric i, deaths[], ymax, dmax; i = 0; dmax = 0; +for n = 1, + 0, 2, 0, 0, 2, 0, 0, + 1, 0, 1, 2, 3,70,127, + 76,71,45,37,32,30,24, + 18,15, 6,13, 6, 8, 6, + 5, 2, 3, 0, 0, 2, 3, + 0, 0, 2, 0, 2, 1, 0: + deaths[incr i] = n; if n > dmax: dmax := n; fi +endfor +numeric ymax; ymax = 20 * ceiling (dmax / 20); +numeric days, day_number[]; days = 0; +for n = 19, + 20,21,22,23,24,25,26, + 27,28,29,30,31, 1, 2, + 3, 4, 5, 6, 7, 8, 9, + 10,11,12,13,14,15,16, + 17,18,19,20,21,22,23, + 24,25,26,27,28,29,30: + day_number[incr days] = n; +endfor +numeric u, v; days * u = 5in = ymax * 2v; +path xx; xx = origin -- (days * u, 0); draw xx; +path yy; yy = origin -- (0, dmax * v); draw yy; +for x = 1 upto days: + cutdraw (x * u, 0) -- (x * u, deaths[x] * v) + withpen pencircle scaled 2 withcolor 5/8[2/3 red, white]; + draw (origin -- 2 down) shifted (x * u, 0); + if x mod 7 = 2: label.bot("\small" & decimal day_number[x], (x*u, -2)); fi + if x = 1: label.lrt("\small August", (x * u + 1, -12)); + elseif x = 15: label.lrt("\small September", (x * u + 1/2 u, -12)); + fi +endfor +for y = 10 step 10 until ymax: + draw (origin -- 2 left) shifted (0, y * v); + undraw xx shifted (0, y * v) withpen pencircle scaled 1/2; + if y mod 20 = 0: label.lft(decimal y, (-2, y * v)); fi +endfor + +label.lrt(btex \vbox{\openup 0pt\halign{#\hss\cr +Deaths from\cr cholera, each\cr day during\cr the epidemic\cr +}} etex, (u, ymax * v + 6)); + +z0 = (21u, deaths[21] * v ) shifted 2 up; +z1 = z0 shifted (13, 34); +draw z0 -- z1 withpen pencircle scaled 1/4; +label.urt(btex \vbox{\openup 0pt\halign{#\hss\cr +Handle removed from\cr +the Broad Street pump,\cr +Friday 8 September 1854\cr +}} etex, z1 shifted 17 left); + +input show_name +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tufte-snow.pdf b/info/drawing-with-metapost/src/tufte-snow.pdf Binary files differnew file mode 100644 index 0000000000..30e1a000c4 --- /dev/null +++ b/info/drawing-with-metapost/src/tufte-snow.pdf diff --git a/info/drawing-with-metapost/src/tufte-srm-damage.mp b/info/drawing-with-metapost/src/tufte-srm-damage.mp new file mode 100644 index 0000000000..c44b647583 --- /dev/null +++ b/info/drawing-with-metapost/src/tufte-srm-damage.mp @@ -0,0 +1,115 @@ +\documentclass{standalone} +\usepackage{fontspec} +\setmainfont[Numbers=OldStyle]{TeX Gyre Pagella} +\usepackage{luamplib} +\begin{document} +\mplibtextextlabel{enable} +\begin{mplibcode} + +% 1985-01-24 51-C 53° 11 +% 1984-02-03 41-B 57° 4 +% 1986-01-12 61-C 58° 4 +% 1984-04-06 41-C 63° 2 +% 1981-04-12 1 66° 0 +% 1983-04-04 6 67° 0 +% 1984-11-08 51-A 67° 0 +% 1985-04-12 51-D 67° 0 +% 1982-11-11 5 68° 0 +% 1982-03-22 3 69° 0 +% 1981-11-12 2 70° 4 +% 1983-11-28 9 70° 0 +% 1984-08-30 41-D 70° 4 +% 1985-06-17 51-G 70° 0 +% 1983-06-18 7 72° 0 +% 1983-08-30 8 73° 0 +% 1985-04-29 51-B 75° 0 +% 1985-10-30 61-A 75° 4 +% 1985-08-27 51-I 76° 0 +% 1985-11-26 61-B 76° 0 +% 1984-10-05 41-G 78° 0 +% 1985-10-03 51-J 79° 0 +% 1982-06-27 4 80° ? +% 1985-07-29 51-F 81° 0 + +numeric r; r = 1/5; % adjustment of the marks where required... +path damage; damage = origin .. +(53, 11).. +(57, 4).. +(58, 4).. +(63, 2).. +(66, 0).. +(67, 0 + 2r).. +(67, 0).. +(67, 0 - 2r).. +(68, 0).. +(69, 0).. +(70, 4 + r).. +(70, 0 + r).. +(70, 4 - r).. +(70, 0 - r).. +(72, 0).. +(73, 0).. +(75, 0).. +(75, 4).. +(76, 0 + r).. +(76, 0 - r).. +(78, 0).. +(79, 0).. +(81, 0); + +input tufte-manila-paper +beginfig(1); + numeric u, v; u = 10.8; 5u = 4v; + damage := damage xscaled u yscaled v; + + path xx, yy; + xx = (25u, 0) -- (85u, 0); + yy = (0, 0) -- (0, 12v); + + for y = 0, 4, 8, 12: + draw xx shifted (0, y * v) withpen pencircle scaled 1/4 withcolor 3/4; + label.lft(decimal y, (25u - 4, y * v)); + label.rt (decimal y, (85u + 4, y * v)); + endfor + for x = 25 step 5 until 85: + draw yy shifted (x * u, 0) withpen pencircle scaled 1/4 withcolor 3/4; + label(decimal x & "°", (x * u, -16)); + endfor + + for i = 1 upto length damage: + draw point i of damage + withpen pencircle scaled (3/2 r * v) + withcolor 2/3 red; + endfor + + labeloffset := 8; + label.bot("\small SRM 15", point 1 of damage); + label.urt("\small SRM 22", point 18 of damage); + + fill unitsquare shifted -(1/2, 1/2) xscaled 3.9u yscaled 3/8v + shifted (27.5u, 0) + withcolor 3/4[blue, white]; + + z0 = (27.5u, 0v); z1 = (31u, 3v); + + ahlength := 2; ahangle := 30; + drawarrow z1 -- z0 cutafter xx shifted (0, 1/2 v) + withpen pencircle scaled 1/4 ; + + label.rt(btex \vbox to 0pt{\vskip-6pt\openup 0pt\halign{\small #\hss\cr + 26°–29° range of forecast temperatures\cr + (as of 27 January 1986) for the launch\cr + of space shuttle Challenger on 28 January\cr + }\vss} etex, z1 shifted 2 left); + + label.rt(btex \vbox to 0pt{\openup 2pt\halign{#\hss\cr + O-ring damage index,\cr + for each launch\cr + }\vss} etex, (23u, 14.4v)); + +undraw point 1 of bbox currentpicture shifted 2 down; +input show_name +endfig; +\end{mplibcode} +\end{document} + diff --git a/info/drawing-with-metapost/src/tufte-srm-damage.pdf b/info/drawing-with-metapost/src/tufte-srm-damage.pdf Binary files differnew file mode 100644 index 0000000000..96e8da9bdd --- /dev/null +++ b/info/drawing-with-metapost/src/tufte-srm-damage.pdf diff --git a/info/drawing-with-metapost/src/twister.mp b/info/drawing-with-metapost/src/twister.mp deleted file mode 100644 index 802d1a1ab8..0000000000 --- a/info/drawing-with-metapost/src/twister.mp +++ /dev/null @@ -1,31 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -input compass-rose -input colorbrewer-rgb -beginfig(1); -picture O; -O = compass_rose(Blues 8 8, Reds 8 7) scaled 1/2; -%O = thelabel(TEX("\TeX"), origin) scaled 3; - -numeric s; pair p; -s = 108; -p = origin; -draw O shifted p; draw bbox O withcolor 3/4[red, white]; label.urt("\small\texttt{bbox P}", point -1 of bbox O) withcolor 3/4[red, white]; -p := (1s, 0); draw O rotated 30 shifted p; label("\small\texttt{rotated 30}", p shifted 54 down); -p := (2s,+15); draw O shifted p; label("\small\texttt{shifted 15 up}", p shifted 54 down); - -p := ( 0, -1s); draw O scaled 3/4 shifted p; label("\small\texttt{scaled 3/4}", p shifted 54 down); -p := (1s, -1s); draw O xscaled 3/4 shifted p; label("\small\texttt{xscaled 3/4}", p shifted 54 down); -p := (2s, -1s); draw O yscaled 3/4 shifted p; label("\small\texttt{yscaled 3/4}", p shifted 54 down); - -p := ( 0, -2s); draw O slanted 3/4 shifted p; label("\small\texttt{slanted 3/4}", p shifted 54 down); -p := (1s, -2s); draw O zscaled 3/4 dir 21 shifted p; label("\small\texttt{zscaled 3/4 dir 21}", p shifted 54 down); -p := (2s, -2s); draw O reflectedabout(up, down) shifted p; label("\small\texttt{reflectedabout(up, down)}", p shifted 54 down); - -endfig; -\end{mplibcode} -\end{document} - diff --git a/info/drawing-with-metapost/src/twister.pdf b/info/drawing-with-metapost/src/twister.pdf Binary files differdeleted file mode 100644 index 24b6fd8341..0000000000 --- a/info/drawing-with-metapost/src/twister.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/utf8.pdf b/info/drawing-with-metapost/src/utf8.pdf Binary files differdeleted file mode 100644 index 521f8dfc66..0000000000 --- a/info/drawing-with-metapost/src/utf8.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/verbatim-listing.pdf b/info/drawing-with-metapost/src/verbatim-listing.pdf Binary files differdeleted file mode 100644 index 438c727086..0000000000 --- a/info/drawing-with-metapost/src/verbatim-listing.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/verbatim-with-infont.mp b/info/drawing-with-metapost/src/verbatim-with-infont.mp deleted file mode 100644 index 7e4081a8e8..0000000000 --- a/info/drawing-with-metapost/src/verbatim-with-infont.mp +++ /dev/null @@ -1,13 +0,0 @@ -prologues := 3; -outputtemplate := "%j.eps"; -beginfig(1); - string s; s = "\TeX\ sets maths like this $e=mc^2$"; - draw ("1. " & s) infont defaultfont; - draw ("2. " & s) infont "texnansi-lmr10" shifted 20 down; - draw ("3. " & s) infont "cmtt10" shifted 40 down; - draw ("4. " & s) infont "texnansi-lmtt10" shifted 60 down; - bboxmargin := 14; - picture p; p = currentpicture; fill bbox currentpicture withcolor (1,1,31/32); draw p; - draw bbox p; -endfig; -end. diff --git a/info/drawing-with-metapost/src/verbatim-with-infont.pdf b/info/drawing-with-metapost/src/verbatim-with-infont.pdf Binary files differdeleted file mode 100644 index b2b3408c13..0000000000 --- a/info/drawing-with-metapost/src/verbatim-with-infont.pdf +++ /dev/null diff --git a/info/drawing-with-metapost/src/whatever.mp b/info/drawing-with-metapost/src/whatever.mp deleted file mode 100644 index 70b4678182..0000000000 --- a/info/drawing-with-metapost/src/whatever.mp +++ /dev/null @@ -1,48 +0,0 @@ -\documentclass[border=1mm]{standalone} -\usepackage{luatex85} -\usepackage{luamplib} -\usepackage{dwmpcode} -\mplibtextextlabel{enable} -\begin{document} -\hbox to 5.3in{$\vcenter{% -\begin{mplibcode} -beginfig(1); - z1 = (10, 50); - z2 = (80, 190); - z3 = (0, 170); - z4 = (60, 10); - - draw z1--z2; - draw z3--z4; - - z0 = alpha [z1, z2] = beta [z3, z4]; - - forsuffixes @=0,1,2,3,4: - dotlabel.rt("$z_" & decimal @ & "$", z@) - withcolor 2/3 if @=0: red else: blue fi; - endfor - - %label.urt(decimal alpha, (x2, y0)); - %label.lrt(decimal beta, (x2, y0)); - -endfig; -\end{mplibcode}} -\qquad\vcenter{ -\begin{code} -beginfig(1); - z1 = (10, 50); - z2 = (80, 190); - z3 = (0, 170); - z4 = (60, 10); - - z0 = whatever [z1, z2] = whatever [z3, z4]; - - draw z1--z2; - draw z3--z4; - forsuffixes @=0,1,2,3,4: - dotlabel.rt("$z_" & decimal @ & "$", z@) - withcolor 2/3 if @=0: red else: blue fi; - endfor -endfig; -\end{code}}$\hss} -\end{document} diff --git a/info/drawing-with-metapost/src/workflow-plain.mp b/info/drawing-with-metapost/src/workflow-plain.mp index 3d29b50e80..b2fc986f8e 100644 --- a/info/drawing-with-metapost/src/workflow-plain.mp +++ b/info/drawing-with-metapost/src/workflow-plain.mp @@ -32,13 +32,13 @@ beginfig(1); drawarrow point 3/2 of bbox EPS -- point 7/2 of bbox pdf; label.top("\texttt{epstopdf}", 1/2[center EPS, center pdf]); - drawarrow center EPS -- center u - cutbefore bbox EPS cutafter bbox u - dashed withdots scaled 1/2; + % drawarrow center EPS -- center u + % cutbefore bbox EPS cutafter bbox u + % dashed withdots scaled 1/2; - draw center EPS -- center p - cutbefore bbox EPS cutafter bbox p - dashed withdots scaled 1/2; + % draw center EPS -- center p + % cutbefore bbox EPS cutafter bbox p + % dashed withdots scaled 1/2; endfig; \end{mplibcode} diff --git a/info/drawing-with-metapost/src/workflow-plain.pdf b/info/drawing-with-metapost/src/workflow-plain.pdf Binary files differindex fc0eac7888..e055fc421b 100644 --- a/info/drawing-with-metapost/src/workflow-plain.pdf +++ b/info/drawing-with-metapost/src/workflow-plain.pdf diff --git a/info/drawing-with-metapost/src/xypic-example.mp b/info/drawing-with-metapost/src/xypic-example.mp deleted file mode 100644 index 074014c82c..0000000000 --- a/info/drawing-with-metapost/src/xypic-example.mp +++ /dev/null @@ -1,53 +0,0 @@ -\documentclass{standalone} -\usepackage{luamplib} -\begin{document} -\mplibtextextlabel{enable} -\begin{mplibcode} -beginfig(1); - - picture U, XY, X, Y, Z; - z1 = -z2 = (-61, 42); - - U = thelabel("$U$", z1); - XY = thelabel("$X\times_ZY$", origin); - X = thelabel("$X$", (x2, 0)); - Y = thelabel("$Y$", (0, y2)); - Z = thelabel("$Z$", z2); - - forsuffixes @=U, XY, X, Y, Z: draw @; endfor - - ahangle := 20; - vardef connect@#(expr s, a, b) = - curved_connect@#(s, a, b, center b - center a) - enddef; - - vardef curved_connect@#(expr s, a, b, d) = - save line, mark; - - path line; - line = center a {d} .. center b; - interim bboxmargin := 4; - drawarrow line cutbefore bbox a cutafter bbox b; - - picture mark; - mark = thelabel@#("$\scriptstyle " & s & "$", point 1/2 of line); - interim bboxmargin := 1; - unfill bbox mark; draw mark; - enddef; - - connect.bot("p", XY, X); - connect.rt ("q", XY, Y); - connect.top("g", Y, Z); - connect.lft("f", X, Z); - - curved_connect.urt("x", U, X, right); - curved_connect.llft("y", U, Y, dir -80); - - drawoptions(dashed withdots scaled 1/2); - connect("(x,y)", U, XY); - drawoptions(); - - -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/youth.mp b/info/drawing-with-metapost/src/youth.mp deleted file mode 100644 index 77830d6629..0000000000 --- a/info/drawing-with-metapost/src/youth.mp +++ /dev/null @@ -1,12 +0,0 @@ -\documentclass[border=5mm]{standalone} -\usepackage{graphicx} -\usepackage{luamplib} -\begin{document} -\begin{mplibcode} -input picture_frame -beginfig(1); - picture F; F = thelabel(TEX("\includegraphics[width=200pt]{youth.jpg}"), origin); - draw F; draw frame F; -endfig; -\end{mplibcode} -\end{document} diff --git a/info/drawing-with-metapost/src/youth.pdf b/info/drawing-with-metapost/src/youth.pdf Binary files differdeleted file mode 100644 index ad0aee97ca..0000000000 --- a/info/drawing-with-metapost/src/youth.pdf +++ /dev/null diff --git a/info/dtk-bibliography/README.md b/info/dtk-bibliography/README.md index 49799b2fcf..e1439d6165 100644 --- a/info/dtk-bibliography/README.md +++ b/info/dtk-bibliography/README.md @@ -3,7 +3,7 @@ This package contains the bibliography for "Die TeXnische Komödie", the journal of the German-speaking user group. -It is updated on a quarterly basis, last update 2024-03-08: updated for issue 2024-01 +It is updated on a quarterly basis, last update 2024-09-14: updated for issue 2024-03 # How to produce dtk-bibliography.pdf @@ -19,4 +19,4 @@ respectively the (local) texmf tree. # License -This material is subject to the LaTeX Project Public License 1.3c.
\ No newline at end of file +This material is subject to the LaTeX Project Public License 1.3c. diff --git a/info/dtk-bibliography/dtk-bibliography.bib b/info/dtk-bibliography/dtk-bibliography.bib index 27124f1df9..950746cc6e 100644 --- a/info/dtk-bibliography/dtk-bibliography.bib +++ b/info/dtk-bibliography/dtk-bibliography.bib @@ -19741,7 +19741,7 @@ to \LaTeX{} quickly and convincingly}, @article {dtk24.1:wehr:schulphysik, author = {Wehr, Keno}, - title = {\LaTeX und Schulphysik 5: Mechanik und Astronomie}, + title = {\LaTeX\ und Schulphysik 5: Mechanik und Astronomie}, journal = dtk, volume = {36}, number = {1}, @@ -19812,4 +19812,228 @@ to \LaTeX{} quickly and convincingly}, keywords = {hinterbuehne} } + +@article {dtk24.2:sievers:grusswort, + author = {Sievers, Martin}, + title = {Grußwort}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {6}, + pages = {4--5}, + keywords = {grusswort} +} + + +@article {dtk24.2:schaa:protokoll, + author = {Schaa, Volker RW}, + title = {Protokoll der 66. Mitgliederversammlung von Dante e.V. am 6. April 2024 im Goethe-Nationalmuseum in Weimar}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {6}, + pages = {6--12}, + keywords = {hinterbuehne} +} + + +@article {dtk24.2:gasmus:weimar, + author = {Gasmus, Henrik}, + title = {Die diesjährige Frühjahrstagung von Dante e.V. vom 4.--6. April 2024 im Goethe-Nationalmuseum in Weimar}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {6}, + pages = {13--24}, + keywords = {hinterbuehne} +} + +@article {dtk24.2:standtem:chemnitz, + author = {{Team Stand Dante e.V.}}, + title = {Chemnitzer Linux-Tage 24}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {6}, + pages = {24--25}, + keywords = {hinterbuehne} +} + +@article {dtk24.2:wehr:schulphysik, + author = {Wehr, Keno}, + title = {\LaTeX und Schulphysik 6: Feldlinienbilder}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {2}, + pages = {27--51}, + keywords = {bretter} +} + + +@article {dtk24.2:mispelhorn:bilder, + author = {Mispelhorn, Ralf}, + title = {Umgang mit Bildern}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {2}, + pages = {51--58}, + keywords = {bretter} +} + + +@article {dtk24.2:niepraschk:markdown, + author = {Niepraschk, Rolf}, + title = {Von Markdown zu PDF}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {2}, + pages = {59--64}, + keywords = {bretter} +} + + +@article {dtk24.2:ramm:context, + author = {Ramm, Henning Hraban}, + title = {ConTeXt kurz notiert}, + journal = dtk, + volume = {36}, + number = {2}, + date = {2024}, + month = {2}, + pages = {64--68}, + keywords = {fremdebuehne} +} + +@article {dtk24.2:fenn:ctan, + author = {Fenn, Jürgen}, + title = {Neue Pakete auf CTAN}, + journal = dtk, + date = {2024}, + volume = {36}, + number = {2}, + month = {6}, + pages = {69--73}, + keywords = {fremdebuehne} +} + + +@article {dtk24.3:sievers:grusswort, + author = {Sievers, Martin}, + title = {Grußwort}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {4}, + keywords = {grusswort} +} + +@article {dtk24.3:behrendt:bericht, + author = {Doris Behrendt}, + title = {Bericht der Schatzmeisterin}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {5--7}, + keywords = {hinterbuehne} +} + +@article {dtk24.3:neukirchen:einladung, + author = {Leah Neukirchen}, + title = {Einladung zur Bay\TeX~2024 in Neu-Ulm}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {8--9}, + keywords = {hinterbuehne} +} + +@article {dtk24.3:wehr:schulphysik, + author = {Wehr, Keno}, + title = {\LaTeX und Schulphysik 7: Optik}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {10--32}, + keywords = {bretter} +} + +@article {dtk24.3:ziegenhagen:diagrammbeispiel, + author = {Ziegenhagen, Uwe}, + title = {Diagramme mit TikZ: Ein Beispiel}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {32--38}, + keywords = {bretter} +} + +@article {dtk24.3:larsson:moloch, + author = {Larsson, Johann}, + title = {Moloch: Die Wieder-Auferstehung des LaTeX-Beamer-Stils Metropolis}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {39--47}, + keywords = {bretter} +} + +@article {dtk24.3:voss:jetbrains, + author = {Voß, Herbert}, + title = {JetBrains Mono}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {48--58}, + keywords = {bretter} +} + + +@article {dtk24.3:ramm:context, + author = {Ramm, Henning Hraban}, + title = {ConTeXt kurz notiert}, + journal = dtk, + volume = {36}, + number = {3}, + date = {2024}, + month = {9}, + pages = {59--62}, + keywords = {fremdebuehne} +} + +@article {dtk24.3:fenn:ctan, + author = {Fenn, Jürgen}, + title = {Neue Pakete auf CTAN}, + journal = dtk, + date = {2024}, + volume = {36}, + number = {3}, + month = {9}, + pages = {63--66}, + keywords = {fremdebuehne} +} + @Comment{jabref-meta: databaseType:biblatex;} diff --git a/info/dtk-bibliography/dtk-bibliography.pdf b/info/dtk-bibliography/dtk-bibliography.pdf Binary files differindex cd39cc02e0..f77ccc648f 100644 --- a/info/dtk-bibliography/dtk-bibliography.pdf +++ b/info/dtk-bibliography/dtk-bibliography.pdf diff --git a/info/dtk-bibliography/dtk-bibliography.tex b/info/dtk-bibliography/dtk-bibliography.tex index 9aea81db0a..9eb85838e0 100644 --- a/info/dtk-bibliography/dtk-bibliography.tex +++ b/info/dtk-bibliography/dtk-bibliography.tex @@ -22,7 +22,7 @@ \begin{document} -\noindent Compiled on \today~ for DTK 2024-01 +\noindent Compiled on \today~ for DTK 2024-03 \nocite{*} diff --git a/info/install-latex-guide-zh-cn/README.md b/info/install-latex-guide-zh-cn/README.md index 0aea05a14b..9ef9ee18b4 100644 --- a/info/install-latex-guide-zh-cn/README.md +++ b/info/install-latex-guide-zh-cn/README.md @@ -3,7 +3,7 @@ This package will introduce the operations related to installing TeX Live (introducing MacTeX in macOS), upgrading packages, and compiling simple documents on Windows 11, Ubuntu 22.04, and macOS systems, and mainly introducing command line operations. At the same time, it briefly introduces the use of several common editors under different operating systems, and additionally adds some related content using Online LaTeX editor, e.g. [Overleaf](www.overleaf.com). -Users are advised to read [texlive-en](https://www.tug.org/texlive/doc/texlive-en/texlive-en.pdf) and [lshort-zh-cn](http://mirrors.ctan.org/info/lshort/chinese/lshort-zh-cn.pdf) for a more comprehensive understanding of the basic content. +Users are advised to read [texlive-zh-cn](https://www.tug.org/texlive/doc/texlive-zh-cn/texlive-zh-cn.pdf) and [lshort-zh-cn](http://mirrors.ctan.org/info/lshort/chinese/lshort-zh-cn.pdf) for a more comprehensive understanding of the basic content. The code involved in this article also asks users to do more, don't simply copy and paste. @@ -25,7 +25,7 @@ This work is released under the LaTeX Project Public License, v1.3c or later. æœ¬æ–‡å°†ä»‹ç» Windows 11ã€Ubuntu 22.04 å’Œ macOS 系统ä¸å®‰è£… TeX Live (macOS ä¸ä»‹ç» MacTeX)ã€å‡çº§å®åŒ…ã€ç¼–译简易文档的相关æ“作, 并多以介ç»å‘½ä»¤è¡Œæ“作为主. åŒæ—¶ç®€è¦ä»‹ç»ä¸åŒæ“ä½œç³»ç»Ÿä¸‹å‡ æ¬¾å¸¸è§ç¼–辑器的使用方法, 并é¢å¤–补充了一些使用在线 LaTeX 编辑器, 如 [Overleaf](www.overleaf.com), 的相关内容. -建议用户阅读 [texlive-en](https://www.tug.org/texlive/doc/texlive-en/texlive-en.pdf) å’Œ [lshort-zh-cn](http://mirrors.ctan.org/info/lshort/chinese/lshort-zh-cn.pdf) 以更全é¢åœ°äº†è§£åŸºç¡€å†…容. +建议用户阅读 [texlive-zh-cn](https://www.tug.org/texlive/doc/texlive-zh-cn/texlive-zh-cn.pdf) å’Œ [lshort-zh-cn](http://mirrors.ctan.org/info/lshort/chinese/lshort-zh-cn.pdf) 以更全é¢åœ°äº†è§£åŸºç¡€å†…容. 本文所涉åŠåˆ°çš„代ç 还请用户多多动手, ä¸è¦ç®€å•åœ°å¤åˆ¶ç²˜è´´. diff --git a/info/install-latex-guide-zh-cn/appendix/updateinfo.tex b/info/install-latex-guide-zh-cn/appendix/updateinfo.tex index 2615af7b8e..16fb23ec17 100644 --- a/info/install-latex-guide-zh-cn/appendix/updateinfo.tex +++ b/info/install-latex-guide-zh-cn/appendix/updateinfo.tex @@ -2,11 +2,12 @@ \chapter{版本信æ¯} -\section*{v2024.6.1} +\section*{v2024.9.1} \begin{itemize} \item æ·»åŠ é•œåƒ \item 修改对于ä¸å®‰è£…第三方安全软件的建议 + \item Overleaf å‡çº§ä¸º 2024 版 \end{itemize} \section*{v2024.4.1} diff --git a/info/install-latex-guide-zh-cn/chapter/overleaf.tex b/info/install-latex-guide-zh-cn/chapter/overleaf.tex index b35e59fe74..cad91ef833 100644 --- a/info/install-latex-guide-zh-cn/chapter/overleaf.tex +++ b/info/install-latex-guide-zh-cn/chapter/overleaf.tex @@ -16,8 +16,8 @@ Overleaf 是全çƒèŒƒå›´å†…首屈一指的在线 \LaTeX{} 编辑平å°. Overleaf æ供了包括% \href{https://cn.overleaf.com}{ä¸æ–‡}% 在内的多ç§è¯è¨€ä¾›ç”¨æˆ·ä½¿ç”¨. -2023å¹´9月6æ—¥, -\href{https://www.overleaf.com/blog/tex-live-2023-now-available}{它将åŽå°çš„ \TeX{} Live å‡çº§ä¸º 2023 版本}, +2024å¹´6月27æ—¥, +\href{https://www.overleaf.com/blog/tex-live-2024-is-now-available}{它将åŽå°çš„ \TeX{} Live å‡çº§ä¸º 2024 版本}, åŒæ—¶, \href{https://www.overleaf.com/blog/new-feature-select-your-tex-live-compiler-version}{Overleaf 还å…许用户自主选择项目ä¸çš„ \TeX{} Live 版本}. diff --git a/info/install-latex-guide-zh-cn/chapter/preface.tex b/info/install-latex-guide-zh-cn/chapter/preface.tex index feef749555..1370585c74 100644 --- a/info/install-latex-guide-zh-cn/chapter/preface.tex +++ b/info/install-latex-guide-zh-cn/chapter/preface.tex @@ -29,7 +29,7 @@ 本手册所涉åŠåˆ°çš„代ç 需结åˆä¸Šä¸‹æ–‡è¯´æ˜Ž, ä¸èƒ½ç®€å•åœ°å¤åˆ¶ç²˜è´´. 红色文å—都是å¯ç‚¹çš„超链接, å¯ç›´æŽ¥è·³è½¬. \menu{èœå•} 表示软件èœå•. \keys{k} 表示键盘按键. -建议用户阅读 \href{https://www.tug.org/texlive/doc/texlive-en/texlive-en.pdf}{texlive-en} +建议用户阅读 \href{https://tug.org/texlive/doc/texlive-zh-cn/texlive-zh-cn.pdf}{texlive-zh-cn} å’Œ \href{http://mirrors.ctan.org/info/lshort/chinese/lshort-zh-cn.pdf}{lshort-zh-cn} 以更全é¢åœ°äº†è§£åŸºç¡€å†…容. diff --git a/info/install-latex-guide-zh-cn/chapter/ubuntu.tex b/info/install-latex-guide-zh-cn/chapter/ubuntu.tex index 2de534b695..e0e2bd8d90 100644 --- a/info/install-latex-guide-zh-cn/chapter/ubuntu.tex +++ b/info/install-latex-guide-zh-cn/chapter/ubuntu.tex @@ -166,7 +166,7 @@ \end{lstlisting} 刷新å—体缓å˜. è¿™æ ·ä¸€æ¥, \TeX{} Live ä¸çš„å—体æ‰èƒ½å¤Ÿè¢«æ£ç¡®è°ƒç”¨. -更多内容请å‚考 \href{https://www.tug.org/texlive/doc/texlive-en/texlive-en.pdf}{texlive-en}. +更多内容请å‚考 \href{https://tug.org/texlive/doc/texlive-zh-cn/texlive-zh-cn.pdf}{texlive-zh-cn}. 如果用户更改了安装路径, è¦æ³¨æ„å°† @@ -195,7 +195,7 @@ export MANPATH=~/texlive/2024/texmf-dist/doc/man:$MANPATH export INFOPATH=~/texlive/2024/texmf-dist/doc/info:$INFOPATH \end{lstlisting} -有关å—体的处ç†å˜ä¸º\footnote{这里并未使用 \href{https://www.tug.org/texlive/doc/texlive-en/texlive-en.pdf}{texlive-en} ä¸å»ºè®®çš„路径 \texttt{\~/.fonts.conf.d/}, +有关å—体的处ç†å˜ä¸º\footnote{这里并未使用 \href{https://tug.org/texlive/doc/texlive-zh-cn/texlive-zh-cn.pdf}{texlive-zh-cn} ä¸å»ºè®®çš„路径 \texttt{\~/.fonts.conf.d/}, å› ä¸ºæ ¹æ® \href{https://www.freedesktop.org/software/fontconfig/fontconfig-user.html}{freedesktop} 的说法, 该路径已废弃, æ•…æ¤å¤„采用新的路径, diff --git a/info/install-latex-guide-zh-cn/install-latex-guide-zh-cn.pdf b/info/install-latex-guide-zh-cn/install-latex-guide-zh-cn.pdf Binary files differindex 6bb0c3e4b9..af6f27ae4f 100644 --- a/info/install-latex-guide-zh-cn/install-latex-guide-zh-cn.pdf +++ b/info/install-latex-guide-zh-cn/install-latex-guide-zh-cn.pdf diff --git a/info/knuth-hint/README.md b/info/knuth-hint/README.md index 2871f31177..ae25729c4d 100644 --- a/info/knuth-hint/README.md +++ b/info/knuth-hint/README.md @@ -10,8 +10,8 @@ sources and their changes in parallel. Also included is the collection of Although not all the texts here are written or maintained by Donald Knuth, it is more convenient for everything to be collected in one place for reading and searching. They all stem from the system that Knuth created. The central -entry point is the ‘index’ file, with links to the individual HINT documents, -either in HTML or in PDF format. +entry point is the ‘index’ file, with links to the individual documents, either +in HTML or in PDF format. If you believe to have found anything that remains technically, historically, typographically, or politically incorrect in any of these files, please feel @@ -21,4 +21,4 @@ The “License†of the `knuth-hint` package is “Public Domain†and it cove the contents of this package, _not_ the various (and varying) “free software†licenses of the presented software codes. -This is version “2.4†of the `knuth-hint` package — 2024-07-10, Andreas Scherer. +This is version “2.5†of the `knuth-hint` package — 2024-08-12, Andreas Scherer. diff --git a/info/knuth-hint/bibtex/bibtex-changes.hnt b/info/knuth-hint/bibtex/bibtex-changes.hnt Binary files differindex af386a05bd..bb7320d22b 100644 --- a/info/knuth-hint/bibtex/bibtex-changes.hnt +++ b/info/knuth-hint/bibtex/bibtex-changes.hnt diff --git a/info/knuth-hint/bibtex/bibtex.hnt b/info/knuth-hint/bibtex/bibtex.hnt Binary files differindex 5ab7689272..2e70fdd291 100644 --- a/info/knuth-hint/bibtex/bibtex.hnt +++ b/info/knuth-hint/bibtex/bibtex.hnt diff 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With the exception of <code>XeTeX</code>, all documents are in the <code>HINT</code> format and can be viewed with the -<code>hintview</code> program; see <a -href="https://github.com/ruckertm/HINT">the HINT homepage</a> for the -latest version.</p> +<code>hintview</code> program, available from <a +href="https://github.com/ruckertm/HINT">the HINT homepage</a>.</p> <p>The <code>NAMED</code> entries represent the unmodified base sources as written by their respective authors, the attached <code>chg</code> links point to only the changed sections (or modules) as applied for @@ -247,7 +246,9 @@ href="web/weave.hnt"><code>WEAVE</code></a>+<a href="web/weave-changes.hnt"><code>chg</code></a> <a href="web/tangle.hnt"><code>TANGLE</code></a>+<a href="web/tangle-changes.hnt"><code>chg</code></a> <a -href="web/twill.hnt"><code>TWILL</code></a> <span>]</span></p></li> +href="web/twill.hnt"><code>TWILL</code></a><a href="#fn1" +class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a> +<span>]</span></p></li> </ul> <h2 id="complementary-web-programs-by-other-authors">Complementary WEB programs by other authors</h2> @@ -286,7 +287,8 @@ href="cweb/ctangle.hnt"><code>CTANGLE</code></a>+<a href="cweb/ctangle-changes.hnt"><code>chg</code></a> <a href="cweb/cweave.hnt"><code>CWEAVE</code></a>+<a href="cweb/cweave-changes.hnt"><code>chg</code></a><br /> -<a href="cweb/ctwill.hnt"><code>CTWILL</code></a> <a +<a href="cweb/ctwill.hnt"><code>CTWILL</code></a><a href="#fn2" +class="footnote-ref" id="fnref2" role="doc-noteref"><sup>2</sup></a> <a href="cweb/refsort.hnt"><code>REFSORT</code></a>+<a href="cweb/refsort-changes.hnt"><code>chg</code></a> <a href="cweb/twinx.hnt"><code>TWINX</code></a>+<a @@ -303,7 +305,9 @@ href="tie/tie-changes.hnt"><code>chg</code></a> <span>]</span></p></li> href="hitex/hitex.hnt"><code>HiTeX</code></a> <span>]</span></p></li> <li><p><code>mp/</code> <span>[</span> <a href="mp/mp.hnt"><code>MP</code></a> <a -href="mp/mpost.hnt"><code>MPOST</code></a> <span>]</span></p></li> +href="mp/mpost.hnt"><code>MPOST</code></a> <span>]</span><a href="#fn3" +class="footnote-ref" id="fnref3" +role="doc-noteref"><sup>3</sup></a></p></li> </ul> <h2 id="errata-for-computers-typesetting-by-donald-e.-knuth">Errata for “Computers & Typesetting†by Donald E. Knuth</h2> @@ -340,6 +344,24 @@ early 2014</a></p></li> </ul></li> </ul> <h2 id="happy-cweb-programming">Happy C/WEB Programming!</h2> -<p>2024-07-09 Andreas Scherer</p> +<p>2024-08-11 Andreas Scherer</p> +<section id="footnotes" class="footnotes footnotes-end-of-document" +role="doc-endnotes"> +<hr /> +<ol> +<li id="fn1"><p><code>TWILL</code> is presented here as a changed +variant of <code>WEAVE</code>.<a href="#fnref1" class="footnote-back" +role="doc-backlink">↩︎</a></p></li> +<li id="fn2"><p><code>CTWILL</code> is presented here in its own format +with a “mini-index†for every single code section.<a href="#fnref2" +class="footnote-back" 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In part `knuth-pdf` is an update and replacement for the `latex-tds` package. -This is version “2.4†of the `knuth-pdf` package — 2024-07-10, Andreas Scherer. +This is version “2.5†of the `knuth-pdf` package — 2024-08-12, Andreas Scherer. diff --git a/info/knuth-pdf/bibtex/bibtex-changes.pdf b/info/knuth-pdf/bibtex/bibtex-changes.pdf Binary files differindex 51afb72828..92952fed92 100644 --- a/info/knuth-pdf/bibtex/bibtex-changes.pdf +++ b/info/knuth-pdf/bibtex/bibtex-changes.pdf diff --git a/info/knuth-pdf/bibtex/bibtex.pdf b/info/knuth-pdf/bibtex/bibtex.pdf Binary files differindex e925af9e09..d0399eac37 100644 --- a/info/knuth-pdf/bibtex/bibtex.pdf +++ b/info/knuth-pdf/bibtex/bibtex.pdf diff --git a/info/knuth-pdf/ctie/ctie-changes.pdf b/info/knuth-pdf/ctie/ctie-changes.pdf Binary files differindex b5d24bfff0..760f704cf3 100644 --- a/info/knuth-pdf/ctie/ctie-changes.pdf +++ b/info/knuth-pdf/ctie/ctie-changes.pdf diff --git a/info/knuth-pdf/ctie/ctie.pdf b/info/knuth-pdf/ctie/ctie.pdf 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b/info/knuth-pdf/hitex/hitex.pdf Binary files differindex 7b82c521de..b4aa53714d 100644 --- a/info/knuth-pdf/hitex/hitex.pdf +++ b/info/knuth-pdf/hitex/hitex.pdf diff --git a/info/knuth-pdf/index.html b/info/knuth-pdf/index.html index 2dc82d621b..0e8abecfa7 100644 --- a/info/knuth-pdf/index.html +++ b/info/knuth-pdf/index.html @@ -241,7 +241,9 @@ href="web/weave.pdf"><code>WEAVE</code></a>+<a href="web/weave-changes.pdf"><code>chg</code></a> <a href="web/tangle.pdf"><code>TANGLE</code></a>+<a href="web/tangle-changes.pdf"><code>chg</code></a> <a -href="web/twill.pdf"><code>TWILL</code></a> <span>]</span></p></li> +href="web/twill.pdf"><code>TWILL</code></a><a href="#fn1" +class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a> +<span>]</span></p></li> </ul> <h2 id="complementary-web-programs-by-other-authors">Complementary WEB programs by other authors</h2> @@ -280,7 +282,8 @@ href="cweb/ctangle.pdf"><code>CTANGLE</code></a>+<a href="cweb/ctangle-changes.pdf"><code>chg</code></a> <a href="cweb/cweave.pdf"><code>CWEAVE</code></a>+<a href="cweb/cweave-changes.pdf"><code>chg</code></a><br /> -<a href="cweb/ctwill.pdf"><code>CTWILL</code></a> <a +<a href="cweb/ctwill.pdf"><code>CTWILL</code></a><a href="#fn2" +class="footnote-ref" id="fnref2" role="doc-noteref"><sup>2</sup></a> <a href="cweb/refsort.pdf"><code>REFSORT</code></a>+<a href="cweb/refsort-changes.pdf"><code>chg</code></a> <a href="cweb/twinx.pdf"><code>TWINX</code></a>+<a @@ -297,7 +300,9 @@ href="tie/tie-changes.pdf"><code>chg</code></a> <span>]</span></p></li> href="hitex/hitex.pdf"><code>HiTeX</code></a> <span>]</span></p></li> <li><p><code>mp/</code> <span>[</span> <a href="mp/mp.pdf"><code>MP</code></a> <a -href="mp/mpost.pdf"><code>MPOST</code></a> <span>]</span></p></li> +href="mp/mpost.pdf"><code>MPOST</code></a> <span>]</span><a href="#fn3" +class="footnote-ref" id="fnref3" +role="doc-noteref"><sup>3</sup></a></p></li> </ul> <h2 id="errata-for-computers-typesetting-by-donald-e.-knuth">Errata for “Computers & Typesetting†by Donald E. Knuth</h2> @@ -334,6 +339,24 @@ early 2014</a></p></li> </ul></li> </ul> <h2 id="happy-cweb-programming">Happy C/WEB Programming!</h2> -<p>2024-07-09 Andreas Scherer</p> +<p>2024-08-11 Andreas Scherer</p> +<section id="footnotes" class="footnotes footnotes-end-of-document" +role="doc-endnotes"> +<hr /> +<ol> +<li id="fn1"><p><code>TWILL</code> is presented here as a changed +variant of <code>WEAVE</code>.<a href="#fnref1" class="footnote-back" +role="doc-backlink">↩︎</a></p></li> +<li id="fn2"><p><code>CTWILL</code> is presented here in its own format +with “mini-indexes†for every two consecutive pages.<a href="#fnref2" +class="footnote-back" role="doc-backlink">↩︎</a></p></li> +<li id="fn3"><p><code>MP</code> and <code>MPOST</code> have received +quite a few changes “behind the scenes†in order to present them in this +collection; see project <a +href="https://github.com/ascherer/mplibdir"><code>mplibdir</code></a> +for details.<a href="#fnref3" class="footnote-back" +role="doc-backlink">↩︎</a></p></li> +</ol> +</section> </body> </html> diff --git a/info/knuth-pdf/index.pdf b/info/knuth-pdf/index.pdf Binary files differindex cdad14512e..85f27f46d9 100644 --- a/info/knuth-pdf/index.pdf +++ b/info/knuth-pdf/index.pdf diff --git a/info/knuth-pdf/mf/mf-changes.pdf b/info/knuth-pdf/mf/mf-changes.pdf Binary files differindex a16ecb16e3..36174d0916 100644 --- a/info/knuth-pdf/mf/mf-changes.pdf +++ b/info/knuth-pdf/mf/mf-changes.pdf diff --git a/info/knuth-pdf/mf/mf.pdf b/info/knuth-pdf/mf/mf.pdf Binary files differindex 1fd069cfcd..bec4c04e24 100644 --- a/info/knuth-pdf/mf/mf.pdf +++ b/info/knuth-pdf/mf/mf.pdf diff --git a/info/knuth-pdf/mf/trapman.pdf b/info/knuth-pdf/mf/trapman.pdf Binary files differindex b97414ec23..33cfe054a4 100644 --- a/info/knuth-pdf/mf/trapman.pdf +++ b/info/knuth-pdf/mf/trapman.pdf diff --git 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If you -are in my situation then try the Makefile, which does a lot of hacking. - Notes: -1) My version of make4ht requires that I change - \def\IfFileExists#1#2#3{% -to - \long\def\IfFileExists#1#2#3{% -in a local copy of tex4ht.sty. See https://tex.stackexchange.com/a/423729/339 - -2) Repo is here. +This document's git repository is here: https://gitlab.com/jim.hefferon/latex-doc-ptr Comments to: - Jim Hefferon email jhefferon@smcvt.edu + Jim Hefferon email: jim.hefferon@gmail.com History: + 2024-Sep-29 JH, KB Add contact information. 2021-Jan-02 JH, KB Merged with another doc, first-packages. 2009-Mar-24 Jim Hefferon, Manuel Pégourié-Gonnard, Karl Berry diff --git a/info/latex-doc-ptr/latex-doc-ptr.css.replacement b/info/latex-doc-ptr/latex-doc-ptr.css.replacement deleted file mode 100644 index db1fcd494c..0000000000 --- a/info/latex-doc-ptr/latex-doc-ptr.css.replacement +++ /dev/null @@ -1,148 +0,0 @@ - -/* start css.sty */ -.Spectral-Light-osf-t-1x-x-109{} -.Spectral-Bold-osf-t-1x-x-172{font-size:156%;} -.ectt-1095{ font-family: monospace;} -.ectt-1095{ font-family: monospace;} -.ectt-1095{ font-family: monospace;} -.Spectral-Bold-osf-t-1x-x-109{} -.cmr-8{font-size:72%;} -.cmr-6{font-size:54%;} -.cmmi-10x-x-109{font-style: italic;} -.Spectral-Light-osf-t-1{font-size:90%;} -.ectt-1000{font-size:90%; 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- } /* make "name" in `texdoc name' */ diff --git a/info/latex-doc-ptr/latex-doc-ptr.html b/info/latex-doc-ptr/latex-doc-ptr.html index 674de5fabb..a91afeddc9 100644 --- a/info/latex-doc-ptr/latex-doc-ptr.html +++ b/info/latex-doc-ptr/latex-doc-ptr.html @@ -1,778 +1,213 @@ -<?xml version="1.0" encoding="iso-8859-1" ?> -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" - "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> -<!--http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd--> -<html xmlns="http://www.w3.org/1999/xhtml" -> +<!DOCTYPE html> +<html lang='en-US' xml:lang='en-US'> <head><title></title> -<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> -<meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)" /> -<meta name="originator" content="TeX4ht (http://www.tug.org/tex4ht/)" /> -<!-- xhtml,html --> -<meta name="src" content="latex-doc-ptr.tex" /> -<link rel="stylesheet" type="text/css" href="latex-doc-ptr.css" /> -</head><body -> -<div class="center" -> -<!--l. 6--><p class="noindent" > -</p><!--l. 7--><p class="noindent" ><span -class="Spectral-Bold-lf-t-1x-x-172">A First Set of </span><span class="LATEX"><span -class="Spectral-Bold-lf-t-1x-x-172">L</span><span class="A"><span -class="Spectral-Bold-lf-t-1x-x-172">A</span></span><span class="TEX"><span -class="Spectral-Bold-lf-t-1x-x-172">T</span><span -class="E"><span -class="Spectral-Bold-lf-t-1x-x-172">E</span></span><span -class="Spectral-Bold-lf-t-1x-x-172">X</span></span></span> <span -class="Spectral-Bold-lf-t-1x-x-172">Resources</span></p></div> - <div class="columns-2"> -<!--l. 17--><p class="indent" > This page suggests documentation, add-on components, and other resources for a beginning <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> +<meta charset='utf-8' /> +<meta content='TeX4ht (https://tug.org/tex4ht/)' name='generator' /> +<meta content='width=device-width,initial-scale=1' name='viewport' /> +<link href='latex-doc-ptr.css' rel='stylesheet' type='text/css' /> +<meta content='latex-doc-ptr.tex' name='src' /> +</head><body> +<div class='center'> +<!-- l. 6 --><p class='noindent'> +</p><!-- l. 7 --><p class='noindent'><span class='Spectral-Bold-lf-t1-x-x-172'>A First Set of LaTeX Resources</span></p></div> + <div class='columns-2'> +<!-- l. 17 --><p class='indent'> This page suggests documentation, add-on components, and other resources for a beginning LaTeX user. -</p><!--l. 20--><p class="indent" > The links here are to freely available materials, so you can click to see the documentation online. Where -the documentation is also available offline in a typical <span class="TEX">T<span -class="E">E</span>X</span> installation, we provide its name as an end note. -View it by running `<span -class="ectt-1095">texdoc </span><span -class="Spectral-LightItalic-lf-t-1x-x-109">name</span>' in a terminal. +</p><!-- l. 20 --><p class='indent'> The links here are to freely available materials, so you can click to see the documentation online. Where +the documentation is also available offline in a typical TeX installation, we provide its name as an end note. +View it by running ‘<span class='ectt-1095'>texdoc </span><span class='Spectral-LightItalic-lf-t1-x-x-109'>name</span>’ in a terminal. </p> -<h3 class="sectionHead"><a - id="x1-1000"></a>Starting</h3> -<!--l. 32--><p class="noindent" >To run <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>, you must use an online service or install a distribution. Online services are commercial; -find them by entering `online latex' in a search engine. For distributions, your choices are <a -href="https://tug.org/texlive/" ><span class="TEX">T<span -class="E">E</span>X</span> Live</a> on a -Unix system, including GNU/Linux, or on Windows, or the related <a -href="https://tug.org/mactex/" >Mac<span class="TEX">T<span -class="E">E</span>X</span></a> on Macintosh, or <a -href="https://miktex.org/" >MiK<span class="TEX">T<span -class="E">E</span>X</span></a> on + <h3 class='sectionHead' id='starting'><a id='x1-1000'></a>Starting</h3> +<!-- l. 32 --><p class='noindent'>To run LaTeX, you must use an online service or install a distribution. Online services are commercial; find +them by entering ‘online latex’ in a search engine. For distributions, your choices are <a href='https://tug.org/texlive/'>TeX Live</a> on a Unix +system, including GNU/Linux, or on Windows, or the related <a href='https://tug.org/mactex/'>MacTeX</a> on Macintosh, or <a href='https://miktex.org/'>MiKTeX</a> on Windows or a Unix system. -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Tutorials </span>The site <a -href="https://www.learnlatex.org/" ><span -class="ectt-1095">learnlatex.org</span></a> teaches you the basics in a sound way, and also lets you play with the -commands to see the results. For a more traditional document, the most widely recommended one is <a -href="https://ctan.org/pkg/lshort-english" >The -Not-So Short Guide to <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>2<span -class="cmmi-10x-x-109">ε</span></a>, available in many languages.<sup><a -href="#ennote-1" id="enmark-1"><span -class="cmr-8">1</span></a></sup> - <p>Many people use <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> to write mathematical text and for this the premier choice is from the -American Mathematical Society. See their <a -href="http://mirror.ctan.org/info/amslatex/primer/amshelp.pdf" >Getting up and running with AMS-<span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span></a>,<sup><a -href="#ennote-2" id="enmark-2"><span -class="cmr-8">2</span></a></sup> and more detail is -in <a -href="http://mirror.ctan.org/macros/latex/required/amsmath/amsldoc.pdf" >Users Guide for the <span -class="ectt-1095">amsmath </span>package</a>.<sup><a -href="#ennote-3" id="enmark-3"><span -class="cmr-8">3</span></a></sup> +</p><!-- l. 44 --><p class='noindent'> </p> -<h3 class="sectionHead"><a - id="x1-2000"></a>Documentation</h3> -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">References </span>The nearest thing to a general reference for <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> is <a -href="http://mirror.ctan.org/info/latex2e-help-texinfo/latex2e.html" ><span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>2<span -class="cmmi-10x-x-109">ε</span> unofficial reference manual</a>.<sup><a -href="#ennote-4" id="enmark-4"><span -class="cmr-8">4</span></a></sup> -Look for symbols in the <a -href="http://mirror.ctan.org/info/symbols/comprehensive/symbols-letter.pdf" >Comprehensive List of Symbols</a>.<sup><a -href="#ennote-5" id="enmark-5"><span -class="cmr-8">5</span></a></sup> And, <a -href="https://tug.org/TUGboat/" >TUGboat</a>, the journal of the <a -href="https://tug.org" ><span class="TEX">T<span -class="E">E</span>X</span> Users -Group</a>, has published many articles, at levels from beginner to expert, almost since the inception of -<span class="TEX">T<span -class="E">E</span>X</span>. -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">FAQs </span>Many web pages offer quick help with <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>, although they can be out of date. Particularly useful -and reliable are the <a -href="https://texfaq.org/" ><span class="TEX">T<span -class="E">E</span>X</span> FAQ</a>,<sup><a -href="#ennote-6" id="enmark-6"><span -class="cmr-8">6</span></a></sup> as well as <a -href="https://tug.org/interest.html" ><span class="TEX">T<span -class="E">E</span>X</span> Resources on the Web</a>. You can also get a handy -general <a -href="http://mirror.ctan.org/info/latexcheat/latexcheat/latexsheet.pdf" ><span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> Cheat Sheet</a>,<sup><a -href="#ennote-7" id="enmark-7"><span -class="cmr-8">7</span></a></sup> as well as the <a -href="http://mirrors.ctan.org/info/undergradmath/undergradmath.pdf" >Math for Undergraduates Cheat Sheet</a>.<sup><a -href="#ennote-8" id="enmark-8"><span -class="cmr-8">8</span></a></sup> Also, -<a -href="http://mirror.ctan.org/info/l2tabu/english/l2tabuen.pdf" >An essential guide to <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>2<span -class="cmmi-10x-x-109">ε</span> usage</a><sup><a -href="#ennote-9" id="enmark-9"><span -class="cmr-8">9</span></a></sup> helps you develop sound habits, by saying what not to + <h4 class='subsectionHead' id='tutorials'><a id='x1-2000'></a>Tutorials</h4> +<!-- l. 45 --><p class='noindent'>The site <a href='https://www.learnlatex.org/'><span class='ectt-1095'>learnlatex.org</span></a> teaches you the basics in a sound way, and also lets you play with the commands +to see the results. For a more traditional document, the most widely recommended one is <a href='https://ctan.org/pkg/lshort-english'>The Not-So Short +Guide to LaTeX2e</a>, available in many languages.<sup class='textsuperscript'><a href='#ennote-1' id='enmark-1'><span class='Spectral-Light-lf-t1-'>1</span></a></sup> +</p><!-- l. 59 --><p class='indent'> <p>Many people use LaTeX to write mathematical text and for this the premier choice is from the +American Mathematical Society. See their <a href='http://mirror.ctan.org/info/amslatex/primer/amshelp.pdf'>Getting up and running with AMS-LaTeX</a>,<sup class='textsuperscript'><a href='#ennote-2' id='enmark-2'><span class='Spectral-Light-lf-t1-'>2</span></a></sup> and more detail is +in <a href='http://mirror.ctan.org/macros/latex/required/amsmath/amsldoc.pdf'>Users Guide for the <span class='ectt-1095'>amsmath </span>package</a>.<sup class='textsuperscript'><a href='#ennote-3' id='enmark-3'><span class='Spectral-Light-lf-t1-'>3</span></a></sup> +</p><!-- l. 72 --><p class='noindent'> +</p> + <h3 class='sectionHead' id='documentation'><a id='x1-3000'></a>Documentation</h3> +<!-- l. 75 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='references'><a id='x1-4000'></a>References</h4> +<!-- l. 76 --><p class='noindent'>The nearest thing to a general reference for LaTeX is <a href='http://mirror.ctan.org/info/latex2e-help-texinfo/latex2e.html'>LaTeX2e unofficial reference manual</a>.<sup class='textsuperscript'><a href='#ennote-4' id='enmark-4'><span class='Spectral-Light-lf-t1-'>4</span></a></sup> Look for +symbols in the <a href='http://mirror.ctan.org/info/symbols/comprehensive/symbols-letter.pdf'>Comprehensive List of Symbols</a>.<sup class='textsuperscript'><a href='#ennote-5' id='enmark-5'><span class='Spectral-Light-lf-t1-'>5</span></a></sup> And, <a href='https://tug.org/TUGboat/'>TUGboat</a>, the journal of the <a href='https://tug.org'>TeX Users Group</a>, +has published many articles, at levels from beginner to expert, almost since the inception of + + +TeX. +</p><!-- l. 90 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='faqs'><a id='x1-5000'></a>FAQs</h4> +<!-- l. 91 --><p class='noindent'>Many web pages offer quick help with LaTeX, although they can be out of date. Particularly useful and +reliable are the <a href='https://texfaq.org/'>TeX FAQ</a>,<sup class='textsuperscript'><a href='#ennote-6' id='enmark-6'><span class='Spectral-Light-lf-t1-'>6</span></a></sup> as well as <a href='https://tug.org/interest.html'>TeX Resources on the Web</a>. You can also get a handy +general <a href='http://mirror.ctan.org/info/latexcheat/latexcheat/latexsheet.pdf'>LaTeX Cheat Sheet</a>,<sup class='textsuperscript'><a href='#ennote-7' id='enmark-7'><span class='Spectral-Light-lf-t1-'>7</span></a></sup> as well as the <a href='http://mirrors.ctan.org/info/undergradmath/undergradmath.pdf'>Math for Undergraduates Cheat Sheet</a>.<sup class='textsuperscript'><a href='#ennote-8' id='enmark-8'><span class='Spectral-Light-lf-t1-'>8</span></a></sup> Also, +<a href='http://mirror.ctan.org/info/l2tabu/english/l2tabuen.pdf'>An essential guide to LaTeX2e usage</a><sup class='textsuperscript'><a href='#ennote-9' id='enmark-9'><span class='Spectral-Light-lf-t1-'>9</span></a></sup> helps you develop sound habits, by saying what not to do. -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Questions </span>If you are stuck on an issue, the <a -href="https://tex.stackexchange.com/" ><span class="TEX">T<span -class="E">E</span>X</span>-<span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> Stack Exchange</a> site and the mailing list -<a -href="https://lists.tug.org/texhax" >texhax@tug.org</a> are where knowledgeable people hang out. You are likely to find an answer in their past -discussions, which cover decades, and if not then you can post a question yourself. -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Books </span>There are many excellent books about <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>. Visit the <a -href="https://tug.org/books/" ><span class="TEX">T<span -class="E">E</span>X</span> Users Group's book list</a> for a -selection, and for discounts. -<h3 class="sectionHead"><a - id="x1-3000"></a>Packages</h3> -<!--l. 131--><p class="noindent" >One of <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>'s strengths is the tremendous number of available add-on packages. This list covers most of +</p><!-- l. 109 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='questions'><a id='x1-6000'></a>Questions</h4> +<!-- l. 110 --><p class='noindent'>If you are stuck on an issue, the <a href='https://tex.stackexchange.com/'>TeX-LaTeX Stack Exchange</a> site and the mailing list <a href='https://lists.tug.org/texhax'>texhax@tug.org</a> are +where knowledgeable people hang out. You are likely to find an answer in their past discussions, which +cover decades, and if not then you can post a question yourself. +</p><!-- l. 119 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='books'><a id='x1-7000'></a>Books</h4> +<!-- l. 120 --><p class='noindent'><p>There are many excellent books about LaTeX. Visit the <a href='https://tug.org/books/'>TeX Users Group’s book list</a> for a selection, and for +discounts. +</p><!-- l. 129 --><p class='noindent'> +</p> + <h3 class='sectionHead' id='packages'><a id='x1-8000'></a>Packages</h3> +<!-- l. 131 --><p class='noindent'>One of LaTeX’s strengths is the tremendous number of available add-on packages. This list covers most of what beginners want to do. (There are some comments in parentheses that often come up in conjunction +with these recommendations.) +</p><!-- l. 139 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='our-archive'><a id='x1-9000'></a>Our archive</h4> +<!-- l. 140 --><p class='noindent'>The Comprehensive TeX Archive Network, <a href='https://ctan.org'><span class='Spectral-Light-lf-t1-'>CTAN</span></a>, has the latest official versions of the packages that are +in the distributions, along with documentation. <a href='https://ctan.org/topics/cloud'>Browsing by topic</a> can be very handy. +</p><!-- l. 149 --><p class='indent'> <p>If you have trouble finding something, it may be the house package of a journal or institution. Look on +their web page as well as on <span class='Spectral-Light-lf-t1-'>CTAN</span>. -with these recommendations.) -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Our archive </span>The Comprehensive <span class="TEX">T<span -class="E">E</span>X</span> Archive Network, <a -href="https://ctan.org" ><span -class="Spectral-Light-lf-t-1">CTAN</span></a>, has the latest official versions of the -packages that are in the distributions, along with documentation. <a -href="https://ctan.org/topics/cloud" >Browsing by topic</a> can be very -handy. - -<p><p>If you have trouble finding something, it may be the house package of a journal or institution. Look on -their web page as well as on <span -class="Spectral-Light-lf-t-1">CTAN</span>. -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Every document </span>To change page size, margins, and orientation, use <a -href="https://ctan.org/pkg/geometry" ><span -class="ectt-1095">geometry</span></a>.<sup><a -href="#ennote-10" id="enmark-10"><span -class="cmr-8">10</span></a></sup> Get multiple columns -with <a -href="https://ctan.org/pkg/multicol" ><span -class="ectt-1095">multicol</span></a>.<sup><a -href="#ennote-11" id="enmark-11"><span -class="cmr-8">11</span></a></sup> - <p>As referred to above, any document containing significant amounts of mathematics should use the -American Mathematical Society's packages <a -href="https://ctan.org/pkg/amsmath" ><span -class="ectt-1095">amsmath</span></a><sup><a -href="#ennote-12" id="enmark-12"><span -class="cmr-8">12</span></a></sup> and <a -href="https://ctan.org/pkg/amsfonts" ><span -class="ectt-1095">amsfonts</span></a>.<sup><a -href="#ennote-13" id="enmark-13"><span -class="cmr-8">13</span></a></sup> Also use their <a -href="https://ctan.org/pkg/amsthm" ><span -class="ectt-1095">amsthm</span></a><sup><a -href="#ennote-14" id="enmark-14"><span -class="cmr-8">14</span></a></sup> for -producing theorem environments. Notes: (1) <a -href="https://ctan.org/pkg/amsfonts" ><span -class="ectt-1095">amssymb</span></a> inputs <a -href="https://ctan.org/pkg/amsfonts" ><span -class="ectt-1095">amsfonts</span></a> so load the former instead of the -latter, (2) many authors also use the calligraphic characters in <a -href="https://ctan.org/pkg/rsfs" ><span -class="ectt-1095">rsfs</span></a>,<sup><a -href="#ennote-15" id="enmark-15"><span -class="cmr-8">15</span></a></sup> (3) get bold math symbols with <a -href="https://ctan.org/pkg/bm" ><span -class="ectt-1095">bm</span></a>,<sup><a -href="#ennote-16" id="enmark-16"><span -class="cmr-8">16</span></a></sup> -(4) don't load <a -href="https://ctan.org/pkg/amsmath" ><span -class="ectt-1095">amsmath</span></a> directly, instead get it by loading <a -href="https://ctan.org/pkg/mathtools" ><span -class="ectt-1095">mathtools</span></a><sup><a -href="#ennote-17" id="enmark-17"><span -class="cmr-8">17</span></a></sup> for some useful improvements, and -(4) load <a -href="https://ctan.org/pkg/amsthm" ><span -class="ectt-1095">amsthm</span></a> after <a -href="https://ctan.org/pkg/mathtools" ><span -class="ectt-1095">mathtools</span></a>. - <p>Also, include <a -href="https://ctan.org/pkg/microtype" ><span -class="ectt-1095">microtype</span></a>.<sup><a -href="#ennote-18" id="enmark-18"><span -class="cmr-8">18</span></a></sup> It will make your document have fewer awkward lines. -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Inside a document </span>Tweak the layout of lists with <a -href="https://ctan.org/pkg/enumitem" ><span -class="ectt-1095">enumitem</span></a>.<sup><a -href="#ennote-19" id="enmark-19"><span -class="cmr-8">19</span></a></sup> - <p>Enhance captions with <a -href="https://ctan.org/pkg/caption" ><span -class="ectt-1095">caption</span></a><sup><a -href="#ennote-20" id="enmark-20"><span -class="cmr-8">20</span></a></sup> and control floating environments with <a -href="https://ctan.org/pkg/float" ><span -class="ectt-1095">float</span></a>.<sup><a -href="#ennote-21" id="enmark-21"><span -class="cmr-8">21</span></a></sup> (In particular, this -package provides the `<span -class="ectt-1095">H</span>' option to override automatic float placement and put something exactly where you +</p><!-- l. 155 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='every-document'><a id='x1-10000'></a>Every document</h4> +<!-- l. 156 --><p class='noindent'>To change page size, margins, and orientation, use <a href='https://ctan.org/pkg/geometry'><span class='ectt-1095'>geometry</span></a>.<sup class='textsuperscript'><a href='#ennote-10' id='enmark-10'><span class='Spectral-Light-lf-t1-'>10</span></a></sup> Get multiple columns with +<a href='https://ctan.org/pkg/multicol'><span class='ectt-1095'>multicol</span></a>.<sup class='textsuperscript'><a href='#ennote-11' id='enmark-11'><span class='Spectral-Light-lf-t1-'>11</span></a></sup> +</p><!-- l. 160 --><p class='indent'> <p>As referred to above, any document containing significant amounts of mathematics should use the +American Mathematical Society’s packages <a href='https://ctan.org/pkg/amsmath'><span class='ectt-1095'>amsmath</span></a><sup class='textsuperscript'><a href='#ennote-12' id='enmark-12'><span class='Spectral-Light-lf-t1-'>12</span></a></sup> and <a href='https://ctan.org/pkg/amsfonts'><span class='ectt-1095'>amsfonts</span></a>.<sup class='textsuperscript'><a href='#ennote-13' id='enmark-13'><span class='Spectral-Light-lf-t1-'>13</span></a></sup> Also use their <a href='https://ctan.org/pkg/amsthm'><span class='ectt-1095'>amsthm</span></a><sup class='textsuperscript'><a href='#ennote-14' id='enmark-14'><span class='Spectral-Light-lf-t1-'>14</span></a></sup> for +producing theorem environments. Notes: (1) <a href='https://ctan.org/pkg/amsfonts'><span class='ectt-1095'>amssymb</span></a> inputs <a href='https://ctan.org/pkg/amsfonts'><span class='ectt-1095'>amsfonts</span></a> so load the former instead of the +latter, (2) many authors also use the calligraphic characters in <a href='https://ctan.org/pkg/rsfs'><span class='ectt-1095'>rsfs</span></a>,<sup class='textsuperscript'><a href='#ennote-15' id='enmark-15'><span class='Spectral-Light-lf-t1-'>15</span></a></sup> (3) get bold math symbols with <a href='https://ctan.org/pkg/bm'><span class='ectt-1095'>bm</span></a>,<sup class='textsuperscript'><a href='#ennote-16' id='enmark-16'><span class='Spectral-Light-lf-t1-'>16</span></a></sup> +(4) don’t load <a href='https://ctan.org/pkg/amsmath'><span class='ectt-1095'>amsmath</span></a> directly, instead get it by loading <a href='https://ctan.org/pkg/mathtools'><span class='ectt-1095'>mathtools</span></a><sup class='textsuperscript'><a href='#ennote-17' id='enmark-17'><span class='Spectral-Light-lf-t1-'>17</span></a></sup> for some useful improvements, and +(4) load <a href='https://ctan.org/pkg/amsthm'><span class='ectt-1095'>amsthm</span></a> after <a href='https://ctan.org/pkg/mathtools'><span class='ectt-1095'>mathtools</span></a>. +</p><!-- l. 178 --><p class='indent'> <p>Also, include <a href='https://ctan.org/pkg/microtype'><span class='ectt-1095'>microtype</span></a>.<sup class='textsuperscript'><a href='#ennote-18' id='enmark-18'><span class='Spectral-Light-lf-t1-'>18</span></a></sup> It will make your document have fewer awkward lines. +</p><!-- l. 185 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='inside-a-document'><a id='x1-11000'></a>Inside a document</h4> +<!-- l. 186 --><p class='noindent'>Tweak the layout of lists with <a href='https://ctan.org/pkg/enumitem'><span class='ectt-1095'>enumitem</span></a>.<sup class='textsuperscript'><a href='#ennote-19' id='enmark-19'><span class='Spectral-Light-lf-t1-'>19</span></a></sup> +</p><!-- l. 188 --><p class='indent'> <p>Enhance captions with <a href='https://ctan.org/pkg/caption'><span class='ectt-1095'>caption</span></a><sup class='textsuperscript'><a href='#ennote-20' id='enmark-20'><span class='Spectral-Light-lf-t1-'>20</span></a></sup> and control floating environments with <a href='https://ctan.org/pkg/float'><span class='ectt-1095'>float</span></a>.<sup class='textsuperscript'><a href='#ennote-21' id='enmark-21'><span class='Spectral-Light-lf-t1-'>21</span></a></sup> (In particular, this +package provides the ‘<span class='ectt-1095'>H</span>’ option to override automatic float placement and put something exactly where you ask. This may cause issues — what if you want to include a two inch tall graphic on a page that has only an inch left? — but it sometimes is what you want.) - <p>Get hyperlinks and turn references into links with <a -href="https://ctan.org/pkg/hyperref" ><span -class="ectt-1095">hyperref</span></a><sup><a -href="#ennote-22" id="enmark-22"><span -class="cmr-8">22</span></a></sup> (make sure to set it up, as with -<span class="lstinline"></span><span -class="ectt-1000">\</span><span -class="ectt-1000">hypersetup</span><span -class="ectt-1000">{</span><span -class="ectt-1000">colorlinks</span><span -class="ectt-1000">=</span><span -class="ectt-1000">true</span><span -class="ectt-1000">}</span>). Have cross-references that say `Theorem 1.2' instead of just `1.2' with -<a -href="https://ctan.org/pkg/cleveref" ><span -class="ectt-1095">cleveref</span></a>.<sup><a -href="#ennote-23" id="enmark-23"><span -class="cmr-8">23</span></a></sup> For <span -class="Spectral-Light-lf-t-1">URL</span>'s and file paths that can break across lines, use <a -href="https://ctan.org/pkg/url" ><span -class="ectt-1095">url</span></a>.<sup><a -href="#ennote-24" id="enmark-24"><span -class="cmr-8">24</span></a></sup> (If you use <a -href="https://ctan.org/pkg/hyperref" ><span -class="ectt-1095">hyperref</span></a> then note -that it has its own commands for the <a -href="https://ctan.org/pkg/cleveref" ><span -class="ectt-1095">cleveref</span></a> and <a -href="https://ctan.org/pkg/url" ><span -class="ectt-1095">url</span></a> functions.) - <p>Inside verbatim text, make single quotes come out correctly with <a -href="https://ctan.org/pkg/upquote" ><span -class="ectt-1095">upquote</span></a>.<sup><a -href="#ennote-25" id="enmark-25"><span -class="cmr-8">25</span></a></sup> For including computer -code, the <a -href="https://ctan.org/pkg/listings" ><span -class="ectt-1095">listings</span></a><sup><a -href="#ennote-26" id="enmark-26"><span -class="cmr-8">26</span></a></sup> package is very popular. (Copy and paste for computer code is especially convenient. -This is a start for the <a -href="https://ctan.org/pkg/listings" ><span -class="ectt-1095">listings</span></a> package. </p><!--l. 219--> - <div class="lstlisting" id="listing-1"><span class="label"><a - id="x1-3001r1"></a></span><span -class="ectt-1000">\</span><span -class="ectt-1000">lstset</span><span -class="ectt-1000">{</span><span -class="ectt-1000">basicstyle</span><span -class="ectt-1000">=\</span><span -class="ectt-1000">ttfamily</span><span -class="ectt-1000">,</span><span -class="ectt-1000"> </span><br /><span class="label"><a - id="x1-3002r2"></a></span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000">keepspaces</span><span -class="ectt-1000">=</span><span -class="ectt-1000">true</span><span -class="ectt-1000">,</span><span -class="ectt-1000"> </span><br /><span class="label"><a - id="x1-3003r3"></a></span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000"> </span><span -class="ectt-1000">columns</span><span -class="ectt-1000">=</span><span -class="ectt-1000">fullflexible</span><span -class="ectt-1000">}</span> +</p><!-- l. 199 --><p class='indent'> <p>Get hyperlinks and turn references into links with <a href='https://ctan.org/pkg/hyperref'><span class='ectt-1095'>hyperref</span></a><sup class='textsuperscript'><a href='#ennote-22' id='enmark-22'><span class='Spectral-Light-lf-t1-'>22</span></a></sup> (make sure to set it up, as with +<code class='lstinline'><span style='color:#000000'>\hypersetup{colorlinks=true}</span></code>). Have cross-references that say ‘Theorem 1.2’ instead of just ‘1.2’ with +<a href='https://ctan.org/pkg/cleveref'><span class='ectt-1095'>cleveref</span></a>.<sup class='textsuperscript'><a href='#ennote-23' id='enmark-23'><span class='Spectral-Light-lf-t1-'>23</span></a></sup> For <span class='Spectral-Light-lf-t1-'>URL</span>’s and file paths that can break across lines, use <a href='https://ctan.org/pkg/url'><span class='ectt-1095'>url</span></a>.<sup class='textsuperscript'><a href='#ennote-24' id='enmark-24'><span class='Spectral-Light-lf-t1-'>24</span></a></sup> (If you use <a href='https://ctan.org/pkg/hyperref'><span class='ectt-1095'>hyperref</span></a> then note +that it has its own commands for the <a href='https://ctan.org/pkg/cleveref'><span class='ectt-1095'>cleveref</span></a> and <a href='https://ctan.org/pkg/url'><span class='ectt-1095'>url</span></a> functions.) +</p><!-- l. 210 --><p class='indent'> <p>Inside verbatim text, make single quotes come out correctly with <a href='https://ctan.org/pkg/upquote'><span class='ectt-1095'>upquote</span></a>.<sup class='textsuperscript'><a href='#ennote-25' id='enmark-25'><span class='Spectral-Light-lf-t1-'>25</span></a></sup> For including computer +code, the <a href='https://ctan.org/pkg/listings'><span class='ectt-1095'>listings</span></a><sup class='textsuperscript'><a href='#ennote-26' id='enmark-26'><span class='Spectral-Light-lf-t1-'>26</span></a></sup> package is very popular. (Copy and paste for computer code is especially convenient. +This is a start for the <a href='https://ctan.org/pkg/listings'><span class='ectt-1095'>listings</span></a> package. </p><!-- l. 219 --> + <pre class='lstlisting' id='listing-2'><span class='label'><a id='x1-11001r1'></a></span><span style='color:#000000'><span class='ectt-1000'>\</span></span><span style='color:#000000'><span class='ectt-1000'>lstset</span></span><span style='color:#000000'><span class='ectt-1000'>{</span></span><span style='color:#000000'><span class='ectt-1000'>basicstyle</span></span><span style='color:#000000'><span class='ectt-1000'>=\</span></span><span style='color:#000000'><span class='ectt-1000'>ttfamily</span></span><span style='color:#000000'><span class='ectt-1000'>,</span></span> +<span class='label'><a id='x1-11002r2'></a></span><span style='color:#000000'> <span class='ectt-1000'>keepspaces=true,</span> +</span><span class='label'><a id='x1-11003r3'></a></span><span style='color:#000000'> <span class='ectt-1000'>columns=fullflexible}</span></span></pre> - </div> - But it is not a full solution. The results depend on the <span -class="Spectral-Light-lf-t-1">PDF </span>viewer and worse, if your code line begins +<!-- l. 224 --><p class='indent'> But it is not a full solution. The results depend on the <span class='Spectral-Light-lf-t1-'>PDF </span>viewer and worse, if your code line begins with blank spaces then after copy and paste those spaces are gone.) - <p>If you use Python, <a -href="https://ctan.org/pkg/pythontex" ><span -class="ectt-1095">pythontex</span></a><sup><a -href="#ennote-27" id="enmark-27"><span -class="cmr-8">27</span></a></sup> will show code listings, but it also allows you to execute Python and put -the results in your output. Do the same for the <span -class="Spectral-LightItalic-lf-t-1x-x-109">Sage </span>mathematics software with <a -href="https://ctan.org/pkg/sagetex" ><span -class="ectt-1095">sagetex</span></a>, and similar +</p><!-- l. 229 --><p class='indent'> <p>If you use Python, <a href='https://ctan.org/pkg/pythontex'><span class='ectt-1095'>pythontex</span></a><sup class='textsuperscript'><a href='#ennote-27' id='enmark-27'><span class='Spectral-Light-lf-t1-'>27</span></a></sup> will show code listings, but it also allows you to execute Python and put +the results in your output. Do the same for the <span class='Spectral-LightItalic-lf-t1-x-x-109'>Sage </span>mathematics software with <a href='https://ctan.org/pkg/sagetex'><span class='ectt-1095'>sagetex</span></a>, and similar support exists for other languages. - <p>There are many packages that add table capabilities, such as multirow entries and breaking across -pages. The first package to try is <a -href="https://ctan.org/pkg/array" ><span -class="ectt-1095">array</span></a>,<sup><a -href="#ennote-28" id="enmark-28"><span -class="cmr-8">28</span></a></sup> which lets you define your own column types. To handle -scientific units, use <a -href="https://ctan.org/pkg/siunitx" ><span -class="ectt-1095">siunitx</span></a><sup><a -href="#ennote-29" id="enmark-29"><span -class="cmr-8">29</span></a></sup> (which also has a table column type for aligning on a decimal +</p><!-- l. 238 --><p class='indent'> <p>There are many packages that add table capabilities, such as multirow entries and breaking across +pages. The first package to try is <a href='https://ctan.org/pkg/array'><span class='ectt-1095'>array</span></a>,<sup class='textsuperscript'><a href='#ennote-28' id='enmark-28'><span class='Spectral-Light-lf-t1-'>28</span></a></sup> which lets you define your own column types. To handle +scientific units, use <a href='https://ctan.org/pkg/siunitx'><span class='ectt-1095'>siunitx</span></a><sup class='textsuperscript'><a href='#ennote-29' id='enmark-29'><span class='Spectral-Light-lf-t1-'>29</span></a></sup> (which also has a table column type for aligning on a decimal point). - <p>Make boxes that are colored or framed, such as boxes for theorems, with <a -href="https://ctan.org/pkg/tcolorbox" ><span -class="ectt-1095">tcolorbox</span></a>.<sup><a -href="#ennote-30" id="enmark-30"><span -class="cmr-8">30</span></a></sup> - <p>Use <a -href="https://ctan.org/pkg/babel" ><span -class="ectt-1095">babel</span></a><sup><a -href="#ennote-31" id="enmark-31"><span -class="cmr-8">31</span></a></sup> for internationalization, including changing the title of the abstract or the bibliography. -(Note that <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> now defaults to UTF-8 encoded input.) - <p>Finally, when developing a document, you often want to generate filler text. Use <a -href="https://ctan.org/pkg/lipsum" ><span -class="ectt-1095">lipsum</span></a>.<sup><a -href="#ennote-32" id="enmark-32"><span -class="cmr-8">32</span></a></sup> -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Color and graphics </span>For colors, use <a -href="https://ctan.org/pkg/xcolor" ><span -class="ectt-1095">xcolor</span></a>.<sup><a -href="#ennote-33" id="enmark-33"><span -class="cmr-8">33</span></a></sup> - <p>To include graphics and do simple manipulations such as resizing, use <a -href="https://ctan.org/pkg/graphicx" ><span -class="ectt-1095">graphicx</span></a>.<sup><a -href="#ennote-34" id="enmark-34"><span -class="cmr-8">34</span></a></sup> Use the <span -class="Spectral-Light-lf-t-1">JPG </span>format -for photos, <span -class="Spectral-Light-lf-t-1">PNG </span>for other kinds of raster graphics, and <span -class="Spectral-Light-lf-t-1">PDF </span>for vector graphics. If your graphic is in another +</p><!-- l. 247 --><p class='indent'> <p>Make boxes that are colored or framed, such as boxes for theorems, with <a href='https://ctan.org/pkg/tcolorbox'><span class='ectt-1095'>tcolorbox</span></a>.<sup class='textsuperscript'><a href='#ennote-30' id='enmark-30'><span class='Spectral-Light-lf-t1-'>30</span></a></sup> +</p><!-- l. 251 --><p class='indent'> Use <a href='https://ctan.org/pkg/babel'><span class='ectt-1095'>babel</span></a><sup class='textsuperscript'><a href='#ennote-31' id='enmark-31'><span class='Spectral-Light-lf-t1-'>31</span></a></sup> for internationalization, including changing the title of the abstract or the bibliography. +(Note that LaTeX now defaults to UTF-8 encoded input.) +</p><!-- l. 256 --><p class='indent'> <p>Finally, when developing a document, you often want to generate filler text. Use <a href='https://ctan.org/pkg/lipsum'><span class='ectt-1095'>lipsum</span></a>.<sup class='textsuperscript'><a href='#ennote-32' id='enmark-32'><span class='Spectral-Light-lf-t1-'>32</span></a></sup> -format then convert it to one of these three. (Usually in your <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> source, you give the file name without -the extension, as with <span class="lstinline"></span><span -class="ectt-1000">\</span><span -class="ectt-1000">includegraphics</span><span -class="ectt-1000">{</span><span -class="ectt-1000">myplot</span><span -class="ectt-1000">}</span>.) Include parts of an outside <span -class="Spectral-Light-lf-t-1">PDF </span>document with -<a -href="https://ctan.org/pkg/pdfpages" ><span -class="ectt-1095">pdfpages</span></a>.<sup><a -href="#ennote-35" id="enmark-35"><span -class="cmr-8">35</span></a></sup> Include video or sound using <a -href="https://ctan.org/pkg/media9" ><span -class="ectt-1095">media9</span></a>.<sup><a -href="#ennote-36" id="enmark-36"><span -class="cmr-8">36</span></a></sup> - <p>In your plots and graphics, you want that the fonts and notations match your document. You have a few -choices. Draw inside your document with <a -href="https://ctan.org/pkg/pgf" >Ti<span -class="Spectral-LightItalic-lf-t-1x-x-109">k</span>Z</a>.<sup><a -href="#ennote-37" id="enmark-37"><span -class="cmr-8">37</span></a></sup> You can instead draw using an external command -language such as <a -href="https://asymptote.sourceforge.io/" >Asymptote</a>,<sup><a -href="#ennote-38" id="enmark-38"><span -class="cmr-8">38</span></a></sup> and bring the results in as graphics. And there are other options, such as -that the <a -href="http://www.gnuplot.info/" >Gnuplot</a> plotting software will output Ti<span -class="Spectral-LightItalic-lf-t-1x-x-109">k</span>Z commands, and the <a -href="https://inkscape.org/" >Inkscape</a> vector graphics editor -allows you to embed <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>-generated equations. -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Front and back matter, headers, footers </span>To style chapter and section titles, use <a -href="https://ctan.org/pkg/titlesec" ><span -class="ectt-1095">titlesec</span></a>.<sup><a -href="#ennote-39" id="enmark-39"><span -class="cmr-8">39</span></a></sup> For page -headers and footers, reach for <a -href="https://ctan.org/pkg/fancyhdr" ><span -class="ectt-1095">fancyhdr</span></a>.<sup><a -href="#ennote-40" id="enmark-40"><span -class="cmr-8">40</span></a></sup> You can tweak the format of tables of contents, lists of figures, -etc., with <a -href="https://ctan.org/pkg/tocloft" ><span -class="ectt-1095">tocloft</span></a>.<sup><a -href="#ennote-41" id="enmark-41"><span -class="cmr-8">41</span></a></sup> - <p>For footnotes, use <a -href="https://ctan.org/pkg/footmisc" ><span -class="ectt-1095">footmisc</span></a>.<sup><a -href="#ennote-42" id="enmark-42"><span -class="cmr-8">42</span></a></sup> Make an index with <a -href="https://ctan.org/pkg/makeindex" ><span -class="ectt-1095">makeindex</span></a>.<sup><a -href="#ennote-43" id="enmark-43"><span -class="cmr-8">43</span></a></sup> With <a -href="https://ctan.org/pkg/answers" ><span -class="ectt-1095">answers</span></a><sup><a -href="#ennote-44" id="enmark-44"><span -class="cmr-8">44</span></a></sup> you can send exercise -answers to an external file, where you can make them a separate document or include them at the end of the -current one. - <p>Bibliographies are a thorny area. Often you have strict requirements, such as from the <a -href="https://ctan.org/pkg/MLA" ><span -class="ectt-1095">MLA</span></a>.<sup><a -href="#ennote-45" id="enmark-45"><span -class="cmr-8">45</span></a></sup> <span -class="Spectral-Light-lf-t-1">CTAN </span>is a -big help here; check out the many styles for both <a -href="https://ctan.org/topic/bibtex-sty" >B<span -class="Spectral-Light-lf-sc-t-1x-x-109">ib</span><span class="TEX">T<span -class="E">E</span>X</span></a><sup><a -href="#ennote-46" id="enmark-46"><span -class="cmr-8">46</span></a></sup> and <a -href="https://ctan.org/topic/biblatex" >B<span -class="Spectral-Light-lf-sc-t-1x-x-109">ib</span><span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span></a>.<sup><a -href="#ennote-47" id="enmark-47"><span -class="cmr-8">47</span></a></sup> -<p class="subsection"><span -class="Spectral-Bold-lf-t-1x-x-109">Special documents </span>Make exams and problem sets with the <a -href="https://ctan.org/pkg/exam" ><span -class="ectt-1095">exam</span></a><sup><a -href="#ennote-48" id="enmark-48"><span -class="cmr-8">48</span></a></sup> class. - <p>There are many, many resume and CV packages. Start with <span -class="Spectral-Light-lf-t-1">CTAN</span>'s <a -href="https://ctan.org/topic/cv" >cv topic</a>. - <p>To make presentations, use the <a -href="https://ctan.org/pkg/beamer" ><span -class="ectt-1095">beamer</span></a><sup><a -href="#ennote-49" id="enmark-49"><span -class="cmr-8">49</span></a></sup> class. (However, with this package you are entering another +</p><!-- l. 263 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='color-and-graphics'><a id='x1-12000'></a>Color and graphics</h4> +<!-- l. 264 --><p class='noindent'>For colors, use <a href='https://ctan.org/pkg/xcolor'><span class='ectt-1095'>xcolor</span></a>.<sup class='textsuperscript'><a href='#ennote-33' id='enmark-33'><span class='Spectral-Light-lf-t1-'>33</span></a></sup> +</p><!-- l. 267 --><p class='indent'> <p>To include graphics and do simple manipulations such as resizing, use <a href='https://ctan.org/pkg/graphicx'><span class='ectt-1095'>graphicx</span></a>.<sup class='textsuperscript'><a href='#ennote-34' id='enmark-34'><span class='Spectral-Light-lf-t1-'>34</span></a></sup> Use the <span class='Spectral-Light-lf-t1-'>JPG </span>format +for photos, <span class='Spectral-Light-lf-t1-'>PNG </span>for other kinds of raster graphics, and <span class='Spectral-Light-lf-t1-'>PDF </span>for vector graphics. If your graphic is in another +format then convert it to one of these three. (Usually in your LaTeX source, you give the file name without +the extension, as with <code class='lstinline'><span style='color:#000000'>\includegraphics{myplot}</span></code>.) Include parts of an outside <span class='Spectral-Light-lf-t1-'>PDF </span>document with +<a href='https://ctan.org/pkg/pdfpages'><span class='ectt-1095'>pdfpages</span></a>.<sup class='textsuperscript'><a href='#ennote-35' id='enmark-35'><span class='Spectral-Light-lf-t1-'>35</span></a></sup> Include video or sound using <a href='https://ctan.org/pkg/media9'><span class='ectt-1095'>media9</span></a>.<sup class='textsuperscript'><a href='#ennote-36' id='enmark-36'><span class='Spectral-Light-lf-t1-'>36</span></a></sup> +</p><!-- l. 280 --><p class='indent'> <p>In your plots and graphics, you want that the fonts and notations match your document. You have a few +choices. Draw inside your document with <a href='https://ctan.org/pkg/pgf'>Ti<span class='Spectral-LightItalic-lf-t1-x-x-109'>k</span>Z</a>.<sup class='textsuperscript'><a href='#ennote-37' id='enmark-37'><span class='Spectral-Light-lf-t1-'>37</span></a></sup> You can instead draw using an external command +language such as <a href='https://asymptote.sourceforge.io/'>Asymptote</a>,<sup class='textsuperscript'><a href='#ennote-38' id='enmark-38'><span class='Spectral-Light-lf-t1-'>38</span></a></sup> and bring the results in as graphics. And there are other options, such as +that the <a href='http://www.gnuplot.info/'>Gnuplot</a> plotting software will output Ti<span class='Spectral-LightItalic-lf-t1-x-x-109'>k</span>Z commands, and the <a href='https://inkscape.org/'>Inkscape</a> vector graphics editor +allows you to embed LaTeX-generated equations. +</p><!-- l. 296 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='front-and-back-matter-headers-footers'><a id='x1-13000'></a>Front and back matter, headers, footers</h4> +<!-- l. 297 --><p class='noindent'>To style chapter and section titles, use <a href='https://ctan.org/pkg/titlesec'><span class='ectt-1095'>titlesec</span></a>.<sup class='textsuperscript'><a href='#ennote-39' id='enmark-39'><span class='Spectral-Light-lf-t1-'>39</span></a></sup> For page headers and footers, reach for <a href='https://ctan.org/pkg/fancyhdr'><span class='ectt-1095'>fancyhdr</span></a>.<sup class='textsuperscript'><a href='#ennote-40' id='enmark-40'><span class='Spectral-Light-lf-t1-'>40</span></a></sup> +You can tweak the format of tables of contents, lists of figures, etc., with <a href='https://ctan.org/pkg/tocloft'><span class='ectt-1095'>tocloft</span></a>.<sup class='textsuperscript'><a href='#ennote-41' id='enmark-41'><span class='Spectral-Light-lf-t1-'>41</span></a></sup> +</p><!-- l. 305 --><p class='indent'> <p>For footnotes, use <a href='https://ctan.org/pkg/footmisc'><span class='ectt-1095'>footmisc</span></a>.<sup class='textsuperscript'><a href='#ennote-42' id='enmark-42'><span class='Spectral-Light-lf-t1-'>42</span></a></sup> Make an index with <a href='https://ctan.org/pkg/makeindex'><span class='ectt-1095'>makeindex</span></a>.<sup class='textsuperscript'><a href='#ennote-43' id='enmark-43'><span class='Spectral-Light-lf-t1-'>43</span></a></sup> With <a href='https://ctan.org/pkg/answers'><span class='ectt-1095'>answers</span></a><sup class='textsuperscript'><a href='#ennote-44' id='enmark-44'><span class='Spectral-Light-lf-t1-'>44</span></a></sup> you can send +exercise answers to an external file, where you can make them a separate document or include them at the +end of the current one. +</p><!-- l. 313 --><p class='indent'> <p>Bibliographies are a thorny area. Often you have strict requirements, such as from the <a href='https://ctan.org/pkg/MLA'><span class='ectt-1095'>MLA</span></a>.<sup class='textsuperscript'><a href='#ennote-45' id='enmark-45'><span class='Spectral-Light-lf-t1-'>45</span></a></sup> <span class='Spectral-Light-lf-t1-'>CTAN </span>is a +big help here; check out the many styles for both <a href='https://ctan.org/topic/bibtex-sty'>B<span class='Spectral-Light-lf-sc-t1-x-x-109'>ib</span>TeX</a><sup class='textsuperscript'><a href='#ennote-46' id='enmark-46'><span class='Spectral-Light-lf-t1-'>46</span></a></sup> and <a href='https://ctan.org/topic/biblatex'>B<span class='Spectral-Light-lf-sc-t1-x-x-109'>ib</span>LaTeX</a>.<sup class='textsuperscript'><a href='#ennote-47' id='enmark-47'><span class='Spectral-Light-lf-t1-'>47</span></a></sup> +</p><!-- l. 324 --><p class='noindent'> +</p> + <h4 class='subsectionHead' id='special-documents'><a id='x1-14000'></a>Special documents</h4> +<!-- l. 325 --><p class='noindent'>Make exams and problem sets with the <a href='https://ctan.org/pkg/exam'><span class='ectt-1095'>exam</span></a><sup class='textsuperscript'><a href='#ennote-48' id='enmark-48'><span class='Spectral-Light-lf-t1-'>48</span></a></sup> class. +</p><!-- l. 329 --><p class='indent'> <p>There are many, many resume and CV packages. Start with <span class='Spectral-Light-lf-t1-'>CTAN</span>’s <a href='https://ctan.org/topic/cv'>cv topic</a>. +</p><!-- l. 333 --><p class='indent'> <p>To make presentations, use the <a href='https://ctan.org/pkg/beamer'><span class='ectt-1095'>beamer</span></a><sup class='textsuperscript'><a href='#ennote-49' id='enmark-49'><span class='Spectral-Light-lf-t1-'>49</span></a></sup> class. (However, with this package you are entering another world, where many of the packages discussed here do not work. For example, section title styling happens via a completely different mechanism.) -<h3 class="sectionHead"><a - id="x1-4000"></a>Fonts and engines</h3> -<!--l. 344--><p class="noindent" >The documentation for font use commands from the <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> developers is <a -href="http://mirror.ctan.org/macros/latex/base/fntguide.pdf" ><span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span>2<span -class="cmmi-10x-x-109">ε</span> font selection</a>.<sup><a -href="#ennote-50" id="enmark-50"><span -class="cmr-8">50</span></a></sup> -</p><!--l. 348--><p class="indent" > To move beyond the default fonts, visit the <a -href="https://tug.org/FontCatalogue/" ><span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> Font Catalogue</a>, which includes copy and paste code +</p><!-- l. 343 --><p class='noindent'> +</p> + <h3 class='sectionHead' id='fonts-and-engines'><a id='x1-15000'></a>Fonts and engines</h3> +<!-- l. 344 --><p class='noindent'>The documentation for font use commands from the LaTeX developers is <a href='http://mirror.ctan.org/macros/latex/base/fntguide.pdf'>LaTeX2e font selection</a>.<sup class='textsuperscript'><a href='#ennote-50' id='enmark-50'><span class='Spectral-Light-lf-t1-'>50</span></a></sup> +</p><!-- l. 348 --><p class='indent'> To move beyond the default fonts, visit the <a href='https://tug.org/FontCatalogue/'>LaTeX Font Catalogue</a>, which includes copy and paste code to make each one work. -</p><!--l. 353--><p class="indent" > Beyond that list, you can also use your computer system's fonts (beware this makes your source -harder to share with friends, though). The background is: to convert <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> source to <span -class="Spectral-Light-lf-t-1">PDF</span> -output there are three varieties of the <span class="TEX">T<span -class="E">E</span>X</span> engine. Currently the most common is <a -href="https://tug.org/applications/pdftex/" >pdf<span class="TEX">T<span -class="E">E</span>X</span></a>.<sup><a -href="#ennote-51" id="enmark-51"><span -class="cmr-8">51</span></a></sup> -For instance, this document was generated with <span class="obeylines-h"><span class="verb"><span -class="ectt-1095">pdflatex</span><span -class="ectt-1095"> latex-doc-ptr.tex</span></span></span>. Two further -developments, <a -href="https://tug.org/xetex/" >Xe<span class="TEX">T<span -class="E">E</span>X</span></a>,<sup><a -href="#ennote-52" id="enmark-52"><span -class="cmr-8">52</span></a></sup> and <a -href="http://www.luatex.org/" >Lua<span class="TEX">T<span -class="E">E</span>X</span></a>,<sup><a -href="#ennote-53" id="enmark-53"><span -class="cmr-8">53</span></a></sup> can leverage the <a -href="https://ctan.org/pkg/fontspec" ><span -class="ectt-1095">fontspec</span></a><sup><a -href="#ennote-54" id="enmark-54"><span -class="cmr-8">54</span></a></sup> package to use your system's fonts, -such as OpenType and TrueType fonts, in addition to the ones from your <span class="TEX">T<span -class="E">E</span>X</span> distribution. +</p><!-- l. 353 --><p class='indent'> Beyond that list, you can also use your computer system’s fonts (this may make your source file harder to +share with friends, though). The background is: to convert LaTeX source to <span class='Spectral-Light-lf-t1-'>PDF </span>output there + + +are three varieties of the TeX engine. Currently the most common is <a href='https://tug.org/applications/pdftex/'>pdfTeX</a>.<sup class='textsuperscript'><a href='#ennote-51' id='enmark-51'><span class='Spectral-Light-lf-t1-'>51</span></a></sup> For instance, +this document was generated with <span class='obeylines-h'><code class='verb'>pdflatex latex-doc-ptr.tex</code></span>. Two further developments, +<a href='https://tug.org/xetex/'>X ETeX</a>,<sup class='textsuperscript'><a href='#ennote-52' id='enmark-52'><span class='Spectral-Light-lf-t1-'>52</span></a></sup> and <a href='http://www.luatex.org/'>LuaTeX</a>,<sup class='textsuperscript'><a href='#ennote-53' id='enmark-53'><span class='Spectral-Light-lf-t1-'>53</span></a></sup> can leverage the <a href='https://ctan.org/pkg/fontspec'><span class='ectt-1095'>fontspec</span></a><sup class='textsuperscript'><a href='#ennote-54' id='enmark-54'><span class='Spectral-Light-lf-t1-'>54</span></a></sup> package to use your system’s fonts, +such as OpenType and TrueType fonts, in addition to the ones from your TeX distribution. (Mathematics requires much special tuning, though, so most of the time you cannot use system fonts for math.) -</p><!--l. 376--><p class="indent" > More is on the <a -href="https://tug.org/fonts/" ><span class="TEX">T<span -class="E">E</span>X</span> Users Group's font page</a>. +</p><!-- l. 376 --><p class='indent'> More is on the <a href='https://tug.org/fonts/'>TeX Users Group’s font page</a>. +</p><!-- l. 384 --><p class='noindent'> </p> -<h3 class="sectionHead"><a - id="x1-5000"></a>Writing <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span></h3> -<!--l. 386--><p class="noindent" ><p>There are many ways to make writing <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> source easier. Most people use a source code editor, such as -<a -href="https://www.texstudio.org/" ><span class="TEX">T<span -class="E">E</span>X</span>studio</a>, or Emacs with the add-on mode <a -href="https://www.gnu.org/software/auctex/" >AUC-<span class="TEX">T<span -class="E">E</span>X</span></a>, or <a -href="https://pages.uoregon.edu/koch/texshop/" ><span class="TEX">T<span -class="E">E</span>X</span>Shop</a> on a Mac. + <h3 class='sectionHead' id='writing-latex'><a id='x1-16000'></a>Writing LaTeX</h3> +<!-- l. 386 --><p class='noindent'><p>There are many ways to make writing LaTeX source easier. Most people use a source code editor, such as +<a href='https://www.texstudio.org/'>TeXstudio</a>, or Emacs with the add-on mode <a href='https://www.gnu.org/software/auctex/'>AUC-TeX</a>, or <a href='https://pages.uoregon.edu/koch/texshop/'>TeXShop</a> on a Mac. +</p><!-- l. 400 --><p class='noindent'> </p> -<h3 class="sectionHead"><a - id="x1-6000"></a>Pronunciation</h3> -<!--l. 401--><p class="noindent" >Pronounce <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span -class="E">E</span>X</span></span> as 'la-tech' or 'lay-tech', with emphasis on either syllable. We prefer the first, with + <h3 class='sectionHead' id='pronunciation'><a id='x1-17000'></a>Pronunciation</h3> +<!-- l. 401 --><p class='noindent'>Pronounce LaTeX as 'la-tech' or 'lay-tech', with emphasis on either syllable. We prefer the first, with emphasis on the first syllable. +</p><!-- l. 408 --><p class='noindent'> </p> -<h3 class="sectionHead"><a - id="x1-7000"></a>Welcome to the community!</h3> -<!--l. 409--><p class="noindent" >One reason that all of these resources are available is the work of the many <a -href="https://tug.org/usergroups.html" >user groups</a>, including the <a -href="https://tug.org/" ><span class="TEX">T<span -class="E">E</span>X</span> - - + <h3 class='sectionHead' id='this-document'><a id='x1-18000'></a>This document</h3> +<!-- l. 409 --><p class='noindent'>To contact this document’s authors with suggestions and corrections please see its page at +<a class='url' href='https://ctan.org/pkg/latex-doc-ptr'><span class='ectt-1095'>https://ctan.org/pkg/latex-doc-ptr</span></a>. +</p><!-- l. 415 --><p class='noindent'> +</p> + <h3 class='sectionHead' id='welcome-to-the-community'><a id='x1-19000'></a>Welcome to the community!</h3> +<!-- l. 417 --><p class='noindent'>One reason that all of these resources are available is the work of the many <a href='https://tug.org/usergroups.html'>user groups</a>, including the <a href='https://tug.org/'>TeX Users Group</a>. Please consider joining. -</p><!--l. 421--><p class="noindent" >_________________________________________________________________________________________ +</p><!-- l. 426 --><p class='noindent'>_________________________________________________________________________________________ +</p><!-- l. 429 --><p class='noindent'> </p> -<h3 class="sectionHead"><a - id="x1-8000"></a>Package names, for texdoc</h3> -<!--l. 424--><p class="noindent" ></p><!--l. 4--><p class="indent" > <a -href="#enmark-1" id="ennote-1"><sup><span -class="cmr-6">1</span></sup></a><a -href="https://ctan.org/pkg/lshort" ><span -class="ectt-0900">lshort</span></a> <a -href="#enmark-2" id="ennote-2"><sup><span -class="cmr-6">2</span></sup></a><a -href="https://ctan.org/pkg/amshelp" ><span -class="ectt-0900">amshelp</span></a> <a -href="#enmark-3" id="ennote-3"><sup><span -class="cmr-6">3</span></sup></a><a -href="https://ctan.org/pkg/amsmath" ><span -class="ectt-0900">amsmath</span></a> <a -href="#enmark-4" id="ennote-4"><sup><span -class="cmr-6">4</span></sup></a><a -href="https://ctan.org/pkg/latex2e" ><span -class="ectt-0900">latex2e</span></a> <a -href="#enmark-5" id="ennote-5"><sup><span -class="cmr-6">5</span></sup></a><a -href="https://ctan.org/pkg/comprehensive" ><span -class="ectt-0900">comprehensive</span></a> <a -href="#enmark-6" id="ennote-6"><sup><span -class="cmr-6">6</span></sup></a><a -href="https://ctan.org/pkg/faq" ><span -class="ectt-0900">faq</span></a> <a -href="#enmark-7" id="ennote-7"><sup><span -class="cmr-6">7</span></sup></a><a -href="https://ctan.org/pkg/latexcheat" ><span -class="ectt-0900">latexcheat</span></a> <a -href="#enmark-8" id="ennote-8"><sup><span -class="cmr-6">8</span></sup></a><a -href="https://ctan.org/pkg/undergradmath" ><span -class="ectt-0900">undergradmath</span></a> <a -href="#enmark-9" id="ennote-9"><sup><span -class="cmr-6">9</span></sup></a><a -href="https://ctan.org/pkg/l2tabuen" ><span -class="ectt-0900">l2tabuen</span></a> <a -href="#enmark-10" id="ennote-10"><sup><span -class="cmr-6">10</span></sup></a><a -href="https://ctan.org/pkg/geometry" ><span -class="ectt-0900">geometry</span></a> -<a -href="#enmark-11" id="ennote-11"><sup><span -class="cmr-6">11</span></sup></a><a -href="https://ctan.org/pkg/multicol" ><span -class="ectt-0900">multicol</span></a> <a -href="#enmark-12" id="ennote-12"><sup><span -class="cmr-6">12</span></sup></a><a -href="https://ctan.org/pkg/amsmath" ><span -class="ectt-0900">amsmath</span></a> <a -href="#enmark-13" id="ennote-13"><sup><span -class="cmr-6">13</span></sup></a><a -href="https://ctan.org/pkg/amssymb" ><span -class="ectt-0900">amssymb</span></a> <a -href="#enmark-14" id="ennote-14"><sup><span -class="cmr-6">14</span></sup></a><a -href="https://ctan.org/pkg/amsthm" ><span -class="ectt-0900">amsthm</span></a> <a -href="#enmark-15" id="ennote-15"><sup><span -class="cmr-6">15</span></sup></a><a -href="https://ctan.org/pkg/rsfs" ><span -class="ectt-0900">rsfs</span></a> <a -href="#enmark-16" id="ennote-16"><sup><span -class="cmr-6">16</span></sup></a><a -href="https://ctan.org/pkg/bm" ><span -class="ectt-0900">bm</span></a> <a -href="#enmark-17" id="ennote-17"><sup><span -class="cmr-6">17</span></sup></a><a -href="https://ctan.org/pkg/mathtools" ><span -class="ectt-0900">mathtools</span></a> <a -href="#enmark-18" id="ennote-18"><sup><span -class="cmr-6">18</span></sup></a><a -href="https://ctan.org/pkg/microtype" ><span -class="ectt-0900">microtype</span></a> <a -href="#enmark-19" id="ennote-19"><sup><span -class="cmr-6">19</span></sup></a><a -href="https://ctan.org/pkg/enumitem" ><span -class="ectt-0900">enumitem</span></a> <a -href="#enmark-20" id="ennote-20"><sup><span -class="cmr-6">20</span></sup></a><a -href="https://ctan.org/pkg/caption" ><span -class="ectt-0900">caption</span></a> <a -href="#enmark-21" id="ennote-21"><sup><span -class="cmr-6">21</span></sup></a><a -href="https://ctan.org/pkg/float" ><span -class="ectt-0900">float</span></a> -<a -href="#enmark-22" id="ennote-22"><sup><span -class="cmr-6">22</span></sup></a><a -href="https://ctan.org/pkg/hyperref" ><span -class="ectt-0900">hyperref</span></a> <a -href="#enmark-23" id="ennote-23"><sup><span -class="cmr-6">23</span></sup></a><a -href="https://ctan.org/pkg/cleveref" ><span -class="ectt-0900">cleveref</span></a> <a -href="#enmark-24" id="ennote-24"><sup><span -class="cmr-6">24</span></sup></a><a -href="https://ctan.org/pkg/url" ><span -class="ectt-0900">url</span></a> <a -href="#enmark-25" id="ennote-25"><sup><span -class="cmr-6">25</span></sup></a><a -href="https://ctan.org/pkg/upquote" ><span -class="ectt-0900">upquote</span></a> <a -href="#enmark-26" id="ennote-26"><sup><span -class="cmr-6">26</span></sup></a><a -href="https://ctan.org/pkg/listings" ><span -class="ectt-0900">listings</span></a> <a -href="#enmark-27" id="ennote-27"><sup><span -class="cmr-6">27</span></sup></a><a -href="https://ctan.org/pkg/pythontex" ><span -class="ectt-0900">pythontex</span></a> <a -href="#enmark-28" id="ennote-28"><sup><span -class="cmr-6">28</span></sup></a><a -href="https://ctan.org/pkg/array" ><span -class="ectt-0900">array</span></a> <a -href="#enmark-29" id="ennote-29"><sup><span -class="cmr-6">29</span></sup></a><a -href="https://ctan.org/pkg/siunitx" ><span -class="ectt-0900">siunitx</span></a> <a -href="#enmark-30" id="ennote-30"><sup><span -class="cmr-6">30</span></sup></a><a -href="https://ctan.org/pkg/tcolorbox" ><span -class="ectt-0900">tcolorbox</span></a> <a -href="#enmark-31" id="ennote-31"><sup><span -class="cmr-6">31</span></sup></a><a -href="https://ctan.org/pkg/babel" ><span -class="ectt-0900">babel</span></a> <a -href="#enmark-32" id="ennote-32"><sup><span -class="cmr-6">32</span></sup></a><a -href="https://ctan.org/pkg/lipsum" ><span -class="ectt-0900">lipsum</span></a> -<a -href="#enmark-33" id="ennote-33"><sup><span -class="cmr-6">33</span></sup></a><a -href="https://ctan.org/pkg/xcolor" ><span -class="ectt-0900">xcolor</span></a> <a -href="#enmark-34" id="ennote-34"><sup><span -class="cmr-6">34</span></sup></a><a -href="https://ctan.org/pkg/graphics" ><span -class="ectt-0900">graphics</span></a> <a -href="#enmark-35" id="ennote-35"><sup><span -class="cmr-6">35</span></sup></a><a -href="https://ctan.org/pkg/pdfpages" ><span -class="ectt-0900">pdfpages</span></a> <a -href="#enmark-36" id="ennote-36"><sup><span -class="cmr-6">36</span></sup></a><a -href="https://ctan.org/pkg/media9" ><span -class="ectt-0900">media9</span></a> <a -href="#enmark-37" id="ennote-37"><sup><span -class="cmr-6">37</span></sup></a><a -href="https://ctan.org/pkg/tikz" ><span -class="ectt-0900">tikz</span></a> <a -href="#enmark-38" id="ennote-38"><sup><span -class="cmr-6">38</span></sup></a><a -href="https://ctan.org/pkg/asymptote" ><span -class="ectt-0900">asymptote</span></a> <a -href="#enmark-39" id="ennote-39"><sup><span -class="cmr-6">39</span></sup></a><a -href="https://ctan.org/pkg/titlesec" ><span -class="ectt-0900">titlesec</span></a> <a -href="#enmark-40" id="ennote-40"><sup><span -class="cmr-6">40</span></sup></a><a -href="https://ctan.org/pkg/fancyhdr" ><span -class="ectt-0900">fancyhdr</span></a> <a -href="#enmark-41" id="ennote-41"><sup><span -class="cmr-6">41</span></sup></a><a -href="https://ctan.org/pkg/tocloft" ><span -class="ectt-0900">tocloft</span></a> <a -href="#enmark-42" id="ennote-42"><sup><span -class="cmr-6">42</span></sup></a><a -href="https://ctan.org/pkg/footmisc" ><span -class="ectt-0900">footmisc</span></a> -<a -href="#enmark-43" id="ennote-43"><sup><span -class="cmr-6">43</span></sup></a><a -href="https://ctan.org/pkg/makeindex" ><span -class="ectt-0900">makeindex</span></a> <a -href="#enmark-44" id="ennote-44"><sup><span -class="cmr-6">44</span></sup></a><a -href="https://ctan.org/pkg/answers" ><span -class="ectt-0900">answers</span></a> <a -href="#enmark-45" id="ennote-45"><sup><span -class="cmr-6">45</span></sup></a><a -href="https://ctan.org/pkg/mla" ><span -class="ectt-0900">mla</span></a> <a -href="#enmark-46" id="ennote-46"><sup><span -class="cmr-6">46</span></sup></a><a -href="https://ctan.org/pkg/bibtex" ><span -class="ectt-0900">bibtex</span></a> <a -href="#enmark-47" id="ennote-47"><sup><span -class="cmr-6">47</span></sup></a><a -href="https://ctan.org/pkg/biblatex" ><span -class="ectt-0900">biblatex</span></a> <a -href="#enmark-48" id="ennote-48"><sup><span -class="cmr-6">48</span></sup></a><a -href="https://ctan.org/pkg/exam" ><span -class="ectt-0900">exam</span></a> <a -href="#enmark-49" id="ennote-49"><sup><span -class="cmr-6">49</span></sup></a><a -href="https://ctan.org/pkg/beamer" ><span -class="ectt-0900">beamer</span></a> <a -href="#enmark-50" id="ennote-50"><sup><span -class="cmr-6">50</span></sup></a><a -href="https://ctan.org/pkg/fntguide" ><span -class="ectt-0900">fntguide</span></a> <a -href="#enmark-51" id="ennote-51"><sup><span -class="cmr-6">51</span></sup></a><a -href="https://ctan.org/pkg/pdftex" ><span -class="ectt-0900">pdftex</span></a> <a -href="#enmark-52" id="ennote-52"><sup><span -class="cmr-6">52</span></sup></a><a -href="https://ctan.org/pkg/xetex" ><span -class="ectt-0900">xetex</span></a> <a -href="#enmark-53" id="ennote-53"><sup><span -class="cmr-6">53</span></sup></a><a -href="https://ctan.org/pkg/luatex" ><span -class="ectt-0900">luatex</span></a> -<a -href="#enmark-54" id="ennote-54"><sup><span -class="cmr-6">54</span></sup></a><a -href="https://ctan.org/pkg/fontspec" ><span -class="ectt-0900">fontspec</span></a> + <h3 class='sectionHead' id='package-names-for-texdoc'><a id='x1-20000'></a>Package names, for texdoc</h3> +<!-- l. 429 --><p class='noindent'> + + +</p><!-- l. 4 --><p class='indent'> <a href='#enmark-1' id='ennote-1'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>1</span></sup></a><a id='x1-20001x'></a> <a href='https://ctan.org/pkg/lshort'><span class='ectt-0900'>lshort</span></a> <a href='#enmark-2' id='ennote-2'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>2</span></sup></a><a id='x1-20002x'></a> <a href='https://ctan.org/pkg/amshelp'><span class='ectt-0900'>amshelp</span></a> <a href='#enmark-3' id='ennote-3'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>3</span></sup></a><a id='x1-20003x'></a> <a href='https://ctan.org/pkg/amsmath'><span class='ectt-0900'>amsmath</span></a> <a href='#enmark-4' id='ennote-4'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>4</span></sup></a><a id='x1-20004x'></a> <a href='https://ctan.org/pkg/latex2e'><span class='ectt-0900'>latex2e</span></a> <a href='#enmark-5' id='ennote-5'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>5</span></sup></a><a id='x1-20005x'></a> <a href='https://ctan.org/pkg/comprehensive'><span class='ectt-0900'>comprehensive</span></a> <a href='#enmark-6' id='ennote-6'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>6</span></sup></a><a id='x1-20006x'></a> <a href='https://ctan.org/pkg/faq'><span class='ectt-0900'>faq</span></a> <a href='#enmark-7' id='ennote-7'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>7</span></sup></a><a id='x1-20007x'></a> <a href='https://ctan.org/pkg/latexcheat'><span class='ectt-0900'>latexcheat</span></a> <a href='#enmark-8' id='ennote-8'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>8</span></sup></a><a id='x1-20008x'></a> <a href='https://ctan.org/pkg/undergradmath'><span class='ectt-0900'>undergradmath</span></a> <a href='#enmark-9' id='ennote-9'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>9</span></sup></a><a id='x1-20009x'></a> <a href='https://ctan.org/pkg/l2tabuen'><span class='ectt-0900'>l2tabuen</span></a> <a href='#enmark-10' id='ennote-10'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>10</span></sup></a><a id='x1-20010x'></a> +<a href='https://ctan.org/pkg/geometry'><span class='ectt-0900'>geometry</span></a> <a href='#enmark-11' id='ennote-11'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>11</span></sup></a><a id='x1-20011x'></a> <a href='https://ctan.org/pkg/multicol'><span class='ectt-0900'>multicol</span></a> <a href='#enmark-12' id='ennote-12'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>12</span></sup></a><a id='x1-20012x'></a> <a href='https://ctan.org/pkg/amsmath'><span class='ectt-0900'>amsmath</span></a> <a href='#enmark-13' id='ennote-13'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>13</span></sup></a><a id='x1-20013x'></a> <a href='https://ctan.org/pkg/amssymb'><span class='ectt-0900'>amssymb</span></a> <a href='#enmark-14' id='ennote-14'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>14</span></sup></a><a id='x1-20014x'></a> <a href='https://ctan.org/pkg/amsthm'><span class='ectt-0900'>amsthm</span></a> <a href='#enmark-15' id='ennote-15'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>15</span></sup></a><a id='x1-20015x'></a> <a href='https://ctan.org/pkg/rsfs'><span class='ectt-0900'>rsfs</span></a> <a href='#enmark-16' id='ennote-16'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>16</span></sup></a><a id='x1-20016x'></a> <a href='https://ctan.org/pkg/bm'><span class='ectt-0900'>bm</span></a> <a href='#enmark-17' id='ennote-17'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>17</span></sup></a><a id='x1-20017x'></a> <a href='https://ctan.org/pkg/mathtools'><span class='ectt-0900'>mathtools</span></a> <a href='#enmark-18' id='ennote-18'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>18</span></sup></a><a id='x1-20018x'></a> <a href='https://ctan.org/pkg/microtype'><span class='ectt-0900'>microtype</span></a> <a href='#enmark-19' id='ennote-19'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>19</span></sup></a><a id='x1-20019x'></a> <a href='https://ctan.org/pkg/enumitem'><span class='ectt-0900'>enumitem</span></a> <a href='#enmark-20' id='ennote-20'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>20</span></sup></a><a id='x1-20020x'></a> <a href='https://ctan.org/pkg/caption'><span class='ectt-0900'>caption</span></a> <a href='#enmark-21' id='ennote-21'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>21</span></sup></a><a id='x1-20021x'></a> +<a href='https://ctan.org/pkg/float'><span class='ectt-0900'>float</span></a> <a href='#enmark-22' id='ennote-22'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>22</span></sup></a><a id='x1-20022x'></a> <a href='https://ctan.org/pkg/hyperref'><span class='ectt-0900'>hyperref</span></a> <a href='#enmark-23' id='ennote-23'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>23</span></sup></a><a id='x1-20023x'></a> <a href='https://ctan.org/pkg/cleveref'><span class='ectt-0900'>cleveref</span></a> <a href='#enmark-24' id='ennote-24'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>24</span></sup></a><a id='x1-20024x'></a> <a href='https://ctan.org/pkg/url'><span class='ectt-0900'>url</span></a> <a href='#enmark-25' id='ennote-25'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>25</span></sup></a><a id='x1-20025x'></a> <a href='https://ctan.org/pkg/upquote'><span class='ectt-0900'>upquote</span></a> <a href='#enmark-26' id='ennote-26'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>26</span></sup></a><a id='x1-20026x'></a> <a href='https://ctan.org/pkg/listings'><span class='ectt-0900'>listings</span></a> <a href='#enmark-27' id='ennote-27'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>27</span></sup></a><a id='x1-20027x'></a> <a href='https://ctan.org/pkg/pythontex'><span class='ectt-0900'>pythontex</span></a> <a href='#enmark-28' id='ennote-28'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>28</span></sup></a><a id='x1-20028x'></a> <a href='https://ctan.org/pkg/array'><span class='ectt-0900'>array</span></a> <a href='#enmark-29' id='ennote-29'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>29</span></sup></a><a id='x1-20029x'></a> <a href='https://ctan.org/pkg/siunitx'><span class='ectt-0900'>siunitx</span></a> <a href='#enmark-30' id='ennote-30'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>30</span></sup></a><a id='x1-20030x'></a> <a href='https://ctan.org/pkg/tcolorbox'><span class='ectt-0900'>tcolorbox</span></a> <a href='#enmark-31' id='ennote-31'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>31</span></sup></a><a id='x1-20031x'></a> <a href='https://ctan.org/pkg/babel'><span class='ectt-0900'>babel</span></a> <a href='#enmark-32' id='ennote-32'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>32</span></sup></a><a id='x1-20032x'></a> +<a href='https://ctan.org/pkg/lipsum'><span class='ectt-0900'>lipsum</span></a> <a href='#enmark-33' id='ennote-33'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>33</span></sup></a><a id='x1-20033x'></a> <a href='https://ctan.org/pkg/xcolor'><span class='ectt-0900'>xcolor</span></a> <a href='#enmark-34' id='ennote-34'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>34</span></sup></a><a id='x1-20034x'></a> <a href='https://ctan.org/pkg/graphics'><span class='ectt-0900'>graphics</span></a> <a href='#enmark-35' id='ennote-35'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>35</span></sup></a><a id='x1-20035x'></a> <a href='https://ctan.org/pkg/pdfpages'><span class='ectt-0900'>pdfpages</span></a> <a href='#enmark-36' id='ennote-36'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>36</span></sup></a><a id='x1-20036x'></a> <a href='https://ctan.org/pkg/media9'><span class='ectt-0900'>media9</span></a> <a href='#enmark-37' id='ennote-37'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>37</span></sup></a><a id='x1-20037x'></a> <a href='https://ctan.org/pkg/tikz'><span class='ectt-0900'>tikz</span></a> <a href='#enmark-38' id='ennote-38'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>38</span></sup></a><a id='x1-20038x'></a> <a href='https://ctan.org/pkg/asymptote'><span class='ectt-0900'>asymptote</span></a> <a href='#enmark-39' id='ennote-39'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>39</span></sup></a><a id='x1-20039x'></a> <a href='https://ctan.org/pkg/titlesec'><span class='ectt-0900'>titlesec</span></a> <a href='#enmark-40' id='ennote-40'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>40</span></sup></a><a id='x1-20040x'></a> <a href='https://ctan.org/pkg/fancyhdr'><span class='ectt-0900'>fancyhdr</span></a> <a href='#enmark-41' id='ennote-41'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>41</span></sup></a><a id='x1-20041x'></a> <a href='https://ctan.org/pkg/tocloft'><span class='ectt-0900'>tocloft</span></a> <a href='#enmark-42' id='ennote-42'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>42</span></sup></a><a id='x1-20042x'></a> <a href='https://ctan.org/pkg/footmisc'><span class='ectt-0900'>footmisc</span></a> <a href='#enmark-43' id='ennote-43'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>43</span></sup></a><a id='x1-20043x'></a> +<a href='https://ctan.org/pkg/makeindex'><span class='ectt-0900'>makeindex</span></a> <a href='#enmark-44' id='ennote-44'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>44</span></sup></a><a id='x1-20044x'></a> <a href='https://ctan.org/pkg/answers'><span class='ectt-0900'>answers</span></a> <a href='#enmark-45' id='ennote-45'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>45</span></sup></a><a id='x1-20045x'></a> <a href='https://ctan.org/pkg/mla'><span class='ectt-0900'>mla</span></a> <a href='#enmark-46' id='ennote-46'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>46</span></sup></a><a id='x1-20046x'></a> <a href='https://ctan.org/pkg/bibtex'><span class='ectt-0900'>bibtex</span></a> <a href='#enmark-47' id='ennote-47'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>47</span></sup></a><a id='x1-20047x'></a> <a href='https://ctan.org/pkg/biblatex'><span class='ectt-0900'>biblatex</span></a> <a href='#enmark-48' id='ennote-48'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>48</span></sup></a><a id='x1-20048x'></a> <a href='https://ctan.org/pkg/exam'><span class='ectt-0900'>exam</span></a> <a href='#enmark-49' id='ennote-49'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>49</span></sup></a><a id='x1-20049x'></a> <a href='https://ctan.org/pkg/beamer'><span class='ectt-0900'>beamer</span></a> <a href='#enmark-50' id='ennote-50'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>50</span></sup></a><a id='x1-20050x'></a> <a href='https://ctan.org/pkg/fntguide'><span class='ectt-0900'>fntguide</span></a> <a href='#enmark-51' id='ennote-51'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>51</span></sup></a><a id='x1-20051x'></a> <a href='https://ctan.org/pkg/pdftex'><span class='ectt-0900'>pdftex</span></a> <a href='#enmark-52' id='ennote-52'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>52</span></sup></a><a id='x1-20052x'></a> <a href='https://ctan.org/pkg/xetex'><span class='ectt-0900'>xetex</span></a> <a href='#enmark-53' id='ennote-53'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>53</span></sup></a><a id='x1-20053x'></a> <a href='https://ctan.org/pkg/luatex'><span class='ectt-0900'>luatex</span></a> <a href='#enmark-54' id='ennote-54'><sup class='textsuperscript'><span class='Spectral-Light-lf-t1-'>54</span></sup></a><a id='x1-20054x'></a> +<a href='https://ctan.org/pkg/fontspec'><span class='ectt-0900'>fontspec</span></a> </p> </div> -</body></html> - - - - +</body> +</html> diff --git a/info/latex-doc-ptr/latex-doc-ptr.pdf b/info/latex-doc-ptr/latex-doc-ptr.pdf Binary files differindex 82a55bfefa..4fc54ddcc5 100644 --- a/info/latex-doc-ptr/latex-doc-ptr.pdf +++ b/info/latex-doc-ptr/latex-doc-ptr.pdf diff --git a/info/latex-doc-ptr/latex-doc-ptr.tex b/info/latex-doc-ptr/latex-doc-ptr.tex index 590bebb76b..387969008d 100644 --- a/info/latex-doc-ptr/latex-doc-ptr.tex +++ b/info/latex-doc-ptr/latex-doc-ptr.tex @@ -351,7 +351,7 @@ visit the which includes copy and paste code to make each one work. Beyond that list, you can also use your computer system's fonts -(beware this makes your source file harder to share with friends, though). +(this may make your source file harder to share with friends, though). The background is:~to convert \LaTeX{} source to \PDF{} output there are three varieties of the \TeX{} engine. Currently the most common is @@ -403,6 +403,14 @@ Pronounce \LaTeX{} as We prefer the first, with emphasis on the first syllable. + +% ==================================================== +\section{This document} +To contact this document's authors with suggestions and corrections +please see its page at +\url{https://ctan.org/pkg/latex-doc-ptr}. + + % ==================================================== \section{Welcome to the community!} @@ -411,9 +419,6 @@ the work of the many \href{https://tug.org/usergroups.html}{user groups}, including the \href{https://tug.org/}{\TeX{} Users Group}. Please consider joining. -% The -% \href{https://www.ctan.org/}{Comprehensive \TeX{} Archive Network} -% contains more packages than any distribution. % \vfill\null % \columnbreak diff --git a/info/russian/basiclatex-ru/BasicLatex.pdf b/info/russian/basiclatex-ru/BasicLatex.pdf Binary files differdeleted file mode 100644 index 3fa1205dcf..0000000000 --- a/info/russian/basiclatex-ru/BasicLatex.pdf +++ /dev/null diff --git a/info/russian/basiclatex-ru/BasicLatex_v2.1.pdf b/info/russian/basiclatex-ru/BasicLatex_v2.1.pdf Binary files differnew file mode 100644 index 0000000000..66402b37b6 --- /dev/null +++ b/info/russian/basiclatex-ru/BasicLatex_v2.1.pdf diff --git a/info/russian/basiclatex-ru/README b/info/russian/basiclatex-ru/README index c1ff42aa46..9220ff5c52 100644 --- a/info/russian/basiclatex-ru/README +++ b/info/russian/basiclatex-ru/README @@ -1,7 +1,8 @@ BasicLatex-ru -version 1.0 Creative Commons Attribution-ShareAlike (CC BY-SA v. 4.0) License +version 1.0 + The textbook "Basic LaTeX" was published by the National Research Nuclear University MEPhI in 2021. The publication is intended for students, postgraduates and scientists. @@ -14,5 +15,22 @@ table of contents and subject index are considered. The book contains a large amount of reference data collected in tables as well as an extensive index. +version 2.0 + +The second edition is expanded to include discussion of the following resources: +– creating indices using the xindex package; +– creating chemical formulae using the chemformula package; +– font management within the NFSS; +– TrueType and OpenType font management using the fontspec package; +– math extensions of the mathtools package; +– creating math formulae using the unicode-math package; +– layout of reports and dissertations according to Russian GOSTs. + +version 2.1 + +Text editing, typo correction: +– fixed typos and formatting errors; +– edited discussion of the thesis layout at the end of Appendix G. + Alexey Kuznetsov -MailToKuznetsov@gmail.com
\ No newline at end of file +MailToKuznetsov@gmail.com diff --git a/info/russian/basiclatex-ru/README.ru b/info/russian/basiclatex-ru/README.ru index 2e73582da1..790989448e 100644 --- a/info/russian/basiclatex-ru/README.ru +++ b/info/russian/basiclatex-ru/README.ru @@ -1,7 +1,8 @@ BasicLatex-ru -ВерÑÐ¸Ñ 1.0 Ð›Ð¸Ñ†ÐµÐ½Ð·Ð¸Ñ Creative Commons Attribution-ShareAlike (CC BY-SA v. 4.0) +ВерÑÐ¸Ñ 1.0 + Учебное поÑобие "ОÑновы LaTeX" опубликовано Ðациональным иÑÑледовательÑким Ñдерным универÑитетом МИФИ в 2021 г. Издание предназначено Ð´Ð»Ñ Ñтудентов, аÑпирантов и научных работников. @@ -14,5 +15,24 @@ BasicLatex-ru Книга Ñодержит большой объем Ñправочной информации, Ñобранной в таблицах, и обширный указатель. +ВерÑÐ¸Ñ 2.0 + +Второе издание дополнено обÑуждением Ñледующих реÑурÑов: +– Ñоздание индекÑов Ñ Ð¸Ñпользованием пакета xindex; +– Ñоздание химичеÑких формул Ñ Ð¸Ñпользованием пакета chemformula; +– управление шрифтами в Ñхеме NFSS; +– управление TrueType и OpenType шрифтами Ñ Ð¸Ñпользованием пакета fontspec; +– математичеÑкие раÑÑˆÐ¸Ñ€ÐµÐ½Ð¸Ñ Ð¿Ð°ÐºÐµÑ‚Ð° mathtools; +– Ñоздание математичеÑких формул Ñ Ð¸Ñпользованием пакета unicode-math; +– оформление отчетов и диÑÑертаций в ÑоответÑтвии Ñ Ñ€Ð¾ÑÑийÑкими ГОСТами. + + +ВерÑÐ¸Ñ 2.1 + +Правка текÑта, иÑправление опечаток: +– иÑправлены опечатки и ошибки форматированиÑ; +– отредактировано обÑуждение верÑтки диÑÑертаций в конце Ð¿Ñ€Ð¸Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð“. + + ÐлекÑей Кузнецов -MailToKuznetsov@gmail.com
\ No newline at end of file +MailToKuznetsov@gmail.com diff --git a/info/tex-vpat/README.md b/info/tex-vpat/README.md index 6eecd0ce9e..168c05e042 100644 --- a/info/tex-vpat/README.md +++ b/info/tex-vpat/README.md @@ -6,7 +6,7 @@ Currently it covers TeXLive. Other distributions can be added if needed. The report is produced by [Tex Users Group](https://tug.org). -TeX VPAT Statement (c) 2021-2023 by TeX Users Group +TeX VPAT Statement (c) 2021-2024 by TeX Users Group TeX VPAT is licensed under a Creative Commons Attribution 3.0 Unported License. @@ -14,6 +14,8 @@ Creative Commons Attribution 3.0 Unported License. You should have received a copy of the license along with this work. If not, see [http://creativecommons.org/licenses/by/3.0/](http://creativecommons.org/licenses/by/3.0/). +Version 2.4: Updated to TeXLive 2024. + Version 2.3: compressed PDF. Makefile now requires lualatex-dev. Version 2.2: new accessible PDF (thanks to Ulrike Fischer and L3 team). Updated to TeXLive 2023 diff --git a/info/tex-vpat/texlive-vpat.css b/info/tex-vpat/texlive-vpat.css index b3712c8b31..f057f36101 100644 --- a/info/tex-vpat/texlive-vpat.css +++ b/info/tex-vpat/texlive-vpat.css @@ -58,6 +58,7 @@ div.flushleft {text-align: left;} .framebox-r {text-align:right;} span.thank-mark{ vertical-align: super } span.footnote-mark sup.textsuperscript, span.footnote-mark a sup.textsuperscript{ font-size:80%; } +code.verb{font-family:monospace,monospace;} div.tabular, div.center div.tabular {text-align: center; margin-top:0.5em; margin-bottom:0.5em; } table.tabular td p{margin-top:0em;} table.tabular {margin-left: auto; margin-right: auto;} @@ -103,7 +104,6 @@ table.pmatrix {width:100%;} span.bar-css {text-decoration:overline;} img.cdots{vertical-align:middle;} .partToc a, .partToc, .likepartToc a, .likepartToc {line-height: 200%; font-weight:bold; font-size:110%;} -.chapterToc a, .chapterToc, .likechapterToc a, .likechapterToc, .appendixToc a, .appendixToc {line-height: 200%; font-weight:bold;} .index-item, .index-subitem, .index-subsubitem {display:block} div.caption {text-indent:-2em; margin-left:3em; margin-right:1em; text-align:left;} div.caption span.id{font-weight: bold; white-space: nowrap; } @@ -123,6 +123,10 @@ div.author{white-space: nowrap;} div.abstract p {margin-left:5%; margin-right:5%;} div.abstract {width:100%;} .abstracttitle{text-align:center;margin-bottom:1em;} +.subsectionToc, .likesubsectionToc {margin-left:1em;} +.subsubsectionToc, .likesubsubsectionToc {margin-left:2em;} +.paragraphToc, .likeparagraphToc {margin-left:3em;} +.subparagraphToc, .likesubparagraphToc {margin-left:4em;} .rotatebox{display: inline-block;} div.tabular, div.center div.tabular {text-align: center; margin-top:0.5em; margin-bottom:0.5em; } table.tabular td p{margin-top:0em;} diff --git a/info/tex-vpat/texlive-vpat.html b/info/tex-vpat/texlive-vpat.html index 4a43ab6389..edc7633488 100644 --- a/info/tex-vpat/texlive-vpat.html +++ b/info/tex-vpat/texlive-vpat.html @@ -24,7 +24,7 @@ class="cmr-12">TeX</span><span class="cmr-12"> Users Group</span></div><br /> <div class="date" ><span -class="cmr-12">Version 2.3, April 2023</span></div> +class="cmr-12">Version 2.4, August 2024</span></div> @@ -36,65 +36,65 @@ class="cmr-12">Version 2.3, April 2023</span></div> <h3 class="likesectionHead"><a id="x1-1000"></a>Contents</h3> <div class="tableofcontents"> -  <span class="sectionToc" ><a + <span class="sectionToc" ><a href="#x1-2000" id="QQ2-1-2">Name of Product/Version</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-3000" id="QQ2-1-3">Report Date</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-4000" id="QQ2-1-4">Product Description</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-5000" id="QQ2-1-5">Contact Information</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-6000" id="QQ2-1-6">Notes</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-7000" id="QQ2-1-7">Evaluation methods used</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-8000" id="QQ2-1-8">Applicable standards and guidelines</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-9000" id="QQ2-1-9">Terms</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-10000" id="QQ2-1-10">WCAG 2.x Report</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-11000" id="QQ2-1-11">Introduction</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-12000" id="QQ2-1-12">Table 1: Success Criteria, Level A</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-13000" id="QQ2-1-13">Table 2: Success Criteria, Level AA</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-14000" id="QQ2-1-14">Table 3: Success Criteria, Level AAA</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-15000" id="QQ2-1-15">Revised Section 508 Report</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-16000" id="QQ2-1-16">Chapter 3: Functional Performance Criteria (FPC)</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-17000" id="QQ2-1-17">Chapter 4: Hardware</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-18000" id="QQ2-1-18">Chapter 5: Software</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-19000" id="QQ2-1-19">Chapter 6: Support Documentation and Services</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-20000" id="QQ2-1-20">EN 301 549 Report</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-21000" id="QQ2-1-21">Chapter 4: Functional Performance Statements (FPS)</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-22000" id="QQ2-1-22">Chapter 5: Generic Requirements</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-23000" id="QQ2-1-23">Chapter 6: ICT with Two-Way Voice Communication </a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-24000" id="QQ2-1-24">Chapter 7: ICT with Video Capabilities </a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-25000" id="QQ2-1-25">Chapter 8: Hardware</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-26000" id="QQ2-1-26">Chapter 9: Web</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-27000" id="QQ2-1-27">Chapter 10: Non-Web Software</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-28000" id="QQ2-1-28">Chapter 11: Software</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-29000" id="QQ2-1-29">Chapter 12: Documentation and Support Services</a></span> -<br />   <span class="subsectionToc" ><a +<br /> <span class="subsectionToc" ><a href="#x1-30000" id="QQ2-1-30">Chapter 13: ICT Providing Relay or Emergency Service Access</a></span> -<br />  <span class="sectionToc" ><a +<br /> <span class="sectionToc" ><a href="#x1-31000" id="QQ2-1-31">Legal Disclaimer</a></span> </div> <!--l. 205--><p class="indent" > @@ -105,13 +105,13 @@ href="#x1-31000" id="QQ2-1-31">Legal Disclaimer</a></span> id="x1-2000"></a>Name of Product/Version</h3> <a id="x1-2000doc"></a> -<!--l. 210--><p class="noindent" >TeXLive 2023. +<!--l. 210--><p class="noindent" >TeXLive 2024. <!--l. 213--><p class="noindent" > <h3 class="sectionHead"><a id="x1-3000"></a>Report Date</h3> <a id="x1-3000doc"></a> -<!--l. 216--><p class="noindent" >March 2023. +<!--l. 216--><p class="noindent" >August 2024. <!--l. 219--><p class="noindent" > <h3 class="sectionHead"><a id="x1-4000"></a>Product Description</h3> @@ -120,8 +120,8 @@ href="#x1-31000" id="QQ2-1-31">Legal Disclaimer</a></span> <!--l. 222--><p class="noindent" >TeXLive is the reference distribution of TeX and related software supported by TeX Users Group, a membership-based not-for-profit organization dedicated to support, promotion and advocacy of TeX typesetting system created by Donald -Knuth and maintained by the international community of developers. As of 2023 -TeXLive contains more than 470 programs and more than 7660 software +Knuth and maintained by the international community of developers. As of 2024 +TeXLive contains more than 490 programs and more than 8000 software packages. <!--l. 229--><p class="noindent" > <h3 class="sectionHead"><a @@ -130,7 +130,6 @@ packages. id="x1-5000doc"></a> <!--l. 232--><p class="noindent" > <dl class="description"><dt class="description"> - <!--l. 233--><p class="noindent" > <span class="cmbx-10">Website:</span> </dt><dd class="description"> @@ -138,51 +137,45 @@ class="description"> href="https://tug.org" class="url" ><span class="cmtt-10">https://tug.org</span></a> </dd><dt class="description"> - <!--l. 234--><p class="noindent" > <span class="cmbx-10">Address:</span> </dt><dd class="description"> <!--l. 234--><p class="noindent" ><br -class="newline" />Robin Laakso, executive director,<br +class="newline" />Sophia Laakso, office manager,<br class="newline" />TeX Users Group,<br class="newline" />PO Box 2311,<br class="newline" />Portland, OR 97208-2311,<br class="newline" />USA - - - </dd><dt class="description"> - <!--l. 240--><p class="noindent" > <span class="cmbx-10">Phone:</span> </dt><dd class="description"> <!--l. 240--><p class="noindent" >+1 503-223-9994 + + + </dd><dt class="description"> - <!--l. 241--><p class="noindent" > <span class="cmbx-10">Fax:</span> </dt><dd class="description"> <!--l. 241--><p class="noindent" >+1 815-301-3568 </dd><dt class="description"> - <!--l. 242--><p class="noindent" > <span class="cmbx-10">Administrative email:</span> </dt><dd class="description"> - <!--l. 242--><p class="noindent" ><a + <!--l. 242--><p class="noindent" > <a href="mailto:office@tug.org" >office@tug.org</a> </dd><dt class="description"> - <!--l. 243--><p class="noindent" > <span class="cmbx-10">Board of directors:</span> </dt><dd class="description"> - <!--l. 243--><p class="noindent" ><a + <!--l. 243--><p class="noindent" > <a href="mailto:board@tug.org" >board@tug.org</a> </dd><dt class="description"> - <!--l. 244--><p class="noindent" > <span class="cmbx-10">President:</span> </dt><dd class="description"> - <!--l. 244--><p class="noindent" ><a + <!--l. 244--><p class="noindent" > <a href="mailto:president@tug.org" >president@tug.org</a></dd></dl> <!--l. 247--><p class="noindent" > @@ -207,15 +200,17 @@ text files created in any authoring tool. TeX Users group is aware about fully accessible authoring tools, and promotes them on its web pages and publications. <!--l. 266--><p class="indent" > A separate issue is the accessibility of the <span -class="cmti-10">output documents </span>created with -TeXLive software. The accessibility features of these documents depend on the -settings in the input code and the packages used, and thus is not covered -by this document. TeX Users Group strives to make the creation of full -accessible documents using its tool as simple as possible, and to make the -accessibility features the default settings of our software. This is an ongoing effort, -involving many developers. TeX Users Group welcomes any help in this -work. -<!--l. 276--><p class="indent" > The tools provided by TeXLive are accompanied by technical documentation, +class="cmti-10">output documents </span>created with TeXLive +software. The accessibility features of these documents depend on the settings in the +input code and the packages used, and thus is not covered by this document. +TeX Users Group strives to make the creation of full accessible documents using its +tool as simple as possible, and to make the accessibility features the default settings +of our software. This is an ongoing effort, involving many developers. TeX Users +Group welcomes any help in this work. The current state of the effort can be found at +<a +href="https://tug.org/twg/accessibility/overview.html" class="url" ><span +class="cmtt-10">https://tug.org/twg/accessibility/overview.html</span></a>. +<!--l. 277--><p class="indent" > The tools provided by TeXLive are accompanied by technical documentation, both included in TeXLive itself, and separate: there are many books, courses and other materials about TeX. Many of the latter a fully accessible. The main documentation of TeXLive, supported by TeXLive team, is accessible as well. Most of @@ -223,15 +218,15 @@ the documentation for several thousand software packages in TeXLive is provided PDF or text format. By requiring machine readable textual sources of all documentation provided by TeXLive packages, we ensure a certain level of accessibility for all documentation. However, the full audit of the documentation for -all 7300+ packages created by many thousands of volunteers is not feasible at this +all 8000+ packages created by many thousands of volunteers is not feasible at this time. TeX Users group supports the efforts of making all TeX documentation fully accessible. -<!--l. 290--><p class="noindent" > +<!--l. 291--><p class="noindent" > <h3 class="sectionHead"><a id="x1-7000"></a>Evaluation methods used</h3> <a id="x1-7000doc"></a> -<!--l. 293--><p class="noindent" >The testing was based on the knowledge of the general product knowledge. +<!--l. 294--><p class="noindent" >The testing was based on the general product knowledge. <!--l. 296--><p class="noindent" > <h3 class="sectionHead"><a id="x1-8000"></a>Applicable standards and guidelines</h3> @@ -249,68 +244,72 @@ id="TBL-2-2"></colgroup><tr style="vertical-align:baseline;" id="TBL-2-1-"><td style="white-space:normal; text-align:left;" id="TBL-2-1-1" class="td11"> </td></tr><tr><td colspan="2"></td></tr><tr style="vertical-align:baseline;" id="TBL-02-1-"><td style="white-space:normal; text-align:left;" id="TBL-02-1-1" -class="td11"> -<!--l. 302--><p class="noindent" > </td> +class="td11"><!--l. 302--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-02-2-"><td style="white-space:normal; text-align:left;" id="TBL-02-2-1" -class="td11"> <!--l. 302--><p class="noindent" > </td> +class="td11"> <!--l. 302--><p class="noindent" > + </td> </tr><tr style="vertical-align:baseline;" id="TBL-02-3-"><td style="white-space:normal; text-align:left;" id="TBL-02-3-1" class="td11"> -<!--l. 304--><p class="noindent" >Standard/Guideline </td><td style="white-space:nowrap; text-align:left;" id="TBL-02-3-2" +<!--l. 304--><p class="noindent" >Standard/Guideline </td><td style="white-space:nowrap; text-align:left;" id="TBL-02-3-2" class="td11"> Included in the report </td> </tr><tr style="vertical-align:baseline;" id="TBL-02-4-"><td style="white-space:normal; text-align:left;" id="TBL-02-4-1" class="td11"> </td></tr><tr><td colspan="2"></td></tr><tr style="vertical-align:baseline;" id="TBL-002-4-"><td style="white-space:normal; text-align:left;" id="TBL-002-4-1" -class="td11"> -<!--l. 307--><p class="noindent" > </td> +class="td11"><!--l. 307--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-5-"><td style="white-space:normal; text-align:left;" id="TBL-002-5-1" -class="td11"> <!--l. 307--><p class="noindent" > </td> +class="td11"> <!--l. 307--><p class="noindent" > + </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-6-"><td style="white-space:normal; text-align:left;" id="TBL-002-6-1" -class="td11"> <!--l. 310--><p class="noindent" ><a -href="http://www.w3.org/TR/2008/REC-WCAG20-20081211" >Web Content Accessibility Guidelines 2.0</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-6-2" +class="td11"> <!--l. 310--><p class="noindent" > <a +href="http://www.w3.org/TR/2008/REC-WCAG20-20081211" >Web Content Accessibility Guidelines 2.0</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-6-2" class="td11"> Level A (Yes) </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-7-"><td style="white-space:normal; text-align:left;" id="TBL-002-7-1" -class="td11"> <!--l. 311--><p class="noindent" > </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-7-2" +class="td11"> <!--l. 311--><p class="noindent" > + </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-7-2" class="td11"> Level AA (Yes) </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-8-"><td style="white-space:normal; text-align:left;" id="TBL-002-8-1" -class="td11"> <!--l. 312--><p class="noindent" > </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-8-2" +class="td11"> <!--l. 312--><p class="noindent" > + </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-8-2" class="td11"> Level AAA (Yes) </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-9-"><td style="white-space:normal; text-align:left;" id="TBL-002-9-1" -class="td11"> <!--l. 314--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21" >Web Content Accessibility Guidelines 2.1</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-9-2" +class="td11"> <!--l. 314--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21" >Web Content Accessibility Guidelines 2.1</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-9-2" class="td11"> Level A (Yes) </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-10-"><td style="white-space:normal; text-align:left;" id="TBL-002-10-1" -class="td11"> <!--l. 315--><p class="noindent" > </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-10-2" +class="td11"> <!--l. 315--><p class="noindent" > + </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-10-2" class="td11"> Level AA (Yes) </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-11-"><td style="white-space:normal; text-align:left;" id="TBL-002-11-1" -class="td11"> <!--l. 316--><p class="noindent" > </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-11-2" +class="td11"> <!--l. 316--><p class="noindent" > + </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-11-2" class="td11"> Level AAA (Yes) </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-12-"><td style="white-space:normal; text-align:left;" id="TBL-002-12-1" -class="td11"> <!--l. 318--><p class="noindent" ><a -href="https://www.access-board.gov/guidelines-and-standards/communications-and-it/about-the-ict-refresh/final-rule/text-of-the-standards-and-guidelines" >Revised Section 508 standards published January 18, 2017 -and corrected January 22, 2018</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-12-2" +class="td11"> <!--l. 318--><p class="noindent" > <a +href="https://www.access-board.gov/guidelines-and-standards/communications-and-it/about-the-ict-refresh/final-rule/text-of-the-standards-and-guidelines" >Revised Section 508 standards published January +18, 2017 and corrected January 22, 2018</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-12-2" class="td11"> Yes </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-13-"><td style="white-space:normal; text-align:left;" id="TBL-002-13-1" -class="td11"> <!--l. 321--><p class="noindent" ><a -href="https://www.etsi.org/deliver/etsi_en/301500_301599/301549/03.01.01_60/en_301549v030101p.pdf" >EN 301 549 Accessibility requirements suitable for public -procurement of ICT products and services in Europe, - -V3.1.1 (2019-11)</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-13-2" +class="td11"> <!--l. 321--><p class="noindent" > <a +href="https://www.etsi.org/deliver/etsi_en/301500_301599/301549/03.01.01_60/en_301549v030101p.pdf" >EN 301 549 Accessibility requirements suitable for +public procurement of ICT products and services in +Europe, - V3.1.1 (2019-11)</a> </td><td style="white-space:nowrap; text-align:left;" id="TBL-002-13-2" class="td11"> Yes </td> </tr><tr style="vertical-align:baseline;" id="TBL-002-14-"><td style="white-space:normal; text-align:left;" id="TBL-002-14-1" -class="td11"> </td></tr></table><!--l. 323--><p class="noindent" ></div> +class="td11"> </td></tr></table><!--l. 323--><p class="noindent" ></div> <!--l. 325--><p class="noindent" > <h3 class="sectionHead"><a id="x1-9000"></a>Terms</h3> @@ -318,35 +317,30 @@ class="td11"> </td></tr></table id="x1-9000doc"></a> <!--l. 328--><p class="noindent" >The terms used in the Conformance Level information are defined as follows: <dl class="description"><dt class="description"> - <!--l. 330--><p class="noindent" > <span class="cmbx-10">Supports:</span> </dt><dd class="description"> <!--l. 330--><p class="noindent" >The functionality of the product has at least one method that meets the criterion without known defects or meets with equivalent facilitation. </dd><dt class="description"> - <!--l. 333--><p class="noindent" > <span class="cmbx-10">Partially Supports:</span> </dt><dd class="description"> <!--l. 333--><p class="noindent" >Some functionality of the product does not meet the criterion. </dd><dt class="description"> - <!--l. 335--><p class="noindent" > <span class="cmbx-10">Does Not Support:</span> </dt><dd class="description"> <!--l. 335--><p class="noindent" >The majority of product functionality does not meet the criterion. - - - </dd><dt class="description"> - <!--l. 337--><p class="noindent" > <span class="cmbx-10">Not Applicable:</span> </dt><dd class="description"> <!--l. 337--><p class="noindent" >The criterion is not relevant to the product. + + + </dd><dt class="description"> - <!--l. 338--><p class="noindent" > <span class="cmbx-10">Not Evaluated:</span> </dt><dd class="description"> @@ -375,7 +369,6 @@ href="#x1-13000doc">2</a> also document conformance with: Editing, and Chapter 6 – 602.3 Electronic Support Documentation.</li></ul> <!--l. 360--><p class="indent" > <dl class="description"><dt class="description"> - <!--l. 361--><p class="noindent" > <span class="cmbx-10">Note:</span> </dt><dd class="description"> @@ -397,7 +390,7 @@ Of course it would be impossible to estimate the accessibility of all this documentation, comprising hundreds thousands of pages written over three decades. <!--l. 380--><p class="indent" > Another way is to count only the documentation for the packages included in -TeXLive. This includes documentation for 7300+ packages, which makes the full +TeXLive. This includes documentation for 8000+ packages, which makes the full audit rather impractical. <!--l. 384--><p class="indent" > In this document we discuss only the main manual for the system, available with the installation and at <a @@ -433,219 +426,216 @@ id="TBL-3-3"></colgroup><tr style="vertical-align:baseline;" id="TBL-3-1-"><td style="white-space:normal; text-align:left;" id="TBL-3-1-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-03-1-"><td style="white-space:normal; text-align:left;" id="TBL-03-1-1" -class="td11"> -<!--l. 399--><p class="noindent" > </td> +class="td11"><!--l. 399--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-03-2-"><td style="white-space:normal; text-align:left;" id="TBL-03-2-1" -class="td11"> <!--l. 399--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 399--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-03-3-"><td colspan="2" style="white-space:nowrap; text-align:left;" id="TBL-03-3-1" -class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-03-3-3" +class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-03-3-3" class="td11"> <div class="multicolumn" style="white-space:normal; text-align:left;">Conformance Level</div> </td></tr><tr style="vertical-align:baseline;" id="TBL-03-4-"><td style="white-space:normal; text-align:left;" id="TBL-03-4-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-003-4-"><td style="white-space:normal; text-align:left;" id="TBL-003-4-1" -class="td11"> -<!--l. 399--><p class="noindent" > </td> +class="td11"><!--l. 399--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-5-"><td style="white-space:normal; text-align:left;" id="TBL-003-5-1" -class="td11"> <!--l. 399--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 399--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-003-6-"><td style="white-space:normal; text-align:left;" id="TBL-003-6-1" class="td11"> <!--l. 400--><p class="noindent" >1.1.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-6-2" -class="td11"> <!--l. 402--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG20/#text-equiv-all" >Non-text Content</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-6-3" +class="td11"> <!--l. 402--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG20/#text-equiv-all" >Non-text Content</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-6-3" class="td11"> <!--l. 402--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-7-"><td style="white-space:normal; text-align:left;" id="TBL-003-7-1" class="td11"> <!--l. 403--><p class="noindent" >1.2.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-7-2" class="td11"> -<!--l. 405--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG20/#media-equiv-av-only-alt" >Audio-only and Video only (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-7-3" +<!--l. 405--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG20/#media-equiv-av-only-alt" >Audio-only and Video only (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-7-3" class="td11"> <!--l. 405--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-8-"><td style="white-space:normal; text-align:left;" id="TBL-003-8-1" class="td11"> <!--l. 406--><p class="noindent" >1.2.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-8-2" -class="td11"> <!--l. 407--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG20/#media-equiv-captions" >Captions Prerecorded</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-8-3" +class="td11"> <!--l. 407--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG20/#media-equiv-captions" >Captions Prerecorded</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-8-3" class="td11"> <!--l. 407--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-9-"><td style="white-space:normal; text-align:left;" id="TBL-003-9-1" class="td11"> <!--l. 408--><p class="noindent" >1.2.3 </td><td style="white-space:normal; text-align:left;" id="TBL-003-9-2" -class="td11"> -<!--l. 410--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#media-equiv-audio-desc" >Audio Description or Media Alternative (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-9-3" +class="td11"> <!--l. 410--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#media-equiv-audio-desc" >Audio Description or Media Alternative +(Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-9-3" class="td11"> <!--l. 411--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-10-"><td style="white-space:normal; text-align:left;" id="TBL-003-10-1" class="td11"> <!--l. 412--><p class="noindent" >1.3.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-10-2" -class="td11"> <!--l. 413--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#content-structure-separation-programmatic" >Info and Relationships</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-10-3" +class="td11"> <!--l. 413--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#content-structure-separation-programmatic" >Info and Relationships</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-10-3" class="td11"> <!--l. 413--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-11-"><td style="white-space:normal; text-align:left;" id="TBL-003-11-1" class="td11"> <!--l. 414--><p class="noindent" >1.3.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-11-2" -class="td11"> <!--l. 415--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#content-structure-separation-programmatic" >Meaningful Sequence</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-11-3" +class="td11"> <!--l. 415--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#content-structure-separation-programmatic" >Meaningful Sequence</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-11-3" class="td11"> <!--l. 415--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-12-"><td style="white-space:normal; text-align:left;" id="TBL-003-12-1" class="td11"> <!--l. 416--><p class="noindent" >1.3.3 </td><td style="white-space:normal; text-align:left;" id="TBL-003-12-2" -class="td11"> <!--l. 417--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#content-structure-separation-understanding" >Sensory Characteristics</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-12-3" +class="td11"> <!--l. 417--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#content-structure-separation-understanding" >Sensory Characteristics</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-12-3" class="td11"> <!--l. 417--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-13-"><td style="white-space:normal; text-align:left;" id="TBL-003-13-1" class="td11"> <!--l. 418--><p class="noindent" >1.4.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-13-2" -class="td11"> <!--l. 419--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-without-color" >Use of Color</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-13-3" +class="td11"> <!--l. 419--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-without-color" >Use of Color</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-13-3" class="td11"> <!--l. 419--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-14-"><td style="white-space:normal; text-align:left;" id="TBL-003-14-1" class="td11"> <!--l. 420--><p class="noindent" >1.4.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-14-2" -class="td11"> <!--l. 421--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-dis-audio" >Audio Control</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-14-3" +class="td11"> <!--l. 421--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-dis-audio" >Audio Control</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-14-3" class="td11"> <!--l. 421--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-15-"><td style="white-space:normal; text-align:left;" id="TBL-003-15-1" class="td11"> <!--l. 422--><p class="noindent" >2.1.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-15-2" -class="td11"> <!--l. 423--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#keyboard-operation-keyboard-operable" >Keyboard</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-15-3" +class="td11"> <!--l. 423--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#keyboard-operation-keyboard-operable" >Keyboard</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-15-3" class="td11"> <!--l. 423--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-16-"><td style="white-space:normal; text-align:left;" id="TBL-003-16-1" class="td11"> <!--l. 424--><p class="noindent" >2.1.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-16-2" -class="td11"> <!--l. 425--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#keyboard-operation-trapping" >No Keyboard Trap</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-16-3" +class="td11"> <!--l. 425--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#keyboard-operation-trapping" >No Keyboard Trap</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-16-3" class="td11"> <!--l. 425--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-17-"><td style="white-space:normal; text-align:left;" id="TBL-003-17-1" class="td11"> <!--l. 426--><p class="noindent" >2.1.4 </td><td style="white-space:normal; text-align:left;" id="TBL-003-17-2" class="td11"> -<!--l. 427--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#character-key-shortcuts" >Character Key Shortcuts</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-17-3" +<!--l. 427--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#character-key-shortcuts" >Character Key Shortcuts</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-17-3" class="td11"> <!--l. 427--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-18-"><td style="white-space:normal; text-align:left;" id="TBL-003-18-1" class="td11"> <!--l. 428--><p class="noindent" >2.2.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-18-2" -class="td11"> <!--l. 429--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#time-limits-required-behaviors" >Timing Adjustable</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-18-3" +class="td11"> <!--l. 429--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#time-limits-required-behaviors" >Timing Adjustable</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-18-3" class="td11"> <!--l. 429--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-19-"><td style="white-space:normal; text-align:left;" id="TBL-003-19-1" class="td11"> <!--l. 430--><p class="noindent" >2.2.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-19-2" -class="td11"> <!--l. 431--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#time-limits-pause" >Pause, Stop, Hide</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-19-3" +class="td11"> <!--l. 431--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#time-limits-pause" >Pause, Stop, Hide</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-19-3" class="td11"> <!--l. 431--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-20-"><td style="white-space:normal; text-align:left;" id="TBL-003-20-1" class="td11"> <!--l. 432--><p class="noindent" >2.3.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-20-2" -class="td11"> <!--l. 433--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#seizure-does-not-violate" >Three Flashes or Below Threshold</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-20-3" +class="td11"> <!--l. 433--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#seizure-does-not-violate" >Three Flashes or Below Threshold</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-20-3" class="td11"> <!--l. 433--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-21-"><td style="white-space:normal; text-align:left;" id="TBL-003-21-1" class="td11"> <!--l. 434--><p class="noindent" >2.4.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-21-2" -class="td11"> <!--l. 435--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-skip" >Bypass Blocks</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-21-3" +class="td11"> <!--l. 435--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-skip" >Bypass Blocks</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-21-3" class="td11"> <!--l. 435--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-22-"><td style="white-space:normal; text-align:left;" id="TBL-003-22-1" class="td11"> <!--l. 436--><p class="noindent" >2.4.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-22-2" -class="td11"> <!--l. 436--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-title" >Page Titled</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-22-3" +class="td11"> <!--l. 436--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-title" >Page Titled</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-22-3" class="td11"> <!--l. 436--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-23-"><td style="white-space:normal; text-align:left;" id="TBL-003-23-1" class="td11"> <!--l. 437--><p class="noindent" >2.4.3 </td><td style="white-space:normal; text-align:left;" id="TBL-003-23-2" -class="td11"> <!--l. 437--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-focus-order" >Focus Order</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-23-3" +class="td11"> <!--l. 437--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-focus-order" >Focus Order</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-23-3" class="td11"> <!--l. 437--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-24-"><td style="white-space:normal; text-align:left;" id="TBL-003-24-1" class="td11"> <!--l. 438--><p class="noindent" >2.4.4 </td><td style="white-space:normal; text-align:left;" id="TBL-003-24-2" class="td11"> -<!--l. 438--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-refs" >Link Purpose (In Context)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-24-3" +<!--l. 438--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-refs" >Link Purpose (In Context)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-24-3" class="td11"> <!--l. 438--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-25-"><td style="white-space:normal; text-align:left;" id="TBL-003-25-1" class="td11"> <!--l. 439--><p class="noindent" >2.5.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-25-2" class="td11"> -<!--l. 439--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#pointer-gestures" >Pointer Gestures</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-25-3" +<!--l. 439--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#pointer-gestures" >Pointer Gestures</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-25-3" class="td11"> <!--l. 439--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-26-"><td style="white-space:normal; text-align:left;" id="TBL-003-26-1" class="td11"> <!--l. 440--><p class="noindent" >2.5.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-26-2" class="td11"> -<!--l. 441--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#pointer-cancellation" >Pointer Cancellation</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-26-3" +<!--l. 441--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#pointer-cancellation" >Pointer Cancellation</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-26-3" class="td11"> <!--l. 441--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-27-"><td style="white-space:normal; text-align:left;" id="TBL-003-27-1" class="td11"> <!--l. 442--><p class="noindent" >2.5.3 </td><td style="white-space:normal; text-align:left;" id="TBL-003-27-2" class="td11"> -<!--l. 442--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#label-in-name" >Label in Name</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-27-3" +<!--l. 442--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#label-in-name" >Label in Name</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-27-3" class="td11"> <!--l. 442--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-28-"><td style="white-space:normal; text-align:left;" id="TBL-003-28-1" class="td11"> <!--l. 443--><p class="noindent" >2.5.4 </td><td style="white-space:normal; text-align:left;" id="TBL-003-28-2" class="td11"> -<!--l. 443--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#motion-actuation" >Motion Actuation</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-28-3" +<!--l. 443--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#motion-actuation" >Motion Actuation</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-003-28-3" class="td11"> <!--l. 443--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-29-"><td style="white-space:normal; text-align:left;" id="TBL-003-29-1" class="td11"> <!--l. 444--><p class="noindent" >3.1.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-29-2" -class="td11"> <!--l. 444--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#meaning-doc-lang-id" >Language of Page</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-29-3" +class="td11"> <!--l. 444--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#meaning-doc-lang-id" >Language of Page</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-29-3" class="td11"> <!--l. 444--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-30-"><td style="white-space:normal; text-align:left;" id="TBL-003-30-1" class="td11"> <!--l. 445--><p class="noindent" >3.2.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-30-2" -class="td11"> <!--l. 445--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#consistent-behavior-receive-focus" >On Focus</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-30-3" +class="td11"> <!--l. 445--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#consistent-behavior-receive-focus" >On Focus</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-30-3" class="td11"> <!--l. 445--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-31-"><td style="white-space:normal; text-align:left;" id="TBL-003-31-1" class="td11"> <!--l. 446--><p class="noindent" >3.2.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-31-2" -class="td11"> <!--l. 446--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#consistent-behavior-unpredictable-change" >On Input</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-31-3" +class="td11"> <!--l. 446--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#consistent-behavior-unpredictable-change" >On Input</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-31-3" class="td11"> <!--l. 446--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-32-"><td style="white-space:normal; text-align:left;" id="TBL-003-32-1" class="td11"> <!--l. 447--><p class="noindent" >3.3.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-32-2" -class="td11"> <!--l. 447--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#minimize-error-identified" >Error Identification</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-32-3" +class="td11"> <!--l. 447--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#minimize-error-identified" >Error Identification</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-32-3" class="td11"> <!--l. 447--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-33-"><td style="white-space:normal; text-align:left;" id="TBL-003-33-1" class="td11"> <!--l. 448--><p class="noindent" >3.3.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-33-2" -class="td11"> <!--l. 448--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#minimize-error-cues" >Labels or Instructions</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-33-3" +class="td11"> <!--l. 448--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#minimize-error-cues" >Labels or Instructions</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-33-3" class="td11"> <!--l. 448--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-34-"><td style="white-space:normal; text-align:left;" id="TBL-003-34-1" class="td11"> <!--l. 449--><p class="noindent" >4.1.1 </td><td style="white-space:normal; text-align:left;" id="TBL-003-34-2" -class="td11"> <!--l. 449--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#ensure-compat-parses" >Parsing</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-34-3" +class="td11"> <!--l. 449--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#ensure-compat-parses" >Parsing</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-34-3" class="td11"> <!--l. 449--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-35-"><td style="white-space:normal; text-align:left;" id="TBL-003-35-1" class="td11"> <!--l. 450--><p class="noindent" >4.1.2 </td><td style="white-space:normal; text-align:left;" id="TBL-003-35-2" -class="td11"> <!--l. 451--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#ensure-compat-rsv" >Name, Role, Value</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-35-3" +class="td11"> <!--l. 451--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#ensure-compat-rsv" >Name, Role, Value</a> </td><td style="white-space:normal; text-align:left;" id="TBL-003-35-3" class="td11"> <!--l. 451--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-003-36-"><td style="white-space:normal; text-align:left;" id="TBL-003-36-1" class="td11"> </td></tr></table><!--l. 453--><p class="noindent" ></div> - - - <!--l. 455--><p class="indent" > @@ -665,154 +655,154 @@ id="TBL-4-3"></colgroup><tr style="vertical-align:baseline;" id="TBL-4-1-"><td style="white-space:normal; text-align:left;" id="TBL-4-1-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-04-1-"><td style="white-space:normal; text-align:left;" id="TBL-04-1-1" -class="td11"> -<!--l. 460--><p class="noindent" > </td> +class="td11"><!--l. 460--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-04-2-"><td style="white-space:normal; text-align:left;" id="TBL-04-2-1" -class="td11"> <!--l. 460--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 460--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-04-3-"><td colspan="2" style="white-space:nowrap; text-align:left;" id="TBL-04-3-1" -class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-04-3-3" +class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-04-3-3" class="td11"> <div class="multicolumn" style="white-space:normal; text-align:left;">Conformance Level</div> </td></tr><tr style="vertical-align:baseline;" id="TBL-04-4-"><td style="white-space:normal; text-align:left;" id="TBL-04-4-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-004-4-"><td style="white-space:normal; text-align:left;" id="TBL-004-4-1" -class="td11"> -<!--l. 460--><p class="noindent" > </td> +class="td11"><!--l. 460--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-5-"><td style="white-space:normal; text-align:left;" id="TBL-004-5-1" -class="td11"> <!--l. 460--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 460--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-004-6-"><td style="white-space:normal; text-align:left;" id="TBL-004-6-1" class="td11"> <!--l. 461--><p class="noindent" >1.2.4 </td><td style="white-space:normal; text-align:left;" id="TBL-004-6-2" class="td11"> -<!--l. 462--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#media-equiv-real-time-captions" >Captions (Live)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-6-3" +<!--l. 462--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#media-equiv-real-time-captions" >Captions (Live)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-6-3" class="td11"> <!--l. 462--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-7-"><td style="white-space:normal; text-align:left;" id="TBL-004-7-1" class="td11"> <!--l. 463--><p class="noindent" >1.2.5 </td><td style="white-space:normal; text-align:left;" id="TBL-004-7-2" class="td11"> -<!--l. 464--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#media-equiv-audio-desc-only" >Audio Description (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-7-3" +<!--l. 464--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#media-equiv-audio-desc-only" >Audio Description (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-7-3" class="td11"> <!--l. 464--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-8-"><td style="white-space:normal; text-align:left;" id="TBL-004-8-1" class="td11"> <!--l. 465--><p class="noindent" >1.3.4 </td><td style="white-space:normal; text-align:left;" id="TBL-004-8-2" class="td11"> -<!--l. 465--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#orientation" >Orientation</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-8-3" +<!--l. 465--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#orientation" >Orientation</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-8-3" class="td11"> <!--l. 466--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-9-"><td style="white-space:normal; text-align:left;" id="TBL-004-9-1" class="td11"> <!--l. 467--><p class="noindent" >1.3.5 </td><td style="white-space:normal; text-align:left;" id="TBL-004-9-2" class="td11"> -<!--l. 468--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#identify-input-purpose" >Identify Input Purpose</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-9-3" +<!--l. 468--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#identify-input-purpose" >Identify Input Purpose</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-9-3" class="td11"> <!--l. 468--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-10-"><td style="white-space:normal; text-align:left;" id="TBL-004-10-1" class="td11"> <!--l. 469--><p class="noindent" >1.4.3 </td><td style="white-space:normal; text-align:left;" id="TBL-004-10-2" class="td11"> -<!--l. 470--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-contrast" >Contrast (Minimum)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-10-3" +<!--l. 470--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-contrast" >Contrast (Minimum)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-10-3" class="td11"> <!--l. 470--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-11-"><td style="white-space:normal; text-align:left;" id="TBL-004-11-1" class="td11"> <!--l. 471--><p class="noindent" >1.4.4 </td><td style="white-space:normal; text-align:left;" id="TBL-004-11-2" -class="td11"> <!--l. 471--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#resize-text" >Resize text</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-11-3" +class="td11"> <!--l. 471--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#resize-text" >Resize text</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-11-3" class="td11"> <!--l. 472--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-12-"><td style="white-space:normal; text-align:left;" id="TBL-004-12-1" class="td11"> <!--l. 473--><p class="noindent" >1.4.5 </td><td style="white-space:normal; text-align:left;" id="TBL-004-12-2" -class="td11"> <!--l. 474--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-text-presentation" >Images of Text</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-12-3" +class="td11"> <!--l. 474--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-text-presentation" >Images of Text</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-12-3" class="td11"> <!--l. 474--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-13-"><td style="white-space:normal; text-align:left;" id="TBL-004-13-1" class="td11"> <!--l. 475--><p class="noindent" >1.4.10 </td><td style="white-space:normal; text-align:left;" id="TBL-004-13-2" class="td11"> -<!--l. 475--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#reflow" >Reflow</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-13-3" +<!--l. 475--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#reflow" >Reflow</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-13-3" class="td11"> <!--l. 475--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-14-"><td style="white-space:normal; text-align:left;" id="TBL-004-14-1" class="td11"> <!--l. 476--><p class="noindent" >1.4.11 </td><td style="white-space:normal; text-align:left;" id="TBL-004-14-2" class="td11"> -<!--l. 477--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#non-text-contrast" >Non-text Contrast</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-14-3" +<!--l. 477--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#non-text-contrast" >Non-text Contrast</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-14-3" class="td11"> <!--l. 477--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-15-"><td style="white-space:normal; text-align:left;" id="TBL-004-15-1" class="td11"> <!--l. 478--><p class="noindent" >1.4.12 </td><td style="white-space:normal; text-align:left;" id="TBL-004-15-2" class="td11"> -<!--l. 479--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#text-spacing" >Text Spacing</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-15-3" +<!--l. 479--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#text-spacing" >Text Spacing</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-15-3" class="td11"> <!--l. 479--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-16-"><td style="white-space:normal; text-align:left;" id="TBL-004-16-1" class="td11"> <!--l. 480--><p class="noindent" >1.4.13 </td><td style="white-space:normal; text-align:left;" id="TBL-004-16-2" class="td11"> -<!--l. 481--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#content-on-hover-or-focus" >Content on Hover or Focus</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-16-3" +<!--l. 481--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#content-on-hover-or-focus" >Content on Hover or Focus</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-16-3" class="td11"> <!--l. 481--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-17-"><td style="white-space:normal; text-align:left;" id="TBL-004-17-1" class="td11"> <!--l. 482--><p class="noindent" >2.4.5 </td><td style="white-space:normal; text-align:left;" id="TBL-004-17-2" -class="td11"> <!--l. 483--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-mult-loc" >Multiple Ways</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-17-3" +class="td11"> <!--l. 483--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-mult-loc" >Multiple Ways</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-17-3" class="td11"> <!--l. 483--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-18-"><td style="white-space:normal; text-align:left;" id="TBL-004-18-1" class="td11"> <!--l. 484--><p class="noindent" >2.4.6 </td><td style="white-space:normal; text-align:left;" id="TBL-004-18-2" -class="td11"> <!--l. 485--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-descriptive" >Headings and Labels</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-18-3" +class="td11"> <!--l. 485--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-descriptive" >Headings and Labels</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-18-3" class="td11"> <!--l. 485--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-19-"><td style="white-space:normal; text-align:left;" id="TBL-004-19-1" class="td11"> <!--l. 486--><p class="noindent" >2.4.7 </td><td style="white-space:normal; text-align:left;" id="TBL-004-19-2" -class="td11"> <!--l. 487--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-focus-visible" >Focus Visible</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-19-3" +class="td11"> <!--l. 487--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-focus-visible" >Focus Visible</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-19-3" class="td11"> <!--l. 487--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-20-"><td style="white-space:normal; text-align:left;" id="TBL-004-20-1" class="td11"> <!--l. 488--><p class="noindent" >3.1.2 </td><td style="white-space:normal; text-align:left;" id="TBL-004-20-2" -class="td11"> <!--l. 489--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#meaning-other-lang-id" >Language of Parts</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-20-3" +class="td11"> <!--l. 489--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#meaning-other-lang-id" >Language of Parts</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-20-3" class="td11"> <!--l. 489--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-21-"><td style="white-space:normal; text-align:left;" id="TBL-004-21-1" class="td11"> <!--l. 490--><p class="noindent" >3.2.3 </td><td style="white-space:normal; text-align:left;" id="TBL-004-21-2" -class="td11"> <!--l. 491--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#consistent-behavior-consistent-locations" >Consistent Navigation</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-21-3" +class="td11"> <!--l. 491--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#consistent-behavior-consistent-locations" >Consistent Navigation</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-21-3" class="td11"> <!--l. 491--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-22-"><td style="white-space:normal; text-align:left;" id="TBL-004-22-1" class="td11"> <!--l. 492--><p class="noindent" >3.2.4 </td><td style="white-space:normal; text-align:left;" id="TBL-004-22-2" -class="td11"> <!--l. 493--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#consistent-behavior-consistent-functionality" >Consistent Identification</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-22-3" +class="td11"> <!--l. 493--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#consistent-behavior-consistent-functionality" >Consistent Identification</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-22-3" class="td11"> <!--l. 493--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-23-"><td style="white-space:normal; text-align:left;" id="TBL-004-23-1" class="td11"> <!--l. 494--><p class="noindent" >3.3.3 </td><td style="white-space:normal; text-align:left;" id="TBL-004-23-2" -class="td11"> <!--l. 495--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#minimize-error-suggestions" >Error Suggestion</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-23-3" +class="td11"> <!--l. 495--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#minimize-error-suggestions" >Error Suggestion</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-23-3" class="td11"> <!--l. 495--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-24-"><td style="white-space:normal; text-align:left;" id="TBL-004-24-1" class="td11"> <!--l. 496--><p class="noindent" >3.3.4 </td><td style="white-space:normal; text-align:left;" id="TBL-004-24-2" class="td11"> -<!--l. 497--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#minimize-error-reversible" >Error Prevention (Legal, Financial, Data)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-24-3" +<!--l. 497--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#minimize-error-reversible" >Error Prevention (Legal, Financial, Data)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-004-24-3" class="td11"> <!--l. 497--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-004-25-"><td style="white-space:normal; text-align:left;" id="TBL-004-25-1" class="td11"> <!--l. 499--><p class="noindent" >4.1.3 </td><td style="white-space:normal; text-align:left;" id="TBL-004-25-2" class="td11"> -<!--l. 500--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#status-messages" >Status Messages</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-25-3" +<!--l. 500--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#status-messages" >Status Messages</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-004-25-3" class="td11"> <!--l. 500--><p class="noindent" >Supports </td> </tr><tr @@ -827,9 +817,6 @@ class="td11"> </td></tr></table><!--l. 502--><p class="noindent" ></div> <a id="x1-14000doc"></a> <div class="tabular"> - - - <!--l. 508--><p class="indent" > <table id="TBL-5" class="tabular" @@ -840,84 +827,84 @@ id="TBL-5-3"></colgroup><tr style="vertical-align:baseline;" id="TBL-5-1-"><td style="white-space:normal; text-align:left;" id="TBL-5-1-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-05-1-"><td style="white-space:normal; text-align:left;" id="TBL-05-1-1" -class="td11"> -<!--l. 509--><p class="noindent" > </td> +class="td11"><!--l. 509--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-05-2-"><td style="white-space:normal; text-align:left;" id="TBL-05-2-1" -class="td11"> <!--l. 509--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 509--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-05-3-"><td colspan="2" style="white-space:nowrap; text-align:left;" id="TBL-05-3-1" -class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-05-3-3" +class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-05-3-3" class="td11"> <div class="multicolumn" style="white-space:normal; text-align:left;">Conformance Level</div> </td></tr><tr style="vertical-align:baseline;" id="TBL-05-4-"><td style="white-space:normal; text-align:left;" id="TBL-05-4-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-005-4-"><td style="white-space:normal; text-align:left;" id="TBL-005-4-1" -class="td11"> -<!--l. 509--><p class="noindent" > </td> +class="td11"><!--l. 509--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-5-"><td style="white-space:normal; text-align:left;" id="TBL-005-5-1" -class="td11"> <!--l. 509--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 509--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-005-6-"><td style="white-space:normal; text-align:left;" id="TBL-005-6-1" class="td11"> <!--l. 510--><p class="noindent" >1.2.6 </td><td style="white-space:normal; text-align:left;" id="TBL-005-6-2" class="td11"> -<!--l. 511--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#media-equiv-sign" >Sign Language (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-6-3" +<!--l. 511--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#media-equiv-sign" >Sign Language (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-6-3" class="td11"> <!--l. 511--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-7-"><td style="white-space:normal; text-align:left;" id="TBL-005-7-1" class="td11"> <!--l. 512--><p class="noindent" >1.2.7 </td><td style="white-space:normal; text-align:left;" id="TBL-005-7-2" class="td11"> -<!--l. 513--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#media-equiv-extended-ad" >Extended Audio Description (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-7-3" +<!--l. 513--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#media-equiv-extended-ad" >Extended Audio Description (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-7-3" class="td11"> <!--l. 513--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-8-"><td style="white-space:normal; text-align:left;" id="TBL-005-8-1" class="td11"> <!--l. 515--><p class="noindent" >1.2.8 </td><td style="white-space:normal; text-align:left;" id="TBL-005-8-2" class="td11"> -<!--l. 516--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#media-equiv-text-doc" >Media Alternative (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-8-3" +<!--l. 516--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#media-equiv-text-doc" >Media Alternative (Prerecorded)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-8-3" class="td11"> <!--l. 516--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-9-"><td style="white-space:normal; text-align:left;" id="TBL-005-9-1" class="td11"> <!--l. 517--><p class="noindent" >1.2.9 </td><td style="white-space:normal; text-align:left;" id="TBL-005-9-2" class="td11"> -<!--l. 518--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#media-equiv-live-audio-only" >Audio-only (Live)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-9-3" +<!--l. 518--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#media-equiv-live-audio-only" >Audio-only (Live)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-9-3" class="td11"> <!--l. 518--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-10-"><td style="white-space:normal; text-align:left;" id="TBL-005-10-1" class="td11"> <!--l. 519--><p class="noindent" >1.3.6 </td><td style="white-space:normal; text-align:left;" id="TBL-005-10-2" class="td11"> -<!--l. 520--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#identify-purpose" >Identify Purpose</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-10-3" +<!--l. 520--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#identify-purpose" >Identify Purpose</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-10-3" class="td11"> <!--l. 520--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-11-"><td style="white-space:normal; text-align:left;" id="TBL-005-11-1" class="td11"> <!--l. 521--><p class="noindent" >1.4.6 </td><td style="white-space:normal; text-align:left;" id="TBL-005-11-2" class="td11"> -<!--l. 522--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast7" >Contrast (Enhanced)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-11-3" +<!--l. 522--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast7" >Contrast (Enhanced)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-11-3" class="td11"> <!--l. 522--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-12-"><td style="white-space:normal; text-align:left;" id="TBL-005-12-1" class="td11"> <!--l. 523--><p class="noindent" >1.4.7 </td><td style="white-space:normal; text-align:left;" id="TBL-005-12-2" -class="td11"> <!--l. 524--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-noaudio" >Low or No Background Audio</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-12-3" +class="td11"> <!--l. 524--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-noaudio" >Low or No Background Audio</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-12-3" class="td11"> <!--l. 524--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-13-"><td style="white-space:normal; text-align:left;" id="TBL-005-13-1" class="td11"> <!--l. 525--><p class="noindent" >1.4.8 </td><td style="white-space:normal; text-align:left;" id="TBL-005-13-2" -class="td11"> <!--l. 526--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-visual-presentation" >Visual Presentation</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-13-3" +class="td11"> <!--l. 526--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-visual-presentation" >Visual Presentation</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-13-3" class="td11"> <!--l. 526--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-14-"><td style="white-space:normal; text-align:left;" id="TBL-005-14-1" class="td11"> <!--l. 527--><p class="noindent" >1.4.9 </td><td style="white-space:normal; text-align:left;" id="TBL-005-14-2" class="td11"> -<!--l. 528--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-text-images" >Images of Text (No Exception)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-14-3" +<!--l. 528--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#visual-audio-contrast-text-images" >Images of Text (No Exception)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-14-3" class="td11"> <!--l. 528--><p class="noindent" >Supports<span class="footnote-mark"><a href="texlive-vpat2.html#fn1x0"><sup class="textsuperscript"> 1</sup></a></span> </td> @@ -925,122 +912,122 @@ href="texlive-vpat2.html#fn1x0"><sup class="textsuperscript"> style="vertical-align:baseline;" id="TBL-005-15-"><td style="white-space:normal; text-align:left;" id="TBL-005-15-1" class="td11"> <!--l. 529--><p class="noindent" >2.1.3 </td><td style="white-space:normal; text-align:left;" id="TBL-005-15-2" class="td11"> -<!--l. 530--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#keyboard-operation-all-funcs" >Keyboard (No Exception)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-15-3" +<!--l. 530--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#keyboard-operation-all-funcs" >Keyboard (No Exception)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-15-3" class="td11"> <!--l. 530--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-16-"><td style="white-space:normal; text-align:left;" id="TBL-005-16-1" class="td11"> <!--l. 531--><p class="noindent" >2.2.3 </td><td style="white-space:normal; text-align:left;" id="TBL-005-16-2" -class="td11"> <!--l. 532--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#time-limits-no-exceptions" >No Timing</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-16-3" +class="td11"> <!--l. 532--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#time-limits-no-exceptions" >No Timing</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-16-3" class="td11"> <!--l. 532--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-17-"><td style="white-space:normal; text-align:left;" id="TBL-005-17-1" class="td11"> <!--l. 533--><p class="noindent" >2.2.4 </td><td style="white-space:normal; text-align:left;" id="TBL-005-17-2" -class="td11"> <!--l. 534--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#time-limits-postponed" >Interruptions</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-17-3" +class="td11"> <!--l. 534--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#time-limits-postponed" >Interruptions</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-17-3" class="td11"> <!--l. 534--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-18-"><td style="white-space:normal; text-align:left;" id="TBL-005-18-1" class="td11"> <!--l. 535--><p class="noindent" >2.2.5 </td><td style="white-space:normal; text-align:left;" id="TBL-005-18-2" -class="td11"> <!--l. 536--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#time-limits-server-timeout" >Re-authenticating</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-18-3" +class="td11"> <!--l. 536--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#time-limits-server-timeout" >Re-authenticating</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-18-3" class="td11"> <!--l. 536--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-19-"><td style="white-space:normal; text-align:left;" id="TBL-005-19-1" class="td11"> <!--l. 537--><p class="noindent" >2.2.6 </td><td style="white-space:normal; text-align:left;" id="TBL-005-19-2" class="td11"> -<!--l. 537--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#timeouts" >Timeouts</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-19-3" +<!--l. 537--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#timeouts" >Timeouts</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-19-3" class="td11"> <!--l. 538--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-20-"><td style="white-space:normal; text-align:left;" id="TBL-005-20-1" class="td11"> <!--l. 539--><p class="noindent" >2.3.2 </td><td style="white-space:normal; text-align:left;" id="TBL-005-20-2" -class="td11"> <!--l. 540--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#seizure-three-times" >Three Flashes</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-20-3" +class="td11"> <!--l. 540--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#seizure-three-times" >Three Flashes</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-20-3" class="td11"> <!--l. 540--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-21-"><td style="white-space:normal; text-align:left;" id="TBL-005-21-1" class="td11"> <!--l. 541--><p class="noindent" >2.3.3 </td><td style="white-space:normal; text-align:left;" id="TBL-005-21-2" class="td11"> -<!--l. 542--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#animation-from-interactions" >Animation from Interactions</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-21-3" +<!--l. 542--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#animation-from-interactions" >Animation from Interactions</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-21-3" class="td11"> <!--l. 542--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-22-"><td style="white-space:normal; text-align:left;" id="TBL-005-22-1" class="td11"> <!--l. 543--><p class="noindent" >2.4.8 </td><td style="white-space:normal; text-align:left;" id="TBL-005-22-2" -class="td11"> <!--l. 544--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-location" >Location</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-22-3" +class="td11"> <!--l. 544--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-location" >Location</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-22-3" class="td11"> <!--l. 544--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-23-"><td style="white-space:normal; text-align:left;" id="TBL-005-23-1" class="td11"> <!--l. 545--><p class="noindent" >2.4.9 </td><td style="white-space:normal; text-align:left;" id="TBL-005-23-2" class="td11"> -<!--l. 546--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-link" >Link Purpose (Link Only)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-23-3" +<!--l. 546--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-link" >Link Purpose (Link Only)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-23-3" class="td11"> <!--l. 546--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-24-"><td style="white-space:normal; text-align:left;" id="TBL-005-24-1" class="td11"> <!--l. 547--><p class="noindent" >2.4.10 </td><td style="white-space:normal; text-align:left;" id="TBL-005-24-2" -class="td11"> <!--l. 548--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-headings" >Section Headings</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-24-3" +class="td11"> <!--l. 548--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#navigation-mechanisms-headings" >Section Headings</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-24-3" class="td11"> <!--l. 548--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-25-"><td style="white-space:normal; text-align:left;" id="TBL-005-25-1" class="td11"> <!--l. 549--><p class="noindent" >2.5.5 </td><td style="white-space:normal; text-align:left;" id="TBL-005-25-2" class="td11"> -<!--l. 549--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#target-size" >Target Size</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-25-3" +<!--l. 549--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#target-size" >Target Size</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-25-3" class="td11"> <!--l. 550--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-26-"><td style="white-space:normal; text-align:left;" id="TBL-005-26-1" class="td11"> <!--l. 551--><p class="noindent" >2.5.6 </td><td style="white-space:normal; text-align:left;" id="TBL-005-26-2" class="td11"> -<!--l. 552--><p class="noindent" ><a -href="https://www.w3.org/TR/WCAG21/#concurrent-input-mechanisms" >Concurrent Input Mechanisms</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-26-3" +<!--l. 552--><p class="noindent" > <a +href="https://www.w3.org/TR/WCAG21/#concurrent-input-mechanisms" >Concurrent Input Mechanisms</a> (2.1 only) </td><td style="white-space:normal; text-align:left;" id="TBL-005-26-3" class="td11"> <!--l. 552--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-27-"><td style="white-space:normal; text-align:left;" id="TBL-005-27-1" class="td11"> <!--l. 553--><p class="noindent" >3.1.3 </td><td style="white-space:normal; text-align:left;" id="TBL-005-27-2" -class="td11"> <!--l. 554--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#meaning-idioms" >Unusual Words</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-27-3" +class="td11"> <!--l. 554--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#meaning-idioms" >Unusual Words</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-27-3" class="td11"> <!--l. 554--><p class="noindent" >Does Not Support </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-28-"><td style="white-space:normal; text-align:left;" id="TBL-005-28-1" class="td11"> <!--l. 555--><p class="noindent" >3.1.4 </td><td style="white-space:normal; text-align:left;" id="TBL-005-28-2" -class="td11"> <!--l. 556--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#meaning-located" >Abbreviations</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-28-3" +class="td11"> <!--l. 556--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#meaning-located" >Abbreviations</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-28-3" class="td11"> <!--l. 556--><p class="noindent" >Does Not Support </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-29-"><td style="white-space:normal; text-align:left;" id="TBL-005-29-1" class="td11"> <!--l. 557--><p class="noindent" >3.1.5 </td><td style="white-space:normal; text-align:left;" id="TBL-005-29-2" -class="td11"> <!--l. 558--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#meaning-supplements" >Reading Level</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-29-3" +class="td11"> <!--l. 558--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#meaning-supplements" >Reading Level</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-29-3" class="td11"> <!--l. 558--><p class="noindent" >Does Not Support </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-30-"><td style="white-space:normal; text-align:left;" id="TBL-005-30-1" class="td11"> <!--l. 559--><p class="noindent" >3.1.6 </td><td style="white-space:normal; text-align:left;" id="TBL-005-30-2" -class="td11"> <!--l. 560--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#meaning-pronunciation" >Pronunciation</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-30-3" +class="td11"> <!--l. 560--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#meaning-pronunciation" >Pronunciation</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-30-3" class="td11"> <!--l. 560--><p class="noindent" >Not Applicable </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-31-"><td style="white-space:normal; text-align:left;" id="TBL-005-31-1" class="td11"> <!--l. 561--><p class="noindent" >3.2.5 </td><td style="white-space:normal; text-align:left;" id="TBL-005-31-2" -class="td11"> <!--l. 562--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#consistent-behavior-no-extreme-changes-context" >Change on Request</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-31-3" +class="td11"> <!--l. 562--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#consistent-behavior-no-extreme-changes-context" >Change on Request</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-31-3" class="td11"> <!--l. 562--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-32-"><td style="white-space:normal; text-align:left;" id="TBL-005-32-1" class="td11"> <!--l. 563--><p class="noindent" >3.3.5 </td><td style="white-space:normal; text-align:left;" id="TBL-005-32-2" -class="td11"> <!--l. 564--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#minimize-error-context-help" >Help</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-32-3" +class="td11"> <!--l. 564--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#minimize-error-context-help" >Help</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-32-3" class="td11"> <!--l. 564--><p class="noindent" >Does Not Support </td> </tr><tr style="vertical-align:baseline;" id="TBL-005-33-"><td style="white-space:normal; text-align:left;" id="TBL-005-33-1" class="td11"> <!--l. 565--><p class="noindent" >3.3.6 </td><td style="white-space:normal; text-align:left;" id="TBL-005-33-2" class="td11"> -<!--l. 566--><p class="noindent" ><a -href="http://www.w3.org/TR/WCAG20/#minimize-error-reversible-all" >Error Prevention (All)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-33-3" +<!--l. 566--><p class="noindent" > <a +href="http://www.w3.org/TR/WCAG20/#minimize-error-reversible-all" >Error Prevention (All)</a> </td><td style="white-space:normal; text-align:left;" id="TBL-005-33-3" class="td11"> <!--l. 566--><p class="noindent" >Not Applicable </td> </tr><tr @@ -1052,7 +1039,6 @@ class="td11"> </td></tr></table> <!--l. 568--><p class="noindent" ></div><a id="x1-14001f1"></a> <dl class="description"><dt class="description"> - <!--l. 574--><p class="noindent" > <span class="cmbx-10">Note:</span> </dt><dd class="description"> @@ -1081,69 +1067,69 @@ id="TBL-6-3"></colgroup><tr style="vertical-align:baseline;" id="TBL-6-1-"><td style="white-space:normal; text-align:left;" id="TBL-6-1-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-06-1-"><td style="white-space:normal; text-align:left;" id="TBL-06-1-1" -class="td11"> -<!--l. 587--><p class="noindent" > </td> +class="td11"><!--l. 587--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-06-2-"><td style="white-space:normal; text-align:left;" id="TBL-06-2-1" -class="td11"> <!--l. 587--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 587--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-06-3-"><td colspan="2" style="white-space:nowrap; text-align:left;" id="TBL-06-3-1" -class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-06-3-3" +class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-06-3-3" class="td11"> <div class="multicolumn" style="white-space:normal; text-align:left;">Conformance Level</div> </td></tr><tr style="vertical-align:baseline;" id="TBL-06-4-"><td style="white-space:normal; text-align:left;" id="TBL-06-4-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-006-4-"><td style="white-space:normal; text-align:left;" id="TBL-006-4-1" -class="td11"> -<!--l. 587--><p class="noindent" > </td> +class="td11"><!--l. 587--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-5-"><td style="white-space:normal; text-align:left;" id="TBL-006-5-1" -class="td11"> <!--l. 587--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 587--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-006-6-"><td style="white-space:normal; text-align:left;" id="TBL-006-6-1" class="td11"> <!--l. 588--><p class="noindent" >302.1 </td><td style="white-space:normal; text-align:left;" id="TBL-006-6-2" -class="td11"> <!--l. 588--><p class="noindent" >Without Vision </td><td style="white-space:normal; text-align:left;" id="TBL-006-6-3" +class="td11"> <!--l. 588--><p class="noindent" >Without Vision </td><td style="white-space:normal; text-align:left;" id="TBL-006-6-3" class="td11"> <!--l. 589--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-7-"><td style="white-space:normal; text-align:left;" id="TBL-006-7-1" class="td11"> <!--l. 590--><p class="noindent" >302.2 </td><td style="white-space:normal; text-align:left;" id="TBL-006-7-2" -class="td11"> <!--l. 590--><p class="noindent" >With Limited Vision </td><td style="white-space:normal; text-align:left;" id="TBL-006-7-3" +class="td11"> <!--l. 590--><p class="noindent" >With Limited Vision </td><td style="white-space:normal; text-align:left;" id="TBL-006-7-3" class="td11"> <!--l. 590--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-8-"><td style="white-space:normal; text-align:left;" id="TBL-006-8-1" class="td11"> <!--l. 591--><p class="noindent" >302.3 </td><td style="white-space:normal; text-align:left;" id="TBL-006-8-2" -class="td11"> <!--l. 591--><p class="noindent" >Without Perception of Color </td><td style="white-space:normal; text-align:left;" id="TBL-006-8-3" +class="td11"> <!--l. 591--><p class="noindent" >Without Perception of Color </td><td style="white-space:normal; text-align:left;" id="TBL-006-8-3" class="td11"> <!--l. 591--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-9-"><td style="white-space:normal; text-align:left;" id="TBL-006-9-1" class="td11"> <!--l. 592--><p class="noindent" >302.4 </td><td style="white-space:normal; text-align:left;" id="TBL-006-9-2" -class="td11"> <!--l. 592--><p class="noindent" >Without Hearing </td><td style="white-space:normal; text-align:left;" id="TBL-006-9-3" +class="td11"> <!--l. 592--><p class="noindent" >Without Hearing </td><td style="white-space:normal; text-align:left;" id="TBL-006-9-3" class="td11"> <!--l. 592--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-10-"><td style="white-space:normal; text-align:left;" id="TBL-006-10-1" class="td11"> <!--l. 593--><p class="noindent" >302.5 </td><td style="white-space:normal; text-align:left;" id="TBL-006-10-2" -class="td11"> <!--l. 593--><p class="noindent" >With Limited Hearing </td><td style="white-space:normal; text-align:left;" id="TBL-006-10-3" +class="td11"> <!--l. 593--><p class="noindent" >With Limited Hearing </td><td style="white-space:normal; text-align:left;" id="TBL-006-10-3" class="td11"> <!--l. 593--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-11-"><td style="white-space:normal; text-align:left;" id="TBL-006-11-1" class="td11"> <!--l. 594--><p class="noindent" >302.6 </td><td style="white-space:normal; text-align:left;" id="TBL-006-11-2" -class="td11"> <!--l. 594--><p class="noindent" >Without Speech </td><td style="white-space:normal; text-align:left;" id="TBL-006-11-3" +class="td11"> <!--l. 594--><p class="noindent" >Without Speech </td><td style="white-space:normal; text-align:left;" id="TBL-006-11-3" class="td11"> <!--l. 594--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-12-"><td style="white-space:normal; text-align:left;" id="TBL-006-12-1" class="td11"> <!--l. 595--><p class="noindent" >302.7 </td><td style="white-space:normal; text-align:left;" id="TBL-006-12-2" -class="td11"> <!--l. 595--><p class="noindent" >With Limited Manipulation </td><td style="white-space:normal; text-align:left;" id="TBL-006-12-3" +class="td11"> <!--l. 595--><p class="noindent" >With Limited Manipulation </td><td style="white-space:normal; text-align:left;" id="TBL-006-12-3" class="td11"> <!--l. 595--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-13-"><td style="white-space:normal; text-align:left;" id="TBL-006-13-1" class="td11"> <!--l. 596--><p class="noindent" >302.8 </td><td style="white-space:normal; text-align:left;" id="TBL-006-13-2" -class="td11"> <!--l. 596--><p class="noindent" >With Limited Reach and Strength </td><td style="white-space:normal; text-align:left;" id="TBL-006-13-3" +class="td11"> <!--l. 596--><p class="noindent" >With Limited Reach and Strength </td><td style="white-space:normal; text-align:left;" id="TBL-006-13-3" class="td11"> <!--l. 596--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-006-14-"><td style="white-space:normal; text-align:left;" id="TBL-006-14-1" class="td11"> <!--l. 597--><p class="noindent" >302.9 </td><td style="white-space:normal; text-align:left;" id="TBL-006-14-2" -class="td11"> <!--l. 597--><p class="noindent" >With Limited Language, Cognitive, and Learning -Abilities </td><td style="white-space:normal; text-align:left;" id="TBL-006-14-3" +class="td11"> <!--l. 597--><p class="noindent" >With Limited Language, Cognitive, and +Learning Abilities </td><td style="white-space:normal; text-align:left;" id="TBL-006-14-3" class="td11"> <!--l. 599--><p class="noindent" >Does Not Support </td> </tr><tr @@ -1179,8 +1165,7 @@ class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></ class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-3-"><td style="white-space:normal; text-align:left;" id="TBL-7-3-1" -class="td11"> -<!--l. 615--><p class="noindent" > </td> +class="td11"> <!--l. 615--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-4-"><td colspan="2" style="white-space:nowrap; text-align:left;" id="TBL-7-4-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-7-4-3" @@ -1194,12 +1179,10 @@ class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></ class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-7-"><td style="white-space:normal; text-align:left;" id="TBL-7-7-1" -class="td11"> -<!--l. 615--><p class="noindent" > </td> +class="td11"> <!--l. 615--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-8-"><td style="white-space:normal; text-align:left;" id="TBL-7-8-1" -class="td11"> -<!--l. 616--><p class="noindent" > </td> +class="td11"> <!--l. 616--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-9-"><td style="white-space:normal; text-align:left;" id="TBL-7-9-1" class="td11"> </td><td style="white-space:normal; text-align:left;" id="TBL-7-9-2" @@ -1361,9 +1344,6 @@ class="td11"> <!--l. 641--><p class="noindent" >Platform Accessibility Features </td><td style="white-space:normal; text-align:left;" id="TBL-7-37-3" class="td11"> <!--l. 641--><p class="noindent" >Supports </td> - - - </tr><tr style="vertical-align:baseline;" id="TBL-7-38-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-7-38-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;"> <span @@ -1385,6 +1365,9 @@ class="td11"> <!--l. 644--><p class="noindent" >Alternative User Interfaces </td><td style="white-space:normal; text-align:left;" id="TBL-7-40-3" class="td11"> <!--l. 644--><p class="noindent" >Supports </td> + + + </tr><tr style="vertical-align:baseline;" id="TBL-7-41-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-7-41-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;"><span @@ -1461,29 +1444,22 @@ class="td11"> </td> class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-52-"><td style="white-space:normal; text-align:left;" id="TBL-7-52-1" -class="td11"> -<!--l. 656--><p class="noindent" > </td> +class="td11"> <!--l. 656--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-53-"><td style="white-space:normal; text-align:left;" id="TBL-7-53-1" -class="td11"> -<!--l. 656--><p class="noindent" > </td> +class="td11"> <!--l. 656--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-54-"><td style="white-space:normal; text-align:left;" id="TBL-7-54-1" -class="td11"> -<!--l. 656--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 656--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-7-15-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-7-15-1" class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-7-16-"><td style="white-space:normal; text-align:left;" id="TBL-7-16-1" -class="td11"> -<!--l. 620--><p class="noindent" > </td> +class="td11"> <!--l. 620--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-7-17-"><td style="white-space:normal; text-align:left;" id="TBL-7-17-1" -class="td11"> -<!--l. 620--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 620--><p class="noindent" > </td></tr> </table></div> <!--l. 659--><p class="noindent" > <h4 class="subsectionHead"><a @@ -1498,9 +1474,6 @@ class="td11"> id="TBL-8-1"><col id="TBL-8-2"><col id="TBL-8-3"></colgroup> - - - <tr style="vertical-align:baseline;" id="TBL-8-10-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-8-10-1" class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> @@ -1514,13 +1487,10 @@ class="td11"> class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-8-13-"><td style="white-space:normal; text-align:left;" id="TBL-8-13-1" -class="td11"> -<!--l. 666--><p class="noindent" > </td> +class="td11"> <!--l. 666--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-8-14-"><td style="white-space:normal; text-align:left;" id="TBL-8-14-1" -class="td11"> -<!--l. 666--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 666--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-8-18-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-8-18-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;"> <span @@ -1567,6 +1537,9 @@ class="td11"> Features </td><td style="white-space:normal; text-align:left;" id="TBL-8-23-3" class="td11"> <!--l. 677--><p class="noindent" >Not Applicable </td> + + + </tr><tr style="vertical-align:baseline;" id="TBL-8-24-"><td style="white-space:normal; text-align:left;" id="TBL-8-24-1" class="td11"> @@ -1583,29 +1556,22 @@ class="td11"> </td> class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-8-27-"><td style="white-space:normal; text-align:left;" id="TBL-8-27-1" -class="td11"> -<!--l. 680--><p class="noindent" > </td> +class="td11"> <!--l. 680--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-8-28-"><td style="white-space:normal; text-align:left;" id="TBL-8-28-1" -class="td11"> -<!--l. 680--><p class="noindent" > </td> +class="td11"> <!--l. 680--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-8-29-"><td style="white-space:normal; text-align:left;" id="TBL-8-29-1" -class="td11"> -<!--l. 680--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 680--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-8-15-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-8-15-1" class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-8-16-"><td style="white-space:normal; text-align:left;" id="TBL-8-16-1" -class="td11"> -<!--l. 668--><p class="noindent" > </td> +class="td11"> <!--l. 668--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-8-17-"><td style="white-space:normal; text-align:left;" id="TBL-8-17-1" -class="td11"> -<!--l. 668--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 668--><p class="noindent" > </td></tr> </table></div> @@ -1630,78 +1596,79 @@ id="TBL-9-3"></colgroup><tr style="vertical-align:baseline;" id="TBL-9-1-"><td style="white-space:normal; text-align:left;" id="TBL-9-1-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-09-1-"><td style="white-space:normal; text-align:left;" id="TBL-09-1-1" -class="td11"> -<!--l. 692--><p class="noindent" > </td> +class="td11"><!--l. 692--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-09-2-"><td style="white-space:normal; text-align:left;" id="TBL-09-2-1" -class="td11"> <!--l. 692--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 692--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-09-3-"><td colspan="2" style="white-space:nowrap; text-align:left;" id="TBL-09-3-1" -class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-09-3-3" +class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;">Criteria</div> </td><td style="white-space:normal; text-align:left;" id="TBL-09-3-3" class="td11"> <div class="multicolumn" style="white-space:normal; text-align:left;">Conformance Level</div> </td></tr><tr style="vertical-align:baseline;" id="TBL-09-4-"><td style="white-space:normal; text-align:left;" id="TBL-09-4-1" class="td11"> </td></tr><tr><td colspan="3"></td></tr><tr style="vertical-align:baseline;" id="TBL-009-4-"><td style="white-space:normal; text-align:left;" id="TBL-009-4-1" -class="td11"> -<!--l. 692--><p class="noindent" > </td> +class="td11"><!--l. 692--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-5-"><td style="white-space:normal; text-align:left;" id="TBL-009-5-1" -class="td11"> <!--l. 692--><p class="noindent" > </td></tr><tr +class="td11"> <!--l. 692--><p class="noindent" > + </td></tr><tr style="vertical-align:baseline;" id="TBL-009-6-"><td style="white-space:normal; text-align:left;" id="TBL-009-6-1" class="td11"> <!--l. 693--><p class="noindent" >4.2.1 </td><td style="white-space:normal; text-align:left;" id="TBL-009-6-2" -class="td11"> <!--l. 693--><p class="noindent" >Usage without vision </td><td style="white-space:normal; text-align:left;" id="TBL-009-6-3" +class="td11"> <!--l. 693--><p class="noindent" >Usage without vision </td><td style="white-space:normal; text-align:left;" id="TBL-009-6-3" class="td11"> <!--l. 693--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-7-"><td style="white-space:normal; text-align:left;" id="TBL-009-7-1" class="td11"> <!--l. 694--><p class="noindent" >4.2.2 </td><td style="white-space:normal; text-align:left;" id="TBL-009-7-2" -class="td11"> <!--l. 694--><p class="noindent" >Usage with limited vision </td><td style="white-space:normal; text-align:left;" id="TBL-009-7-3" +class="td11"> <!--l. 694--><p class="noindent" >Usage with limited vision </td><td style="white-space:normal; text-align:left;" id="TBL-009-7-3" class="td11"> <!--l. 694--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-8-"><td style="white-space:normal; text-align:left;" id="TBL-009-8-1" class="td11"> <!--l. 695--><p class="noindent" >4.2.3 </td><td style="white-space:normal; text-align:left;" id="TBL-009-8-2" -class="td11"> <!--l. 695--><p class="noindent" >Usage without perception of colour </td><td style="white-space:normal; text-align:left;" id="TBL-009-8-3" +class="td11"> <!--l. 695--><p class="noindent" >Usage without perception of colour </td><td style="white-space:normal; text-align:left;" id="TBL-009-8-3" class="td11"> <!--l. 695--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-9-"><td style="white-space:normal; text-align:left;" id="TBL-009-9-1" class="td11"> <!--l. 696--><p class="noindent" >4.2.4 </td><td style="white-space:normal; text-align:left;" id="TBL-009-9-2" -class="td11"> <!--l. 696--><p class="noindent" >Usage without hearing </td><td style="white-space:normal; text-align:left;" id="TBL-009-9-3" +class="td11"> <!--l. 696--><p class="noindent" >Usage without hearing </td><td style="white-space:normal; text-align:left;" id="TBL-009-9-3" class="td11"> <!--l. 696--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-10-"><td style="white-space:normal; text-align:left;" id="TBL-009-10-1" class="td11"> <!--l. 697--><p class="noindent" >4.2.5 </td><td style="white-space:normal; text-align:left;" id="TBL-009-10-2" -class="td11"> <!--l. 697--><p class="noindent" >Usage with limited hearing </td><td style="white-space:normal; text-align:left;" id="TBL-009-10-3" +class="td11"> <!--l. 697--><p class="noindent" >Usage with limited hearing </td><td style="white-space:normal; text-align:left;" id="TBL-009-10-3" class="td11"> <!--l. 697--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-11-"><td style="white-space:normal; text-align:left;" id="TBL-009-11-1" class="td11"> <!--l. 698--><p class="noindent" >4.2.6 </td><td style="white-space:normal; text-align:left;" id="TBL-009-11-2" -class="td11"> <!--l. 698--><p class="noindent" >Usage with no or limited vocal capability </td><td style="white-space:normal; text-align:left;" id="TBL-009-11-3" +class="td11"> <!--l. 698--><p class="noindent" >Usage with no or limited vocal capability </td><td style="white-space:normal; text-align:left;" id="TBL-009-11-3" class="td11"> <!--l. 698--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-12-"><td style="white-space:normal; text-align:left;" id="TBL-009-12-1" class="td11"> <!--l. 699--><p class="noindent" >4.2.7 </td><td style="white-space:normal; text-align:left;" id="TBL-009-12-2" -class="td11"> <!--l. 699--><p class="noindent" >Usage with limited manipulation or strength </td><td style="white-space:normal; text-align:left;" id="TBL-009-12-3" +class="td11"> <!--l. 699--><p class="noindent" >Usage with limited manipulation or strength </td><td style="white-space:normal; text-align:left;" id="TBL-009-12-3" class="td11"> <!--l. 699--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-13-"><td style="white-space:normal; text-align:left;" id="TBL-009-13-1" class="td11"> <!--l. 700--><p class="noindent" >4.2.8 </td><td style="white-space:normal; text-align:left;" id="TBL-009-13-2" -class="td11"> <!--l. 700--><p class="noindent" >Usage with limited reach </td><td style="white-space:normal; text-align:left;" id="TBL-009-13-3" +class="td11"> <!--l. 700--><p class="noindent" >Usage with limited reach </td><td style="white-space:normal; text-align:left;" id="TBL-009-13-3" class="td11"> <!--l. 700--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-14-"><td style="white-space:normal; text-align:left;" id="TBL-009-14-1" class="td11"> <!--l. 701--><p class="noindent" >4.2.9 </td><td style="white-space:normal; text-align:left;" id="TBL-009-14-2" -class="td11"> <!--l. 701--><p class="noindent" >Minimize photosensitive seizure triggers </td><td style="white-space:normal; text-align:left;" id="TBL-009-14-3" +class="td11"> <!--l. 701--><p class="noindent" >Minimize photosensitive seizure triggers </td><td style="white-space:normal; text-align:left;" id="TBL-009-14-3" class="td11"> <!--l. 701--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-15-"><td style="white-space:normal; text-align:left;" id="TBL-009-15-1" class="td11"> <!--l. 702--><p class="noindent" >4.2.10 </td><td style="white-space:normal; text-align:left;" id="TBL-009-15-2" -class="td11"> <!--l. 702--><p class="noindent" >Usage with limited cognition, language or learning </td><td style="white-space:normal; text-align:left;" id="TBL-009-15-3" -class="td11"> <!--l. 702--><p class="noindent" >Does not support </td> +class="td11"> <!--l. 702--><p class="noindent" >Usage with limited cognition, language or +learning </td><td style="white-space:normal; text-align:left;" id="TBL-009-15-3" +class="td11"> <!--l. 702--><p class="noindent" >Does Not Support </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-16-"><td style="white-space:normal; text-align:left;" id="TBL-009-16-1" class="td11"> <!--l. 704--><p class="noindent" >4.2.11 </td><td style="white-space:normal; text-align:left;" id="TBL-009-16-2" -class="td11"> <!--l. 704--><p class="noindent" >Privacy </td><td style="white-space:normal; text-align:left;" id="TBL-009-16-3" +class="td11"> <!--l. 704--><p class="noindent" >Privacy </td><td style="white-space:normal; text-align:left;" id="TBL-009-16-3" class="td11"> <!--l. 704--><p class="noindent" >Supports </td> </tr><tr style="vertical-align:baseline;" id="TBL-009-17-"><td style="white-space:normal; text-align:left;" id="TBL-009-17-1" @@ -1713,7 +1680,6 @@ class="td11"> </td></tr></table><!--l. 705--><p class="noindent" ></div> id="x1-22000doc"></a> <!--l. 710--><p class="noindent" > <dl class="description"><dt class="description"> - <!--l. 711--><p class="noindent" > <span class="cmbx-10">Note:</span> </dt><dd class="description"> @@ -1722,10 +1688,10 @@ class="description"> assistive technology”. Since TeXLive utilities do not prevent users from attaching, installing or using assistive technology, most of requirements in this chapter are not applicable to them.</dd></dl> +<!--l. 720--><p class="noindent" > -<!--l. 720--><p class="noindent" > <a id="x1-22001r3"></a> <!--l. 721--><div class="longtable"> <table id="TBL-10" class="longtable" @@ -1746,28 +1712,21 @@ class="td11"> class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-10-13-"><td style="white-space:normal; text-align:left;" id="TBL-10-13-1" -class="td11"> -<!--l. 724--><p class="noindent" > </td> +class="td11"> <!--l. 724--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-14-"><td style="white-space:normal; text-align:left;" id="TBL-10-14-1" -class="td11"> -<!--l. 724--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 724--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-10-18-"><td style="white-space:normal; text-align:left;" id="TBL-10-18-1" -class="td11"> -<!--l. 727--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-10-18-2" -class="td11"> -<!--l. 727--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-10-18-3" -class="td11"> -<!--l. 727--><p class="noindent" > </td> +class="td11"> <!--l. 727--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-10-18-2" +class="td11"> <!--l. 727--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-10-18-3" +class="td11"> <!--l. 727--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-19-"><td style="white-space:normal; text-align:left;" id="TBL-10-19-1" class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-20-"><td style="white-space:normal; text-align:left;" id="TBL-10-20-1" -class="td11"> -<!--l. 727--><p class="noindent" > </td> +class="td11"> <!--l. 727--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-21-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-10-21-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;"> <span @@ -1919,9 +1878,6 @@ class="td11"> <!--l. 746--><p class="noindent" >Non-visual error identification </td><td style="white-space:normal; text-align:left;" id="TBL-10-40-3" class="td11"> <!--l. 746--><p class="noindent" >Not Applicable </td> - - - </tr><tr style="vertical-align:baseline;" id="TBL-10-41-"><td style="white-space:normal; text-align:left;" id="TBL-10-41-1" class="td11"> @@ -1946,6 +1902,9 @@ class="td11"> <!--l. 749--><p class="noindent" >Visual output for auditory information </td><td style="white-space:normal; text-align:left;" id="TBL-10-43-3" class="td11"> <!--l. 749--><p class="noindent" >Not Applicable </td> + + + </tr><tr style="vertical-align:baseline;" id="TBL-10-44-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-10-44-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;"><span @@ -2066,33 +2025,23 @@ class="td11"> </td> class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-61-"><td style="white-space:normal; text-align:left;" id="TBL-10-61-1" -class="td11"> -<!--l. 766--><p class="noindent" > </td> +class="td11"> <!--l. 766--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-62-"><td style="white-space:normal; text-align:left;" id="TBL-10-62-1" -class="td11"> -<!--l. 766--><p class="noindent" > </td> +class="td11"> <!--l. 766--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-63-"><td style="white-space:normal; text-align:left;" id="TBL-10-63-1" -class="td11"> -<!--l. 766--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 766--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-10-15-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-10-15-1" class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-10-16-"><td style="white-space:normal; text-align:left;" id="TBL-10-16-1" -class="td11"> -<!--l. 726--><p class="noindent" > </td> +class="td11"> <!--l. 726--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-10-17-"><td style="white-space:normal; text-align:left;" id="TBL-10-17-1" -class="td11"> -<!--l. 726--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 726--><p class="noindent" > </td></tr> </table></div> - - - <!--l. 768--><p class="noindent" > <h4 class="subsectionHead"><a id="x1-23000"></a>Chapter 6: ICT with Two-Way Voice Communication </h4> @@ -2105,6 +2054,9 @@ class="td11"> <a id="x1-24000doc"></a> <!--l. 776--><p class="noindent" >Not Applicable. + + + <!--l. 779--><p class="noindent" > <h4 class="subsectionHead"><a id="x1-25000"></a>Chapter 8: Hardware</h4> @@ -2143,13 +2095,10 @@ class="td11"> class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-11-13-"><td style="white-space:normal; text-align:left;" id="TBL-11-13-1" -class="td11"> -<!--l. 799--><p class="noindent" > </td> +class="td11"> <!--l. 799--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-11-14-"><td style="white-space:normal; text-align:left;" id="TBL-11-14-1" -class="td11"> -<!--l. 799--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 799--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-11-18-"><td style="white-space:normal; text-align:left;" id="TBL-11-18-1" class="td11"> @@ -2179,37 +2128,27 @@ class="td11"> </tr><tr style="vertical-align:baseline;" id="TBL-11-21-"><td style="white-space:normal; text-align:left;" id="TBL-11-21-1" class="td11"> </td> - - - </tr><tr style="vertical-align:baseline;" id="TBL-11-22-"><td style="white-space:normal; text-align:left;" id="TBL-11-22-1" class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-11-23-"><td style="white-space:normal; text-align:left;" id="TBL-11-23-1" -class="td11"> -<!--l. 805--><p class="noindent" > </td> +class="td11"> <!--l. 805--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-11-24-"><td style="white-space:normal; text-align:left;" id="TBL-11-24-1" -class="td11"> -<!--l. 805--><p class="noindent" > </td> +class="td11"> <!--l. 805--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-11-25-"><td style="white-space:normal; text-align:left;" id="TBL-11-25-1" -class="td11"> -<!--l. 805--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 805--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-11-15-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-11-15-1" class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-11-16-"><td style="white-space:normal; text-align:left;" id="TBL-11-16-1" -class="td11"> -<!--l. 801--><p class="noindent" > </td> +class="td11"> <!--l. 801--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-11-17-"><td style="white-space:normal; text-align:left;" id="TBL-11-17-1" -class="td11"> -<!--l. 801--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 801--><p class="noindent" > </td></tr> </table></div> <!--l. 808--><p class="noindent" > <h4 class="subsectionHead"><a @@ -2224,6 +2163,9 @@ class="td11"> id="TBL-12-1"><col id="TBL-12-2"><col id="TBL-12-3"></colgroup> + + + <tr style="vertical-align:baseline;" id="TBL-12-10-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-12-10-1" class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> @@ -2237,20 +2179,15 @@ class="td11"> class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-12-13-"><td style="white-space:normal; text-align:left;" id="TBL-12-13-1" -class="td11"> -<!--l. 817--><p class="noindent" > </td> +class="td11"> <!--l. 817--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-12-14-"><td style="white-space:normal; text-align:left;" id="TBL-12-14-1" -class="td11"> -<!--l. 817--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 817--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-12-18-"><td style="white-space:normal; text-align:left;" id="TBL-12-18-1" class="td11"> -11.1.1.1 through 11.4.1.3 -<!--l. 820--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-18-2" -class="td11"> -<!--l. 820--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-18-3" +11.1.1.1 through 11.4.1.3<!--l. 820--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-18-2" +class="td11"> <!--l. 820--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-18-3" class="td11"> <!--l. 820--><p class="noindent" >Supports<span class="footnote-mark"><a href="texlive-vpat6.html#fn5x0"><sup class="textsuperscript">5</sup></a></span> <a @@ -2324,9 +2261,6 @@ class="td11"> <!--l. 832--><p class="noindent" >Row, column, and headers </td><td style="white-space:normal; text-align:left;" id="TBL-12-27-3" class="td11"> <!--l. 832--><p class="noindent" >Not Applicable </td> - - - </tr><tr style="vertical-align:baseline;" id="TBL-12-28-"><td style="white-space:normal; text-align:left;" id="TBL-12-28-1" class="td11"> @@ -2444,6 +2378,9 @@ class="td11"> <!--l. 849--><p class="noindent" >User preferences </td><td style="white-space:normal; text-align:left;" id="TBL-12-42-3" class="td11"> <!--l. 849--><p class="noindent" >Not Applicable </td> + + + </tr><tr style="vertical-align:baseline;" id="TBL-12-43-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-12-43-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;"> <span @@ -2490,32 +2427,22 @@ class="td11"> </td> class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-12-50-"><td style="white-space:normal; text-align:left;" id="TBL-12-50-1" -class="td11"> -<!--l. 856--><p class="noindent" > </td> +class="td11"> <!--l. 856--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-12-51-"><td style="white-space:normal; text-align:left;" id="TBL-12-51-1" -class="td11"> -<!--l. 856--><p class="noindent" > </td> +class="td11"> <!--l. 856--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-12-52-"><td style="white-space:normal; text-align:left;" id="TBL-12-52-1" -class="td11"> -<!--l. 856--><p class="noindent" > </td> - </tr> - - - +class="td11"> <!--l. 856--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-12-15-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-12-15-1" class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-12-16-"><td style="white-space:normal; text-align:left;" id="TBL-12-16-1" -class="td11"> -<!--l. 819--><p class="noindent" > </td> +class="td11"> <!--l. 819--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-12-17-"><td style="white-space:normal; text-align:left;" id="TBL-12-17-1" -class="td11"> -<!--l. 819--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 819--><p class="noindent" > </td></tr> </table></div> <!--l. 859--><p class="noindent" > <h4 class="subsectionHead"><a @@ -2543,28 +2470,21 @@ class="td11"> class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-13-13-"><td style="white-space:normal; text-align:left;" id="TBL-13-13-1" -class="td11"> -<!--l. 866--><p class="noindent" > </td> +class="td11"> <!--l. 866--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-14-"><td style="white-space:normal; text-align:left;" id="TBL-13-14-1" -class="td11"> -<!--l. 866--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 866--><p class="noindent" > </td></tr> <tr style="vertical-align:baseline;" id="TBL-13-18-"><td style="white-space:normal; text-align:left;" id="TBL-13-18-1" -class="td11"> -<!--l. 869--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-18-2" -class="td11"> -<!--l. 869--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-18-3" -class="td11"> -<!--l. 869--><p class="noindent" > </td> +class="td11"> <!--l. 869--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-18-2" +class="td11"> <!--l. 869--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-18-3" +class="td11"> <!--l. 869--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-19-"><td style="white-space:normal; text-align:left;" id="TBL-13-19-1" class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-20-"><td style="white-space:normal; text-align:left;" id="TBL-13-20-1" -class="td11"> -<!--l. 869--><p class="noindent" > </td> +class="td11"> <!--l. 869--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-21-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-13-21-1" class="td11"> <div class="multicolumn" style="white-space:nowrap; text-align:left;"> <span @@ -2625,17 +2545,13 @@ class="td11"> </td> class="td11"> </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-30-"><td style="white-space:normal; text-align:left;" id="TBL-13-30-1" -class="td11"> -<!--l. 877--><p class="noindent" > </td> +class="td11"> <!--l. 877--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-31-"><td style="white-space:normal; text-align:left;" id="TBL-13-31-1" -class="td11"> -<!--l. 877--><p class="noindent" > </td> +class="td11"> <!--l. 877--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-32-"><td style="white-space:normal; text-align:left;" id="TBL-13-32-1" -class="td11"> -<!--l. 877--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 877--><p class="noindent" > </td></tr> @@ -2644,13 +2560,10 @@ class="td11"> class="td11"><span class="cmidrule"><!-- enable post-processing of cmidrule--></span> </td></tr><tr style="vertical-align:baseline;" id="TBL-13-16-"><td style="white-space:normal; text-align:left;" id="TBL-13-16-1" -class="td11"> -<!--l. 868--><p class="noindent" > </td> +class="td11"> <!--l. 868--><p class="noindent" > </td> </tr><tr style="vertical-align:baseline;" id="TBL-13-17-"><td style="white-space:normal; text-align:left;" id="TBL-13-17-1" -class="td11"> -<!--l. 868--><p class="noindent" > </td> - </tr> +class="td11"> <!--l. 868--><p class="noindent" > </td></tr> </table></div> <!--l. 880--><p class="noindent" > <h4 class="subsectionHead"><a diff --git a/info/tex-vpat/texlive-vpat.pdf b/info/tex-vpat/texlive-vpat.pdf Binary files differindex 370e8e4a35..d27a1c5b6a 100644 --- a/info/tex-vpat/texlive-vpat.pdf +++ b/info/tex-vpat/texlive-vpat.pdf diff --git a/info/tex-vpat/texlive-vpat.tex b/info/tex-vpat/texlive-vpat.tex index 6eefcde301..700b7eefda 100644 --- a/info/tex-vpat/texlive-vpat.tex +++ b/info/tex-vpat/texlive-vpat.tex @@ -190,7 +190,7 @@ (International Edition)\\ (Based upon VPAT\textsuperscript{\textregistered} version~2.4)} \author{\TeX\ Users Group} -\date{Version 2.3, April 2023} +\date{Version 2.4, August 2024} \hypersetup{ pdftitle=TeX Live Accessibility Conformance Report, @@ -207,13 +207,13 @@ \section{Name of Product/Version} \label{sec:name} -\TeX Live 2023. +\TeX Live 2024. \section{Report Date} \label{sec:date} -March 2023. +August 2024. \section{Product Description} @@ -223,8 +223,8 @@ March 2023. supported by \TeX\ Users Group, a membership-based not-for-profit organization dedicated to support, promotion and advocacy of \TeX\ typesetting system created by Donald Knuth and maintained by the -international community of developers. As of 2023 \TeX Live contains -more than 470~programs and more than 7660~software packages. +international community of developers. As of 2024 \TeX Live contains +more than 490~programs and more than 8000~software packages. \section{Contact Information} \label{sec:contact_info} @@ -232,7 +232,7 @@ more than 470~programs and more than 7660~software packages. \begin{description} \item[Website:] \url{https://tug.org} \item[Address:] \leavevmode\\ - Robin Laakso, executive director,\\ + Sophia Laakso, office manager,\\ \TeX\ Users Group,\\ PO Box 2311,\\ Portland, OR~97208-2311,\\ @@ -271,7 +271,8 @@ strives to make the creation of full accessible documents using its tool as simple as possible, and to make the accessibility features the default settings of our software. This is an ongoing effort, involving many developers. \TeX\ Users Group welcomes any help in -this work. +this work. The current state of the effort can be found at +\url{https://tug.org/twg/accessibility/overview.html}. The tools provided by \TeX Live are accompanied by technical documentation, both included in \TeX Live itself, and separate: there @@ -282,7 +283,7 @@ documentation for several thousand software packages in \TeX Live is provided in PDF or text format. By requiring machine readable textual sources of all documentation provided by \TeX Live packages, we ensure a certain level of accessibility for all documentation. However, the -full audit of the documentation for all 7300+ packages created by many +full audit of the documentation for all 8000+ packages created by many thousands of volunteers is not feasible at this time. \TeX\ Users group supports the efforts of making all \TeX\ documentation fully accessible. @@ -290,8 +291,7 @@ accessible. \section{Evaluation methods used} \label{sec:methods} -The testing was based on the knowledge of the general product -knowledge. +The testing was based on the general product knowledge. \section{Applicable standards and guidelines} \label{sec:standards} @@ -378,7 +378,7 @@ impossible to estimate the accessibility of all this documentation, comprising hundreds thousands of pages written over three decades. Another way is to count only the documentation for the packages -included in \TeX Live. This includes documentation for 7300+ +included in \TeX Live. This includes documentation for 8000+ packages, which makes the full audit rather impractical. In this document we discuss only the main manual for the system, @@ -699,8 +699,8 @@ Does Not Apply. 4.2.7& Usage with limited manipulation or strength & Supports \\ 4.2.8& Usage with limited reach & Supports \\ 4.2.9& Minimize photosensitive seizure triggers & Supports \\ - 4.2.10 &Usage with limited cognition, language or learning & Does not - support \\ + 4.2.10 &Usage with limited cognition, language or learning & Does Not + Support \\ 4.2.11& Privacy & Supports\\ \end{tabular} diff --git a/info/tex-vpat/texlive-vpat2.html b/info/tex-vpat/texlive-vpat2.html index 11cd93099c..f507ddbabe 100644 --- a/info/tex-vpat/texlive-vpat2.html +++ b/info/tex-vpat/texlive-vpat2.html @@ -12,8 +12,8 @@ > <div class="footnote-text"> <!--l. 570--><p class="indent" > <span class="footnote-mark"><a - id="fn1x0"><a - id="x2-14002x"></a> <sup class="textsuperscript">1</sup></a></span><span + id="x2-14002x"></a><a + id="fn1x0"> <sup class="textsuperscript">1</sup></a></span><span class="cmr-8">Images of GUI screens are used only when essential to the information being</span> <span class="cmr-8">conveyed.</span></div> diff --git a/info/tex-vpat/texlive-vpat3.html b/info/tex-vpat/texlive-vpat3.html index 06caa9f153..67b2d0e6ed 100644 --- a/info/tex-vpat/texlive-vpat3.html +++ b/info/tex-vpat/texlive-vpat3.html @@ -10,8 +10,8 @@ <link rel="stylesheet" type="text/css" href="texlive-vpat.css"> </head><body > <div class="footnote-text"><span class="footnote-mark"><a - id="fn2x0"><a - id="x3-18003x2"></a> <sup class="textsuperscript">2</sup></a></span><span + id="x3-18003x2"></a><a + id="fn2x0"> <sup class="textsuperscript">2</sup></a></span><span class="cmr-8">See Table</span><span class="cmr-8"> 2: Success Criteria, Level</span><span class="cmr-8"> AA</span></div> diff --git a/info/tex-vpat/texlive-vpat4.html b/info/tex-vpat/texlive-vpat4.html index d0d3ad6104..4c976d8267 100644 --- a/info/tex-vpat/texlive-vpat4.html +++ b/info/tex-vpat/texlive-vpat4.html @@ -10,8 +10,8 @@ <link rel="stylesheet" type="text/css" href="texlive-vpat.css"> </head><body > <div class="footnote-text"><span class="footnote-mark"><a - id="fn3x0"><a - id="x4-19003x3"></a> <sup class="textsuperscript">3</sup></a></span><span + id="x4-19003x3"></a><a + id="fn3x0"> <sup class="textsuperscript">3</sup></a></span><span class="cmr-8">See WCAG</span><span class="cmr-8"> 2.x Report</span></div> </body></html> diff --git a/info/tex-vpat/texlive-vpat5.html b/info/tex-vpat/texlive-vpat5.html index e411503b40..e018e209d0 100644 --- a/info/tex-vpat/texlive-vpat5.html +++ b/info/tex-vpat/texlive-vpat5.html @@ -10,8 +10,8 @@ <link rel="stylesheet" type="text/css" href="texlive-vpat.css"> </head><body > <div class="footnote-text"><span class="footnote-mark"><a - id="fn4x0"><a - id="x5-27003x4"></a> <sup class="textsuperscript">4</sup></a></span><span + id="x5-27003x4"></a><a + id="fn4x0"> <sup class="textsuperscript">4</sup></a></span><span class="cmr-8">WCAG</span><span class="cmr-8"> 2.x Report</span></div> </body></html> diff --git a/info/tex-vpat/texlive-vpat6.html b/info/tex-vpat/texlive-vpat6.html index fec5b8464d..657c41f649 100644 --- a/info/tex-vpat/texlive-vpat6.html +++ b/info/tex-vpat/texlive-vpat6.html @@ -10,8 +10,8 @@ <link rel="stylesheet" type="text/css" href="texlive-vpat.css"> </head><body > <div class="footnote-text"><span class="footnote-mark"><a - id="fn5x0"><a - id="x6-28003x5"></a> <sup class="textsuperscript">5</sup></a></span><span + id="x6-28003x5"></a><a + id="fn5x0"> <sup class="textsuperscript">5</sup></a></span><span class="cmr-8">See WCAG</span><span class="cmr-8"> 2.x Report</span></div> </body></html> diff --git a/info/tex-vpat/texlive-vpat7.html b/info/tex-vpat/texlive-vpat7.html index 6d73328b06..cd73d2682e 100644 --- a/info/tex-vpat/texlive-vpat7.html +++ b/info/tex-vpat/texlive-vpat7.html @@ -10,7 +10,7 @@ <link rel="stylesheet" type="text/css" href="texlive-vpat.css"> </head><body > <div class="footnote-text"><span class="footnote-mark"><a - id="fn6x0"><a - id="x7-28005x6"></a> <sup class="textsuperscript">6</sup></a></span><span + id="x7-28005x6"></a><a + id="fn6x0"> <sup class="textsuperscript">6</sup></a></span><span class="cmr-8">See information in 11.5.2.5 through 11.5.2.17</span></div> </body></html> diff --git a/info/tex-vpat/texlive-vpat8.html b/info/tex-vpat/texlive-vpat8.html index 6ecaccd575..7630b7f5f9 100644 --- a/info/tex-vpat/texlive-vpat8.html +++ b/info/tex-vpat/texlive-vpat8.html @@ -10,7 +10,7 @@ <link rel="stylesheet" type="text/css" href="texlive-vpat.css"> </head><body > <div class="footnote-text"><span class="footnote-mark"><a - id="fn7x0"><a - id="x8-28007x7"></a> <sup class="textsuperscript">7</sup></a></span><span + id="x8-28007x7"></a><a + id="fn7x0"> <sup class="textsuperscript">7</sup></a></span><span class="cmr-8">See information in 11.5.2.5 through 11.5.2.17</span></div> </body></html> diff --git a/info/tex-vpat/texlive-vpat9.html b/info/tex-vpat/texlive-vpat9.html index 4021c71011..62e7b096fc 100644 --- a/info/tex-vpat/texlive-vpat9.html +++ b/info/tex-vpat/texlive-vpat9.html @@ -10,8 +10,8 @@ <link rel="stylesheet" type="text/css" href="texlive-vpat.css"> </head><body > <div class="footnote-text"><span class="footnote-mark"><a - id="fn8x0"><a - id="x9-29003x8"></a> <sup class="textsuperscript">8</sup></a></span><span + id="x9-29003x8"></a><a + id="fn8x0"> <sup class="textsuperscript">8</sup></a></span><span class="cmr-8">See WCAG</span><span class="cmr-8"> 2.x Report</span></div> </body></html> |