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diff --git a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-tikz-plots.tex b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-tikz-plots.tex new file mode 100644 index 00000000000..043ba4c5312 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-tikz-plots.tex @@ -0,0 +1,577 @@ +% Copyright 2007 by Till Tantau +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Free Documentation License. +% +% See the file doc/generic/pgf/licenses/LICENSE for more details. + + +\section{Plots of Functions} + +\label{section-tikz-plots} + +\subsection{When Should One Use \tikzname\ for Generating Plots? } + +\label{section-why-pgname-for-plots} + +There exist many powerful programs that produce plots, examples are +\textsc{gnuplot} or \textsc{mathematica}. These programs can produce +two different kinds of output: First, they can output a complete plot +picture in a certain format (like \pdf) that includes all low-level +commands necessary for drawing the complete plot (including axes and +labels). Second, they can usually also produce ``just plain data'' in +the form of a long list of coordinates. Most of the powerful programs +consider it a to be ``a bit boring'' to just output tabled data and +very much prefer to produce fancy pictures. Nevertheless, when coaxed, +they can also provide the plain data. + +\emph{Note that is often not necessary to use \tikzname\ for plots.} +Programs like \textsc{gnuplot} can produce very sophisticated plots +and it is usually much easier to simply include these plots as a +finished \textsc{pdf} or PostScript graphics. + +However, there are a number of reasons why you may wish to invest time +and energy into mastering the \pgfname\ commands for creating plots: + +\begin{itemize} +\item + Virtually all plots produced by ``external programs'' use different + fonts from the one used in your document. +\item + Even worse, formulas will look totally different, if they can be + rendered at all. +\item + Line width will usually be too large or too small. +\item + Scaling effects upon inclusion can create a mismatch between sizes + in the plot and sizes in the text. +\item + The automatic grid generated by most programs is mostly + distracting. +\item + The automatic ticks generated by most programs are cryptic + numerics. (Try adding a tick reading ``$\pi$'' at the right point.) +\item + Most programs make it very easy to create ``chart junk'' in a most + convenient fashion. All show, no content. +\item + Arrows and plot marks will almost never match the arrows used in the + rest of the document. +\end{itemize} + +The above list is not exhaustive, unfortunately. + + +\subsection{The Plot Path Operation} + +The |plot| path operation can be used to append a line or curve to the path +that goes through a large number of coordinates. These coordinates are +either given in a simple list of coordinates, read from some file, or +they are computed on the fly. + +The syntax of the |plot| comes in different versions. + +\begin{pathoperation}{--plot}{\meta{further arguments}} + This operation plots the curve through the coordinates specified in + the \meta{further arguments}. The current (sub)path is simply + continued, that is, a line-to operation to the first point of the + curve is implicitly added. The details of the \meta{further + arguments} will be explained in a moment. +\end{pathoperation} + +\begin{pathoperation}{plot}{\meta{further arguments}} + This operation plots the curve through the coordinates specified in + the \meta{further arguments} by first ``moving'' to the first + coordinate of the curve. +\end{pathoperation} + +The \meta{further arguments} are used in three different ways to +specifying the coordinates of the points to be plotted: + +\begin{enumerate} +\item + \opt{|--|}|plot|\oarg{local options}\declare{|coordinates{|\meta{coordinate + 1}\meta{coordinate 2}\dots\meta{coordinate $n$}|}|} +\item + \opt{|--|}|plot|\oarg{local options}\declare{|file{|\meta{filename}|}|} +\item + \opt{|--|}|plot|\oarg{local options}\declare{\meta{coordinate expression}} +\item + \opt{|--|}|plot|\oarg{local options}\declare{|function{|\meta{gnuplot formula}|}|} +\end{enumerate} + +These different ways are explained in the following. + + +\subsection{Plotting Points Given Inline} + +In the first two cases, the points are given directly in the \TeX-file +as in the following example: + +\begin{codeexample}[] +\tikz \draw plot coordinates {(0,0) (1,1) (2,0) (3,1) (2,1) (10:2cm)}; +\end{codeexample} + +Here is an example showing the difference between |plot| and |--plot|: + +\begin{codeexample}[] +\begin{tikzpicture} + \draw (0,0) -- (1,1) plot coordinates {(2,0) (4,0)}; + \draw[color=red,xshift=5cm] + (0,0) -- (1,1) -- plot coordinates {(2,0) (4,0)}; +\end{tikzpicture} +\end{codeexample} + + +\subsection{Plotting Points Read From an External File} + +The second way of specifying points is to put them in an external +file named \meta{filename}. Currently, the only file format that +\tikzname\ allows is the following: Each line of the \meta{filename} +should contain one line starting with two numbers, separated by a +space. Anything following the two numbers on the line is +ignored. Also, lines starting with a |%| or a |#| are ignored as well +as empty lines. (This is exactly the format that \textsc{gnuplot} +produces when you say |set terminal table|.) If necessary, more +formats will be supported in the future, but it is usually easy to +produce a file containing data in this form. + +\begin{codeexample}[] +\tikz \draw plot[mark=x,smooth] file {plots/pgfmanual-sine.table}; +\end{codeexample} + +The file |plots/pgfmanual-sine.table| reads: +\begin{codeexample}[code only] +#Curve 0, 20 points +#x y type +0.00000 0.00000 i +0.52632 0.50235 i +1.05263 0.86873 i +1.57895 0.99997 i +... +9.47368 -0.04889 i +10.00000 -0.54402 i +\end{codeexample} +It was produced from the following source, using |gnuplot|: +\begin{codeexample}[code only] +set terminal table +set output "../plots/pgfmanual-sine.table" +set format "%.5f" +set samples 20 +plot [x=0:10] sin(x) +\end{codeexample} + +The \meta{local options} of the |plot| operation are local to each +plot and do not affect other plots ``on the same path.'' For example, +|plot[yshift=1cm]| will locally shift the plot 1cm upward. Remember, +however, that most options can only be applied to paths as a +whole. For example, |plot[red]| does not have the effect of making the +plot red. After all, you are trying to ``locally'' make part of the +path red, which is not possible. + +\subsection{Plotting a Function} +\label{section-tikz-plot} + +When you plot a function, the coordinates of the plot data can be +computed by evaluating a mathematical expression. Since \pgfname\ +comes with a mathematical engine, you can specify this expression and +then have \tikzname\ produce the desired coordinates for you, +automatically. + +Since this case is quite common when plotting a function, the syntax +is easy: Following the |plot| command and its local options, you +directly provide a \meta{coordinate expression}. It looks like a +normal coordinate, but inside you may use a special macro, which is +|\x| by default, but this can be changed using the |variable| +option. The \meta{coordinate expression} is then evaluated for +different values for |\x| and the resulting coordinates are plotted. + +Note that you will often have to put the $x$- or $y$-coordinate inside +braces, namely whenever you use an expression involving a paranthesis. + +The following options influence how the \meta{coordinate expression} +is evaluated: +\begin{itemize} + \itemoption{variable}|=|\meta{macro} + sets the macro whose value is set to the different values when + \meta{coordinate expression} is evaluated. + \itemoption{samples}|=|\meta{number} + sets the number of samples used in the plot. The default is 25. + \itemoption{domain}|=|\meta{start}|:|\meta{end} + sets the domain between which the samples are taken. The default is + |-5:5|. + \itemoption{samples at}|=|\meta{sample list} + This option specifies a list of positions for which the + variable should be evaluated. For instance, you can say + |samples at={1,2,8,9,10}| to have the variable evaluated exactly for + values $1$, $2$, $8$, $9$, and $10$. You can use the |\foreach| + syntax, so you can use |...| inside the \meta{sample list}. + + When this option is used, the |samples| and |domain| option are + overruled. The other ways round, setting either |samples| or + |domain| will overrule this option. +\end{itemize} + +\begin{codeexample}[] +\begin{tikzpicture}[domain=0:4] + \draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9); + + \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$}; + \draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$}; + + \draw[color=red] plot (\x,\x) node[right] {$f(x) =x$}; + \draw[color=blue] plot (\x,{sin(\x r)}) node[right] {$f(x) = \sin x$}; + \draw[color=orange] plot (\x,{0.05*exp(\x)}) node[right] {$f(x) = \frac{1}{20} \mathrm e^x$}; +\end{tikzpicture} +\end{codeexample} + +\begin{codeexample}[] +\tikz \draw[scale=0.5,domain=-3.141:3.141,smooth,variable=\t] + plot ({\t*sin(\t r)},{\t*cos(\t r)}); +\end{codeexample} + +\begin{codeexample}[] +\tikz \draw[domain=0:360,smooth,variable=\t] + plot ({sin(\t)},\t/360,{cos(\t)}); +\end{codeexample} + + +\subsection{Plotting a Function Using Gnuplot} +\label{section-tikz-gnuplot} + +Often, you will want to plot points that are given via a function like +$f(x) = x \sin x$. Unfortunately, \TeX\ does not really have enough +computational power to generate the points on such a function +efficiently (it is a text processing program, after all). However, +if you allow it, \TeX\ can try to call external programs that can +easily produce the necessary points. Currently, \tikzname\ knows how to +call \textsc{gnuplot}. + +When \tikzname\ encounters your operation +|plot[id=|\meta{id}|] function{x*sin(x)}| for +the first time, it will create a file called +\meta{prefix}\meta{id}|.gnuplot|, where \meta{prefix} is |\jobname.| by +default, that is, the name of you main |.tex| file. If no \meta{id} is +given, it will be empty, which is alright, but it is better when each +plot has a unique \meta{id} for reasons explained in a moment. Next, +\tikzname\ writes some initialization code into this file followed by +|plot x*sin(x)|. The initialization code sets up things +such that the |plot| operation will write the coordinates into another +file called \meta{prefix}\meta{id}|.table|. Finally, this table file +is read as if you had said |plot file{|\meta{prefix}\meta{id}|.table}|. + +For the plotting mechanism to work, two conditions must be met: +\begin{enumerate} +\item + You must have allowed \TeX\ to call external programs. This is often + switched off by default since this is a security risk (you might, + without knowing, run a \TeX\ file that calls all sorts of ``bad'' + commands). To enable this ``calling external programs'' a command + line option must be given to the \TeX\ program. Usually, it is + called something like |shell-escape| or |enable-write18|. For + example, for my |pdflatex| the option |--shell-escape| can be + given. +\item + You must have installed the |gnuplot| program and \TeX\ must find it + when compiling your file. +\end{enumerate} + +Unfortunately, these conditions will not always be met. Especially if +you pass some source to a coauthor and the coauthor does not have +\textsc{gnuplot} installed, he or she will have trouble compiling your +files. + +For this reason, \tikzname\ behaves differently when you compile your +graphic for the second time: If upon reaching +|plot[id=|\meta{id}|] function{...}| the file \meta{prefix}\meta{id}|.table| +already exists \emph{and} if the \meta{prefix}\meta{id}|.gnuplot| file +contains what \tikzname\ thinks that it ``should'' contain, the |.table| +file is immediately read without trying to call a |gnuplot| +program. This approach has the following advantages: +\begin{enumerate} +\item + If you pass a bundle of your |.tex| file and all |.gnuplot| and + |.table| files to someone else, that person can \TeX\ the |.tex| + file without having to have |gnuplot| installed. +\item + If the |\write18| feature is switched off for security reasons (a + good idea), then, upon the first compilation of the |.tex| file, the + |.gnuplot| will still be generated, but not the |.table| + file. You can then simply call |gnuplot| ``by hand'' for each + |.gnuplot| file, which will produce all necessary |.table| files. +\item + If you change the function that you wish to plot or its + domain, \tikzname\ will automatically try to regenerate the |.table| + file. +\item + If, out of laziness, you do not provide an |id|, the same |.gnuplot| + will be used for different plots, but this is not a problem since + the |.table| will automatically be regenerated for each plot + on-the-fly. \emph{Note: If you intend to share your files with + someone else, always use an id, so that the file can by typeset + without having \textsc{gnuplot} installed.} Also, having unique ids + for each plot will improve compilation speed since no external + programs need to be called, unless it is really necessary. +\end{enumerate} + +When you use |plot function{|\meta{gnuplot formula}|}|, the \meta{gnuplot + formula} must be given in the |gnuplot| syntax, whose details are +beyond the scope of this manual. Here is the ultra-condensed +essence: Use |x| as the variable and use the C-syntax for normal +plots, use |t| as the variable for parametric plots. Here are some examples: + +\begin{codeexample}[] +\begin{tikzpicture}[domain=0:4] + \draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9); + + \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$}; + \draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$}; + + \draw[color=red] plot[id=x] function{x} node[right] {$f(x) =x$}; + \draw[color=blue] plot[id=sin] function{sin(x)} node[right] {$f(x) = \sin x$}; + \draw[color=orange] plot[id=exp] function{0.05*exp(x)} node[right] {$f(x) = \frac{1}{20} \mathrm e^x$}; +\end{tikzpicture} +\end{codeexample} + + +The following options influence the plot: + +\begin{itemize} + \itemoption{samples}|=|\meta{number} + sets the number of samples used in the plot. The default is 25. + \itemoption{domain}|=|\meta{start}|:|\meta{end} + sets the domain between which the samples are taken. The default is + |-5:5|. + \itemoption{parametric}\opt{|=|\meta{true or false}} + sets whether the plot is a parametric plot. If true, then |t| must + be used instead of |x| as the parameter and two comma-separated + functions must be given in the \meta{gnuplot formula}. An example is + the following: +\begin{codeexample}[] +\tikz \draw[scale=0.5,domain=-3.141:3.141,smooth] + plot[parametric,id=parametric-example] function{t*sin(t),t*cos(t)}; +\end{codeexample} + + \itemoption{id}|=|\meta{id} + sets the identifier of the current plot. This should be a unique + identifier for each plot (though things will also work if it is not, + but not as well, see the explanations above). The \meta{id} will be + part of a filename, so it should not contain anything fancy like |*| + or |$|.%$ + \itemoption{prefix}|=|\meta{prefix} + is put before each plot file name. The default is |\jobname.|, but + if you have many plots, it might be better to use, say |plots/| and + have all plots placed in a directory. You have to create the + directory yourself. + \itemoption{raw gnuplot} + causes the \meta{gnuplot formula} to be passed on to + \textsc{gnuplot} without setting up the samples or the |plot| + operation. Thus, you could write +\begin{codeexample}[code only] +plot[raw gnuplot,id=raw-example] function{set samples 25; plot sin(x)} +\end{codeexample} + This can be + useful for complicated things that need to be passed to + \textsc{gnuplot}. However, for really complicated situations you + should create a special external generating \textsc{gnuplot} file + and use the |file|-syntax to include the table ``by hand.'' +\end{itemize} + +The following styles influence the plot: +\begin{itemize} + \itemstyle{every plot} + This style is installed in each plot, that is, as if you always said +\begin{codeexample}[code only] + plot[style=every plot,...] +\end{codeexample} + This is most useful for globally setting a prefix for all plots by saying: +\begin{codeexample}[code only] +\tikzstyle{every plot}=[prefix=plots/] +\end{codeexample} +\end{itemize} + + + +\subsection{Placing Marks on the Plot} + +As we saw already, it is possible to add \emph{marks} to a plot using +the |mark| option. When this option is used, a copy of the plot +mark is placed on each point of the plot. Note that the marks are +placed \emph{after} the whole path has been drawn/filled/shaded. In +this respect, they are handled like text nodes. + +In detail, the following options govern how marks are drawn: +\begin{itemize} + \itemoption{mark}|=|\meta{mark mnemonic} + Sets the mark to a mnemonic that has previously been defined using + the |\pgfdeclareplotmark|. By default, |*|, |+|, and |x| are available, + which draw a filled circle, a plus, and a cross as marks. Many more + marks become available when the library |pgflibraryplotmarks| is + loaded. Section~\ref{section-plot-marks} lists the available plot + marks. + + One plot mark is special: the |ball| plot mark is available only + it \tikzname. The |ball color| determines the balls's color. Do not use + this option with a large number of marks since it will take very long + to render in PostScript. + + \begin{tabular}{lc} + Option & Effect \\\hline \vrule height14pt width0pt + \plotmarkentrytikz{ball} + \end{tabular} + + \itemoption{mark repeat}|=|\meta{r} + This option tells \tikzname\ that only every $r$th mark should be + drawn. + +\begin{codeexample}[] +\tikz \draw plot[mark=x,mark repeat=3,smooth] file {plots/pgfmanual-sine.table}; +\end{codeexample} + + \itemoption{mark phase}|=|\meta{p} + This option tells \tikzname\ that the first mark to be draw should + be the $p$th, followed by the $(p+r)$th, then the $(p+2r)$th, and so + on. + +\begin{codeexample}[] +\tikz \draw plot[mark=x,mark repeat=3,mark phase=6,smooth] file {plots/pgfmanual-sine.table}; +\end{codeexample} + + \itemoption{mark indices}|=|\meta{list} + This option allows you to specify explicitly the indices at which a + mark should be placed. Counting starts with 1. You can use the + |\foreach| syntax, that is, |...| can be used. + +\begin{codeexample}[] +\tikz \draw plot[mark=x,mark indices={1,4,...,10,11,12,...,16,20},smooth] + file {plots/pgfmanual-sine.table}; +\end{codeexample} + + \itemoption{mark size}|=|\meta{dimension} + Sets the size of the plot marks. For circular plot marks, + \meta{dimension} is the radius, for other plot marks + \meta{dimension} should be about half the width and height. + + This option is not really necessary, since you achieve the same + effect by specifying |scale=|\meta{factor} as a local option, where + \meta{factor} is the quotient of the desired size and the default + size. However, using |mark size| is a bit faster and more natural. + + \itemoption{mark options}|=|\meta{options} + These options are applied to marks when they are drawn. For example, + you can scale (or otherwise transform) the plot mark or set its + color. +\begin{codeexample}[] +\tikz \fill[fill=blue!20] + plot[mark=triangle*,mark options={color=blue,rotate=180}] + file{plots/pgfmanual-sine.table} |- (0,0); +\end{codeexample} +\end{itemize} + + + +\subsection{Smooth Plots, Sharp Plots, and Comb Plots} + +There are different things the |plot| operation can do with the points +it reads from a file or from the inlined list of points. By default, +it will connect these points by straight lines. However, you can also +use options to change the behavior of |plot|. + +\begin{itemize} + \itemoption{sharp plot} + This is the default and causes the points to be connected by + straight lines. This option is included only so that you can + ``switch back'' if you ``globally'' install, say, |smooth|. + + \itemoption{smooth} + This option causes the points on the path to be connected using a + smooth curve: + +\begin{codeexample}[] +\tikz\draw plot[smooth] file{plots/pgfmanual-sine.table}; +\end{codeexample} + + Note that the smoothing algorithm is not very intelligent. You will + get the best results if the bending angles are small, that is, less + than about $30^\circ$ and, even more importantly, if the distances + between points are about the same all over the plotting path. + + \itemoption{tension}|=|\meta{value} + This option influences how ``tight'' the smoothing is. A lower value + will result in sharper corners, a higher value in more ``round'' + curves. A value of $1$ results in a circle if four points at + quarter-positions on a circle are given. The default is $0.55$. The + ``correct'' value depends on the details of plot. + +\begin{codeexample}[] +\begin{tikzpicture}[smooth cycle] + \draw plot[tension=0.2] + coordinates{(0,0) (1,1) (2,0) (1,-1)}; + \draw[yshift=-2.25cm] plot[tension=0.5] + coordinates{(0,0) (1,1) (2,0) (1,-1)}; + \draw[yshift=-4.5cm] plot[tension=1] + coordinates{(0,0) (1,1) (2,0) (1,-1)}; +\end{tikzpicture} +\end{codeexample} + + \itemoption{smooth cycle} + This option causes the points on the path to be connected using a + closed smooth curve. + +\begin{codeexample}[] +\tikz[scale=0.5] + \draw plot[smooth cycle] coordinates{(0,0) (1,0) (2,1) (1,2)} + plot coordinates{(0,0) (1,0) (2,1) (1,2)} -- cycle; +\end{codeexample} + + \itemoption{ycomb} + This option causes the |plot| operation to interpret the plotting + points differently. Instead of connecting them, for each point of + the plot a straight line is added to the path from the $x$-axis to the point, + resulting in a sort of ``comb'' or ``bar diagram.'' + +\begin{codeexample}[] +\tikz\draw[ultra thick] plot[ycomb,thin,mark=*] file{plots/pgfmanual-sine.table}; +\end{codeexample} + +\begin{codeexample}[] +\begin{tikzpicture}[ycomb] + \draw[color=red,line width=6pt] + plot coordinates{(0,1) (.5,1.2) (1,.6) (1.5,.7) (2,.9)}; + \draw[color=red!50,line width=4pt,xshift=3pt] + plot coordinates{(0,1.2) (.5,1.3) (1,.5) (1.5,.2) (2,.5)}; +\end{tikzpicture} +\end{codeexample} + + \itemoption{xcomb} + This option works like |ycomb| except that the bars are horizontal. + +\begin{codeexample}[] +\tikz \draw plot[xcomb,mark=x] coordinates{(1,0) (0.8,0.2) (0.6,0.4) (0.2,1)}; +\end{codeexample} + + \itemoption{polar comb} + This option causes a line from the origin to the point to be added + to the path for each plot point. + +\begin{codeexample}[] +\tikz \draw plot[polar comb, + mark=pentagon*,mark options={fill=white,draw=red},mark size=4pt] + coordinates {(0:1cm) (30:1.5cm) (160:.5cm) (250:2cm) (-60:.8cm)}; +\end{codeexample} + + + \itemoption{only marks} + This option causes only marks to be shown; no path segments are + added to the actual path. This can be useful for quickly adding some + marks to a path. + +\begin{codeexample}[] +\tikz \draw (0,0) sin (1,1) cos (2,0) + plot[only marks,mark=x] coordinates{(0,0) (1,1) (2,0) (3,-1)}; +\end{codeexample} +\end{itemize} + + |