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diff --git a/Build/source/utils/asymptote/doc/extra/intro.asy b/Build/source/utils/asymptote/doc/extra/intro.asy index 4234b8cee8e..20b03c578dc 100644 --- a/Build/source/utils/asymptote/doc/extra/intro.asy +++ b/Build/source/utils/asymptote/doc/extra/intro.asy @@ -1,5 +1,3 @@ -// Introduction to Asymptote - orientation=Landscape; settings.tex="pdflatex"; @@ -8,6 +6,10 @@ import slide; import three; import animate; +bool long=true; + +usepackage("mflogo"); + usersetting(); viewportsize=pagewidth-2pagemargin; @@ -18,23 +20,39 @@ viewportsize=pagewidth-2pagemargin; bibliographystyle("alpha"); itempen=fontsize(22pt); - -titlepage("Asymptote: The Vector Graphics Language", - "Andy Hammerlindl and John Bowman", - "University of Toronto and University of Alberta","August 16, 2007", - "http://asymptote.sf.net"); +defaultpen(itempen); +viewportmargin=(2,2); + +titlepage(long ? "Asymptote: The Vector Graphics Language" : + "Interactive TeX-Aware 3D Vector Graphics", + "John Bowman and Andy Hammerlindl", +"Department of Mathematical and Statistical Sciences\\ + University of Alberta\\ +%and Instituto Nacional de Matem\'atica Pura e Aplicada (IMPA) +\medskip\Green{Collaborators: Orest Shardt, Michail Vidiassov}", +"June 30, 2010", +"http://asymptote.sf.net/intro.pdf"); title("History"); -item("\TeX\ and METAFONT (Knuth, 1979)"); -item("MetaPost (Hobby, 1989): 2D Bezier Control Point Selection"); -item("Asymptote (Hammerlindl, Bowman, Prince, 2004): 2D \& 3D Graphics"); - -title("Statistics (as of April, 2007)"); -item("Runs on Windows, Mac OS X, Linux, etc."); -item("1800 downloads a month from {\tt asymptote.sourceforge.net}."); -item("33\ 000 lines of C++ code."); -item("18\ 000 lines of Asymptote code."); - +item("1979: \TeX\ and \MF\ (Knuth)"); +item("1986: 2D B\'ezier control point selection (Hobby)"); +item("1989: MetaPost (Hobby)"); +item("2004: Asymptote"); +subitem("2004: initial public release (Hammerlindl, Bowman, \& Prince)"); +subitem("2005: 3D B\'ezier control point selection (Bowman)"); +subitem("2008: 3D interactive \TeX\ within PDF files (Shardt \& Bowman)"); +subitem("2009: 3D billboard labels that always face camera (Bowman)"); +subitem("2010: 3D PDF enhancements (Vidiassov \& Bowman)"); + +title("Statistics (as of June, 2010)"); +item("Runs under Linux/UNIX, Mac OS X, Microsoft Windows."); +item("4000 downloads/month from primary\hfill\\ + {\tt asymptote.sourceforge.net} site alone."); +item("80\ 000 lines of low-level C++ code."); +item("36\ 000 lines of high-level Asymptote code."); +item("Latest stable release: Version 2.00 (LGPL)."); + +if(long) { title("Vector Graphics"); item("Raster graphics assign colors to a grid of pixels."); figure("pixel.pdf"); @@ -61,17 +79,24 @@ add(zoom(100), (0,0)); add(zoom(10), (200,0)); add(zoom(1), (400,0)); ")); +} title("Cartesian Coordinates"); + +item("Asymptote's graphical capabilities are based on four primitive + commands: {\tt draw}, {\tt label}, {\tt fill}, {\tt clip} \cite{Bowman08}"); + asyfilecode("diagonal"); item("units are {\tt PostScript} {\it big points\/} (1 {\tt bp} = 1/72 {\tt inch})"); item("{\tt --} means join the points with a linear segment to create a {\it path}"); -item("cyclic path:"); +item("{\it cyclic\/} path:"); -asyfilecode("square"); +asycode(" +draw((0,0)--(100,0)--(100,100)--(0,100)--cycle); +"); title("Scaling to a Given Size"); @@ -79,11 +104,7 @@ item("{\tt PostScript} units are often inconvenient."); item("Instead, scale user coordinates to a specified final size:"); -code(" -size(101,101); -draw((0,0)--(1,0)--(1,1)--(0,1)--cycle); -"); -asyfigure("square"); +asyfilecode("square"); item("One can also specify the size in {\tt cm}:"); @@ -96,18 +117,36 @@ title("Labels"); item("Adding and aligning \LaTeX\ labels is easy:"); -asyfilecode("labelsquare","height=6cm"); - +asycode(preamble="defaultpen(fontsize("+string(fontsize(itempen))+"));", +"size(6cm); +draw(unitsquare); +label(\"$A$\",(0,0),SW); +label(\"$B$\",(1,0),SE); +label(\"$C$\",(1,1),NE); +label(\"$D$\",(0,1),NW); +"); -title("2D Bezier Splines"); +title("2D B\'ezier Splines"); -item("Using {\tt ..} instead of {\tt --} specifies a {\it Bezier cubic +item("Using {\tt ..} instead of {\tt --} specifies a {\it B\'ezier cubic spline}:"); code(" draw(z0 .. controls c0 and c1 .. z1,blue); "); -asyfigure("beziercurve","height=7cm"); +asyfigure(asywrite("defaultpen(fontsize("+string(fontsize(itempen))+")); +size(0,7cm); +pair z0=(0,0); +pair c0=(1,1); +pair c1=(2,1); +pair z1=(3,0); +draw(z0..controls c0 and c1 .. z1,blue); +draw(z0--c0--c1--z1,dashed); +dot(\"$z_0$\",z0,W,red); +dot(\"$c_0$\",c0,NW,red); +dot(\"$c_1$\",c1,NE,red); +dot(\"$z_1$\",z1,red); +")); equation("(1-t)^3 z_0+3t(1-t)^2 c_0+3t^2(1-t) c_1+t^3 z_1, \qquad t\in [0,1]."); @@ -139,7 +178,7 @@ dot(z); picture output; save(); -for (int i=0; i<length(p); ++i) { +for(int i=0; i<length(p); ++i) { pair z=point(p,i), dir=dir(p,i); draw((z-0.3dir)--(z+0.3dir), Arrow); } @@ -148,7 +187,7 @@ restore(); save(); guide g; -for (int i=0; i<length(p); ++i) { +for(int i=0; i<length(p); ++i) { dot(precontrol(p,i)); dot(postcontrol(p,i)); g=g--precontrol(p,i)--point(p,i)--postcontrol(p,i); @@ -161,16 +200,18 @@ shipout(output); ")); title("Filling"); -item("Use {\tt fill} to fill the inside of a path:"); +item("The {\tt fill} primitive to fill the inside of a path:"); asycode(preamble="size(0,200);"," path star; -for (int i=0; i<5; ++i) +for(int i=0; i < 5; ++i) star=star--dir(90+144i); star=star--cycle; -fill(shift(-1,0)*star,orange+zerowinding); -draw(shift(-1,0)*star,linewidth(3)); -fill(shift(1,0)*star,blue+evenodd); -draw(shift(1,0)*star,linewidth(3)); + +fill(star,orange+zerowinding); +draw(star,linewidth(3)); + +fill(shift(2,0)*star,blue+evenodd); +draw(shift(2,0)*star,linewidth(3)); "); title("Filling"); @@ -181,29 +222,23 @@ fill(p,green+zerowinding); "); title("Clipping"); -item("Pictures can be clipped to lie inside a path:"); +item("Pictures can be clipped to a path:"); asycode(preamble=" size(0,200); guide star; -for (int i=0; i<5; ++i) +for(int i=0; i<5; ++i) star=star--dir(90+144i); star=star--cycle;"," fill(star,orange+zerowinding); clip(scale(0.7)*unitcircle); draw(scale(0.7)*unitcircle); "); -item("All of Asymptote's graphical capabilities are based on four primitive - commands: {\tt draw}, {\tt fill}, {\tt clip}, and {\tt label}."); title("Affine Transforms"); -item("Affine transformations: shifts, rotations, reflections, and scalings."); -code(" -transform t=rotate(90); -write(t*(1,0)); // Writes (0,1). -"); +item("Affine transformations: shifts, rotations, reflections, and scalings + can be applied to pairs, paths, pens, strings, and even whole pictures:"); -item("Pairs, paths, pens, strings, and whole pictures can be transformed."); code(" fill(P,blue); fill(shift(2,0)*reflect((0,0),(0,1))*P, red); @@ -231,6 +266,7 @@ fill(shift(4,0)*rotate(30)*P, yellow); fill(shift(6,0)*yscale(0.7)*xscale(2)*P, green); ")); +if(long) { title("C++/Java-like Programming Syntax"); code("// Declaration: Declare x to be real: @@ -250,287 +286,11 @@ if(x == 1.0) { for(int i=0; i < 10; ++i) { write(i); }"); - -title("Helpful Math Notation"); - -item("Integer division returns a {\tt real}. Use {\tt quotient} for an integer - result:"); -code("3/4==0.75 quotient(3,4)==0"); - -item("Caret for real and integer exponentiation:"); -code("2^3 2.7^3 2.7^3.2"); - -item("Many expressions can be implicitly scaled by a numeric constant:"); -code("2pi 10cm 2x^2 3sin(x) 2(a+b)"); - -item("Pairs are complex numbers:"); -code("(0,1)*(0,1)==(-1,0)"); - -title("Function Calls"); - -item("Functions can take default arguments in any position. Arguments are - matched to the first possible location:"); -string unitsize="unitsize(0.65cm);"; -string preamble="void drawEllipse(real xsize=1, real ysize=xsize, pen p=blue) { - draw(xscale(xsize)*yscale(ysize)*unitcircle, p); -} -"; - -asycode(preamble=unitsize,preamble+" -drawEllipse(2); -drawEllipse(red); -"); - -item("Arguments can be given by name:"); -asycode(preamble=unitsize+preamble," -drawEllipse(xsize=2, ysize=1); -drawEllipse(ysize=2, xsize=3, green); -"); - -title("Rest Arguments"); -item("Rest arguments allow one to write a function that takes an arbitrary - number of arguments:"); -code(" -int sum(... int[] nums) { - int total=0; - for (int i=0; i < nums.length; ++i) - total += nums[i]; - return total; -} - -sum(1,2,3,4); // returns 10 -sum(); // returns 0 -sum(1,2,3 ... new int[] {4,5,6}); // returns 21 - -int subtract(int start ... int[] subs) { - return start - sum(... subs); -} -"); - -title("Higher-Order Functions"); - -item("Functions are first-class values. They can be passed to other - functions:"); -code("real f(real x) { - return x*sin(10x); -} -draw(graph(f,-3,3,300),red);"); -asyfigure(asywrite(" -import graph; -size(300,0); -real f(real x) { - return x*sin(10x); -} -draw(graph(f,-3,3,300),red); -")); - -title("Higher-Order Functions"); -item("Functions can return functions:"); -equation("f_n(x)=n\sin\left(\frac{x}{n}\right)."); -skip(); -string preamble=" -import graph; -size(300,0); -"; -string graphfunc2=" -typedef real func(real); -func f(int n) { - real fn(real x) { - return n*sin(x/n); - } - return fn; -} - -func f1=f(1); -real y=f1(pi); - -for (int i=1; i<=5; ++i) - draw(graph(f(i),-10,10),red); -"; -code(graphfunc2); -string name=asywrite(graphfunc2,preamble=preamble); -asy(nativeformat(),name+".asy"); -label(graphic(name+"."+nativeformat()),(0.5,0), - Fill(figureborder,figuremattpen)); - -title("Anonymous Functions"); - -item("Create new functions with {\tt new}:"); -code(" -path p=graph(new real (real x) { return x*sin(10x); },-3,3,red); - -func f(int n) { - return new real (real x) { return n*sin(x/n); }; -}"); - -item("Function definitions are just syntactic sugar for assigning function -objects to variables."); -code(" -real square(real x) { - return x^2; -} -"); - -remark("is equivalent to"); -code(" -real square(real x); -square=new real (real x) { - return x^2; -}; -"); - -title("Structures"); - -item("As in other languages, structures group together data."); -code(" -struct Person { - string firstname, lastname; - int age; -} -Person bob=new Person; -bob.firstname=\"Bob\"; -bob.lastname=\"Chesterton\"; -bob.age=24; -"); - -item("Any code in the structure body will be executed every time a new structure - is allocated..."); -code(" -struct Person { - write(\"Making a person.\"); - string firstname, lastname; - int age=18; -} -Person eve=new Person; // Writes \"Making a person.\" -write(eve.age); // Writes 18. -"); - -title("Object-Oriented Programming"); -item("Functions are defined for each instance of a structure."); -code(" -struct Quadratic { - real a,b,c; - real discriminant() { - return b^2-4*a*c; - } - real eval(real x) { - return a*x^2 + b*x + c; - } -} -"); - -item("This allows us to construct ``methods'' which are just normal functions - declared in the environment of a particular object:"); -code(" -Quadratic poly=new Quadratic; -poly.a=-1; poly.b=1; poly.c=2; - -real f(real x)=poly.eval; -real y=f(2); -draw(graph(poly.eval, -5, 5)); -"); - -title("Specialization"); - -item("Can create specialized objects just by redefining methods:"); -code(" -struct Shape { - void draw(); - real area(); -} - -Shape rectangle(real w, real h) { - Shape s=new Shape; - s.draw = new void () { - fill((0,0)--(w,0)--(w,h)--(0,h)--cycle); }; - s.area = new real () { return w*h; }; - return s; -} - -Shape circle(real radius) { - Shape s=new Shape; - s.draw = new void () { fill(scale(radius)*unitcircle); }; - s.area = new real () { return pi*radius^2; } - return s; -} -"); - -title("Overloading"); -item("Consider the code:"); -code(" -int x1=2; -int x2() { - return 7; -} -int x3(int y) { - return 2y; -} - -write(x1+x2()); // Writes 9. -write(x3(x1)+x2()); // Writes 11. -"); - -title("Overloading"); -item("{\tt x1}, {\tt x2}, and {\tt x3} are never used in the same context, so - they can all be renamed {\tt x} without ambiguity:"); -code(" -int x=2; -int x() { - return 7; -} -int x(int y) { - return 2y; } -write(x+x()); // Writes 9. -write(x(x)+x()); // Writes 11. -"); - -item("Function definitions are just variable definitions, but variables are - distinguished by their signatures to allow overloading."); - -title("Operators"); -item("Operators are just syntactic sugar for functions, and can be addressed or - defined as functions with the {\tt operator} keyword."); -code(" -int add(int x, int y)=operator +; -write(add(2,3)); // Writes 5. - -// Don't try this at home. -int operator +(int x, int y) { - return add(2x,y); -} -write(2+3); // Writes 7. -"); -item("This allows operators to be defined for new types."); - -title("Operators"); -item("Operators for constructing paths are also functions:"); -code("a.. controls b and c .. d--e"); -remark("is equivalent to"); -code( - "operator --(operator ..(a, operator controls(b,c), d), e)"); -item("This allowed us to redefine all of the path operators for 3D paths."); -asyfigure("helix","height=10cm"); - -title("Packages"); - -item("Function and structure definitions can be grouped into packages:"); -code(" -// powers.asy -real square(real x) { return x^2; } -real cube(real x) { return x^3; } -"); -remark("and imported:"); -code(" -import powers; -real eight=cube(2.0); -draw(graph(powers.square, -1, 1)); -"); - -title("Packages"); +title("Modules"); -item("There are packages for Feynman diagrams,"); +item("There are modules for Feynman diagrams,"); asyfigure("eetomumu","height=6cm"); remark("data structures,"); asyfigure(asywrite(" @@ -547,6 +307,7 @@ equations("\Phi\Phi(x_1,x_2,x_3,x_4,x_5) + &\rho_{4a}(x_1,x_2+x_3,x_4,x_5) - \rho_{4b}(x_1,x_2,x_3,x_4+x_5) \\ - &\rho_{4a}(x_1+x_2,x_3,x_4,x_5) - \rho_{4a}(x_1,x_2,x_4,x_5)."); +if(long) { title("Textbook Graph"); asy(nativeformat(),"exp"); filecode("exp.asy"); @@ -564,18 +325,20 @@ asyfilecode("filegraph","height=15cm",newslide=true); title("Logarithmic Graph"); asyfilecode("loggraph","height=15cm",newslide=true); - title("Secondary Axis"); +} else +title("Scientific Graph"); + asyfigure("secondaryaxis","height=15cm"); -title("Images"); +title("Images and Contours"); asyfigure("imagecontour","height=17cm"); title("Multiple Graphs"); asyfigure("diatom","height=17cm"); title("Hobby's 2D Direction Algorithm"); -item("A tridiagonal system of linear equations is solved to determine any unspecified directions $\theta_k$ and $\phi_k$ through each knot $z_k$:"); +item("A tridiagonal system of linear equations is solved to determine any unspecified directions $\phi_k$ and $\theta_k$ through each knot $z_k$:"); equation("\frac{\theta_{k-1}-2\phi_k}{\ell_k}= \frac{\phi_{k+1}-2\theta_k}{\ell_{k+1}}."); @@ -584,39 +347,43 @@ asyfigure("Hobbydir","height=9cm"); item("The resulting shape may be adjusted by modifying optional {\it tension\/} parameters and {\it curl\/} boundary conditions."); -//involving the curvature - title("Hobby's 2D Control Point Algorithm"); item("Having prescribed outgoing and incoming path directions $e^{i\theta}$ at node~$z_0$ and $e^{i\phi}$ at node $z_1$ relative to the vector $z_1-z_0$, the control points are determined as:"); +skip(-3); + equations("u&=&z_0+e^{i\theta}(z_1-z_0)f(\theta,-\phi),\nonumber\\ v&=&z_1-e^{i\phi}(z_1-z_0)f(-\phi,\theta),"); +skip(-3); + remark("where the relative distance function $f(\theta,\phi)$ is given by Hobby [1986]."); asyfigure("Hobbycontrol","height=9cm"); -title("Bezier Curves in 3D"); +if(long) { +title("B\'ezier Curves in 3D"); item("Apply an affine transformation"); equation("x'_i=A_{ij} x_j+C_i"); -remark("to a Bezier curve:"); +remark("to a B\'ezier curve:"); -equation("x(t)=\sum_{k=0}^3 B_k(t) P_k, \qquad t\in [0,1]."); +equation("\displaystyle x(t)=\sum_{k=0}^3 B_k(t) P_k, \qquad t\in [0,1]."); -item("The resulting curve is also a Bezier curve:"); +item("The resulting curve is also a B\'ezier curve:"); equations("x'_i(t)&=&\sum_{k=0}^3 B_k(t) A_{ij}(P_k)_j+C_i\nonumber\\ &=&\sum_{k=0}^3 B_k(t) P'_k,"); remark("where $P'_k$ is the transformed $k^{\rm th}$ control point, noting $\displaystyle\sum_{k=0}^3 B_k(t)=1.$"); +} -title("3D Generalization of Hobby's algorithm"); +title("3D Generalization of Direction Algorithm"); item("Must reduce to 2D algorithm in planar case."); @@ -625,12 +392,12 @@ item("Determine directions by applying Hobby's algorithm in the plane containing // Reformulate Hobby's equations in terms of the angle $\psi_k=$ item("The only ambiguity that can arise is the overall sign of the angles, which relates to viewing each 2D plane from opposing normal directions."); -item("A reference vector based on the mean unit normal of successive segments can be used to resolve such ambiguities."); +item("A reference vector based on the mean unit normal of successive segments can be used to resolve such ambiguities \cite{Bowman07,Bowman09}"); title("3D Control Point Algorithm"); -item("Hobby's control point algorithm can be generalized to 3D by expressing it in terms of the absolute directions $\omega_0$ and $\omega_1$:"); - +item("Express Hobby's algorithm in terms of the absolute directions $\omega_0$ and~$\omega_1$:"); +skip(-1); equation("u=z_0+\omega_0\left|z_1-z_0\right|f(\theta,-\phi),"); equation("v=z_1-\omega_1\left|z_1-z_0\right|f(-\phi,\theta),"); @@ -638,29 +405,46 @@ asyfigure("Hobbycontrol"); remark("interpreting $\theta$ and $\phi$ as the angle between the corresponding path direction vector and $z_1-z_0$."); -item("In this case there is an unambiguous reference vector for determining the relative sign of the angles $\phi$ and $\theta$."); +item("Here there is an unambiguous reference vector for determining the relative sign of the angles $\phi$ and $\theta$."); -viewportmargin=(0,0.5cm); -defaultpen(1.0); +viewportmargin=(2,0.5cm); +//defaultpen(1.0); title("Interactive 3D Saddle"); -item("A unit circle in the $X$--$Y$ plane may be filled and drawn with: -(1,0,0)..(0,1,0)..(-1,0,0)..(0,-1,0)..cycle"); +item("A unit circle in the $X$--$Y$ plane may be constructed with: +{\tt (1,0,0)..(0,1,0)..(-1,0,0)..(0,-1,0)..cycle}:"); asyinclude("unitcircle3",8cm); -remark("and then distorted into a saddle:\\ (1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle"); +remark("and then distorted into the saddle\\ +{\tt (1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle}:"); asyinclude("saddle",8cm); +//defaultpen(0.5); + +title("Lifting TeX to 3D"); +item("Glyphs are first split into simply connected regions and then decomposed into planar B\'ezier surface patches \cite{Bowman09,Shardt10}:"); +asyfigure("../examples/partitionExample"); + +viewportmargin=(2,1cm); +title("Label Manipulation"); +item("They can then be extruded and/or arbitrarily transformed:"); +asyinclude("../examples/label3solid"); + +title("Billboard Labels"); +defaultpen(fontsize(36pt)); +asyinclude("../examples/billboard",15cm); +defaultpen(itempen); -viewportmargin=(0,2cm); title("Smooth 3D surfaces"); -asyinclude("GaussianSurface",15cm); -defaultpen(0.5); +asyinclude("../examples/sinc",25cm); + +title("Curved 3D Arrows"); +asyinclude("../examples/arrows3",20cm); title("Slide Presentations"); -item("Asymptote has a package for preparing slides."); +item("Asymptote has a module for preparing slides."); item("It even supports embedded high-resolution PDF movies."); code(' title("Slide Presentations"); -item("Asymptote has a package for preparing slides."); +item("Asymptote has a module for preparing slides."); item("It even supports embedded high-resolution PDF movies."); '); remark("\quad\ldots"); @@ -729,8 +513,8 @@ frame cardsize(real w=0, real h=0, bool keepAspect=Aspect) { guide g=polargraph(f,0,2pi,operator ..)--cycle; filldraw(pic,g,pink); - xaxis(pic,\"$x$\"); - yaxis(pic,\"$y$\"); + xaxis(pic,\"$x$\",above=true); + yaxis(pic,\"$y$\",above=true); dot(pic,\"$(a,0)$\",(1,0),N); dot(pic,\"$(2a,0)$\",(2,0),N+E); @@ -748,7 +532,7 @@ add(cardsize(0,200), (540,0)); title("Deferred Drawing"); item("We can't draw a graphical object until we know the scaling factors for the user coordinates."); -item("Instead, store a function that when given the scaling information, draws +item("Instead, store a function that, given the scaling information, draws the scaled object."); code(" void draw(picture pic=currentpicture, path g, pen p=currentpen) { @@ -791,7 +575,7 @@ pic.addPoint(max(g),max(p));"); item("Filling ignores the pen width:"); code("pic.addPoint(min(g),(0,0)); pic.addPoint(max(g),(0,0));"); -item("Communicate with \LaTeX\ to determine label sizes:"); +item("Communicate with \LaTeX\ {\it via\/} a pipe to determine label sizes:"); asyfigure(asywrite(" size(0,100); @@ -807,14 +591,16 @@ title("Sizing"); item("When scaling the final figure to a given size $S$, we first need to determine a scaling factor $a>0$ and a shift $b$ so that all of the - coordinates when transformed will lie in the interval $[0,S]$. That is, if - $u$ and $t$ are the user and truesize components:"); + coordinates when transformed will lie in the interval $[0,S]$."); + +item("That is, if $u$ and $t$ are the user and truesize components:"); equation("0\le au+t+b \le S."); -item("We are maximizing the variable $a$ subject to a number of inequalities. - This is a linear programming problem that can be solved by the simplex - method."); +item("Maximize the variable $a$ subject to a number of inequalities."); +item("Use the simplex method to solve the resulting linear programming problem."); + +if(long) { title("Sizing"); item("Every addition of a coordinate $(t,u)$ adds two restrictions"); equation("au+t+b\ge 0,"); @@ -829,7 +615,7 @@ asyfigure(asywrite(" import palette; size(160,0); pen[] p=Rainbow(NColors=11); -for (int i=1; i<10; ++i) { +for(int i=1; i<10; ++i) { draw(scale(i)*unitcircle, p[i]+linewidth(2)); } ")); @@ -845,6 +631,7 @@ item("This defines a partial ordering on coordinates. When sizing a picture, item("In practice, the linear programming problem will have less than a dozen restraints."); item("All picture sizing is implemented in Asymptote code."); +} title("Infinite Lines"); item("Deferred drawing allows us to draw infinite lines."); @@ -852,59 +639,321 @@ code("drawline(P, Q);"); asyfigure("elliptic","height=12cm"); -title("A Final Example: Quilting"); +title("Helpful Math Notation"); + +item("Integer division returns a {\tt real}. Use {\tt quotient} for an integer + result:"); +code("3/4 == 0.75 quotient(3,4) == 0"); + +item("Caret for real and integer exponentiation:"); +code("2^3 2.7^3 2.7^3.2"); + +item("Many expressions can be implicitly scaled by a numeric constant:"); +code("2pi 10cm 2x^2 3sin(x) 2(a+b)"); + +item("Pairs are complex numbers:"); +code("(0,1)*(0,1) == (-1,0)"); + +title("Function Calls"); + +item("Functions can take default arguments in any position. Arguments are + matched to the first possible location:"); +string unitsize="unitsize(0.65cm);"; +string preamble="void drawEllipse(real xsize=1, real ysize=xsize, pen p=blue) { + draw(xscale(xsize)*yscale(ysize)*unitcircle, p); +} +"; + +asycode(preamble=unitsize,preamble+" +drawEllipse(2); +drawEllipse(red); +"); + +item("Arguments can be given by name:"); +asycode(preamble=unitsize+preamble," +drawEllipse(xsize=2, ysize=1); +drawEllipse(ysize=2, xsize=3, green); +"); + +if(long) { +title("Rest Arguments"); +item("Rest arguments allow one to write a function that takes an arbitrary + number of arguments:"); +code(" +int sum(... int[] nums) { + int total=0; + for(int i=0; i < nums.length; ++i) + total += nums[i]; + return total; +} + +sum(1,2,3,4); // returns 10 +sum(); // returns 0 +sum(1,2,3 ... new int[] {4,5,6}); // returns 21 + +int subtract(int start ... int[] subs) { + return start - sum(... subs); +} +"); +} + +title("High-Order Functions"); + +item("Functions are first-class values. They can be passed to other + functions:"); +code("import graph; +real f(real x) { + return x*sin(10x); +} +draw(graph(f,-3,3,300),red);"); asyfigure(asywrite(" -import math; +import graph; +size(300,0); +real f(real x) { + return x*sin(10x); +} +draw(graph(f,-3,3,300),red); +")); -int n=8, skip=3; +if(long) { +title("Higher-Order Functions"); +item("Functions can return functions:"); +equation("f_n(x)=n\sin\left(\frac{x}{n}\right)."); +skip(); +string preamble=" +import graph; +size(300,0); +"; +string graphfunc2=" +typedef real func(real); +func f(int n) { + real fn(real x) { + return n*sin(x/n); + } + return fn; +} -pair r(int k) { return unityroot(n,k); } +func f1=f(1); +real y=f1(pi); + +for(int i=1; i<=5; ++i) + draw(graph(f(i),-10,10),red); +"; +code(graphfunc2); +string name=asywrite(graphfunc2,preamble=preamble); +asy(nativeformat(),name+".asy"); +label(graphic(name+"."+nativeformat()),(0.5,0), + Fill(figureborder,figuremattpen)); -pen col=blue, col2=purple; +title("Anonymous Functions"); -guide square=box((1,1),(-1,-1)); +item("Create new functions with {\tt new}:"); +code(" +path p=graph(new real (real x) { return x*sin(10x); },-3,3,red); -guide step(int mult) -{ - guide g; - for (int k=0; k<n; ++k) - g=g--r(mult*k); - g=g--cycle; - return g; +func f(int n) { + return new real (real x) { return n*sin(x/n); }; +}"); + +item("Function definitions are just syntactic sugar for assigning function +objects to variables."); +code(" +real square(real x) { + return x^2; } +"); -guide oct=step(1), star=step(skip); +remark("is equivalent to"); +code(" +real square(real x); +square=new real (real x) { + return x^2; +}; +"); -guide wedge(pair z, pair v, real r, real a) -{ - pair w=expi(a/2.0); - v=unit(v)*r; - return shift(z)*((0,0)--v*w--v*conj(w)--cycle); +title("Structures"); + +item("As in other languages, structures group together data."); +code(" +struct Person { + string firstname, lastname; + int age; } +Person bob=new Person; +bob.firstname=\"Bob\"; +bob.lastname=\"Chesterton\"; +bob.age=24; +"); -filldraw(square, col); -filldraw(oct, yellow); +item("Any code in the structure body will be executed every time a new structure + is allocated..."); +code(" +struct Person { + write(\"Making a person.\"); + string firstname, lastname; + int age=18; +} +Person eve=new Person; // Writes \"Making a person.\" +write(eve.age); // Writes 18. +"); -// The interior angle of the points of the star. -real intang=pi*(1-((real)2skip)/((real)n)); +title("Modules"); -for (int k=0; k<n; ++k) { - pair z=midpoint(r(k)--r(k+1)); - guide g=wedge(z,-z,1,intang); - filldraw(g,col2); +item("Function and structure definitions can be grouped into modules:"); +code(" +// powers.asy +real square(real x) { return x^2; } +real cube(real x) { return x^3; } +"); +remark("and imported:"); +code(" +import powers; +real eight=cube(2.0); +draw(graph(powers.square, -1, 1)); +"); } -fill(star,yellow); -filldraw(star,evenodd+col); +title("Object-Oriented Programming"); +item("Functions are defined for each instance of a structure."); +code(" +struct Quadratic { + real a,b,c; + real discriminant() { + return b^2-4*a*c; + } + real eval(real x) { + return a*x^2 + b*x + c; + } +} +"); -size(5inch,0); -")); +item("This allows us to construct ``methods'' which are just normal functions + declared in the environment of a particular object:"); +code(" +Quadratic poly=new Quadratic; +poly.a=-1; poly.b=1; poly.c=2; + +real f(real x)=poly.eval; +real y=f(2); +draw(graph(poly.eval, -5, 5)); +"); + +title("Specialization"); + +item("Can create specialized objects just by redefining methods:"); +code(" +struct Shape { + void draw(); + real area(); +} + +Shape rectangle(real w, real h) { + Shape s=new Shape; + s.draw = new void () { + fill((0,0)--(w,0)--(w,h)--(0,h)--cycle); }; + s.area = new real () { return w*h; }; + return s; +} + +Shape circle(real radius) { + Shape s=new Shape; + s.draw = new void () { fill(scale(radius)*unitcircle); }; + s.area = new real () { return pi*radius^2; } + return s; +} +"); + +title("Overloading"); +item("Consider the code:"); +code(" +int x1=2; +int x2() { + return 7; +} +int x3(int y) { + return 2y; +} + +write(x1+x2()); // Writes 9. +write(x3(x1)+x2()); // Writes 11. +"); + +title("Overloading"); +item("{\tt x1}, {\tt x2}, and {\tt x3} are never used in the same context, so + they can all be renamed {\tt x} without ambiguity:"); +code(" +int x=2; +int x() { + return 7; +} +int x(int y) { + return 2y; +} + +write(x+x()); // Writes 9. +write(x(x)+x()); // Writes 11. +"); + +item("Function definitions are just variable definitions, but variables are + distinguished by their signatures to allow overloading."); + +title("Operators"); +item("Operators are just syntactic sugar for functions, and can be addressed or + defined as functions with the {\tt operator} keyword."); +code(" +int add(int x, int y)=operator +; +write(add(2,3)); // Writes 5. + +// Don't try this at home. +int operator +(int x, int y) { + return add(2x,y); +} +write(2+3); // Writes 7. +"); +item("This allows operators to be defined for new types."); + +title("Operators"); +item("Operators for constructing paths are also functions:"); +code("a.. controls b and c .. d--e"); +remark("is equivalent to"); +code( + "operator --(operator ..(a, operator controls(b,c), d), e)"); +item("This allowed us to redefine all of the path operators for 3D paths."); + +title("Summary"); + +item("Asymptote:"); +subitem("uses IEEE floating point numerics;"); +subitem("uses C++/Java-like syntax;"); +subitem("supports deferred drawing for automatic picture sizing;"); +subitem("supports Grayscale, RGB, CMYK, and HSV colour spaces;"); +subitem("supports PostScript shading, pattern fills, and function shading;"); +subitem("can fill nonsimply connected regions;"); +subitem("generalizes MetaPost path construction algorithms to 3D;"); +subitem("lifts \TeX\ to 3D;"); +subitem("supports 3D billboard labels and PDF grouping."); bibliography("refs"); -viewportsize=viewportmargin=0; +viewportmargin=(2,2); +viewportsize=0; +defaultpen(0.5); title("\mbox{Asymptote: 2D \& 3D Vector Graphics Language}"); asyinclude("../examples/logo3"); skip(); center("\tt http://asymptote.sf.net"); -center("(freely available under the GNU public license)"); +center("(freely available under the LGPL license)"); + +// LocalWords: pdflatex mflogo viewportsize pagewidth pagemargin goysr bibtex +// LocalWords: itempen defaultrender medskip Orest Shardt Vidiassov MF ezier +// LocalWords: Hammerlindl MetaPost PDF hfill LGPL pdf asywrite zoombox LaTeX +// LocalWords: asyfilecode PostScript asycode unitsquare beziercurve grey bw +// LocalWords: lightgrey zerowinding evenodd sw unitsize drawEllipse nums fn +// LocalWords: frac graphfunc func nativeformat figureborder figuremattpen bt +// LocalWords: firstname lastname eval eetomumu binarytree filecode datagraph +// LocalWords: lineargraph filegraph loggraph secondaryaxis imagecontour ij +// LocalWords: tridiagonal Hobbydir nonumber Hobbycontrol th viewportmargin +// LocalWords: asyinclude dotpen wheelpoint yequals xaxis yaxis cardsize mc +// LocalWords: polargraph filldraw addPoint lightblue truesize le au NColors +// LocalWords: drawline unityroot mult oct intang IEEE numerics HSV colour +// LocalWords: nonsimply |