diff options
| author | Karl Berry <karl@freefriends.org> | 2009-09-29 18:35:31 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2009-09-29 18:35:31 +0000 |
| commit | 20dceaaefed2eb0aaacb38e00618f26f0d50786d (patch) | |
| tree | cbf55bc2418663140593d4a6223556807fba5f40 /Build | |
| parent | 222b0c6dbb8b237abac6d5a9e1d80b33e11dde08 (diff) | |
remove deleted asy files
git-svn-id: svn://tug.org/texlive/trunk@15557 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build')
| -rw-r--r-- | Build/source/utils/asymptote/backtrace.cc | 84 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/backtrace.h | 8 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/backtrace.in | 32 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/base/splinetype.asy | 240 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/png/asymptote/asymptote.info | 9565 |
5 files changed, 0 insertions, 9929 deletions
diff --git a/Build/source/utils/asymptote/backtrace.cc b/Build/source/utils/asymptote/backtrace.cc deleted file mode 100644 index 45bf8c4604a..00000000000 --- a/Build/source/utils/asymptote/backtrace.cc +++ /dev/null @@ -1,84 +0,0 @@ -/***** Autogenerated from backtrace.in; changes will be overwritten *****/ - -#line 1 "runtimebase.in" -/***** - * runtimebase.in - * Andy Hammerlindl 2009/07/28 - * - * Common declarations needed for all code-generating .in files. - * - *****/ - - -#line 1 "backtrace.in" -/***** - * backtrace.in - * Andy Hammerlindl 2009/07/28 - * - * Runtime functions for printing garbage collector backtraces. - * - *****/ - -#line 1 "runtimebase.in" -#include "stack.h" -#include "types.h" -#include "builtin.h" -#include "entry.h" -#include "errormsg.h" - -using vm::stack; -using vm::error; -using types::formal; - -#define PRIMITIVE(name,Name,asyName) using types::prim##Name; -#include <primitives.h> -#undef PRIMITIVE - -void unused(void *); - -#line 11 "backtrace.in" -// No extra code for .cc file. - - -namespace run { -#line 13 "backtrace.in" -// void generate_random_backtrace(); -void gen_backtrace0(stack *) -{ -#line 14 "backtrace.in" -#if defined(USEGC) && defined(GC_DEBUG) && defined(GC_BACKTRACE) - GC_generate_random_backtrace(); -#else - error("generate_random_backtrace() requires ./configure --enable-gc-debug"); -#endif -} - -#line 22 "backtrace.in" -// void print_random_addresses(Int n=1); -void gen_backtrace1(stack *Stack) -{ - Int n=vm::pop<Int>(Stack,1); -#line 23 "backtrace.in" -#if defined(USEGC) && defined(GC_DEBUG) && defined(GC_BACKTRACE) - GC_gcollect(); - for (Int i=0; i < n; ++i) - GC_debug_print_heap_obj_proc(GC_base(GC_generate_random_valid_address())); -#else - error("print_random_addresses() requires ./configure --enable-gc-debug"); - unused(&n); // Avoid unused variable warning message. -#endif -} - -} // namespace run - -namespace trans { - -void gen_backtrace_venv(venv &ve) -{ -#line 13 "backtrace.in" - addFunc(ve, run::gen_backtrace0, primVoid(), "generate_random_backtrace"); -#line 22 "backtrace.in" - addFunc(ve, run::gen_backtrace1, primVoid(), "print_random_addresses", formal(primInt(), "n", true, false)); -} - -} // namespace trans diff --git a/Build/source/utils/asymptote/backtrace.h b/Build/source/utils/asymptote/backtrace.h deleted file mode 100644 index f052679a6d6..00000000000 --- a/Build/source/utils/asymptote/backtrace.h +++ /dev/null @@ -1,8 +0,0 @@ -/***** Autogenerated from backtrace.in; changes will be overwritten *****/ - -#ifndef backtrace_H -#define backtrace_H -namespace run { -} - -#endif // backtrace_H diff --git a/Build/source/utils/asymptote/backtrace.in b/Build/source/utils/asymptote/backtrace.in deleted file mode 100644 index 4547355f965..00000000000 --- a/Build/source/utils/asymptote/backtrace.in +++ /dev/null @@ -1,32 +0,0 @@ -/***** - * backtrace.in - * Andy Hammerlindl 2009/07/28 - * - * Runtime functions for printing garbage collector backtraces. - * - *****/ - -// No extra types defined. - -// No extra code for .cc file. - -void generate_random_backtrace() -{ -#if defined(USEGC) && defined(GC_DEBUG) && defined(GC_BACKTRACE) - GC_generate_random_backtrace(); -#else - error("generate_random_backtrace() requires ./configure --enable-gc-debug"); -#endif -} - -void print_random_addresses(Int n=1) -{ -#if defined(USEGC) && defined(GC_DEBUG) && defined(GC_BACKTRACE) - GC_gcollect(); - for (Int i=0; i < n; ++i) - GC_debug_print_heap_obj_proc(GC_base(GC_generate_random_valid_address())); -#else - error("print_random_addresses() requires ./configure --enable-gc-debug"); - unused(&n); // Avoid unused variable warning message. -#endif -} diff --git a/Build/source/utils/asymptote/base/splinetype.asy b/Build/source/utils/asymptote/base/splinetype.asy deleted file mode 100644 index 08263ddf4ca..00000000000 --- a/Build/source/utils/asymptote/base/splinetype.asy +++ /dev/null @@ -1,240 +0,0 @@ -typedef real[] splinetype(real[], real[]); - -restricted real[] defaultspline(real[] x, real[] y); -restricted real[] Spline(real[] x, real[] y); -restricted splinetype[] Spline; - -string morepoints="interpolation requires at least 2 points"; -string differentlengths="arrays have different lengths"; -void checklengths(int x, int y, string text=differentlengths) -{ - if(x != y) - abort(text+": "+string(x)+" != "+string(y)); -} - -// Standard cubic spline interpolation with not-a-knot condition: -// s'''(x_2^-)=s'''(x_2^+) et s'''(x_(n_2)^-)=s'''(x_(n-2)^+) -// if n=2, linear interpolation is returned -// if n=3, an interpolation polynomial of degree <= 2 is returned: -// p(x_1)=y_1, p(x_2)=y_2, p(x_3)=y_3 -real[] notaknot(real[] x, real[] y) -{ - int n=x.length; - checklengths(n,y.length); - real[] d; - if(n > 3) { - real[] a=new real[n]; - real[] b=new real[n]; - real[] c=new real[n]; - real[] g=new real[n]; - b[0]=x[2]-x[1]; - c[0]=x[2]-x[0]; - a[0]=0; - g[0]=((x[1]-x[0])^2*(y[2]-y[1])/b[0]+b[0]*(2*b[0]+3*(x[1]-x[0]))* - (y[1]-y[0])/(x[1]-x[0]))/c[0]; - for(int i=1; i < n-1; ++i) { - a[i]=x[i+1]-x[i]; - c[i]=x[i]-x[i-1]; - b[i]=2*(a[i]+c[i]); - g[i]=3*(c[i]*(y[i+1]-y[i])/a[i]+a[i]*(y[i]-y[i-1])/c[i]); - } - c[n-1]=0; - b[n-1]=x[n-2]-x[n-3]; - a[n-1]=x[n-1]-x[n-3]; - g[n-1]=((x[n-1]-x[n-2])^2*(y[n-2]-y[n-3])/b[n-1]+ - b[n-1]*(2*b[n-1]+3(x[n-1]-x[n-2]))* - (y[n-1]-y[n-2])/(x[n-1]-x[n-2]))/a[n-1]; - d=tridiagonal(a,b,c,g); - } else if(n == 2) { - real val=(y[1]-y[0])/(x[1]-x[0]); - d=new real[] {val,val}; - } else if(n == 3) { - real a=(y[1]-y[0])/(x[1]-x[0]); - real b=(y[2]-y[1])/(x[2]-x[1]); - real c=(b-a)/(x[2]-x[0]); - d=new real[] {a+c*(x[0]-x[1]),a+c*(x[1]-x[0]),a+c*(2*x[2]-x[0]-x[1])}; - } else abort(morepoints); - return d; -} - -// Standard cubic spline interpolation with periodic condition -// s'(a)=s'(b), s''(a)=s''(b), assuming that f(a)=f(b) -// if n=2, linear interpolation is returned -real[] periodic(real[] x, real[] y) -{ - int n=x.length; - checklengths(n,y.length); - if(abs(y[n-1]-y[0]) > sqrtEpsilon*max(abs(y))) - abort("function values are not periodic"); - real[] d; - if(n > 2) { - real[] a=new real[n-1]; - real[] b=new real[n-1]; - real[] c=new real[n-1]; - real[] g=new real[n-1]; - c[0]=x[n-1]-x[n-2]; - a[0]=x[1]-x[0]; - b[0]=2*(a[0]+c[0]); - g[0]=3*c[0]*(y[1]-y[0])/a[0]+3*a[0]*(y[n-1]-y[n-2])/c[0]; - for(int i=1; i < n-1; ++i) { - a[i]=x[i+1]-x[i]; - c[i]=x[i]-x[i-1]; - b[i]=2*(a[i]+c[i]); - g[i]=3*(c[i]*(y[i+1]-y[i])/a[i]+a[i]*(y[i]-y[i-1])/c[i]); - } - d=tridiagonal(a,b,c,g); - d.push(d[0]); - } else if(n == 2) { - d=new real[] {0,0}; - } else abort(morepoints); - return d; -} - -// Standard cubic spline interpolation with the natural condition -// s''(a)=s''(b)=0. -// if n=2, linear interpolation is returned -// Don't use the natural type unless the underlying function -// has zero second end points derivatives. -real[] natural(real[] x, real[] y) -{ - int n=x.length; - checklengths(n,y.length); - real[] d; - if(n > 2) { - real[] a=new real[n]; - real[] b=new real[n]; - real[] c=new real[n]; - real[] g=new real[n]; - b[0]=2*(x[1]-x[0]); - c[0]=x[1]-x[0]; - a[0]=0; - g[0]=3*(y[1]-y[0]); - for(int i=1; i < n-1; ++i) { - a[i]=x[i+1]-x[i]; - c[i]=x[i]-x[i-1]; - b[i]=2*(a[i]+c[i]); - g[i]=3*(c[i]*(y[i+1]-y[i])/a[i]+a[i]*(y[i]-y[i-1])/c[i]); - } - c[n-1]=0; - a[n-1]=x[n-1]-x[n-2]; - b[n-1]=2*a[n-1]; - g[n-1]=3*(y[n-1]-y[n-2]); - d=tridiagonal(a,b,c,g); - } else if(n == 2) { - real val=(y[1]-y[0])/(x[1]-x[0]); - d=new real[] {val,val}; - } else abort(morepoints); - return d; -} - -// Standard cubic spline interpolation with clamped conditions f'(a), f'(b) -splinetype clamped(real slopea, real slopeb) -{ - return new real[] (real[] x, real[] y) { - int n=x.length; - checklengths(n,y.length); - real[] d; - if(n > 2) { - real[] a=new real[n]; - real[] b=new real[n]; - real[] c=new real[n]; - real[] g=new real[n]; - b[0]=x[1]-x[0]; - g[0]=b[0]*slopea; - c[0]=0; - a[0]=0; - for(int i=1; i < n-1; ++i) { - a[i]=x[i+1]-x[i]; - c[i]=x[i]-x[i-1]; - b[i]=2*(a[i]+c[i]); - g[i]=3*(c[i]*(y[i+1]-y[i])/a[i]+a[i]*(y[i]-y[i-1])/c[i]); - } - c[n-1]=0; - a[n-1]=0; - b[n-1]=x[n-1]-x[n-2]; - g[n-1]=b[n-1]*slopeb; - d=tridiagonal(a,b,c,g); - } else if(n == 2) { - d=new real[] {slopea,slopeb}; - } else abort(morepoints); - return d; - }; -} - -// Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) -// Modified MATLAB code -// [1] Fritsch, F. N. and R. E. Carlson, -// "Monotone Piecewise Cubic Interpolation," -// SIAM J. Numerical Analysis, Vol. 17, 1980, pp.238-246. -// [2] Kahaner, David, Cleve Moler, Stephen Nash, -// Numerical Methods and Software, Prentice Hall, 1988. -real[] monotonic(real[] x, real[] y) -{ - int n=x.length; - checklengths(n,y.length); - real[] d=new real[n]; - if(n > 2) { - real[] h=new real[n-1]; - real[] del=new real[n-1]; - for(int i=0; i < n-1; ++i) { - h[i]=x[i+1]-x[i]; - del[i]=(y[i+1]-y[i])/h[i]; - } - int j=0; - int k[]=new int[]; - for(int i=0; i < n-2; ++i) - if((sgn(del[i])*sgn(del[i+1])) > 0) {k[j]=i; j=j+1;} - - real[] hs=new real[j]; - for(int i=0; i < j; ++i) hs[i]=h[k[i]]+h[k[i]+1]; - real w1[]=new real[j]; - real w2[]=new real[j]; - real dmax[]=new real[j]; - real dmin[]=new real[j]; - for(int i=0; i < j; ++i) { - w1[i]=(h[k[i]]+hs[i])/(3*hs[i]); - w2[i]=(h[k[i]+1]+hs[i])/(3*hs[i]); - dmax[i]=max(abs(del[k[i]]),abs(del[k[i]+1])); - dmin[i]=min(abs(del[k[i]]),abs(del[k[i]+1])); - } - for(int i=0; i < n; ++i) d[i]=0; - for(int i=0; i < j; ++i) - d[k[i]+1]=dmin[i]/(w1[i]*(del[k[i]]/dmax[i])+w2[i]*(del[k[i]+1]/dmax[i])); - d[0]=((2*h[0]+h[1])*del[0]-h[0]*del[1])/(h[0]+h[1]); - if(sgn(d[0]) != sgn(del[0])) {d[0]=0;} - else if((sgn(del[0]) != sgn(del[1])) && (abs(d[0]) > abs(3*del[0]))) - d[0]=3*del[0]; - - d[n-1]=((2*h[n-2]+h[n-3])*del[n-2]-h[n-2]*del[n-2])/(h[n-2]+h[n-3]); - if(sgn(d[n-1]) != sgn(del[n-2])) {d[n-1]=0;} - else if((sgn(del[n-2]) != sgn(del[n-3])) && - (abs(d[n-1]) > abs(3*del[n-2]))) - d[n-1]=3*del[n-2]; - } else if(n == 2) { - d[0]=d[1]=(y[1]-y[0])/(x[1]-x[0]); - } else abort(morepoints); - return d; -} - -// Return standard cubic spline interpolation as a guide -guide hermite(real[] x, real[] y, splinetype splinetype=null) -{ - int n=x.length; - if(n == 0) return nullpath; - - guide g=(x[0],y[0]); - if(n == 1) return g; - if(n == 2) return g--(x[1],y[1]); - - if(splinetype == null) - splinetype=(x[0] == x[x.length-1] && y[0] == y[y.length-1]) ? - periodic : notaknot; - - real[] dy=splinetype(x,y); - for(int i=1; i < n; ++i) { - pair z=(x[i],y[i]); - real dx=x[i]-x[i-1]; - g=g..controls((x[i-1],y[i-1])+dx*(1,dy[i-1])/3) and (z-dx*(1,dy[i])/3)..z; - } - return g; -} diff --git a/Build/source/utils/asymptote/doc/png/asymptote/asymptote.info b/Build/source/utils/asymptote/doc/png/asymptote/asymptote.info deleted file mode 100644 index ce277160bfd..00000000000 --- a/Build/source/utils/asymptote/doc/png/asymptote/asymptote.info +++ /dev/null @@ -1,9565 +0,0 @@ -This is asymptote.info, produced by makeinfo version 4.13 from -../asymptote.texi. - -This file documents `Asymptote', version 1.78. - - `http://asymptote.sourceforge.net' - - Copyright (C) 2004-9 Andy Hammerlindl, John Bowman, and Tom Prince. - - Permission is granted to copy, distribute and/or modify this - document under the terms of the GNU Lesser General Public License - (see the file LICENSE in the top-level source directory). - - -INFO-DIR-SECTION Languages -START-INFO-DIR-ENTRY -* asymptote: (asymptote/asymptote). Vector graphics language. -END-INFO-DIR-ENTRY - - -File: asymptote.info, Node: Top, Next: Description, Up: (dir) - -Asymptote -********* - -This file documents `Asymptote', version 1.78. - - `http://asymptote.sourceforge.net' - - Copyright (C) 2004-9 Andy Hammerlindl, John Bowman, and Tom Prince. - - Permission is granted to copy, distribute and/or modify this - document under the terms of the GNU Lesser General Public License - (see the file LICENSE in the top-level source directory). - - -* Menu: - -* Description:: What is `Asymptote'? -* Installation:: Downloading and installing -* Tutorial:: Getting started -* Drawing commands:: Four primitive graphics commands -* Programming:: The `Asymptote' vector graphics language -* LaTeX usage:: Embedding `Asymptote' commands within `LaTeX' -* Base modules:: Base modules shipped with `Asymptote' -* Options:: Command-line options -* Interactive mode:: Typing `Asymptote' commands interactively -* GUI:: Graphical user interface -* PostScript to Asymptote:: `Asymptote' backend to `pstoedit' -* Help:: Where to get help and submit bug reports -* Debugger:: Squish those bugs! -* Credits:: Contributions and acknowledgments -* Index:: General index - - --- The Detailed Node Listing --- - -Installation - -* UNIX binary distributions:: Prebuilt `UNIX' binaries -* MacOS X binary distributions:: Prebuilt `MacOS X' binaries -* Microsoft Windows:: Prebuilt `Microsoft Windows' binary -* Configuring:: Configuring `Asymptote' for your system -* Search paths:: Where `Asymptote' looks for your files -* Compiling from UNIX source:: Building `Asymptote' from scratch -* Editing modes:: Convenient `emacs' and `vim' modes -* Subversion:: Getting the latest development source -* Uninstall:: Goodbye, `Asymptote'! - -Drawing commands - -* draw:: Draw a path on a picture or frame -* fill:: Fill a cyclic path on a picture or frame -* clip:: Clip a picture or frame to a cyclic path -* label:: Label a point on a picture - -Programming - -* Data types:: void, bool, int, real, pair, triple, string -* Paths and guides:: -* Pens:: Colors, line types, line widths, font sizes -* Transforms:: Affine transforms -* Frames and pictures:: Canvases for immediate and deferred drawing -* Files:: Reading and writing your data -* Variable initializers:: Initialize your variables -* Structures:: Organize your data -* Operators:: Arithmetic and logical operators -* Implicit scaling:: Avoiding those ugly *s -* Functions:: Traditional and high-order functions -* Arrays:: Dynamic vectors -* Casts:: Implicit and explicit casts -* Import:: Importing external `Asymptote' packages -* Static:: Where to allocate your variable? - -Operators - -* Arithmetic & logical:: Basic mathematical operators -* Self & prefix operators:: Increment and decrement -* User-defined operators:: Overloading operators - -Functions - -* Default arguments:: Default values can appear anywhere -* Named arguments:: Assigning function arguments by keyword -* Rest arguments:: Functions with a variable number of arguments -* Mathematical functions:: Standard libm functions - - -Arrays - -* Slices:: Python-style array slices - -Base modules - -* plain:: Default `Asymptote' base file -* simplex:: Linear programming: simplex method -* math:: Extend `Asymptote''s math capabilities -* interpolate:: Interpolation routines -* geometry:: Geometry routines -* trembling:: Wavy lines -* stats:: Statistics routines and histograms -* patterns:: Custom fill and draw patterns -* markers:: Custom path marker routines -* tree:: Dynamic binary search tree -* binarytree:: Binary tree drawing module -* drawtree:: Tree drawing module -* syzygy:: Syzygy and braid drawing module -* feynman:: Feynman diagrams -* roundedpath:: Round the sharp corners of paths -* animation:: Embedded PDF and MPEG movies -* embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with `Asymptote' -* MetaPost:: `MetaPost' compatibility routines -* unicode:: Accept `unicode' (UTF-8) characters -* latin1:: Accept `ISO 8859-1' characters -* babel:: Interface to `LaTeX' `babel' package -* labelpath:: Drawing curved labels -* labelpath3:: Drawing curved labels in 3D -* annotate:: Annotate your PDF files -* CAD:: 2D CAD pen and measurement functions (DIN 15) -* graph:: 2D linear & logarithmic graphs -* palette:: Color density images and palettes -* three:: 3D vector graphics -* obj:: 3D obj files -* graph3:: 3D linear & logarithmic graphs -* grid3:: 3D grids -* solids:: 3D solid geometry -* tube:: 3D rotation minimizing tubes -* flowchart:: Flowchart drawing routines -* contour:: Contour lines -* contour3:: Contour surfaces -* slopefield:: Slope fields -* ode:: Ordinary differential equations - -Graphical User Interface - -* GUI Installation:: Installing `xasy' -* GUI Usage:: - - -File: asymptote.info, Node: Description, Next: Installation, Prev: Top, Up: Top - -1 Description -************* - -`Asymptote' is a powerful descriptive vector graphics language that -provides a mathematical coordinate-based framework for technical -drawings. Labels and equations are typeset with `LaTeX', for overall -document consistency, yielding the same high-quality level of -typesetting that `LaTeX' provides for scientific text. By default it -produces `PostScript' output, but it can also generate any format that -the `ImageMagick' package can produce. - - A major advantage of `Asymptote' over other graphics packages is -that it is a high-level programming language, as opposed to just a -graphics program: it can therefore exploit the best features of the -script (command-driven) and graphical-user-interface (GUI) methods for -producing figures. The rudimentary GUI `xasy' included with the package -allows one to move script-generated objects around. To make `Asymptote' -accessible to the average user, this GUI is currently being developed -into a full-fledged interface that can generate objects directly. -However, the script portion of the language is now ready for general -use by users who are willing to learn a few simple `Asymptote' graphics -commands (*note Drawing commands::). - - `Asymptote' is mathematically oriented (e.g. one can use complex -multiplication to rotate a vector) and uses `LaTeX' to do the -typesetting of labels. This is an important feature for scientific -applications. It was inspired by an earlier drawing program (with a -weaker syntax and capabilities) called `MetaPost'. - - The `Asymptote' vector graphics language provides: - - * a standard for typesetting mathematical figures, just as - TeX/`LaTeX' is the de-facto standard for typesetting equations. - - * `LaTeX' typesetting of labels, for overall document consistency; - - * the ability to generate and embed 3D vector PRC graphics into PDF - files; - - * a natural coordinate-based framework for technical drawings, - inspired by `MetaPost', with a much cleaner, powerful C++-like - programming syntax; - - * compilation of figures into virtual machine code for speed, without - sacrificing portability; - - * the power of a script-based language coupled to the convenience of - a GUI; - - * customization using its own C++-like graphics programming language; - - * sensible defaults for graphical features, with the ability to - override; - - * a high-level mathematically oriented interface to the `PostScript' - language for vector graphics, including affine transforms and - complex variables; - - * functions that can create new (anonymous) functions; - - * deferred drawing that uses the simplex method to solve overall size - constraint issues between fixed-sized objects (labels and - arrowheads) and objects that should scale with figure size; - - - Many of the features of `Asymptote' are written in the `Asymptote' -language itself. While the stock version of `Asymptote' is designed for -mathematics typesetting needs, one can write `Asymptote' modules that -tailor it to specific applications. A scientific graphing module has -already been written (*note graph::). Examples of `Asymptote' code and -output, including animations, are available at - - `http://asymptote.sourceforge.net/gallery/'. - Links to many external resources, including an excellent user-written -`Asymptote' tutorial can be found at - - `http://asymptote.sourceforge.net/links.html'. - - -File: asymptote.info, Node: Installation, Next: Tutorial, Prev: Description, Up: Top - -2 Installation -************** - -* Menu: - -* UNIX binary distributions:: Prebuilt `UNIX' binaries -* MacOS X binary distributions:: Prebuilt `MacOS X' binaries -* Microsoft Windows:: Prebuilt `Microsoft Windows' binary -* Configuring:: Configuring `Asymptote' for your system -* Search paths:: Where `Asymptote' looks for your files -* Compiling from UNIX source:: Building `Asymptote' from scratch -* Editing modes:: Convenient `emacs' and `vim' modes -* Subversion:: Getting the latest development source -* Uninstall:: Goodbye, `Asymptote'! - - After following the instructions for your specific distribution, -please see also *note Configuring::. - -We recommend subscribing to new release announcements at - - `http://freshmeat.net/projects/asy' - Users may also wish to monitor the `Asymptote' forum: - - `http://sourceforge.net/forum/monitor.php?forum_id=409349' - - -File: asymptote.info, Node: UNIX binary distributions, Next: MacOS X binary distributions, Up: Installation - -2.1 UNIX binary distributions -============================= - -We release both `tgz' and RPM binary distributions of `Asymptote'. The -root user can install the `Linux i386' `tgz' distribution of version -`x.xx' of `Asymptote' with the commands: -tar -C / -zxf asymptote-x.xx.i386.tgz -texhash - The `texhash' command, which installs LaTeX style files, is optional. -The executable file will be `/usr/local/bin/asy') and example code will -be installed by default in `/usr/local/share/doc/asymptote/examples'. - -Fedora users can easily install the most recent version of `Asymptote' -with the command -yum --enablerepo=rawhide install asymptote - -To install the latest version of `Asymptote' on a Debian-based -distribution (e.g. Ubuntu, Mepis, Linspire) follow the instructions for -compiling from `UNIX' source (*note Compiling from UNIX source::). -Alternatively, Debian users can install one of Hubert Chan's prebuilt -`Asymptote' binaries from - - `http://ftp.debian.org/debian/pool/main/a/asymptote' - - -File: asymptote.info, Node: MacOS X binary distributions, Next: Microsoft Windows, Prev: UNIX binary distributions, Up: Installation - -2.2 MacOS X binary distributions -================================ - -`MacOS X' users can either compile the `UNIX' source code (*note -Compiling from UNIX source::) or install the contributed `Asymptote' -binary available at - -`http://www.hmug.org/pub/MacOS_X/X/Applications/Publishing/asymptote/' - -Because these preconfigured binary distributions have strict -architecture and library dependencies that many installations do not -satisfy, we recommend installing `Asymptote' directly from the official -source: - - `http://sourceforge.net/project/showfiles.php?group_id=120000' - -Note that many `MacOS X' (and FreeBSD) systems inexplicably ship with -an extremely old GNU `readline' version (4.1, dated 21 March 2000). For -full interactive functionality, `readline' version 4.2 or later (16 -April 2001) is required. - - -File: asymptote.info, Node: Microsoft Windows, Next: Configuring, Prev: MacOS X binary distributions, Up: Installation - -2.3 Microsoft Windows -===================== - -Users of the `Microsoft Windows' operating system can install the -self-extracting `Asymptote' executable `asymptote-x.xx-setup.exe', -where `x.xx' denotes the latest version. - - A working TeX implementation (such as the one available at -`http://www.miktex.org') will be required to typeset labels. You will -also need to install `GPL Ghostscript' from -`http://sourceforge.net/projects/ghostscript/'. To view the default -`PostScript' output, you can install the program `gsview' available from -`http://www.cs.wisc.edu/~ghost/gsview/'. - - The `ImageMagick' package from - - `http://www.imagemagick.org/script/binary-releases.php' - -is required to support output formats other than EPS and PDF (*note -convert::). The `Python' interpreter from `http://www.python.org' is -only required if you wish to try out the graphical user interface -(*note GUI::). - -Example code will be installed by default in the `examples' -subdirectory of the installation directory (by default, `C:\Program -Files\Asymptote'). - - -File: asymptote.info, Node: Configuring, Next: Search paths, Prev: Microsoft Windows, Up: Installation - -2.4 Configuring -=============== - -In interactive mode, or when given the `-V' option (the default when -running `Asymptote' on a single file under `MSDOS'), `Asymptote' will -automatically invoke the `PostScript' viewer `gv' (under `UNIX') or -`gsview' (under `MSDOS' to display graphical output. These defaults may -be overridden with the configuration variable `psviewer'. The -`PostScript' viewer should be capable of automatically redrawing -whenever the output file is updated. The default `UNIX' `PostScript' -viewer `gv' supports this (via a `SIGHUP' signal). Version `gv-3.6.3' -or later (from `http://ftp.gnu.org/gnu/gv/') is required for -interactive mode to work properly. Users of `ggv' will need to enable -`Watch file' under `Edit/Postscript Viewer Preferences'. Users of -`gsview' will need to enable `Options/Auto Redisplay' (however, under -`MSDOS' it is still necessary to click on the `gsview' window; under -`UNIX' one must manually redisplay by pressing the `r' key). - - Configuration variables are most easily set as `Asymptote' variables -in an optional configuration file (by default, `.asy/config.asy' in the -user's home directory or `%USERPROFILE%\.asy\config.asy' under -`MSDOS'); *note configuration file::. Here are the default values of -several important configuration variables under `UNIX': - - -import settings; -psviewer="gv"; -pdfviewer="acroread"; -gs="gs"; -python=""; - -The (installation-dependent) default values of these configuration -variables under `MSDOS' are determined automatically from the -`Microsoft Windows' registry. - - For PDF format output, the `gs' setting specifies the location of -the `PostScript'-to-PDF processor `Ghostscript', available from -`http://sourceforge.net/projects/ghostscript/'. - - The setting `pdfviewer' specifies the location of the PDF viewer. On -`UNIX' systems, to support automatic document reloading in `Adobe -Reader', we recommend copying the file `reload.js' from the `Asymptote' -system directory (by default, `/usr/local/share/asymptote' under `UNIX' -to `~/.adobe/Acrobat/x.x/JavaScripts/', where `x.x' represents the -appropriate `Adobe Reader' version number. The automatic document -reload feature must then be explicitly enabled by putting -import settings; -pdfreload=true; -pdfreloadOptions="-tempFile"; - in the `Asymptote' configuration file. This reload feature is not -useful under `MSDOS' since the document cannot be updated anyway on -that operating system until it is first closed by `Adobe Reader'. - - The graphical user interface may also require setting the variable -`python' if `Python' is installed in a nonstandard location. - - The configuration variable `dir' can be used to adjust the search -path (*note Search paths::). - - By default, `Asymptote' attempts to center the figure on the page, -assuming that the paper type is `letter'. The default paper type may be -changed to `a4' with the configuration variable `papertype'. Alignment -to other paper sizes can be obtained by setting the configuration -variables `paperwidth' and `paperheight'. - - The following configuration variables normally do not require -adjustment: -texpath -texcommand -texdvicommand -dvips -convert -display -animate -xasy - The `texdvicommand' is used for `3D' label typesetting, which requires -`dvips' output. An empty string indicates the default setting of -`latex'/`tex', depending on the setting of `texengine'. - - Configuration variables may also be set or overwritten with a -command-line option: -asy -psviewer=gsview -V venn - - Alternatively, system environment versions of the above configuration -variables may be set in the conventional way. The corresponding -environment variable name is obtained by converting the configuration -variable name to upper case and prepending `ASYMPTOTE_': for example, -to set the environment variable -ASYMPTOTE_PSVIEWER="C:\Program Files\Ghostgum\gsview\gsview32.exe"; - under `Microsoft Windows XP': - 1. Click on the `Start' button; - - 2. Right-click on `My Computer'; - - 3. Choose `Properties' from the popup menu; - - 4. Click the `Advanced' tab; - - 5. Click the `Environment Variables' button. - - -File: asymptote.info, Node: Search paths, Next: Compiling from UNIX source, Prev: Configuring, Up: Installation - -2.5 Search paths -================ - -In looking for `Asymptote' system files, `asy' will search the -following paths, in the order listed: - 1. The current directory; - - 2. A list of one or more directories specified by the configuration - variable `dir' (separated by `:' under UNIX and `;' under `MSDOS'); - - 3. The directory `.asy' in the user's home directory - (`%USERPROFILE%\.asy' under `MSDOS'); - - 4. The `Asymptote' system directory (by default, - `/usr/local/share/asymptote' under `UNIX' and `C:\Program - Files\Asymptote' under `MSDOS'). - - -File: asymptote.info, Node: Compiling from UNIX source, Next: Editing modes, Prev: Search paths, Up: Installation - -2.6 Compiling from UNIX source -============================== - -To compile and install a `UNIX' executable from a source release -`x.xx', first execute the commands: -gunzip asymptote-x.xx.src.tgz -tar -xf asymptote-x.xx.src.tar -cd asymptote-x.xx - By default the system version of the Boehm garbage collector will be -used; if it is old we recommend first putting -`http://www.hpl.hp.com/personal/Hans_Boehm/gc/gc_source/gc-7.1.tar.gz' -in the `Asymptote' source directory. - -If your graphics card supports multisampling, we recommend using version -`2.6.0-rc1' (or later) of `freeglut' to support antialiasing in -`Asymptote''s adaptive `OpenGL' 3D renderer (`MacOS X' users can skip -this step since `Asymptote' is configured to use the native glut -library on that platform). Download - - `http://prdownloads.sourceforge.net/freeglut/freeglut-2.6.0-rc1.tar.gz' - and type (as the root user): -tar -zxf freeglut-2.6.0-rc1.tar.gz -cd freeglut-2.6.0 -./configure --prefix=/usr -make install -cd .. - Then compile `Asymptote' with the commands -./configure -make all -make install - Be sure to use GNU `make' (on non-GNU systems this command may be -called `gmake'). To build the documentation, you may need to install -the `texinfo-tex' package. If you get errors from a broken `texinfo' or -`pdftex' installation, simply put - - `http://asymptote.sourceforge.net/asymptote.pdf' - in the directory `doc' and repeat the command `make all'. - -For a (default) system-wide installation, the last command should be -done as the root user. To install without root privileges, change the -`./configure' command to -./configure --prefix=$HOME/asymptote - One can disable use of the Boehm garbage collector by configuring with -`./configure --disable-gc'. For a list of other configuration options, -say `./configure --help'. For example, one can tell configure to look -for header files and libraries in nonstandard locations: -./configure CFLAGS=-I/opt/usr/include LDFLAGS=-L/opt/usr/lib - - If you are compiling `Asymptote' with `gcc', you will need a -relatively recent version (e.g. 3.4.4 or later). For full interactive -functionality, you will need version 4.2 or later of the GNU `readline' -library. The file `gcc3.3.2curses.patch' in the `patches' directory can -be used to patch the broken curses.h header file (or a local copy -thereof in the current directory) on some `AIX' and `IRIX' systems. - - The `FFTW' library is only required if you want `Asymptote' to be -able to take Fourier transforms of data (say, to compute an audio power -spectrum). The `GSL' library is only required if you require the -special functions that it supports. - - If you don't want to install `Asymptote' system wide, just make sure -the compiled binary `asy' and GUI script `xasy' are in your path and -set the configuration variable `dir' to point to the directory `base' -(in the top level directory of the `Asymptote' source code). - - -File: asymptote.info, Node: Editing modes, Next: Subversion, Prev: Compiling from UNIX source, Up: Installation - -2.7 Editing modes -================= - -Users of `emacs' can edit `Asymptote' code with the mode `asy-mode', -after enabling it by putting the following lines in their `.emacs' -initialization file, replacing `ASYDIR' with the location of the -`Asymptote' system directory (by default, `/usr/local/share/asymptote' -or `C:\Program Files\Asymptote' under `MSDOS'): -(add-to-list 'load-path "ASYDIR") -(autoload 'asy-mode "asy-mode.el" "Asymptote major mode." t) -(autoload 'lasy-mode "asy-mode.el" "hybrid Asymptote/Latex major mode." t) -(autoload 'asy-insinuate-latex "asy-mode.el" "Asymptote insinuate LaTeX." t) -(add-to-list 'auto-mode-alist '("\\.asy$" . asy-mode)) - - Particularly useful key bindings in this mode are `C-c C-c', which -compiles and displays the current buffer, and the key binding `C-c ?', -which shows the available function prototypes for the command at the -cursor. For full functionality you should also install the Apache -Software Foundation package `two-mode-mode': - - `http://www.dedasys.com/freesoftware/files/two-mode-mode.el' - Once installed, you can use the hybrid mode `lasy-mode' to edit a -LaTeX file containing embedded `Asymptote' code (*note LaTeX usage::). -This mode can be enabled within `latex-mode' with the key sequence `M-x -lasy-mode <RET>'. On `UNIX' systems, additional keywords will be -generated from all `asy' files in the space-separated list of -directories specified by the environment variable `ASYMPTOTE_SITEDIR'. -Further documentation of `asy-mode' is available within `emacs' by -pressing the sequence keys `C-h f asy-mode <RET>'. - - Fans of `vim' can customize `vim' for `Asymptote' with - -`cp /usr/local/share/asymptote/asy.vim ~/.vim/syntax/asy.vim' - -and add the following to their `~/.vimrc' file: -augroup filetypedetect -au BufNewFile,BufRead *.asy setf asy -augroup END -filetype plugin on - - If any of these directories or files don't exist, just create them. -To set `vim' up to run the current asymptote script using `:make' just -add to `~/.vim/ftplugin/asy.vim': -setlocal makeprg=asy\ % -setlocal errorformat=%f:\ %l.%c:\ %m - - Syntax highlighting support for the KDE editor `Kate' can be enabled -by running `asy-kate.sh' in the `/usr/local/share/asymptote' directory -and putting the generated `asymptote.xml' file in -`~/.kde/share/apps/katepart/syntax/'. - - -File: asymptote.info, Node: Subversion, Next: Uninstall, Prev: Editing modes, Up: Installation - -2.8 Subversion (SVN) -==================== - -The following commands are needed to install the latest development -version of `Asymptote' using `Subversion': -svn co http://asymptote.svn.sourceforge.net/svnroot/asymptote/trunk/asymptote -cd asymptote -./autogen.sh -./configure -make all -make install - -To compile without optimization, use the command `make CFLAGS=-g'. - - -File: asymptote.info, Node: Uninstall, Prev: Subversion, Up: Installation - -2.9 Uninstall -============= - -To uninstall an `Linux i386' binary distribution, use the commands -tar -zxvf asymptote-x.xx.i386.tgz | xargs --replace=% rm /% -texhash - -To uninstall all `Asymptote' files installed from a source -distribution, use the command -make uninstall - - -File: asymptote.info, Node: Tutorial, Next: Drawing commands, Prev: Installation, Up: Top - -3 Tutorial -********** - -_An excellent user-written `Asymptote' tutorial is also available from_ - - `http://www.artofproblemsolving.com/Wiki/index.php/Asymptote:_Basics' - -To draw a line from coordinate (0,0) to coordinate (100,100) using -`Asymptote''s interactive mode, type at the command prompt: -asy -draw((0,0)--(100,100)); - - - -The units here are `PostScript' "big points" (1 `bp' = 1/72 `inch'); -`--' means join with a linear segment. In `Asymptote' coordinates like -`(0,0)' and `(1000,100)' are called _pairs_. - - At this point you can type in further draw commands, which will be -added to the displayed figure, or type `quit' to exit interactive mode. -You can use the arrow keys in interactive mode to edit previous lines -(assuming that you have support for the GNU `readline' library -enabled). The tab key will automatically complete unambiguous words; -otherwise, hitting tab again will show the possible choices. Further -commands specific to interactive mode are described in *note -Interactive mode::. - - In batch mode, `Asymptote' reads commands directly from a file. To -try this out, type - -draw((0,0)--(100,100)); - into a file, say test.asy. Then execute this file with the `MSDOS' or -`UNIX' command -asy -V test - `MSDOS' users can drag and drop the file onto the Desktop `asy' icon -or make `Asymptote' the default application for files with the -extension `asy'. - -The `-V' option opens up a `PostScript' viewer window so you can -immediately view the encapsulated `PostScript' output. By default the -output will be written to the file `test.eps'; the prefix of the output -file may be changed with the `-o' command-line option. - - One can draw a line with more than two points and create a cyclic -path like this square: - -draw((0,0)--(100,0)--(100,100)--(0,100)--cycle); - - - -It is often inconvenient to work directly with `PostScript' coordinates. -The next example draws a unit square scaled to width 101 bp and height -101 bp. The output is identical to that of the previous example. -size(101,101); -draw((0,0)--(1,0)--(1,1)--(0,1)--cycle); - - For convenience, the path `(0,0)--(1,0)--(1,1)--(0,1)--cycle' may be -replaced with the predefined variable `unitsquare', or equivalently, -`box((0,0),(1,1))'. - - One can also specify the size in `pt' (1 `pt' = 1/72.27 `inch'), -`cm', `mm', or `inches'. If 0 is given as a size argument, no -restriction is made in that direction; the overall scaling will be -determined by the other direction (*note size::): - -size(0,3cm); -draw(unitsquare); - - - -To make the user coordinates represent multiples of exactly `1cm': -unitsize(1cm); -draw(unitsquare); - - One can also specify different x and y unit sizes: -unitsize(1cm,2cm); -draw(unitsquare); - - Adding labels is easy in `Asymptote'; one specifies the label as a -double-quoted `LaTeX' string, a coordinate, and an optional alignment -direction: - -size(0,3cm); -draw(unitsquare); -label("$A$",(0,0),SW); -label("$B$",(1,0),SE); -label("$C$",(1,1),NE); -label("$D$",(0,1),NW); - - - -`Asymptote' uses the standard compass directions `E=(1,0)', `N=(0,1)', -`NE=unit(N+E)', and `ENE=unit(E+NE)', etc., which along with the -directions `up', `down', `right', and `left' are defined as pairs in -the `Asymptote' base module `plain'. A user who has a local variable -named `E' may access the compass direction `E' by prefixing it with the -name of the module where it is defined: `plain.E'. - - This example draws a path that approximates a quarter circle: - -size(100,0); -draw((1,0){up}..{left}(0,1)); - - - -In general, a path is specified as a list of pairs (or other paths) -interconnected with `--', which denotes a straight line segment, or -`..', which denotes a cubic spline. Specifying a final node `cycle' -creates a cyclic path that connects smoothly back to the initial node, -as in this approximation (accurate to within 0.06%) of a unit circle: -path unitcircle=E..N..W..S..cycle; - - Each interior node of a cubic spline may be given a direction prefix -or suffix `{dir}': the direction of the pair `dir' specifies the -direction of the incoming or outgoing tangent, respectively, to the -curve at that node. Exterior nodes may be given direction specifiers -only on their interior side. - - A cubic spline between the node z_0, with postcontrol point c_0, and -the node z_1, with precontrol point c_1, is computed as the Bezier curve - - - -As illustrated in the diagram below, the third-order midpoint (m_5) -constructed from two endpoints z_0 and z_1 and two control points c_0 -and c_1, is the point corresponding to t=1/2 on the Bezier curve formed -by the quadruple (z_0, c_0, c_1, z_1). This allows one to recursively -construct the desired curve, by using the newly extracted third-order -midpoint as an endpoint and the respective second- and first-order -midpoints as control points: - - - -Here m_0, m_1 and m_2 are the first-order midpoints, m_3 and m_4 are -the second-order midpoints, and m_5 is the third-order midpoint. The -curve is then constructed by recursively applying the algorithm to -(z_0, m_0, m_3, m_5) and (m_5, m_4, m_2, z_1). - - In fact, an analogous property holds for points located at any -fraction t in [0,1] of each segment, not just for midpoints (t=1/2). - - The Bezier curve constructed in this manner has the following -properties: - * It is entirely contained in the convex hull of the given four - points. - - * It starts heading from the first endpoint to the first control - point and finishes heading from the second control point to the - second endpoint. - - - The user can specify explicit control points between two nodes like -this: -draw((0,0)..controls (0,100) and (100,100)..(100,0)); - - However, it is usually more convenient to just use the `..' -operator, which tells `Asymptote' to choose its own control points -using the algorithms described in Donald Knuth's monograph, The -MetaFontbook, Chapter 14. The user can still customize the guide (or -path) by specifying direction, tension, and curl values. - - The higher the tension, the straighter the curve is, and the more it -approximates a straight line. One can change the spline tension from -its default value of 1 to any real value greater than or equal to 0.75 -(cf. John D. Hobby, Discrete and Computational Geometry 1, 1986): -draw((100,0)..tension 2 ..(100,100)..(0,100)); -draw((100,0)..tension 2 and 1 ..(100,100)..(0,100)); -draw((100,0)..tension atleast 1 ..(100,100)..(0,100)); - - The curl parameter specifies the curvature at the endpoints of a path -(0 means straight; the default value of 1 means approximately circular): -draw((100,0){curl 0}..(100,100)..{curl 0}(0,100)); - - The `MetaPost ...' path connector, which requests, when possible, an -inflection-free curve confined to a triangle defined by the endpoints -and directions, is implemented in `Asymptote' as the convenient -abbreviation `::' for `..tension atleast 1 ..' (the ellipsis `...' is -used in `Asymptote' to indicate a variable number of arguments; *note -Rest arguments::). For example, compare - -draw((0,0){up}..(100,25){right}..(200,0){down}); - - -with - -draw((0,0){up}::(100,25){right}::(200,0){down}); - - - -The `---' connector is an abbreviation for `..tension atleast -infinity..' and the `&' connector concatenates two paths, after first -stripping off the last node of the first path (which normally should -coincide with the first node of the second path). - - An `Asymptote' path, being connected, is equivalent to a `Postscript -subpath'. The `^^' binary operator, which requests that the pen be -moved (without drawing or affecting endpoint curvatures) from the final -point of the left-hand path to the initial point of the right-hand -path, may be used to group several `Asymptote' paths into a `path[]' -array (equivalent to a `PostScript' path): - -size(0,100); -path unitcircle=E..N..W..S..cycle; -path g=scale(2)*unitcircle; -filldraw(unitcircle^^g,evenodd+yellow,black); - - - -The `PostScript' even-odd fill rule here specifies that only the region -bounded between the two unit circles is filled (*note fillrule::). In -this example, the same effect can be achieved by using the default zero -winding number fill rule, if one is careful to alternate the -orientation of the paths: -filldraw(unitcircle^^reverse(g),yellow,black); - - The `^^' operator is used by the `box(triple, triple)' function in -`three.asy' to construct the edges of a cube `unitbox' without -retracing steps: - -import three; -dotgranularity=0; // Render dots as spheres. - -currentprojection=orthographic(5,4,2,center=true); - -size(5cm); -size3(3cm,5cm,8cm); - -draw(unitbox); - -dot(unitbox,red); - -label("$O$",(0,0,0),NW); -label("(1,0,0)",(1,0,0),S); -label("(0,1,0)",(0,1,0),E); -label("(0,0,1)",(0,0,1),Z); - - - -See section *note graph:: (or the online `Asymptote' gallery and -external links posted at `http://asymptote.sourceforge.net') for -further examples, including two and three-dimensional scientific -graphs. Additional examples have been posted by Philippe Ivaldi at -`http://piprim.tuxfamily.org/asymptote/'. - - -File: asymptote.info, Node: Drawing commands, Next: Programming, Prev: Tutorial, Up: Top - -4 Drawing commands -****************** - -All of `Asymptote''s graphical capabilities are based on four primitive -commands. The three `PostScript' drawing commands `draw', `fill', and -`clip' add objects to a picture in the order in which they are -executed, with the most recently drawn object appearing on top. The -labeling command `label' can be used to add text labels and external -EPS images, which will appear on top of the `PostScript' objects (since -this is normally what one wants), but again in the relative order in -which they were executed. After drawing objects on a picture, the -picture can be output with the `shipout' function (*note shipout::). - - If you wish to draw `PostScript' objects on top of labels (or -verbatim `tex' commands; *note tex::), the `layer' command may be used -to start a new `PostScript/LaTeX' layer: -void layer(picture pic=currentpicture); - - The `layer' function gives one full control over the order in which -objects are drawn. Layers are drawn sequentially, with the most recent -layer appearing on top. Within each layer, labels, images, and verbatim -`tex' commands are always drawn after the `PostScript' objects in that -layer. - - While some of these drawing commands take many options, they all -have sensible default values (for example, the picture argument -defaults to currentpicture). - -* Menu: - -* draw:: Draw a path on a picture or frame -* fill:: Fill a cyclic path on a picture or frame -* clip:: Clip a picture or frame to a cyclic path -* label:: Label a point on a picture - - -File: asymptote.info, Node: draw, Next: fill, Up: Drawing commands - -4.1 draw -======== - -void draw(picture pic=currentpicture, Label L="", path g, - align align=NoAlign, pen p=currentpen, - arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin, - Label legend="", marker marker=nomarker); - -Draw the path `g' on the picture `pic' using pen `p' for drawing, with -optional drawing attributes (Label `L', explicit label alignment -`align', arrows and bars `arrow' and `bar', margins `margin', legend, -and markers `marker'). Only one parameter, the path, is required. For -convenience, the arguments `arrow' and `bar' may be specified in either -order. The argument `legend' is a Label to use in constructing an -optional legend entry. - - Bars are useful for indicating dimensions. The possible values of -`bar' are `None', `BeginBar', `EndBar' (or equivalently `Bar'), and -`Bars' (which draws a bar at both ends of the path). Each of these bar -specifiers (except for `None') will accept an optional real argument -that denotes the length of the bar in `PostScript' coordinates. The -default bar length is `barsize(pen)'. - - The possible values of `arrow' are `None', `Blank' (which draws no -arrows or path), `BeginArrow', `MidArrow', `EndArrow' (or equivalently -`Arrow'), and `Arrows' (which draws an arrow at both ends of the path). -All of the arrow specifiers except for `None' and `Blank' may be given -the optional arguments arrowhead `arrowhead' (one of the predefined -arrowhead styles `DefaultHead', `SimpleHead', `HookHead', `TeXHead'), -real `size' (arrowhead size in `PostScript' coordinates), real `angle' -(arrowhead angle in degrees), filltype `filltype' (one of `FillDraw', -`Fill', `NoFill', `UnFill', `Draw') and (except for `MidArrow' and -`Arrows') a relative real `position' along the path (an `arctime') where -the tip of the arrow should be placed. The default arrowhead size when -drawn with a pen `p' is `arrowsize(p)'. There are also arrow versions -with slightly modified default values of `size' and `angle' suitable for -curved arrows: `BeginArcArrow', `EndArcArrow' (or equivalently -`ArcArrow'), `MidArcArrow', and `ArcArrows'. - - Margins can be used to shrink the visible portion of a path by -`labelmargin(p)' to avoid overlap with other drawn objects. Typical -values of `margin' are `NoMargin', `BeginMargin', `EndMargin' (or -equivalently `Margin'), and `Margins' (which leaves a margin at both -ends of the path). One may use `Margin(real begin, real end)' to -specify the size of the beginning and ending margin, respectively, in -multiples of the units `labelmargin(p)' used for aligning labels. -Alternatively, `BeginPenMargin', `EndPenMargin' (or equivalently -`PenMargin'), `PenMargins', `PenMargin(real begin, real end)' specify a -margin in units of the pen line width, taking account of the pen line -width when drawing the path or arrow. For example, use `DotMargin', an -abbreviation for `PenMargin(-0.5*dotfactor,0.5*dotfactor)', to draw -from the usual beginning point just up to the boundary of an end dot of -width `dotfactor*linewidth(p)'. The qualifiers `BeginDotMargin', -`EndDotMargin', and `DotMargins' work similarly. The qualifier -`TrueMargin(real begin, real end)' allows one to specify a margin -directly in `PostScript' units, independent of the pen line width. - - The use of arrows, bars, and margins is illustrated by the examples -`Pythagoras.asy', `sqrtx01.asy', and `triads.asy'. - - The legend for a picture `pic' can be fit and aligned to a frame -with the routine: -frame legend(picture pic=currentpicture, int perline=1, - real xmargin=legendmargin, real ymargin=xmargin, - real linelength=legendlinelength, - real hskip=legendhskip, real vskip=legendvskip, - real maxwidth=0, real maxheight=0, - bool hstretch=false, bool vstretch=false, pen p=currentpen); - Here `xmargin' and `ymargin' specify the surrounding x and y margins, -`perline' specifies the number of entries per line (default 1; 0 means -choose this number automatically), `linelength' specifies the length of -the path lines, `hskip' and `vskip' specify the line skip (as a -multiple of the legend entry size), `maxwidth' and `maxheight' specify -optional upper limits on the width and height of the resulting legend -(0 means unlimited), `hstretch' and `vstretch' allow the legend to -stretch horizontally or vertically, and `p' specifies the pen used to -draw the bounding box. The legend frame can then be added and aligned -about a point on a picture `dest' using `add' or `attach' (*note add -about::). - - To draw a dot, simply draw a path containing a single point. The -`dot' command defined in the module `plain' draws a dot having a -diameter equal to an explicit pen line width or the default line width -magnified by `dotfactor' (6 by default), using the specified filltype -(*note filltype::): -void dot(picture pic=currentpicture, pair z, pen p=currentpen, - filltype filltype=Fill); -void dot(picture pic=currentpicture, Label L, pair z, align align=NoAlign, - string format=defaultformat, pen p=currentpen, filltype filltype=Fill); -void dot(picture pic=currentpicture, Label[] L=new Label[], pair[] z, - align align=NoAlign, string format=defaultformat, pen p=currentpen, - filltype filltype=Fill) -void dot(picture pic=currentpicture, Label L, pen p=currentpen, - filltype filltype=Fill); - - If the variable `Label' is given as the `Label' argument to the -second routine, the `format' argument will be used to format a string -based on the dot location (here `defaultformat' is `"$%.4g$"'). The -third routine draws a dot at every point of a pair array `z'. One can -also draw a dot at every node of a path: -void dot(picture pic=currentpicture, Label[] L=new Label[], - path g, align align=RightSide, string format=defaultformat, - pen p=currentpen, filltype filltype=Fill); - See *note pathmarkers:: and *note markers:: for more general methods -for marking path nodes. - - To draw a fixed-sized object (in `PostScript' coordinates) about the -user coordinate `origin', use the routine -void draw(pair origin, picture pic=currentpicture, Label L="", path g, - align align=NoAlign, pen p=currentpen, arrowbar arrow=None, - arrowbar bar=None, margin margin=NoMargin, Label legend="", - marker marker=nomarker); - - -File: asymptote.info, Node: fill, Next: clip, Prev: draw, Up: Drawing commands - -4.2 fill -======== - -void fill(picture pic=currentpicture, path g, pen p=currentpen); - -Fill the interior region bounded by the cyclic path `g' on the picture -`pic', using the pen `p'. - - There is also a convenient `filldraw' command, which fills the path -and then draws in the boundary. One can specify separate pens for each -operation: -void filldraw(picture pic=currentpicture, path g, pen fillpen=currentpen, - pen drawpen=currentpen); - - This fixed-size version of `fill' allows one to fill an object -described in `PostScript' coordinates about the user coordinate -`origin': -void fill(pair origin, picture pic=currentpicture, path g, pen p=currentpen); - -This is just a convenient abbreviation for the commands: -picture opic; -fill(opic,g,p); -add(pic,opic,origin); - - The routine -void filloutside(picture pic=currentpicture, path g, pen p=currentpen); - fills the region exterior to the path `g', out to the current boundary -of picture `pic'. - - Lattice gradient shading varying smoothly over a two-dimensional -array of pens `p', using fill rule `fillrule', can be produced with -void latticeshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[][] p) - If `stroke=true', the region filled is the same as the region that -would be drawn by `draw(pic,g,fillrule+zerowinding)'; in this case the -path `g' need not be cyclic. The pens in `p' must belong to the same -color space. One can use the functions `rgb(pen)' or `cmyk(pen)' to -promote pens to a higher color space, as illustrated in the example file -`latticeshading.asy'. - - Axial gradient shading varying smoothly from `pena' to `penb' in the -direction of the line segment `a--b' can be achieved with -void axialshade(picture pic=currentpicture, path g, bool stroke=false, - pen pena, pair a, - pen penb, pair b); - - Radial gradient shading varying smoothly from `pena' on the circle -with center `a' and radius `ra' to `penb' on the circle with center `b' -and radius `rb' is similar: -void radialshade(picture pic=currentpicture, path g, bool stroke=false, - pen pena, pair a, real ra, - pen penb, pair b, real rb); - Illustrations of radial shading are provided in the example files -`shade.asy', `ring.asy', and `shadestroke.asy'. - - Gouraud shading using fill rule `fillrule' and the vertex colors in -the pen array `p' on a triangular lattice defined by the vertices `z' -and edge flags `edges' is implemented with -void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, pair[] z, - int[] edges); -void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, int[] edges); - In the second form, the elements of `z' are taken to be successive -nodes of path `g'. The pens in `p' must belong to the same color space. -Illustrations of Gouraud shading are provided in the example file -`Gouraud.asy' and in the solid geometry module `solids.asy'. The edge -flags used in Gouraud shading are documented here: - - `http://partners.adobe.com/public/developer/en/ps/sdk/TN5600.SmoothShading.pdf'. - - Tensor product shading using fill rule `fillrule' on patches bounded -by the n cyclic paths of length 4 in path array `b', using the vertex -colors specified in the n \times 4 pen array `p' and internal control -points in the n \times 4 array `z', is implemented with -void tensorshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[][] p, path[] b=g, - pair[][] z=new pair[][]); - If the array `z' is empty, Coons shading, in which the color control -points are calculated automatically, is used. The pens in `p' must -belong to the same color space. A simpler interface for the case of a -single patch (n=1) is also available: -void tensorshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, path b=g, - pair[] z=new pair[]); - One can also smoothly shade the regions between consecutive paths of a -sequence using a given array of pens: -void draw(picture pic=currentpicture, path[] g, pen[] p); - Illustrations of tensor product and Coons shading are provided in the -example files `tensor.asy', `Coons.asy', `BezierSurface.asy', and -`rainbow.asy'. - - More general shading possibilities are available with the `pdflatex', -`context', and `pdftex' TeX engines: the routine -void functionshade(picture pic=currentpicture, path[] g, bool stroke=false, - pen fillrule=currentpen, string shader); - shades on picture `pic' the interior of path `g' according to fill -rule `fillrule' using the `PostScript' calculator routine specified by -the string `shader'; this routine takes 2 arguments, each in [0,1], and -returns `colors(fillrule).length' color components. Function shading -is illustrated in the example `functionshading.asy'. - - The following routine uses `evenodd' clipping together with the `^^' -operator to unfill a region: - -void unfill(picture pic=currentpicture, path g); - - -File: asymptote.info, Node: clip, Next: label, Prev: fill, Up: Drawing commands - -4.3 clip -======== - -void clip(picture pic=currentpicture, path g, stroke=false, - pen fillrule=currentpen); - -Clip the current contents of picture `pic' to the region bounded by the -path `g', using fill rule `fillrule' (*note fillrule::). If -`stroke=true', the clipped portion is the same as the region that would -be drawn with `draw(pic,g,fillrule+zerowinding)'; in this case the path -`g' need not be cyclic. For an illustration of picture clipping, see -the first example in *note LaTeX usage::. - - -File: asymptote.info, Node: label, Prev: clip, Up: Drawing commands - -4.4 label -========= - -void label(picture pic=currentpicture, Label L, pair position, - align align=NoAlign, pen p=nullpen, filltype filltype=NoFill) - -Draw Label `L' on picture `pic' using pen `p'. If `align' is `NoAlign', -the label will be centered at user coordinate `position'; otherwise it -will be aligned in the direction of `align' and displaced from -`position' by the `PostScript' offset `align*labelmargin(p)'. The -constant `Align' can be used to align the bottom-left corner of the -label at `position'. If `p' is `nullpen', the pen specified within the -Label, which defaults to `currentpen', will be used. The Label `L' can -either be a string or the structure obtained by calling one of the -functions -Label Label(string s="", pair position, align align=NoAlign, - pen p=nullpen, embed embed=Rotate, filltype filltype=NoFill); -Label Label(string s="", align align=NoAlign, - pen p=nullpen, embed embed=Rotate, filltype filltype=NoFill); -Label Label(Label L, pair position, align align=NoAlign, - pen p=nullpen, embed embed=L.embed, filltype filltype=NoFill); -Label Label(Label L, align align=NoAlign, - pen p=nullpen, embed embed=L.embed, filltype filltype=NoFill); - The text of a Label can be scaled, slanted, rotated, or shifted by -multiplying it on the left by an affine transform (*note Transforms::). -For example, `rotate(45)*xscale(2)*L' first scales `L' in the x -direction and then rotates it counterclockwise by 45 degrees. The final -position of a Label can also be shifted by a `PostScript' coordinate -translation: `shift(10,0)*L'. The `embed' argument determines how the -Label should transform with the embedding picture: -`Shift' - only shift with embedding picture; - -`Rotate' - only shift and rotate with embedding picture (default); - -`Rotate(pair z)' - rotate with (picture-transformed) vector `z'. - -`Slant' - only shift, rotate, slant, and reflect with embedding picture; - -`Scale' - shift, rotate, slant, reflect, and scale with embedding picture. - - - To add a label to a path, use -void label(picture pic=currentpicture, Label L, path g, align align=NoAlign, - pen p=nullpen, filltype filltype=NoFill); - By default the label will be positioned at the midpoint of the path. -An alternative label location (an `arctime' value between 0 and -`length(g)' *note arctime::) may be specified as real value for -`position' in constructing the Label. The position `Relative(real)' -specifies a location relative to the total arclength of the path. These -convenient abbreviations are predefined: -position BeginPoint=Relative(0); -position MidPoint=Relative(0.5); -position EndPoint=Relative(1); - - Path labels are aligned in the direction `align', which may be -specified as an absolute compass direction (pair) or a direction -`Relative(pair)' measured relative to a north axis in the local -direction of the path. For convenience `LeftSide', `Center', and -`RightSide' are defined as `Relative(W)', `Relative((0,0))', and -`Relative(E)', respectively. Multiplying `LeftSide', `Center', -`RightSide' on the left by a real scaling factor will move the label -further away from or closer to the path. - - A label with a fixed-size arrow of length `arrowlength' pointing to -`b' from direction `dir' can be produced with the routine -void arrow(picture pic=currentpicture, Label L="", pair b, pair dir, - real length=arrowlength, align align=NoAlign, - pen p=currentpen, arrowbar arrow=Arrow, margin margin=EndMargin); - If no alignment is specified (either in the Label or as an explicit -argument), the optional Label will be aligned in the direction `dir', -using margin `margin'. - - The function `string graphic(string name, string options="")' -returns a string that can be used to include an encapsulated -`PostScript' (EPS) file. Here, `name' is the name of the file to -include and `options' is a string containing a comma-separated list of -optional bounding box (`bb=llx lly urx ury'), width (`width=value'), -height (`height=value'), rotation (`angle=value'), scaling -(`scale=factor'), clipping (`clip=bool'), and draft mode (`draft=bool') -parameters. The `layer()' function can be used to force future objects -to be drawn on top of the included image: -label(graphic("file.eps","width=1cm"),(0,0),NE); -layer(); - - The `string baseline(string s, string template="\strut")' function -can be used to enlarge the bounding box of labels to match a given -template, so that their baselines will be typeset on a horizontal line. -See `Pythagoras.asy' for an example. - - One can prevent labels from overwriting one another with the -`overwrite' pen attribute (*note overwrite::). - - The structure `object' defined in `plain_Label.asy' allows Labels -and frames to be treated in a uniform manner. A group of objects may -be packed together into single frame with the routine -frame pack(pair align=2S ... object inset[]); - To draw or fill a box (or ellipse or other path) around a Label and -return the bounding object, use one of the routines -object draw(picture pic=currentpicture, Label L, envelope e, - real xmargin=0, real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); -object draw(picture pic=currentpicture, Label L, envelope e, pair position, - real xmargin=0, real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); - Here `envelope' is a boundary-drawing routine such as `box', -`roundbox', or `ellipse' defined in `plain_boxes.asy' (*note -envelope::). - - The function `path[] texpath(Label L)' returns the path array that -TeX would fill to draw the Label `L'. - - The `string minipage(string s, width=100pt)' function can be used to -format string `s' into a paragraph of width `width'. This example uses -`minipage', `clip', and `graphic' to produce a CD label: - - -size(11.7cm,11.7cm); -asy(nativeformat(),"logo"); -fill(unitcircle^^(scale(2/11.7)*unitcircle), - evenodd+rgb(124/255,205/255,124/255)); -label(scale(1.1)*minipage( -"\centering\scriptsize \textbf{\LARGE {\tt Asymptote}\\ -\smallskip -\small The Vector Graphics Language}\\ -\smallskip -\textsc{Andy Hammerlindl, John Bowman, and Tom Prince} -http://asymptote.sourceforge.net\\ -",8cm),(0,0.6)); -label(graphic("logo."+nativeformat(),"height=7cm"),(0,-0.22)); -clip(unitcircle^^(scale(2/11.7)*unitcircle),evenodd); - - -File: asymptote.info, Node: Programming, Next: LaTeX usage, Prev: Drawing commands, Up: Top - -5 Programming -************* - -Here is a short introductory example to the `Asymptote' programming -language that highlights the similarity of its control structures with -those of C, C++, and Java: -// This is a comment. - -// Declaration: Declare x to be a real variable; -real x; - -// Assignment: Assign the real variable x the value 1. -x=1.0; - -// Conditional: Test if x equals 1 or not. -if(x == 1.0) { - write("x equals 1.0"); -} else { - write("x is not equal to 1.0"); -} - -// Loop: iterate 10 times -for(int i=0; i < 10; ++i) { - write(i); -} - - `Asymptote' supports `while', `do', `break', and `continue' -statements just as in C/C++. It also supports the Java-style shorthand -for iterating over all elements of an array: - -// Iterate over an array -int[] array={1,1,2,3,5}; -for(int k : array) { - write(k); -} - In addition, it supports many features beyond the ones found in those -languages. - -* Menu: - -* Data types:: void, bool, int, real, pair, triple, string -* Paths and guides:: -* Pens:: Colors, line types, line widths, font sizes -* Transforms:: Affine transforms -* Frames and pictures:: Canvases for immediate and deferred drawing -* Files:: Reading and writing your data -* Variable initializers:: Initialize your variables -* Structures:: Organize your data -* Operators:: Arithmetic and logical operators -* Implicit scaling:: Avoiding those ugly *s -* Functions:: Traditional and high-order functions -* Arrays:: Dynamic vectors -* Casts:: Implicit and explicit casts -* Import:: Importing external `Asymptote' packages -* Static:: Where to allocate your variable? - - -File: asymptote.info, Node: Data types, Next: Paths and guides, Up: Programming - -5.1 Data types -============== - -`Asymptote' supports the following data types (in addition to -user-defined types): - -`void' - The void type is used only by functions that take or return no - arguments. - -`bool' - a boolean type that can only take on the values `true' or `false'. - For example: bool b=true; - - defines a boolean variable `b' and initializes it to the value - `true'. If no initializer is given: bool b; - - the value `false' is assumed. - -`bool3' - an extended boolean type that can take on the values `true', - `default', or `false'. A bool3 type can be cast to or from a bool. - The default initializer for bool3 is `default'. - -`int' - an integer type; if no initializer is given, the implicit value `0' - is assumed. The minimum allowed value of an integer is `intMin' - and the maximum value is `intMax'. - -`real' - a real number; this should be set to the highest-precision native - floating-point type on the architecture. The implicit initializer - for reals is `0.0'. Real numbers have precision `realEpsilon', - with `realDigits' significant digits. The smallest positive real - number is `realMin' and the largest positive real number is - `realMax'. - -`pair' - complex number, that is, an ordered pair of real components - `(x,y)'. The real and imaginary parts of a pair `z' can read as - `z.x' and `z.y'. We say that `x' and `y' are virtual members of - the data element pair; they cannot be directly modified, however. - The implicit initializer for pairs is `(0.0,0.0)'. - - There are a number of ways to take the complex conjugate of a pair: - pair z=(3,4); - z=(z.x,-z.y); - z=z.x-I*z.y; - z=conj(z); - - Here `I' is the pair `(0,1)'. A number of built-in functions are - defined for pairs: - - `pair conj(pair z)' - returns the conjugate of `z'; - - `real length(pair z)' - returns the complex modulus `|z|' of its argument `z'. For - example, - pair z=(3,4); - length(z); - returns the result 5. A synonym for `length(pair)' is - `abs(pair)'; - - `real angle(pair z, bool warn=true)' - returns the angle of `z' in radians in the interval - [-`pi',`pi'] or `0' if `warn' is `false' and `z=(0,0)' - (rather than producing an error); - - `real degrees(pair z, bool warn=true)' - returns the angle of `z' in degrees in the interval [0,360) - or `0' if `warn' is `false' and `z=(0,0)' (rather than - producing an error); - - `pair unit(pair z)' - returns a unit vector in the direction of the pair `z'; - - `pair expi(real angle)' - returns a unit vector in the direction `angle' measured in - radians; - - `pair dir(real degrees)' - returns a unit vector in the direction `degrees' measured in - degrees; - - `real xpart(pair z)' - returns `z.x'; - - `real ypart(pair z)' - returns `z.y'; - - `pair realmult(pair z, pair w)' - returns the element-by-element product `(z.x*w.x,z.y*w.y)'; - - `real dot(pair z, pair w)' - returns the dot product `z.x*w.x+z.y*w.y'; - - `pair minbound(pair z, pair w)' - returns `(min(z.x,w.x),min(z.y,w.y))'; - - `pair maxbound(pair z, pair w)' - returns `(max(z.x,w.x),max(z.y,w.y))'. - - -`triple' - an ordered triple of real components `(x,y,z)' used for - three-dimensional drawings. The respective components of a triple - `v' can read as `v.x', `v.y', and `v.z'. The implicit initializer - for triples is `(0.0,0.0,0.0)'. - - Here are the built-in functions for triples: - `real length(triple v)' - returns the length `|v|' of the vector `v'. A synonym for - `length(triple)' is `abs(triple)'; - - `real polar(triple v, bool warn=true)' - returns the colatitude of `v' measured from the z axis in - radians or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real azimuth(triple v, bool warn=true)' - returns the longitude of `v' measured from the x axis in - radians or `0' if `warn' is `false' and `v.x=v.y=0' (rather - than producing an error); - - `real colatitude(triple v, bool warn=true)' - returns the colatitude of `v' measured from the z axis in - degrees or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real latitude(triple v, bool warn=true)' - returns the latitude of `v' measured from the xy plane in - degrees or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real longitude(triple v, bool warn=true)' - returns the longitude of `v' measured from the x axis in - degrees or `0' if `warn' is `false' and `v.x=v.y=0' (rather - than producing an error); - - `triple unit(triple v)' - returns a unit triple in the direction of the triple `v'; - - `triple expi(real polar, real azimuth)' - returns a unit triple in the direction `(polar,azimuth)' - measured in radians; - - `triple dir(real colatitude, real longitude)' - returns a unit triple in the direction - `(colatitude,longitude)' measured in degrees; - - `real xpart(triple v)' - returns `v.x'; - - `real ypart(triple v)' - returns `v.y'; - - `real zpart(triple v)' - returns `v.z'; - - `real dot(triple u, triple v)' - returns the dot product `u.x*v.x+u.y*v.y+u.z*v.z'; - - `triple cross(triple u, triple v)' - returns the cross product - - `(u.y*v.z-u.z*v.y,u.z*v.x-u.x*v.z,u.x*v.y-v.x*u.y)'; - - `triple minbound(triple u, triple v)' - returns `(min(u.x,v.x),min(u.y,v.y),min(u.z,v.z))'; - - `triple maxbound(triple u, triple v)' - returns `(max(u.x,v.x),max(u.y,v.y),max(u.z,v.z)'). - - -`string' - a character string, implemented using the STL `string' class. - - Strings delimited by double quotes (`"') are subject to the - following mappings to allow the use of double quotes in TeX (e.g. - for using the `babel' package, *note babel::): - - * \" maps to " - - * \\ maps to \\ - - Strings delimited by single quotes (`'') have the same mappings as - character strings in ANSI `C': - - * \' maps to ' - - * \" maps to " - - * \? maps to ? - - * \\ maps to backslash - - * \a maps to alert - - * \b maps to backspace - - * \f maps to form feed - - * \n maps to newline - - * \r maps to carriage return - - * \t maps to tab - - * \v maps to vertical tab - - * \0-\377 map to corresponding octal byte - - * \x0-\xFF map to corresponding hexadecimal byte - - The implicit initializer for strings is the empty string `""'. - Strings may be concatenated with the `+' operator. In the following - string functions, position `0' denotes the start of the string: - `int length(string s)' - returns the length of the string `s'; - - `int find(string s, string t, int pos=0)' - returns the position of the first occurrence of string `t' in - string `s' at or after position `pos', or -1 if `t' is not a - substring of `s'; - - `int rfind(string s, string t, int pos=-1)' - returns the position of the last occurrence of string `t' in - string `s' at or before position `pos' (if `pos'=-1, at the - end of the string `s'), or -1 if `t' is not a substring of - `s'; - - `string insert(string s, int pos, string t)' - returns the string formed by inserting string `t' at position - `pos' in `s'; - - `string erase(string s, int pos, int n)' - returns the string formed by erasing the string of length `n' - (if `n'=-1, to the end of the string `s') at position `pos' - in `s'; - - `string substr(string s, int pos, int n=-1)' - returns the substring of `s' starting at position `pos' and - of length `n' (if `n'=-1, until the end of the string `s'); - - `string reverse(string s)' - returns the string formed by reversing string `s'; - - `string replace(string s, string before, string after)' - returns a string with all occurrences of the string `before' - in the string `s' changed to the string `after'; - - `string replace(string s, string[][] table)' - returns a string constructed by translating in string `s' all - occurrences of the string `before' in an array `table' of - string pairs {`before',`after'} to the corresponding string - `after'; - - `string[] split(string s, string delimiter)' - returns an array of strings obtained by splitting `s' into - substrings delimited by `delimiter'; - - `string format(string s, int n)' - returns a string containing `n' formatted according to the - C-style format string `s' using the current locale; - - `string format(string s=defaultformat, real x, string locale="")' - returns a string containing `x' formatted according to the - C-style format string `s' using locale `locale' (or the - current locale if an empty string is specified), following - the behaviour of the C function `fprintf'), except that only - one data field is allowed, trailing zeros are removed by - default (unless `#' is specified), and (if the format string - specifies math mode) TeX is used to typeset scientific - notation; - - `int hex(string s);' - casts a hexidecimal string `s' to an integer. - - `string string(real x, int digits=realDigits)' - casts `x' to a string using precision `digits' and the C - locale; - - `string locale(string s="")' - sets the locale to the given string, if nonempty, and returns - the current locale. - - `string time(string format="%a %b %d %T %Z %Y")' - returns the current time formatted by the ANSI C routine - `strftime' according to the string `format' using the current - locale. Thus time(); - time("%a %b %d %H:%M:%S %Z %Y"); - - are equivalent ways of returning the current time in the - default format used by the `UNIX' `date' command; - - `int seconds(string t="", string format="")' - returns the time measured in seconds after the Epoch (Thu Jan - 01 00:00:00 UTC 1970) as determined by the ANSI C routine - `strptime' according to the string `format' using the current - locale, or the current time if `t' is the empty string. Note - that the `"%Z"' extension to the POSIX `strptime' - specification is ignored by the current GNU C Library. If an - error occurs, the value -1 is returned. Here are some - examples: seconds("Mar 02 11:12:36 AM PST 2007","%b %d %r PST %Y"); - seconds(time("%b %d %r %z %Y"),"%b %d %r %z %Y"); - seconds(time("%b %d %r %Z %Y"),"%b %d %r "+time("%Z")+" %Y"); - 1+(seconds()-seconds("Jan 1","%b %d"))/(24*60*60); - The last example returns today's ordinal date, measured from - the beginning of the year. - - `string time(int seconds, string format="%a %b %d %T %Z %Y")' - returns the time corresponding to `seconds' seconds after the - Epoch (Thu Jan 01 00:00:00 UTC 1970) formatted by the ANSI C - routine `strftime' according to the string `format' using the - current locale. For example, to return the date corresponding - to 24 hours ago: time(seconds()-24*60*60); - - `void abort(string s)' - aborts execution (with a non-zero return code in batch mode); - if string `s' is nonempty, a diagnostic message constructed - from the source file, line number, and `s' is printed; - - `void exit()' - exits with a zero error return code in batch mode; - - `void sleep(int seconds)' - pauses for the given number of seconds; - - `void usleep(int microseconds)' - pauses for the given number of microseconds; - - `void beep()' - produces a beep on the console; - - - - As in C/C++, complicated types may be abbreviated with `typedef' -(see the example in *note Functions::). - - -File: asymptote.info, Node: Paths and guides, Next: Pens, Prev: Data types, Up: Programming - -5.2 Paths and guides -==================== - -`path' - a cubic spline resolved into a fixed path. The implicit - initializer for paths is `nullpath'. - - For example, the routine `circle(pair c, real r)', which returns a - Bezier curve approximating a circle of radius `r' centered on `c', - is based on `unitcircle' (*note unitcircle::): path circle(pair c, real r) - { - return shift(c)*scale(r)*unitcircle; - } - If high accuracy is needed, a true circle may be produced with the - routine `Circle' defined in the module `graph.asy': import graph; - path Circle(pair c, real r, int n=nCircle); - - A circular arc consistent with `circle' centered on `c' with - radius `r' from `angle1' to `angle2' degrees, drawing - counterclockwise if `angle2 >= angle1', can be constructed with path arc(pair c, real r, real angle1, real angle2); - One may also specify the direction explicitly: path arc(pair c, real r, real angle1, real angle2, bool direction); - Here the direction can be specified as CCW (counter-clockwise) or - CW (clockwise). For convenience, an arc centered at `c' from pair - `z1' to `z2' (assuming `|z2-c|=|z1-c|') in the may also be - constructed with path arc(pair c, explicit pair z1, explicit pair z2, - bool direction=CCW) - - If high accuracy is needed, true arcs may be produced with routines - in the module `graph.asy' that produce Bezier curves with `n' - control points: import graph; - path Arc(pair c, real r, real angle1, real angle2, bool direction, - int n=nCircle); - path Arc(pair c, real r, real angle1, real angle2, int n=nCircle); - path Arc(pair c, explicit pair z1, explicit pair z2, - bool direction=CCW, int n=nCircle); - - An ellipse can be drawn with the routine @cindex @code{ellipse} - path ellipse(pair c, real a, real b) - { - return shift(c)*scale(a,b)*unitcircle; - } - - This example illustrates the use of all five guide connectors - discussed in *note Tutorial::: size(300,0); - pair[] z=new pair[10]; - - z[0]=(0,100); z[1]=(50,0); z[2]=(180,0); - - for(int n=3; n <= 9; ++n) - z[n]=z[n-3]+(200,0); - - path p=z[0]..z[1]---z[2]::{up}z[3] - &z[3]..z[4]--z[5]::{up}z[6] - &z[6]::z[7]---z[8]..{up}z[9]; - - draw(p,grey+linewidth(4mm)); - - dot(z); - - - - Here are some useful functions for paths: - - `int length(path p);' - This is the number of (linear or cubic) segments in path `p'. - If `p' is cyclic, this is the same as the number of nodes in - `p'. - - `int size(path p);' - This is the number of nodes in the path `p'. If `p' is - cyclic, this is the same as `length(p)'. - - `bool cyclic(path p);' - returns `true' iff path `p' is cyclic. - - `bool straight(path p, int i);' - returns `true' iff the segment of path `p' between node `i' - and node `i+1' is straight. - - `bool piecewisestraight(path p)' - returns `true' iff the path `p' is piecewise straight. - - `pair point(path p, int t);' - If `p' is cyclic, return the coordinates of node `t' mod - `length(p)'. Otherwise, return the coordinates of node `t', - unless `t' < 0 (in which case `point(0)' is returned) or `t' - > `length(p)' (in which case `point(length(p))' is returned). - - `pair point(path p, real t);' - This returns the coordinates of the point between node - `floor(t)' and `floor(t)+1' corresponding to the cubic spline - parameter `t-floor(t)' (*note Bezier::). If `t' lies outside - the range [0,`length(p)'], it is first reduced modulo - `length(p)' in the case where `p' is cyclic or else converted - to the corresponding endpoint of `p'. - - `pair dir(path p, int t, int sign=0, bool normalize=true);' - If `sign < 0', return the direction (as a pair) of the - incoming tangent to path `p' at node `t'; if `sign > 0', - return the direction of the outgoing tangent. If `sign=0', - the mean of these two directions is returned. - - `pair dir(path p, real t, bool normalize=true);' - returns the direction of the tangent to path `p' at the point - between node `floor(t)' and `floor(t)+1' corresponding to the - cubic spline parameter `t-floor(t)' (*note Bezier::). - - `pair accel(path p, int t, int sign=0);' - If `sign < 0', return the acceleration of the incoming path - `p' at node `t'; if `sign > 0', return the acceleration of - the outgoing path. If `sign=0', the mean of these two - accelerations is returned. - - `pair accel(path p, real t);' - returns the acceleration of the path `p' at the point `t'. - - `pair radius(path p, real t);' - returns the radius of curvature of the path `p' at the point - `t'. - - `pair precontrol(path p, int t);' - returns the precontrol point of `p' at node `t'. - - `pair precontrol(path p, real t);' - returns the effective precontrol point of `p' at parameter - `t'. - - `pair postcontrol(path p, int t);' - returns the postcontrol point of `p' at node `t'. - - `pair postcontrol(path p, real t);' - returns the effective postcontrol point of `p' at parameter - `t'. - - `real arclength(path p);' - returns the length (in user coordinates) of the piecewise - linear or cubic curve that path `p' represents. - - `real arctime(path p, real L);' - returns the path "time", a real number between 0 and the - length of the path in the sense of `point(path p, real t)', - at which the cumulative arclength (measured from the - beginning of the path) equals `L'. - - `real dirtime(path p, pair z);' - returns the first "time", a real number between 0 and the - length of the path in the sense of `point(path, real)', at - which the tangent to the path has the direction of pair `z', - or -1 if this never happens. - - `real reltime(path p, real l);' - returns the time on path `p' at the relative fraction `l' of - its arclength. - - `pair relpoint(path p, real l);' - returns the point on path `p' at the relative fraction `l' of - its arclength. - - `pair midpoint(path p);' - returns the point on path `p' at half of its arclength. - - `path reverse(path p);' - returns a path running backwards along `p'. - - `path subpath(path p, int a, int b);' - returns the subpath of `p' running from node `a' to node `b'. - If `a' < `b', the direction of the subpath is reversed. - - `path subpath(path p, real a, real b);' - returns the subpath of `p' running from path time `a' to path - time `b', in the sense of `point(path, real)'. If `a' < `b', - the direction of the subpath is reversed. - - `real[] intersect(path p, path q, real fuzz=-1);' - If `p' and `q' have at least one intersection point, return a - real array of length 2 containing the times representing the - respective path times along `p' and `q', in the sense of - `point(path, real)', for one such intersection point (as - chosen by the algorithm described on page 137 of `The - MetaFontbook'). The computations are performed to the - absolute error specified by `fuzz', or if `fuzz < 0', to - machine precision. If the paths do not intersect, return a - real array of length 0. - - `real[][] intersections(path p, path q, real fuzz=-1);' - Return all (unless there are infinitely many) intersection - times of paths `p' and `q' as a sorted array of real arrays - of length 2 (*note sort::). The computations are performed to - the absolute error specified by `fuzz', or if `fuzz < 0', to - machine precision. - - `real[] intersections(path p, explicit pair a, explicit pair b,' - real fuzz=-1); Return all (unless there are infinitely many) - intersection times of path `p' with the (infinite) line - through points `a' and `b' as a sorted array. The - intersections returned are guaranteed to be correct to within - the absolute error specified by `fuzz', or if `fuzz < 0', to - machine precision. - - `real[] times(path p, real x)' - returns all intersection times of path `p' with the vertical - line through `(x,0)'. - - `real[] times(path p, explicit pair z)' - returns all intersection times of path `p' with the - horizontal line through `(0,z.y)'. - - `real[] mintimes(path p)' - returns an array of length 2 containing times at which path - `p' reaches its minimal horizontal and vertical extents, - respectively. - - `real[] maxtimes(path p)' - returns an array of length 2 containing the times at which - path `p' reaches its maximal horizontal and vertical extents, - respectively. - - `pair intersectionpoint(path p, path q, real fuzz=-1);' - returns the intersection point - `point(p,intersect(p,q,fuzz)[0])'. - - `pair[] intersectionpoints(path p, path q, real fuzz=-1);' - returns an array containing all intersection points of the - paths `p' and `q'. - - `pair extension(pair P, pair Q, pair p, pair q);' - returns the intersection point of the extensions of the line - segments `P--Q' and `p--q', or if the lines are parallel, - `(infinity,infinity)'. - - `slice cut(path p, path knife, int n);' - returns the portions of path `p' before and after the `n'th - intersection of `p' with path `knife' as a structure `slice' - (if no intersection exist is found, the entire path is - considered to be `before' the intersection): struct slice { - path before,after; - } - The argument `n' is treated as modulo the number of - intersections. - - `slice firstcut(path p, path knife);' - equivalent to `cut(p,knife,0);' Note that `firstcut.after' - plays the role of the `MetaPost cutbefore' command. - - `slice lastcut(path p, path knife);' - equivalent to `cut(p,knife,-1);' Note that `lastcut.before' - plays the role of the `MetaPost cutafter' command. - - `path buildcycle(... path[] p);' - This returns the path surrounding a region bounded by a list - of two or more consecutively intersecting paths, following - the behaviour of the `MetaPost buildcycle' command. - - `pair min(path p);' - returns the pair (left,bottom) for the path bounding box of - path `p'. - - `pair max(path p);' - returns the pair (right,top) for the path bounding box of - path `p'. - - `int windingnumber(path p, pair z);' - returns the winding number of the cyclic path `p' relative to - the point `z'. The winding number is positive if the path - encircles `z' in the counterclockwise direction. If `z' lies - on `p' the constant `undefined' (defined to be the largest - odd integer) is returned. - - `bool interior(int windingnumber, pen fillrule)' - returns true if `windingnumber' corresponds to an interior - point according to `fillrule'. - - `bool inside(path p, pair z, pen fillrule=currentpen);' - returns `true' iff the point `z' lies inside or on the edge of - the region bounded by the cyclic path `p' according to the - fill rule `fillrule' (*note fillrule::). - - `int inside(path p, path q, pen fillrule=currentpen);' - returns `1' if the cyclic path `p' strictly contains `q' - according to the fill rule `fillrule' (*note fillrule::), `-1' - if the cyclic path `q' strictly contains `p', and `0' - otherwise. - - `pair inside(path p, pen fillrule=currentpen);' - returns an arbitrary point strictly inside a cyclic path `p' - according to the fill rule `fillrule' (*note fillrule::). - - `path[] strokepath(path g, pen p=currentpen);' - returns the path array that `PostScript' would fill in - drawing path `g' with pen `p'. - - -`guide' - an unresolved cubic spline (list of cubic-spline nodes and control - points). The implicit initializer for a guide is `nullpath'; this - is useful for building up a guide within a loop. - - A guide is similar to a path except that the computation of the - cubic spline is deferred until drawing time (when it is resolved - into a path); this allows two guides with free endpoint conditions - to be joined together smoothly. The solid curve in the following - example is built up incrementally as a guide, but only resolved at - drawing time; the dashed curve is incrementally resolved at each - iteration, before the entire set of nodes (shown in red) is known: - - size(200); - - real mexican(real x) {return (1-8x^2)*exp(-(4x^2));} - - int n=30; - real a=1.5; - real width=2a/n; - - guide hat; - path solved; - - for(int i=0; i < n; ++i) { - real t=-a+i*width; - pair z=(t,mexican(t)); - hat=hat..z; - solved=solved..z; - } - - draw(hat); - dot(hat,red); - draw(solved,dashed); - - - - We point out an efficiency distinction in the use of guides and - paths: guide g; - for(int i=0; i < 10; ++i) - g=g--(i,i); - path p=g; - - runs in linear time, whereas path p; - for(int i=0; i < 10; ++i) - p=p--(i,i); - - runs in quadratic time, as the entire path up to that point is - copied at each step of the iteration. - - The following routines can be used to examine the individual - elements of a guide without actually resolving the guide to a - fixed path (except for internal cycles, which are resolved): - - `int size(guide g);' - Analogous to `size(path p)'. - - `int length(guide g);' - Analogous to `length(path p)'. - - `bool cyclic(path p);' - Analogous to `cyclic(path p)'. - - `pair point(guide g, int t);' - Analogous to `point(path p, int t)'. - - `guide reverse(guide g);' - Analogous to `reverse(path p)'. If `g' is cyclic and also - contains a secondary cycle, it is first solved to a path, - then reversed. If `g' is not cyclic but contains an internal - cycle, only the internal cycle is solved before reversal. If - there are no internal cycles, the guide is reversed but not - solved to a path. - - `pair[] dirSpecifier(guide g, int i);' - This returns a pair array of length 2 containing the outgoing - (in element 0) and incoming (in element 1) direction - specifiers (or `(0,0)' if none specified) for the segment of - guide `g' between nodes `i' and `i+1'. - - `pair[] controlSpecifier(guide g, int i);' - If the segment of guide `g' between nodes `i' and `i+1' has - explicit outgoing and incoming control points, they are - returned as elements 0 and 1, respectively, of a two-element - array. Otherwise, an empty array is returned. - - `tensionSpecifier tensionSpecifier(guide g, int i);' - This returns the tension specifier for the segment of guide - `g' between nodes `i' and `i+1'. The individual components of - the `tensionSpecifier' type can be accessed as the virtual - members `in', `out', and `atLeast'. - - `real[] curlSpecifier(guide g);' - This returns an array containing the initial curl specifier - (in element 0) and final curl specifier (in element 1) for - guide `g'. - - - As a technical detail we note that a direction specifier given to - `nullpath' modifies the node on the other side: the guides a..{up}nullpath..b; - c..nullpath{up}..d; - e..{up}nullpath{down}..f; - are respectively equivalent to a..nullpath..{up}b; - c{up}..nullpath..d; - e{down}..nullpath..{up}f; - - - -File: asymptote.info, Node: Pens, Next: Transforms, Prev: Paths and guides, Up: Programming - -5.3 Pens -======== - -In `Asymptote', pens provide a context for the four basic drawing -commands (*note Drawing commands::). They are used to specify the -following drawing attributes: color, line type, line width, line cap, -line join, fill rule, text alignment, font, font size, pattern, -overwrite mode, and calligraphic transforms on the pen nib. The default -pen used by the drawing routines is called `currentpen'. This provides -the same functionality as the `MetaPost' command `pickup'. The -implicit initializer for pens is `defaultpen'. - - Pens may be added together with the nonassociative binary operator -`+'. This will add the colors of the two pens. All other non-default -attributes of the rightmost pen will override those of the leftmost -pen. Thus, one can obtain a yellow dashed pen by saying -`dashed+red+green' or `red+green+dashed' or `red+dashed+green'. The -binary operator `*' can be used to scale the color of a pen by a real -number, until it saturates with one or more color components equal to 1. - - * Colors are specified using one of the following colorspaces: - `pen gray(real g);' - This produces a grayscale color, where the intensity `g' lies - in the interval [0,1], with 0.0 denoting black and 1.0 - denoting white. - - `pen rgb(real r, real g, real b);' - This produces an RGB color, where each of the red, green, and - blue intensities `r', `g', `b', lies in the interval [0,1]. - - `pen cmyk(real c, real m, real y, real k);' - This produces a CMYK color, where each of the cyan, magenta, - yellow, and black intensities `c', `m', `y', `k', lies in the - interval [0,1]. - - `pen invisible;' - This special pen writes in invisible ink, but adjusts the - bounding box as if something had been drawn (like the - `\phantom' command in TeX). The function `bool - invisible(pen)' can be used to test whether a pen is - invisible. - - - The default color is `black'; this may be changed with the routine - `defaultpen(pen)'. The function `colorspace(pen p)' returns the - colorspace of pen `p' as a string (`"gray"', `"rgb"', `"cmyk"', or - `""'). - - The function `real[] colors(pen)' returns the color components of - a pen. The functions `pen gray(pen)', `pen rgb(pen)', and `pen - cmyk(pen)' return new pens obtained by converting their arguments - to the respective color spaces. The function - `colorless(pen=currentpen)' returns a copy of its argument with - the color attributes stripped (to avoid color mixing). - - A 6-character RGB hexidecimal string can be converted to a pen with - the routine pen rgb(string s); - - Various shades and mixtures of the grayscale primary colors - `black' and `white', RGB primary colors `red', `green', and - `blue', and RGB secondary colors `cyan', `magenta', and `yellow' - are defined as named colors, along with the CMYK primary colors - `Cyan', `Magenta', `Yellow', and `Black', in the module `plain': - - - - The standard 140 RGB `X11' colors can be imported with the command import x11colors; - and the standard 68 CMYK TeX colors can be imported with the - command import texcolors; - Note that there is some overlap between these two standards and - the definitions of some colors (e.g. `Green') actually disagree. - - `Asymptote' also comes with a `asycolors.sty' `LaTeX' package that - defines to `LaTeX' CMYK versions of `Asymptote''s predefined - colors, so that they can be used directly within `LaTeX' strings. - Normally, such colors are passed to `LaTeX' via a pen argument; - however, to change the color of only a portion of a string, say - for a slide presentation, (*note slide::) it may be desirable to - specify the color directly to `LaTeX'. This file can be passed to - `LaTeX' with the `Asymptote' command usepackage("asycolors"); - - The structure `hsv' defined in `plain_pens.asy' may be used to - convert between HSV and RGB spaces, where the hue `h' is an angle - in [0,360) and the saturation `s' and value `v' lie in `[0,1]': pen p=hsv(180,0.5,0.75); - write(p); // ([default], red=0.375, green=0.75, blue=0.75) - hsv q=p; - write(q.h,q.s,q.v); // 180 0.5 0.75 - - * Line types are specified with the function `pen linetype(string s, - real offset=0, bool scale=true, bool adjust=true)', where `s' is a - string of integer or real numbers separated by spaces. The - optional parameter `offset' specifies where in the pattern to - begin. The first number specifies how far (if `scale' is `true', - in units of the pen line width; otherwise in `PostScript' units) - to draw with the pen on, the second number specifies how far to - draw with the pen off, and so on. If `adjust' is `true', these - spacings are automatically adjusted by `Asymptote' to fit the - arclength of the path. Here are the predefined line types: pen solid=linetype(""); - pen dotted=linetype("0 4"); - pen dashed=linetype("8 8"); - pen longdashed=linetype("24 8"); - pen dashdotted=linetype("8 8 0 8"); - pen longdashdotted=linetype("24 8 0 8"); - pen Dotted=dotted+1.0; - pen Dotted(pen p=currentpen) {return dotted+2*linewidth(p);} - - - - The default line type is `solid'; this may be changed with - `defaultpen(pen)'. The line type of a pen is returned by `int - linetype(pen p=currentpen)'. - - * The pen line width is specified in `PostScript' units with `pen - linewidth(real)'. The default line width is 0.5 bp; this value may - be changed with `defaultpen(pen)'. The line width of a pen is - returned by `real linewidth(pen p=currentpen)'. For convenience, - in the module `plain' we define static void defaultpen(real w) {defaultpen(linewidth(w));} - static pen operator +(pen p, real w) {return p+linewidth(w);} - static pen operator +(real w, pen p) {return linewidth(w)+p;} - so that one may set the line width like this: defaultpen(2); - pen p=red+0.5; - - * A pen with a specific `PostScript' line cap is returned on calling - `linecap' with an integer argument: pen squarecap=linecap(0); - pen roundcap=linecap(1); - pen extendcap=linecap(2); - - The default line cap, `roundcap', may be changed with - `defaultpen(pen)'. The line cap of a pen is returned by `int - linecap(pen p=currentpen)'. - - * A pen with a specific `PostScript' join style is returned on - calling `linejoin' with an integer argument: pen miterjoin=linejoin(0); - pen roundjoin=linejoin(1); - pen beveljoin=linejoin(2); - - The default join style, `roundjoin', may be changed with - `defaultpen(pen)'.The join style of a pen is returned by `int - linejoin(pen p=currentpen)'. - - * A pen with a specific `PostScript' miter limit is returned by - calling `miterlimit(real)'. The default miterlimit, `10.0', may - be changed with `defaultpen(pen)'. The miter limit of a pen is - returned by `real miterlimit(pen p=currentpen)'. - - * A pen with a specific `PostScript' fill rule is returned on - calling `fillrule' with an integer argument: pen zerowinding=fillrule(0); - pen evenodd=fillrule(1); - - The fill rule, which identifies the algorithm used to determine the - insideness of a path or array of paths, only affects the `clip', - `fill', and `inside' functions. For the `zerowinding' fill rule, a - point `z' is outside the region bounded by a path if the number of - upward intersections of the path with the horizontal line - `z--z+infinity' minus the number of downward intersections is - zero. For the `evenodd' fill rule, `z' is considered to be outside - the region if the total number of such intersections is even. The - default fill rule, `zerowinding', may be changed with - `defaultpen(pen)'. The fill rule of a pen is returned by `int - fillrule(pen p=currentpen)'. - - * A pen with a specific text alignment setting is returned on - calling `basealign' with an integer argument: pen nobasealign=basealign(0); - pen basealign=basealign(1); - - The default setting, `nobasealign',which may be changed with - `defaultpen(pen)', causes the label alignment routines to use the - full label bounding box for alignment. In contrast, `basealign' - requests that the TeX baseline be respected. The base align - setting of a pen is returned by `int basealigin(pen p=currentpen)'. - - * The font size is specified in TeX points (1 pt = 1/72.27 inches) - with the function `pen fontsize(real size, real - lineskip=1.2*size)'. The default font size, 12pt, may be changed - with `defaultpen(pen)'. Nonstandard font sizes may require - inserting import fontsize; - at the beginning of the file (this requires the `fix-cm' package - available from - - `http://www.ctan.org/tex-archive/help/Catalogue/entries/fix-cm' - and included in recent `LaTeX' distributions). The font size and - line skip of a pen can be examined with the routines `real - fontsize(pen p=currentpen)' and `real lineskip(pen p=currentpen)', - respectively. - - * A pen using a specific `LaTeX' `NFSS' font is returned by calling - the function `pen font(string encoding, string family, string - series, string shape)'. The default setting, - `font("OT1","cmr","m","n")', corresponds to 12pt Computer Modern - Roman; this may be changed with `defaultpen(pen)'. The font - setting of a pen is returned by `string font(pen p=currentpen)'. - Support for standardized international characters is provided by - the `unicode' package (*note unicode::). - - Alternatively, one may select a fixed-size TeX font (on which - `fontsize' has no effect) like `"cmr12"' (12pt Computer Modern - Roman) or `"pcrr"' (Courier) using the function `pen font(string - name)'. An optional size argument can also be given to scale the - font to the requested size: `pen font(string name, real size)'. - - A nonstandard font command can be generated with `pen - fontcommand(string)'. - - A convenient interface to the following standard `PostScript' - fonts is also provided: pen AvantGarde(string series="m", string shape="n"); - pen Bookman(string series="m", string shape="n"); - pen Courier(string series="m", string shape="n"); - pen Helvetica(string series="m", string shape="n"); - pen NewCenturySchoolBook(string series="m", string shape="n"); - pen Palatino(string series="m", string shape="n"); - pen TimesRoman(string series="m", string shape="n"); - pen ZapfChancery(string series="m", string shape="n"); - pen Symbol(string series="m", string shape="n"); - pen ZapfDingbats(string series="m", string shape="n"); - - * The transparency of a pen can be changed with the command: pen opacity(real opacity=1, string blend="Compatible"); - The opacity can be varied from `0' (fully transparent) to the - default value of `1' (opaque), and `blend' specifies one of the - following foreground-background blending operations: "Compatible","Normal","Multiply","Screen","Overlay","SoftLight", - "HardLight","ColorDodge","ColorBurn","Darken","Lighten","Difference", - "Exclusion","Hue","Saturation","Color","Luminosity", - as described in - - `http://partners.adobe.com/public/developer/en/pdf/PDFReference16.pdf'. - Since `PostScript' does not support transparency, this feature is - only effective with the `-f pdf' output format option; other - formats can be produced from the resulting PDF file with the - `ImageMagick' `convert' program. Labels are always drawn with an - `opacity' of 1. A simple example of transparent filling is - provided in the example file `transparency.asy'. - - * `PostScript' commands within a `picture' may be used to create a - tiling pattern, identified by the string `name', for `fill' and - `draw' operations by adding it to the global `PostScript' frame - `currentpatterns', with optional left-bottom margin `lb' and - right-top margin `rt'. import patterns; - void add(string name, picture pic, pair lb=0, pair rt=0); - - To `fill' or `draw' using pattern `name', use the pen - `pattern("name")'. For example, rectangular tilings can be - constructed using the routines `picture tile(real Hx=5mm, real - Hy=0, pen p=currentpen, filltype filltype=NoFill)', `picture - checker(real Hx=5mm, real Hy=0, pen p=currentpen)', and `picture - brick(real Hx=5mm, real Hy=0, pen p=currentpen)' defined in - `patterns.asy': size(0,90); - import patterns; - - add("tile",tile()); - add("filledtilewithmargin",tile(6mm,4mm,red,Fill),(1mm,1mm),(1mm,1mm)); - add("checker",checker()); - add("brick",brick()); - - real s=2.5; - filldraw(unitcircle,pattern("tile")); - filldraw(shift(s,0)*unitcircle,pattern("filledtilewithmargin")); - filldraw(shift(2s,0)*unitcircle,pattern("checker")); - filldraw(shift(3s,0)*unitcircle,pattern("brick")); - - - - Hatch patterns can be generated with the routines `picture - hatch(real H=5mm, pair dir=NE, pen p=currentpen)', `picture - crosshatch(real H=5mm, pen p=currentpen)': size(0,100); - import patterns; - - add("hatch",hatch()); - add("hatchback",hatch(NW)); - add("crosshatch",crosshatch(3mm)); - - real s=1.25; - filldraw(unitsquare,pattern("hatch")); - filldraw(shift(s,0)*unitsquare,pattern("hatchback")); - filldraw(shift(2s,0)*unitsquare,pattern("crosshatch")); - - - - You may need to turn off aliasing in your `PostScript' viewer for - patterns to appear correctly. Custom patterns can easily be - constructed, following the examples in `patterns.asy'. The tiled - pattern can even incorporate shading (*note gradient shading::), - as illustrated in this example (not included in the manual because - not all printers support `PostScript' 3): size(0,100); - import patterns; - - real d=4mm; - picture tiling; - path square=scale(d)*unitsquare; - axialshade(tiling,square,white,(0,0),black,(d,d)); - fill(tiling,shift(d,d)*square,blue); - add("shadedtiling",tiling); - - filldraw(unitcircle,pattern("shadedtiling")); - - - - * One can specify a custom pen nib as an arbitrary polygonal path - with `pen makepen(path)'; this path represents the mark to be - drawn for paths containing a single point. This pen nib path can be - recovered from a pen with `path nib(pen)'. Unlike in `MetaPost', - the path need not be convex: - - size(200); - pen convex=makepen(scale(10)*polygon(8))+grey; - draw((1,0.4),convex); - draw((0,0)---(1,1)..(2,0)--cycle,convex); - - pen nonconvex=scale(10)* - makepen((0,0)--(0.25,-1)--(0.5,0.25)--(1,0)--(0.5,1.25)--cycle)+red; - draw((0.5,-1.5),nonconvex); - draw((0,-1.5)..(1,-0.5)..(2,-1.5),nonconvex); - - - - The value `nullpath' represents a circular pen nib (the default); - an elliptical pen can be achieved simply by multiplying the pen by - a transform: `yscale(2)*currentpen'. - - * One can prevent labels from overwriting one another by using the - pen attribute `overwrite', which takes a single argument: - - `Allow' - Allow labels to overwrite one another. This is the default - behaviour (unless overridden with `defaultpen(pen)'. - - `Suppress' - Suppress, with a warning, each label that would overwrite - another label. - - `SuppressQuiet' - Suppress, without warning, each label that would overwrite - another label. - - `Move' - Move a label that would overwrite another out of the way and - issue a warning. As this adjustment is during the final - output phase (in `PostScript' coordinates) it could result in - a larger figure than requested. - - `MoveQuiet' - Move a label that would overwrite another out of the way, - without warning. As this adjustment is during the final - output phase (in `PostScript' coordinates) it could result in - a larger figure than requested. - - - - The routine `defaultpen()' returns the current default pen -attributes. Calling the routine `resetdefaultpen()' resets all pen -default attributes to their initial values. - - -File: asymptote.info, Node: Transforms, Next: Frames and pictures, Prev: Pens, Up: Programming - -5.4 Transforms -============== - -`Asymptote' makes extensive use of affine transforms. A pair `(x,y)' is -transformed by the transform `t=(t.x,t.y,t.xx,t.xy,t.yx,t.yy)' to -`(x',y')', where -x' = t.x + t.xx * x + t.xy * y -y' = t.y + t.yx * x + t.yy * y - This is equivalent to the `PostScript' transformation `[t.xx t.yx t.xy -t.yy t.x t.y]'. - - Transforms can be applied to pairs, guides, paths, pens, strings, -transforms, frames, and pictures by multiplication (via the binary -operator `*') on the left (*note circle:: for an example). Transforms -can be composed with one another and inverted with the function -`transform inverse(transform t)'; they can also be raised to any -integer power with the `^' operator. - - The built-in transforms are: - -`transform identity();' - the identity transform; - -`transform shift(pair z);' - translates by the pair `z'; - -`transform shift(real x, real y);' - translates by the pair `(x,y)'; - -`transform xscale(real x);' - scales by `x' in the x direction; - -`transform yscale(real y);' - scales by `y' in the y direction; - -`transform scale(real s);' - scale by `s' in both x and y directions; - -`transform scale(real x, real y);' - scale by `x' in the x direction and by `y' in the y direction; - -`transform slant(real s);' - maps `(x,y)' -> `(x+s*y,y)'; - -`transform rotate(real angle, pair z=(0,0));' - rotates by `angle' in degrees about `z'; - -`transform reflect(pair a, pair b);' - reflects about the line `a--b'. - - The implicit initializer for transforms is `identity()'. The -routines `shift(transform t)' and `shiftless(transform t)' return the -transforms `(t.x,t.y,0,0,0,0)' and `(0,0,t.xx,t.xy,t.yx,t.yy)' -respectively. - - -File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transforms, Up: Programming - -5.5 Frames and pictures -======================= - -`frame' - Frames are canvases for drawing in `PostScript' coordinates. While - working with frames directly is occasionally necessary for - constructing deferred drawing routines, pictures are usually more - convenient to work with. The implicit initializer for frames is - `newframe'. The function `bool empty(frame f)' returns `true' only - if the frame `f' is empty. A frame may be erased with the - `erase(frame)' routine. The functions `pair min(frame)' and `pair - max(frame)' return the (left,bottom) and (right,top) coordinates - of the frame bounding box, respectively. The contents of frame - `src' may be appended to frame `dest' with the command void add(frame dest, frame src); - or prepended with void prepend(frame dest, frame src); - A frame obtained by aligning frame `f' in the direction `align', - in a manner analogous to the `align' argument of `label' (*note - label::), is returned by frame align(frame f, pair align); - - To draw or fill a box or ellipse around a label or frame and - return the boundary as a path, use one of the predefined - `envelope' routines path box(frame f, Label L="", real xmargin=0, - real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); - path roundbox(frame f, Label L="", real xmargin=0, - real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); - path ellipse(frame f, Label L="", real xmargin=0, - real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); - -`picture' - Pictures are high-level structures (*note Structures::) defined in - the module `plain' that provide canvases for drawing in user - coordinates. The default picture is called `currentpicture'. A - new picture can be created like this: picture pic; - Anonymous pictures can be made by the expression `new picture'. - - The `size' routine specifies the dimensions of the desired picture: - - void size(picture pic=currentpicture, real x, real y=x, - bool keepAspect=Aspect); - - If the `x' and `y' sizes are both 0, user coordinates will be - interpreted as `PostScript' coordinates. In this case, the - transform mapping `pic' to the final output frame is `identity()'. - - If exactly one of `x' or `y' is 0, no size restriction is imposed - in that direction; it will be scaled the same as the other - direction. - - If `keepAspect' is set to `Aspect' or `true', the picture will be - scaled with its aspect ratio preserved such that the final width - is no more than `x' and the final height is no more than `y'. - - If `keepAspect' is set to `IgnoreAspect' or `false', the picture - will be scaled in both directions so that the final width is `x' - and the height is `y'. - - To make the user coordinates of picture `pic' represent multiples - of `x' units in the x direction and `y' units in the y direction, - use void unitsize(picture pic=currentpicture, real x, real y=x); - When nonzero, these `x' and `y' values override the corresponding - size parameters of picture `pic'. - - The routine void size(picture pic=currentpicture, real xsize, real ysize, - pair min, pair max); - forces the final picture scaling to map the user coordinates - `box(min,max)' to a region of width `xsize' and height `ysize' - (when these parameters are nonzero). - - Alternatively, calling the routine transform fixedscaling(picture pic=currentpicture, pair min, - pair max, pen p=nullpen, bool warn=false); - will cause picture `pic' to use a fixed scaling to map user - coordinates in `box(min,max)' to the (already specified) picture - size, taking account of the width of pen `p'. A warning will be - issued if the final picture exceeds the specified size. - - A picture `pic' can be fit to a frame and output to a file - `prefix'.`format' using image format `format' by calling the - `shipout' function: void shipout(string prefix=defaultfilename, picture pic=currentpicture, - orientation orientation=orientation, - string format="", bool wait=false, bool view=true, - string options="", string script="", - projection P=currentprojection); - The default output format, `PostScript', may be changed with the - `-f' or `-tex' command-line options. The `options', `script', and - `projection' parameters are only relevant for 3D pictures. If - `defaultfilename' is an empty string, the prefix `outprefix()' - will be used. - - A `shipout()' command is added implicitly at file exit if no - previous `shipout' commands have been executed. The default page - orientation is `Portrait'; this may be modified by changing the - variable `orientation'. To output in landscape mode, simply set - the variable `orientation=Landscape' or issue the command shipout(Landscape); - - To rotate the page by -90 degrees, use the orientation `Seascape'. The - orientation `UpsideDown' rotates the page by 180 degrees. - - A picture `pic' can be explicitly fit to a frame by calling frame pic.fit(real xsize=pic.xsize, real ysize=pic.ysize, - bool keepAspect=pic.keepAspect); - The default size and aspect ratio settings are those given to the - `size' command (which default to `0', `0', and `true', - respectively). The transformation that would currently be used to - fit a picture `pic' to a frame is returned by the member function - `pic.calculateTransform()'. - - In certain cases (e.g. 2D graphs) where only an approximate size - estimate for `pic' is available, the picture fitting routine frame pic.scale(real xsize=this.xsize, real ysize=this.ysize, - bool keepAspect=this.keepAspect); - (which scales the resulting frame, including labels and fixed-size - objects) will enforce perfect compliance with the requested size - specification, but should not normally be required. - - To draw a bounding box with margins around a picture, fit the - picture to a frame using the function frame bbox(picture pic=currentpicture, real xmargin=0, - real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill); - Here `filltype' specifies one of the following fill types: - `FillDraw' - Fill the interior and draw the boundary. - - `FillDraw(real xmargin=0, real ymargin=xmargin, pen fillpen=nullpen,' - `pen drawpen=nullpen);' If `fillpen' is `nullpen', fill with - the drawing pen; otherwise fill with pen `fillpen'. If - `drawpen' is `nullpen', draw the boundary with `fillpen'; - otherwise with `drawpen'. An optional margin of `xmargin' and - `ymargin' can be specified. - - `Fill' - Fill the interior. - - `Fill(real xmargin=0, real ymargin=xmargin, pen p=nullpen)' - If `p' is `nullpen', fill with the drawing pen; otherwise - fill with pen `p'. An optional margin of `xmargin' and - `ymargin' can be specified. - - `NoFill' - Do not fill. - - `Draw' - Draw only the boundary. - - `Draw(real xmargin=0, real ymargin=xmargin, pen p=nullpen)' - If `p' is `nullpen', draw the boundary with the drawing pen; - otherwise draw with pen `p'. An optional margin of `xmargin' - and `ymargin' can be specified. - - `UnFill' - Clip the region. - - `UnFill(real xmargin=0, real ymargin=xmargin)' - Clip the region and surrounding margins `xmargin' and - `ymargin'. - - `RadialShade(pen penc, pen penr)' - Fill varying radially from `penc' at the center of the - bounding box to `penr' at the edge. - - - For example, to draw a bounding box around a picture with a 0.25 cm - margin and output the resulting frame, use the command: shipout(bbox(0.25cm)); - A `picture' may be fit to a frame with the background color of - pen `p' with the function `bbox(p,Fill)'. - - The functions pair min(picture pic, user=false); - pair max(picture pic, user=false); - pair size(picture pic, user=false); - calculate the `PostScript' bounds that picture `pic' would have - if it were currently fit to a frame using its default size - specification. If `user' is `false' the returned value is in - `PostScript' coordinates, otherwise it is in user coordinates. - - The function pair point(picture pic=currentpicture, pair dir, bool user=true); - is a convenient way of determining the point on the bounding box - of `pic' in the direction `dir' relative to its center, ignoring - the contributions from fixed-size objects (such as labels and - arrowheads). If `user' is `true' the returned value is in user - coordinates, otherwise it is in `PostScript' coordinates. - - The function pair truepoint(picture pic=currentpicture, pair dir, bool user=true); - is identical to `point', except that it also accounts for - fixed-size objects, using the scaling transform that picture `pic' - would have if currently fit to a frame using its default size - specification. If `user' is `true' the returned value is in user - coordinates, otherwise it is in `PostScript' coordinates. - - Sometimes it is useful to draw objects on separate pictures and - add one picture to another using the `add' function: void add(picture src, bool group=true, - filltype filltype=NoFill, bool above=true); - void add(picture dest, picture src, bool group=true, - filltype filltype=NoFill, bool above=true); - The first example adds `src' to `currentpicture'; the second one - adds `src' to `dest'. The `group' option specifies whether or not - the graphical user interface `xasy' should treat all of the - elements of `src' as a single entity (*note GUI::), `filltype' - requests optional background filling or clipping, and `above' - specifies whether to add `src' above or below existing objects. - - There are also routines to add a picture or frame `src' specified - in postscript coordinates to another picture `dest' (or - `currentpicture') about the user coordinate `position': void add(picture src, pair position, bool group=true, - filltype filltype=NoFill, bool above=true); - void add(picture dest, picture src, pair position, - bool group=true, filltype filltype=NoFill, bool above=true); - void add(picture dest=currentpicture, frame src, pair position=0, - bool group=true, filltype filltype=NoFill, bool above=true); - void add(picture dest=currentpicture, frame src, pair position, - pair align, bool group=true, filltype filltype=NoFill, - bool above=true); - - The optional `align' argument in the last three forms specifies a - direction to use for aligning the frame, in a manner analogous to - the `align' argument of `label' (*note label::). However, one key - difference is that when `align' is not specified, labels are - centered, whereas frames and pictures are aligned so that their - origin is at `position'. Illustrations of frame alignment can be - found in the examples *note errorbars:: and *note image::. If you - want to align three or more subpictures, group them two at a time: - - picture pic1; - real size=50; - size(pic1,size); - fill(pic1,(0,0)--(50,100)--(100,0)--cycle,red); - - picture pic2; - size(pic2,size); - fill(pic2,unitcircle,green); - - picture pic3; - size(pic3,size); - fill(pic3,unitsquare,blue); - - picture pic; - add(pic,pic1.fit(),(0,0),N); - add(pic,pic2.fit(),(0,0),10S); - - add(pic.fit(),(0,0),N); - add(pic3.fit(),(0,0),10S); - - - - Alternatively, one can use `attach' to automatically increase the - size of picture `dest' to accommodate adding a frame `src' about - the user coordinate `position': void attach(picture dest=currentpicture, frame src, - pair position=0, bool group=true, - filltype filltype=NoFill, bool above=true); - void attach(picture dest=currentpicture, frame src, - pair position, pair align, bool group=true, - filltype filltype=NoFill, bool above=true); - - To erase the contents of a picture (but not the size - specification), use the function void erase(picture pic=currentpicture); - - To save a snapshot of `currentpicture', `currentpen', and - `currentprojection', use the function `save()'. - - To restore a snapshot of `currentpicture', `currentpen', and - `currentprojection', use the function `restore()'. - - Many further examples of picture and frame operations are provided - in the base module `plain'. - - It is possible to insert verbatim `PostScript' commands in a - picture with one of the routines void postscript(picture pic=currentpicture, string s); - void postscript(picture pic=currentpicture, string s, pair min, - pair max) - Here `min' and `max' can be used to specify explicit bounds - associated with the resulting `PostScript' code. - - Verbatim TeX commands can be inserted in the intermediate `LaTeX' - output file with one of the functions void tex(picture pic=currentpicture, string s); - void tex(picture pic=currentpicture, string s, pair min, pair max) - Here `min' and `max' can be used to specify explicit bounds - associated with the resulting TeX code. - - To issue a global TeX command (such as a TeX macro definition) in - the TeX preamble (valid for the remainder of the top-level module) - use: void texpreamble(string s); - - The TeX environment can be reset to its initial state, clearing all - macro definitions, with the function void texreset(); - - The routine void usepackage(string s, string options=""); - provides a convenient abbreviation for texpreamble("\usepackage["+options+"]{"+s+"}"); - that can be used for importing `LaTeX' packages. - - - -File: asymptote.info, Node: Files, Next: Variable initializers, Prev: Frames and pictures, Up: Programming - -5.6 Files -========= - -`Asymptote' can read and write text files (including comma-separated -value) files and portable XDR (External Data Representation) binary -files. - - An input file must first be opened with `input(string name, bool -check=true, string comment="#")'; reading is then done by assignment: -file fin=input("test.txt"); -real a=fin; - - If the optional boolean argument `check' is `false', no check will -be made that the file exists. If the file does not exist or is not -readable, the function `bool error(file)' will return `true'. The -first character of the string `comment' specifies a comment character. -If this character is encountered in a data file, the remainder of the -line is ignored. When reading strings, a comment character followed -immediately by another comment character is treated as a single literal -comment character. - - If the `-globalwrite' (or `-nosafe') option is enabled, one can -change the current working directory to the contents of the string `s' -with the function `string cd(string s)', which returns the new working -directory. If `string s' is empty, the path is reset to the value it -had at program startup. - - When reading pairs, the enclosing parenthesis are optional. Strings -are also read by assignment, by reading characters up to but not -including a newline. In addition, `Asymptote' provides the function -`string getc(file)' to read the next character (treating the comment -character as an ordinary character) and return it as a string. - - A file named `name' can be open for output with -file output(string name, bool update=false); - If `update=false', any existing data in the file will be erased and -only write operations can be used on the file. If `update=true', any -existing data will be preserved, the position will be set to the -end-of-file, and both reading and writing operations will be enabled. -For security reasons, writing to files in directories other than the -current directory is allowed only if the `-globalwrite' (or `-nosafe') -command-line option is specified. - - There are two special files: `stdin', which reads from the keyboard, -and `stdout', which writes to the terminal. The implicit initializer -for files is `null'. - - Data of a built-in type `T' can be written to an output file by -calling one of the functions -write(string s="", T x, suffix suffix=endl ... T[]); -write(file file, string s="", T x, suffix suffix=none ... T[]); -write(file file=stdout, string s="", explicit T[] x ... T[][]); -write(file file=stdout, T[][]); -write(file file=stdout, T[][][]); -write(suffix suffix=endl); -write(file file, suffix suffix=none); - If `file' is not specified, `stdout' is used and terminated by default -with a newline. If specified, the optional identifying string `s' is -written before the data `x'. An arbitrary number of data values may be -listed when writing scalars or one-dimensional arrays. The `suffix' may -be one of the following: `none' (do nothing), `flush' (output buffered -data), `endl' (terminate with a newline and flush), `newl' (terminate -with a newline), `tab' (terminate with a tab), or `comma' (terminate -with a comma). Here are some simple examples of data output: -file fout=output("test.txt"); -write(fout,1); // Writes "1" -write(fout); // Writes a new line -write(fout,"List: ",1,2,3); // Writes "List: 1 2 3" - A file may also be opened with `xinput' or `xoutput', instead of -`input' or `output', to read or write double precision (64-bit) real -values and single precision (32-bit) integer values in Sun -Microsystem's XDR (External Data Representation) portable binary format -(available on all `UNIX' platforms). A file may also be opened with -`binput' or `boutput' to read or write double precision values in the -native (nonportable) machine binary format. The function `file -single(file,0.0)' may be used to set a file to read single precision -real XDR or binary values; calling `file single(file,0.0,false)' sets -it back to read doubles again. The functions `file single(file,0)' and -`file single(file,0,false)' can be used to change the default integer -precision (single). The functions `file single(file)' and `file -single(file,false)' may be used to set the precision for both real and -integer values. - - One can test a file for end-of-file with the boolean function -`eof(file)', end-of-line with `eol(file)', and for I/O errors with -`error(file)'. One can flush the output buffers with `flush(file)', -clear a previous I/O error with `clear(file)', and close the file with -`close(file)'. The function `int precision(file file=stdout, int -digits=0)' sets the number of digits of output precision for `file' to -`digits', provided `digits' is nonzero, and returns the previous -precision setting. The function `int tell(file)' returns the current -position in a file relative to the beginning. The routine `seek(file -file, int pos)' can be used to change this position, where a negative -value for the position `pos' is interpreted as relative to the -end-of-file. For example, one can rewind a file `file' with the command -`seek(file,0)' and position to the final character in the file with -`seek(file,-1)'. The command `seekeof(file)' sets the position to the -end of the file. - - Assigning `settings.scroll=n' for a positive integer `n' requests a -pause after every `n' output lines to `stdout'. One may then press -`Enter' to continue to the next `n' output lines, `s' followed by -`Enter' to scroll without further interruption, or `q' followed by -`Enter' to quit the current output operation. If `n' is negative, the -output scrolls a page at a time (i.e. by one less than the current -number of display lines). The default value, `settings.scroll=0', -specifies continuous scrolling. - - The routines -string getstring(string name="", string default="", string prompt="", - bool store=true); -int getint(string name="", int default=0, string prompt="", - bool store=true); -real getreal(string name="", real default=0, string prompt="", - bool store=true); -pair getpair(string name="", pair default=0, string prompt="", - bool store=true); -triple gettriple(string name="", triple default=(0,0,0), string prompt="", - bool store=true); - defined in the module `plain' may be used to prompt for a value from -`stdin' using the GNU `readline' library. If `store=true', the history -of values for `name' is stored in the file `".asy_history_"+name' -(*note history::). The most recent value in the history will be used to -provide a default value for subsequent runs. The default value -(initially `default') is displayed after `prompt'. These functions are -based on the internal routines -string readline(string prompt="", string name="", bool tabcompletion=false); -void saveline(string name, string value, bool store=true); - Here, `readline' prompts the user with the default value formatted -according to `prompt', while `saveline' is used to save the string -`value' in a local history named `name', optionally storing the local -history in a file `".asy_history_"+name'. - - The routine `history(string name, int n=1)' can be used to look up -the `n' most recent values (or all values up to `historylines' if -`n=0') entered for string `name'. The routine `history(int n=0)' -returns the interactive history. For example, -write(output("transcript.asy"),history()); - outputs the interactive history to the file `transcript.asy'. - - The function `int delete(string s)' deletes the file named by the -string `s'. Unless the `-globalwrite' (or `-nosafe') option is enabled, -the file must reside in the current directory. The function `int -rename(string from, string to)' may be used to rename file `from' to -file `to'. Unless the `-globalwrite' (or `-nosafe') option is enabled, -this operation is restricted to the current directory. The functions -int convert(string args="", string file="", string format=""); -int animate(string args="", string file="", string format=""); - call the `ImageMagick' commands `convert' and `animate', respectively, -with the arguments `args' and the file name constructed from the -strings `file' and `format'. If the setting `safe' is false, then the -function `int system(string s)' can be used to call the arbitrary system -command `s'. - - -File: asymptote.info, Node: Variable initializers, Next: Structures, Prev: Files, Up: Programming - -5.7 Variable initializers -========================= - -A variable can be assigned a value when it is declared, as in `int -x=3;' where the variable `x' is assigned the value `3'. As well as -literal constants such as `3', arbitary expressions can be used as -initializers, as in `real x=2*sin(pi/2);'. - - A variable is not added to the namespace until after the initializer -is evaluated, so for example, in - -int x=2; -int x=5*x; - the `x' in the initializer on the second line refers to the variable -`x' declared on the first line. The second line, then, declares a -variable `x' shadowing the original `x' and initializes it to the value -`10'. - - Variables of most types can be declared without an explicit -initializer and they will be initialized by the default initializer of -that type: - - * Variables of the numeric types `int', `real', and `pair' are all - initialized to zero; variables of type `triple' are initialized to - `O=(0,0,0)'. - - * `boolean' variables are initialized to `false'. - - * `string' variables are initialized to the empty string. - - * `transform' variables are initialized to the identity - transformation. - - * `path' and `guide' variables are initialized to `nullpath'. - - * `pen' variables are initialized to the default pen. - - * `frame' and `picture' variables are initialized to empty frames - and pictures, respectively. - - * `file' variables are initialized to `null'. - - The default initializers for user-defined array, structure, and -function types are explained in their respective sections. Some types, -such as `code', do not have default initializers. When a variable of -such a type is introduced, the user must initialize it by explicitly -giving it a value. - - The default initializer for any type `T' can be redeclared by -defining the function `T operator init()'. For instance, `int' -variables are usually initialized to zero, but in - -int operator init() { - return 3; -} -int y; - -the variable `y' is initialized to `3'. This example was given for -illustrative purposes; redeclaring the initializers of built-in types -is not recommended. Typically, `operator init' is used to define -sensible defaults for user-defined types. - - -File: asymptote.info, Node: Structures, Next: Operators, Prev: Variable initializers, Up: Programming - -5.8 Structures -============== - -Users may also define their own data types as structures, along with -user-defined operators, much as in C++. By default, structure members -are `public' (may be read and modified anywhere in the code), but may be -optionally declared `restricted' (readable anywhere but writeable only -inside the structure where they are defined) or `private' (readable and -writable only inside the structure). In a structure definition, the -keyword `this' can be used as an expression to refer to the enclosing -structure. Any code at the top-level scope within the structure is -executed on initialization. - - Variables hold references to structures. That is, in the example: - -struct T { - int x; -} - -T foo=new T; -T bar=foo; -bar.x=5; - - The variable `foo' holds a reference to an instance of the structure -`T'. When `bar' is assigned the value of `foo', it too now holds a -reference to the same instance as `foo' does. The assignment `bar.x=5' -changes the value of the field `x' in that instance, so that `foo.x' -will also be equal to `5'. - - The expression `new T' creates a new instance of the structure `T' -and returns a reference to that instance. In creating the new -instance, any code in the body of the record definition is executed. -For example: - -int Tcount=0; -struct T { - int x; - ++Tcount; -} - -T foo=new T; - - Here, the expression `new T' will produce a new instance of the -class, but will also cause `Tcount' to be incremented, so that it keeps -track of the number of instances produced. - - The expression `null' can be cast to any structure type to yield a -null reference, a reference that does not actually refer to any -instance of the structure. Trying to use a field of a null reference -will cause an error. - - The function `bool alias(T,T)' checks to see if two structure -references refer to the same instance of the structure (or both to -`null'). For example, in the example code at the start of the section, -`alias(foo,bar)' would return true, but `alias(foo,new T)' would return -false, as `new T' creates a new instance of the structure `T'. The -boolean operators `==' and `!=' are by default equivalent to `alias' and -`!alias' respectively, but may be overwritten for a particular type -(for example, to do a deep comparison). - - After the definition of a structure `T', a variable of type `T' is -initialized to a new instance (`new T') by default. During the -definition of the structure, however, variables of type `T' are -initialized to `null' by default. This special behaviour is to avoid -infinite recursion of creating new instances in code such as - -struct tree { - int value; - tree left; - tree right; -} - - Here is a simple example that illustrates the use of structures: - -struct S { - real a=1; - real f(real a) {return a+this.a;} -} - -S s; // Initializes s with new S; - -write(s.f(2)); // Outputs 3 - -S operator + (S s1, S s2) -{ - S result; - result.a=s1.a+s2.a; - return result; -} - -write((s+s).f(0)); // Outputs 2 - - It is often convenient to have functions that construct new -instances of a structure. Say we have a `Person' structure: - -struct Person { - string firstname; - string lastname; -} - -Person joe=new Person; -joe.firstname="Joe"; -joe.lastname="Jones"; - Creating a new Person is a chore; it takes three lines to create a new -instance and to initialize its fields (that's still considerably less -effort than creating a new person in real life, though). - - We can reduce the work by defining a constructor function -`Person(string,string)': - -struct Person { - string firstname; - string lastname; - - static Person Person(string firstname, string lastname) { - Person p=new Person; - p.firstname=firstname; - p.lastname=lastname; - return p; - } -} - -Person joe=Person.Person("Joe", "Jones"); - - While it is now easier than before to create a new instance, we still -have to refer to the constructor by the qualified name `Person.Person'. -If we add the line - -from Person unravel Person; - immediately after the structure definition, then the constructor can -be used without qualification: `Person joe=Person("Joe", "Jones");'. - - The constructor is now easy to use, but it is quite a hassle to -define. If you write a lot of constructors, you will find that you are -repeating a lot of code in each of them. Fortunately, your friendly -neighbourhood Asymptote developers have devised a way to automate much -of the process. - - If, in the body of a structure, Asymptote encounters the definition -of a function of the form `void operator init(ARGS)', it implicitly -defines a constructor function of the arguments `ARGS' that uses the -`void operator init' function to initialize a new instance of the -structure. That is, it essentially defines the following constructor -(assuming the structure is called `Foo'): - - static Foo Foo(ARGS) { - Foo instance=new Foo; - instance.operator init(ARGS); - return instance; - } - - This constructor is also implicitly copied to the enclosing scope -after the end of the structure definition, so that it can used -subsequently without qualifying it by the structure name. Our `Person' -example can thus be implemented as: - -struct Person { - string firstname; - string lastname; - - void operator init(string firstname, string lastname) { - this.firstname=firstname; - this.lastname=lastname; - } -} - -Person joe=Person("Joe", "Jones"); - - The use of `operator init' to implicitly define constructors should -not be confused with its use to define default values for variables -(*note Variable initializers::). Indeed, in the first case, the return -type of the `operator init' must be `void' while in the second, it must -be the (non-`void') type of the variable. - - The function `cputime()' returns a structure `cputime' with -cumulative CPU times broken down into the fields `parent.user', -`parent.system', `child.user', and `child.system'. For convenience, the -incremental fields `change.user' and `change.system' indicate the -change in the corresponding total parent and child CPU times since the -last call to `cputime()'. The function -void write(file file=stdout, string s="", cputime c, - string format=cputimeformat, suffix suffix=none); - displays the incremental user cputime followed by "u", the incremental -system cputime followed by "s", the total user cputime followed by "U", -and the total system cputime followed by "S". - - Much like in C++, casting (*note Casts::) provides for an elegant -implementation of structure inheritance, including virtual functions: -struct parent { - real x; - void operator init(int x) {this.x=x;} - void virtual(int) {write(0);} - void f() {virtual(1);} -} - -void write(parent p) {write(p.x);} - -struct child { - parent parent; - real y=3; - void operator init(int x) {parent.operator init(x);} - void virtual(int x) {write(x);} - parent.virtual=virtual; - void f()=parent.f; -} - -parent operator cast(child child) {return child.parent;} - -parent p=parent(1); -child c=child(2); - -write(c); // Outputs 2; - -p.f(); // Outputs 0; -c.f(); // Outputs 1; - -write(c.parent.x); // Outputs 2; -write(c.y); // Outputs 3; - - For further examples of structures, see `Legend' and `picture' in -the `Asymptote' base module `plain'. - - -File: asymptote.info, Node: Operators, Next: Implicit scaling, Prev: Structures, Up: Programming - -5.9 Operators -============= - -* Menu: - -* Arithmetic & logical:: Basic mathematical operators -* Self & prefix operators:: Increment and decrement -* User-defined operators:: Overloading operators - - -File: asymptote.info, Node: Arithmetic & logical, Next: Self & prefix operators, Up: Operators - -5.9.1 Arithmetic & logical operators ------------------------------------- - -`Asymptote' uses the standard binary arithmetic operators. However, -when one integer is divided by another, both arguments are converted to -real values before dividing and a real quotient is returned (since this -is usually what is intended). The function `int quotient(int x, int y)' -returns the greatest integer less than or equal to `x/y'. In all other -cases both operands are promoted to the same type, which will also be -the type of the result: -`+' - addition - -`-' - subtraction - -`*' - multiplication - -`/' - division - -`%' - modulo; the result always has the same sign as the divisor. In - particular, this makes `q*quotient(p,q)+p%q == p' for all integers - `p' and nonzero integers `q'. - -`^' - power; if the exponent (second argument) is an int, recursive - multiplication is used; otherwise, logarithms and exponentials are - used (`**' is a synonym for `^'). - - - The usual boolean operators are also defined: -`==' - equals - -`!=' - not equals - -`<' - less than - -`<=' - less than or equals - -`>=' - greater than or equals - -`>' - greater than - -`&&' - and (with conditional evaluation of right-hand argument) - -`&' - and - -`||' - or (with conditional evaluation of right-hand argument) - -`|' - or - -`^' - xor - -`!' - not - - `Asymptote' also supports the C-like conditional syntax: -bool positive=(pi >= 0) ? true : false; - - The function `T interp(T a, T b, real t)' returns `(1-t)*a+t*b' for -nonintegral built-in arithmetic types `T'. If `a' and `b' are pens, -they are first promoted to the same color space. - - `Asymptote' also defines bitwise functions `int AND(int,int)', `int -OR(int,int)', `int XOR(int,int)', and `int NOT(int)'. - - -File: asymptote.info, Node: Self & prefix operators, Next: User-defined operators, Prev: Arithmetic & logical, Up: Operators - -5.9.2 Self & prefix operators ------------------------------ - -As in C, each of the arithmetic operators `+', `-', `*', `/', `%', and -`^' can be used as a self operator. The prefix operators `++' -(increment by one) and `--' (decrement by one) are also defined. For -example, -int i=1; -i += 2; -int j=++i; - -is equivalent to the code -int i=1; -i=i+2; -int j=i=i+1; - - However, postfix operators like `i++' and `i--' are not defined -(because of the inherent ambiguities that would arise with the `--' -path-joining operator). In the rare instances where `i++' and `i--' are -really needed, one can substitute the expressions `(++i-1)' and -`(--i+1)', respectively. - - -File: asymptote.info, Node: User-defined operators, Prev: Self & prefix operators, Up: Operators - -5.9.3 User-defined operators ----------------------------- - -The following symbols may be used with `operator' to define or redefine -operators on structures and built-in types: -- + * / % ^ ! < > == != <= >= & | ^^ .. :: -- --- ++ -<< >> $ $$ @ @@ - The operators on the second line have precedence one higher than the -boolean operators `<', `>', `<=', and `>='. - - Guide operators like `..' may be overloaded, say, to write a user -function that produces a new guide from a given guide: -guide dots(... guide[] g)=operator ..; - -guide operator ..(... guide[] g) { - guide G; - if(g.length > 0) { - write(g[0]); - G=g[0]; - } - for(int i=1; i < g.length; ++i) { - write(g[i]); - write(); - G=dots(G,g[i]); - } - return G; -} - -guide g=(0,0){up}..{SW}(100,100){NE}..{curl 3}(50,50)..(10,10); -write("g=",g); - - -File: asymptote.info, Node: Implicit scaling, Next: Functions, Prev: Operators, Up: Programming - -5.10 Implicit scaling -===================== - -If a numeric literal is in front of certain types of expressions, then -the two are multiplied: -int x=2; -real y=2.0; -real cm=72/2.540005; - -write(3x); -write(2.5x); -write(3y); -write(-1.602e-19 y); -write(0.5(x,y)); -write(2x^2); -write(3x+2y); -write(3(x+2y)); -write(3sin(x)); -write(3(sin(x))^2); -write(10cm); - - This produces the output -6 -5 -6 --3.204e-19 -(1,1) -8 -10 -18 -2.72789228047704 -2.48046543129542 -283.464008929116 - - -File: asymptote.info, Node: Functions, Next: Arrays, Prev: Implicit scaling, Up: Programming - -5.11 Functions -============== - -`Asymptote' functions are treated as variables with a signature -(non-function variables have null signatures). Variables with the same -name are allowed, so long as they have distinct signatures. - - Functions arguments are passed by value. To pass an argument by -reference, simply enclose it in a structure (*note Structures::). - - Here are some significant features of `Asymptote' functions: - - 1. Variables with signatures (functions) and without signatures - (nonfunction variables) are distinct: int x, x(); - x=5; - x=new int() {return 17;}; - x=x(); // calls x() and puts the result, 17, in the scalar x - - 2. Traditional function definitions are allowed: int sqr(int x) - { - return x*x; - } - sqr=null; // but the function is still just a variable. - - 3. Casting can be used to resolve ambiguities: int a, a(), b, b(); // Valid: creates four variables. - a=b; // Invalid: assignment is ambiguous. - a=(int) b; // Valid: resolves ambiguity. - (int) (a=b); // Valid: resolves ambiguity. - (int) a=b; // Invalid: cast expressions cannot be L-values. - - int c(); - c=a; // Valid: only one possible assignment. - - 4. Anonymous (so-called "high-order") functions are also allowed: typedef int intop(int); - intop adder(int m) - { - return new int(int n) {return m+n;}; - } - intop addby7=adder(7); - write(addby7(1)); // Writes 8. - - 5. One may redefine a function `f', even for calls to `f' in - previously declared functions, by assigning another (anonymous or - named) function to it. However, if `f' is overloaded by a new - function definition, previous calls will still access the original - version of `f', as illustrated in this example: void f() { - write("hi"); - } - - void g() { - f(); - } - - g(); // writes "hi" - - f=new void() {write("bye");}; - - g(); // writes "bye" - - void f() {write("overloaded");}; - - f(); // writes "overloaded" - g(); // writes "bye" - - 6. Anonymous functions can be used to redefine a function variable - that has been declared (and implicitly initialized to the null - function) but not yet explicitly defined: void f(bool b); - - void g(bool b) { - if(b) f(b); - else write(b); - } - - f=new void(bool b) { - write(b); - g(false); - }; - - g(true); // Writes true, then writes false. - - - `Asymptote' is the only language we know of that treats functions as -variables, but allows overloading by distinguishing variables based on -their signatures. - - Functions are allowed to call themselves recursively. As in C++, -infinite nested recursion will generate a stack overflow (reported as a -segmentation fault, unless a fully working version of the GNU library -`libsigsegv' (e.g. 2.4 or later) is installed at configuration time). - -* Menu: - -* Default arguments:: Default values can appear anywhere -* Named arguments:: Assigning function arguments by keyword -* Rest arguments:: Functions with a variable number of arguments -* Mathematical functions:: Standard libm functions - - -File: asymptote.info, Node: Default arguments, Next: Named arguments, Up: Functions - -5.11.1 Default arguments ------------------------- - -`Asymptote' supports a more flexible mechanism for default function -arguments than C++: they may appear anywhere in the function prototype. -Because certain data types are implicitly cast to more sophisticated -types (*note Casts::) one can often avoid ambiguities by ordering -function arguments from the simplest to the most complicated. For -example, given -real f(int a=1, real b=0) {return a+b;} - then `f(1)' returns 1.0, but `f(1.0)' returns 2.0. - - The value of a default argument is determined by evaluating the -given `Asymptote' expression in the scope where the called function is -defined. - - -File: asymptote.info, Node: Named arguments, Next: Rest arguments, Prev: Default arguments, Up: Functions - -5.11.2 Named arguments ----------------------- - -It is sometimes difficult to remember the order in which arguments -appear in a function declaration. Named (keyword) arguments make calling -functions with multiple arguments easier. Unlike in the C and C++ -languages, an assignment in a function argument is interpreted as an -assignment to a parameter of the same name in the function signature, -_not within the local scope_. The command-line option `-d' may be used -to check `Asymptote' code for cases where a named argument may be -mistaken for a local assignment. - - When matching arguments to signatures, first all of the keywords are -matched, then the arguments without names are matched against the -unmatched formals as usual. For example, -int f(int x, int y) { - return 10x+y; -} -write(f(4,x=3)); - outputs 34, as `x' is already matched when we try to match the unnamed -argument `4', so it gets matched to the next item, `y'. - - For the rare occasions where it is desirable to assign a value to -local variable within a function argument (generally _not_ a good -programming practice), simply enclose the assignment in parentheses. -For example, given the definition of `f' in the previous example, -int x; -write(f(4,(x=3))); - is equivalent to the statements -int x; -x=3; -write(f(4,3)); - and outputs 43. - - As a technical detail, we point out that, since variables of the same -name but different signatures are allowed in the same scope, the code -int f(int x, int x()) { - return x+x(); -} -int seven() {return 7;} - is legal in `Asymptote', with `f(2,seven)' returning 9. A named -argument matches the first unmatched formal of the same name, so -`f(x=2,x=seven)' is an equivalent call, but `f(x=seven,2)' is not, as -the first argument is matched to the first formal, and `int ()' cannot -be implicitly cast to `int'. Default arguments do not affect which -formal a named argument is matched to, so if `f' were defined as -int f(int x=3, int x()) { - return x+x(); -} - then `f(x=seven)' would be illegal, even though `f(seven)' obviously -would be allowed. - - -File: asymptote.info, Node: Rest arguments, Next: Mathematical functions, Prev: Named arguments, Up: Functions - -5.11.3 Rest arguments ---------------------- - -Rest arguments allow one to write functions that take a variable number -of arguments: -// This function sums its arguments. -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 - -// This function subtracts subsequent arguments from the first. -int subtract(int start ... int[] subs) { - for(int i=0; i < subs.length; ++i) - start -= subs[i]; - return start; -} - -subtract(10,1,2); // returns 7 -subtract(10); // returns 10 -subtract(); // illegal - - Putting an argument into a rest array is called _packing_. One can -give an explicit list of arguments for the rest argument, so `subtract' -could alternatively be implemented as -int subtract(int start ... int[] subs) { - return start - sum(... subs); -} - - One can even combine normal arguments with rest arguments: -sum(1,2,3 ... new int[] {4,5,6}); // returns 21 - This builds a new six-element array that is passed to `sum' as `nums'. -The opposite operation, _unpacking_, is not allowed: -subtract(... new int[] {10, 1, 2}); - is illegal, as the start formal is not matched. - - If no arguments are packed, then a zero-length array (as opposed to -`null') is bound to the rest parameter. Note that default arguments are -ignored for rest formals and the rest argument is not bound to a -keyword. - - The overloading resolution in `Asymptote' is similar to the function -matching rules used in C++. Every argument match is given a score. -Exact matches score better than matches with casting, and matches with -formals (regardless of casting) score better than packing an argument -into the rest array. A candidate is maximal if all of the arguments -score as well in it as with any other candidate. If there is one -unique maximal candidate, it is chosen; otherwise, there is an -ambiguity error. - -int f(path g); -int f(guide g); -f((0,0)--(100,100)); // matches the second; the argument is a guide - -int g(int x, real y); -int g(real x, int x); - -g(3,4); // ambiguous; the first candidate is better for the first argument, - // but the second candidate is better for the second argument - -int h(... int[] rest); -int h(real x ... int[] rest); - -h(1,2); // the second definition matches, even though there is a cast, - // because casting is preferred over packing - -int i(int x ... int[] rest); -int i(real x, real y ... int[] rest); - -i(3,4); // ambiguous; the first candidate is better for the first argument, - // but the second candidate is better for the second one - - -File: asymptote.info, Node: Mathematical functions, Prev: Rest arguments, Up: Functions - -5.11.4 Mathematical functions ------------------------------ - -`Asymptote' has built-in versions of the standard `libm' mathematical -real(real) functions `sin', `cos', `tan', `asin', `acos', `atan', -`exp', `log', `pow10', `log10', `sinh', `cosh', `tanh', `asinh', -`acosh', `atanh', `sqrt', `cbrt', `fabs', `expm1', `log1p', as well as -the identity function `identity'. `Asymptote' also defines the order -`n' Bessel functions of the first kind `J(int n, real)' and second kind -`Y(int n, real)', as well as the gamma function `gamma', the error -function `erf', and the complementary error function `erfc'. The -standard real(real, real) functions `atan2', `hypot', `fmod', -`remainder' are also included. - - The functions `degrees(real radians)' and `radians(real degrees)' -can be used to convert between radians and degrees. The function -`Degrees(real radians)' returns the angle in degrees in the interval -[0,360). For convenience, `Asymptote' defines variants `Sin', `Cos', -`Tan', `aSin', `aCos', and `aTan' of the standard trigonometric -functions that use degrees rather than radians. We also define complex -versions of the `sqrt', `sin', `cos', `exp', `log', and `gamma' -functions. - - The functions `floor', `ceil', and `round' differ from their usual -definitions in that they all return an int value rather than a real -(since that is normally what one wants). The functions `Floor', -`Ceil', and `Round' are respectively similar, except that if the result -cannot be converted to a valid int, they return `intMax' for positive -arguments and `intMin' for negative arguments, rather than generating -an integer overflow. We also define a function `sgn', which returns -the sign of its real argument as an integer (-1, 0, or 1). - - There is an `abs(int)' function, as well as an `abs(real)' function -(equivalent to `fabs(real)'), an `abs(pair)' function (equivalent to -`length(pair)'). - - Random numbers can be seeded with `srand(int)' and generated with -the `int rand()' function, which returns a random integer between 0 and -the integer `randMax'. The `unitrand()' function returns a random -number uniformly distributed in the interval [0,1]. A Gaussian random -number generator `Gaussrand' and a collection of statistics routines, -including `histogram', are provided in the base file `stats.asy'. The -functions `factorial(int n)', which returns n!, and `choose(int n, int -k)', which returns n!/(k!(n-k)!), are also defined. - - When configured with the GNU Scientific Library (GSL), available from -`http://www.gnu.org/software/gsl/', `Asymptote' contains an internal -module `gsl' that defines the airy functions `Ai(real)', `Bi(real)', -`Ai_deriv(real)', `Bi_deriv(real)', `zero_Ai(int)', `zero_Bi(int)', -`zero_Ai_deriv(int)', `zero_Bi_deriv(int)', the Bessel functions -`I(int, real)', `K(int, real)', `j(int, real)', `y(int, real)', -`i_scaled(int, real)', `k_scaled(int, real)', `J(real, real)', `Y(real, -real)', `I(real, real)', `K(real, real)', `zero_J(real, int)', the -elliptic functions `F(real, real)', `E(real, real)', and `P(real, -real)', the exponential/trigonometric integrals `Ei', `Si', and `Ci', -the Legendre polynomials `Pl(int, real)', and the Riemann zeta function -`zeta(real)'. For example, to compute the sine integral `Si' of 1.0: -import gsl; -write(Si(1.0)); - - `Asymptote' also provides a few general purpose numerical routines: - -``real newton(int iterations=100, real f(real), real fprime(real), real x, bool verbose=false);'' - Use Newton-Raphson iteration to solve for a root of a real-valued - differentiable function `f', given its derivative `fprime' and an - initial guess `x'. Diagnostics for each iteration are printed if - `verbose=true'. If the iteration fails after the maximum allowed - number of loops (`iterations'), `realMax' is returned. - -``real newton(int iterations=100, real f(real), real fprime(real), real x1, real x2, bool verbose=false);'' - Use bracketed Newton-Raphson bisection to solve for a root of a - real-valued differentiable function `f' within an interval - [`x1',`x2'] (on which the endpoint values of `f' have opposite - signs), given its derivative `fprime'. Diagnostics for each - iteration are printed if `verbose=true'. If the iteration fails - after the maximum allowed number of loops (`iterations'), - `realMax' is returned. - -``real simpson(real f(real), real a, real b, real acc=realEpsilon, real dxmax=b-a)'' - returns the integral of `f' from `a' to `b' using adaptive Simpson - integration. - - - -File: asymptote.info, Node: Arrays, Next: Casts, Prev: Functions, Up: Programming - -5.12 Arrays -=========== - -* Menu: - -* Slices:: Python-style array slices - - Appending `[]' to a built-in or user-defined type yields an array. -The array element `i' of an array `A' can be accessed as `A[i]'. By -default, attempts to access or assign to an array element using a -negative index generates an error. Reading an array element with an -index beyond the length of the array also generates an error; however, -assignment to an element beyond the length of the array causes the -array to be resized to accommodate the new element. One can also index -an array `A' with an integer array `B': the array `A[B]' is formed by -indexing array `A' with successive elements of array `B'. A convenient -Java-style shorthand exists for iterating over all elements of an -array; see *note array iteration::. - - The declaration -real[] A; - -initializes `A' to be an empty (zero-length) array. Empty arrays should -be distinguished from null arrays. If we say -real[] A=null; - -then `A' cannot be dereferenced at all (null arrays have no length and -cannot be read from or assigned to). - - Arrays can be explicitly initialized like this: -real[] A={0,1,2}; - - Array assignment in `Asymptote' does a shallow copy: only the -pointer is copied (if one copy if modified, the other will be too). -The `copy' function listed below provides a deep copy of an array. - - Every array `A' of type `T[]' has the virtual members - * `int length', - - * `void cyclic(bool b)', - - * `bool cyclicflag', - - * `int[] keys', - - * `T push(T x)', - - * `void append(T[] a)', - - * `T pop()', - - * `void insert(int i ... T[] x)', - - * `void delete(int i, int j=i)', - - * `void delete()', and - - * `bool initialized(int n)'. - - The member `A.length' evaluates to the length of the array. Setting -`A.cyclic(true)' signifies that array indices should be reduced modulo -the current array length. Reading from or writing to a nonempty cyclic -array never leads to out-of-bounds errors or array resizing. The member -`A.cyclicflag' returns the current setting of the `cyclic' flag. - - The member `A.keys' evaluates to an array of integers containing the -indices of initialized entries in the array in ascending order. Hence, -for an array of length `n' with all entries initialized, `A.keys' -evaluates to the array of integers from `0' to `n-1' inclusive. A new -keys array is produced each time `A.keys' is evaluated. - - The functions `A.push' and `A.append' append their arguments onto -the end of the array, while `A.insert(int i ... T[] x)' inserts `x' -into the array at index `i'. For convenience `A.push' returns the -pushed item. The function `A.pop()' pops and returns the last element, -while `A.delete(int i, int j=i)' deletes elements with indices in the -range [`i',`j'], shifting the position of all higher-indexed elements -down. If no arguments are given, `A.delete()' provides a convenient way -of deleting all elements of `A'. The routine `A.initialized(int n)' can -be used to examine whether the element at index `n' is initialized. -Like all `Asymptote' functions, `cyclic', `push', `append', `pop', -`insert', `delete', and `initialized' can be "pulled off" of the array -and used on their own. For example, -int[] A={1}; -A.push(2); // A now contains {1,2}. -A.append(A); // A now contains {1,2,1,2}. -int f(int)=A.push; -f(3); // A now contains {1,2,1,2,3}. -int g()=A.pop; -write(g()); // Outputs 3. -A.delete(0); // A now contains {2,1,2}. -A.delete(0,1); // A now contains {2}. -A.insert(1,3); // A now contains {2,3}. -A.insert(1 ... A); // A now contains {2,2,3,3} -A.insert(2,4,5); // A now contains {2,2,4,5,3,3}. - - The `[]' suffix can also appear after the variable name; this is -sometimes convenient for declaring a list of variables and arrays of -the same type: -real a,A[]; - This declares `a' to be `real' and implicitly declares `A' to be of -type `real[]'. - - In the following list of built-in array functions, `T' represents a -generic type. Note that the internal functions `alias', `array', -`copy', `concat', `sequence', `map', and `transpose', which depend on -type `T[]', are defined only after the first declaration of a variable -of type `T[]'. - -`new T[]' - returns a new empty array of type `T[]'; - -`new T[] {list}' - returns a new array of type `T[]' initialized with `list' (a comma - delimited list of elements). - -`new T[n]' - returns a new array of `n' elements of type `T[]'. These `n' - array elements are not initialized unless they are arrays - themselves (in which case they are each initialized to empty - arrays). - -`T[] array(int n, T value, int depth=intMax)' - returns an array consisting of `n' copies of value. By default, if - `value' is itself an array, a deep copy of that array is made for - each entry in the new array. If `depth' is specified, this deep - copying only recurses to the number of levels specified. - -`int[] sequence(int n)' - if `n >= 1' returns the array `{0,1,...,n-1}' (otherwise returns a - null array); - -`int[] sequence(int n, int m)' - if `m >= n' returns an array `{n,n+1,...,m}' (otherwise returns a - null array); - -`T[] sequence(T f(int), int n)' - if `n >= 1' returns the sequence `{f_i :i=0,1,...n-1}' given a - function `T f(int)' and integer `int n' (otherwise returns a null - array); - -`T[] map(T f(T), T[] a)' - returns the array obtained by applying the function `f' to each - element of the array `a'. This is equivalent to `sequence(new - T(int i) {return f(a[i]);},a.length)'. - -`int[] reverse(int n)' - if `n >= 1' returns the array `{n-1,n-2,...,0}' (otherwise returns - a null array); - -`int[] complement(int[] a, int n)' - returns the complement of the integer array `a' in - `{0,1,2,...,n-1}', so that `b[complement(a,b.length)]' yields the - complement of `b[a]'. - -`real[] uniform(real a, real b, int n)' - if `n >= 1' returns a uniform partition of `[a,b]' into `n' - subintervals (otherwise returns a null array); - -`int find(bool[], int n=1)' - returns the index of the `n'th `true' value or -1 if not found. - If `n' is negative, search backwards from the end of the array for - the `-n'th value; - -`int search(T[] a, T key)' - For built-in ordered types `T', searches a sorted ordered array - `a' of `n' elements to find an interval containing `key', - returning `-1' if `key' is less than the first element, `n-1' if - `key' is greater than or equal to the last element, and otherwise - the index corresponding to the left-hand (smaller) endpoint. - -`T[] copy(T[] a)' - returns a deep copy of the array `a'; - -`T[][] copy(T[][] a)' - returns a deep copy of the array `a'; - -`T[][][] copy(T[][][] a)' - returns a deep copy of the array `a'; - -`T[] concat(... T[][] a)' - returns a new array formed by concatenating the arrays given as - arguments; - -`bool alias(T[] a, T[] b)' - returns `true' if the arrays `a' and `b' are identical; - -`T[] sort(T[] a)' - For built-in ordered types `T', returns a copy of `a' sorted in - ascending order; - -`T[][] sort(T[][] a)' - For built-in ordered types `T', returns a copy of `a' with the rows - sorted by the first column, breaking ties with successively higher - columns. For example: string[][] a={{"bob","9"},{"alice","5"},{"pete","7"}, - {"alice","4"}}; - // Row sort (by column 0, using column 1 to break ties): - write(sort(a)); - - produces alice 4 - alice 5 - bob 9 - pete 7 - -`T[] sort(T[] a, bool compare(T i, T j))' - returns a copy of `a' stably sorted in ascending order such that - element `i' precedes element `j' if `compare(i,j)' is true. - -`T[][] transpose(T[][] a)' - returns the transpose of `a'. - -`T[][][] transpose(T[][][] a, int[] perm)' - returns the 3D transpose of `a' obtained by applying the - permutation `perm' of `new int[]{0,1,2}' to the indices of each - entry. - -`T sum(T[] a)' - For arithmetic types `T', returns the sum of `a'. In the case - where `T' is `bool', the number of true elements in `a' is - returned. - -`T min(T[] a)' - -`T min(T[][] a)' - -`T min(T[][][] a)' - For built-in ordered types `T', returns the minimum element of `a'. - -`T max(T[] a)' - -`T max(T[][] a)' - -`T max(T[][][] a)' - For built-in ordered types `T', returns the maximum element of `a'. - -`T[] min(T[] a, T[] b)' - For built-in ordered types `T', and arrays `a' and `b' of the same - length, returns an array composed of the minimum of the - corresponding elements of `a' and `b'. - -`T[] max(T[] a, T[] b)' - For built-in ordered types `T', and arrays `a' and `b' of the same - length, returns an array composed of the maximum of the - corresponding elements of `a' and `b'. - -`pair[] pairs(real[] x, real[] y);' - For arrays `x' and `y' of the same length, returns the pair array - `sequence(new pair(int i) {return (x[i],y[i]);},x.length)'. - -`pair[] fft(pair[] a, int sign=1)' - returns the Fast Fourier Transform of `a' (if the optional `FFTW' - package is installed), using the given `sign'. Here is a simple - example: int n=4; - pair[] f=sequence(n); - write(f); - pair[] g=fft(f,-1); - write(); - write(g); - f=fft(g,1); - write(); - write(f/n); - -`real dot(real[] a, real[] b)' - returns the dot product of the vectors `a' and `b'. - -`real[] tridiagonal(real[] a, real[] b, real[] c, real[] f);' - Solve the periodic tridiagonal problem L`x'=`f' and return the - solution `x', where `f' is an n vector and L is the n \times n - matrix [ b[0] c[0] a[0] ] - [ a[1] b[1] c[1] ] - [ a[2] b[2] c[2] ] - [ ... ] - [ c[n-1] a[n-1] b[n-1] ] - For Dirichlet boundary conditions (denoted here by `u[-1]' and - `u[n]'), replace `f[0]' by `f[0]-a[0]u[-1]' and - `f[n-1]-c[n-1]u[n]'; then set `a[0]=c[n-1]=0'. - -`real[] solve(real[][] a, real[] b, bool warn=true)' - Solve the linear equation `a'x=`b' by LU decomposition and return - the solution x, where `a' is an n \times n matrix and `b' is an - array of length n. For example: import math; - real[][] a={{1,-2,3,0},{4,-5,6,2},{-7,-8,10,5},{1,50,1,-2}}; - real[] b={7,19,33,3}; - real[] x=solve(a,b); - write(a); write(); - write(b); write(); - write(x); write(); - write(a*x); - If `a' is a singular matrix and `warn' is `false', return an - empty array. If the matrix `a' is tridiagonal, the routine - `tridiagonal' provides a more efficient algorithm (*note - tridiagonal::). - -`real[][] solve(real[][] a, real[][] b, bool warn=true)' - Solve the linear equation `a'x=`b' and return the solution x, - where `a' is an n \times n matrix and `b' is an n \times m matrix. - If `a' is a singular matrix and `warn' is `false', return an empty - matrix. - -`real[][] identity(int n);' - returns the n \times n identity matrix. - -`real[][] diagonal(... real[] a)' - returns the diagonal matrix with diagonal entries given by a. - -`real[][] inverse(real[][] a)' - returns the inverse of a square matrix `a'. - -``real[] quadraticroots(real a, real b, real c);'' - This numerically robust solver returns the real roots of the - quadratic equation ax^2+bx+c=0, in ascending order. Multiple roots - are listed separately. - -``pair[] quadraticroots(explicit pair a, explicit pair b, explicit pair c);'' - This numerically robust solver returns the two complex roots of the - quadratic equation ax^2+bx+c=0. - -``real[] cubicroots(real a, real b, real c, real d);'' - This numerically robust solver returns the real roots of the cubic - equation ax^3+bx^2+cx+d=0. Multiple roots are listed separately. - - - `Asymptote' includes a full set of vectorized array instructions for -arithmetic (including self) and logical operations. These -element-by-element instructions are implemented in C++ code for speed. -Given -real[] a={1,2}; -real[] b={3,2}; - then `a == b' and `a >= 2' both evaluate to the vector `{false, true}'. To -test whether all components of `a' and `b' agree, use the boolean -function `all(a == b)'. One can also use conditionals like `(a >= 2) ? -a : b', which returns the array `{3,2}', or `write((a >= 2) ? a : -null', which returns the array `{2}'. - - All of the standard built-in `libm' functions of signature -`real(real)' also take a real array as an argument, effectively like an -implicit call to `map'. - - As with other built-in types, arrays of the basic data types can be -read in by assignment. In this example, the code -file fin=input("test.txt"); -real[] A=fin; - -reads real values into `A' until the end-of-file is reached (or an I/O -error occurs). If line mode is set with `line(file)', then reading will -stop once the end of the line is reached instead (line mode may be -cleared with `line(file,false)'): -file fin=input("test.txt"); -real[] A=line(fin); - - Since string reads by default read up to the end of line anyway, -line mode normally has no effect on string array reads. However, there -is a white-space delimiter mode for reading strings, set with -`word(file)' and cleared with `word(file,false)', which causes string -reads to respect white-space delimiters, instead of the default -end-of-line delimiter: -file fin=word(line(input("test.txt"))); -real[] A=fin; - - Another useful mode is comma-separated-value mode, set with -`csv(file)' and cleared with `csv(file,false)', which causes reads to -respect comma delimiters: -file fin=csv(input("test.txt")); -real[] A=fin; - - To restrict the number of values read, use the `dimension(file,int)' -function: -file fin=input("test.txt"); -real[] A=dimension(fin,10); - - This reads 10 values into A, unless end-of-file (or end-of-line in -line mode) occurs first. Attempting to read beyond the end of the file -will produce a runtime error message. Specifying a value of 0 for the -integer limit is equivalent to the previous example of reading until -end-of-file (or end-of-line in line mode) is encountered. - - Two- and three-dimensional arrays of the basic data types can be read -in like this: -file fin=input("test.txt"); -real[][] A=dimension(fin,2,3); -real[][][] B=dimension(fin,2,3,4); - Again, an integer limit of zero means no restriction. - - Sometimes the array dimensions are stored with the data as integer -fields at the beginning of an array. Such arrays can be read in with the -functions `read1', `read2', and `read3', respectively: -file fin=input("test.txt"); -real[] A=read1(fin); -real[][] B=read2(fin); -real[][][] C=read3(fin); - - One, two, and three-dimensional arrays of the basic data types can be -output with the functions `write(file,T[])', `write(file,T[][])', -`write(file,T[][][])', respectively. - - -File: asymptote.info, Node: Slices, Up: Arrays - -5.12.1 Slices -------------- - -Asymptote allows a section of an array to be addressed as a slice using -a Python-like syntax. If `A' is an array, the expression `A[m:n]' -returns a new array consisting of the elements of `A' with indices from -`m' up to but not including `n'. For example, - -int[] x={0,1,2,3,4,5,6,7,8,9}; -int[] y=x[2:6]; // y={2,3,4,5}; -int[] z=x[5:10]; // z={5,6,7,8,9}; - - If the left index is omitted, it is taken be `0'. If the right -index is omitted it is taken to be the length of the array. If both -are omitted, the slice then goes from the start of the array to the -end, producing a non-cyclic deep copy of the array. For example: - -int[] x={0,1,2,3,4,5,6,7,8,9}; -int[] y=x[:4]; // y={0,1,2,3} -int[] z=x[5:]; // z={5,6,7,8,9} -int[] w=x[:]; // w={0,1,2,3,4,5,6,7,8,9}, distinct from array x. - - If A is a non-cyclic array, it is illegal to use negative values for -either of the indices. If the indices exceed the length of the array, -however, they are politely truncated to that length. - - For cyclic arrays, the slice `A[m:n]' still consists of the cells -with indices in the set [`m',`n'), but now negative values and values -beyond the length of the array are allowed. The indices simply wrap -around. For example: - -int[] x={0,1,2,3,4,5,6,7,8,9}; -x.cyclic(true); -int[] y=x[8:15]; // y={8,9,0,1,2,3,4}. -int[] z=x[-5:5]; // z={5,6,7,8,9,0,1,2,3,4} -int[] w=x[-3:17]; // w={7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6} - - Notice that with cyclic arrays, it is possible to include the same -element of the original array multiple times within a slice. -Regardless of the original array, arrays produced by slices are always -non-cyclic. - - If the left and right indices of a slice are the same, the result is -an empty array. If the array being sliced is empty, the result is an -empty array. Any slice with a left index greater than its right index -will yield an error. - - Slices can also be assigned to, changing the value of the original -array. If the array being assigned to the slice has a different length -than the slice itself, elements will be inserted or removed from the -array to accommodate it. For instance: - -string[] toppings={"mayo", "salt", "ham", "lettuce"}; -toppings[0:2]=new string[] {"mustard", "pepper"}; - // Now toppings={"mustard", "pepper", "ham", "lettuce"} -toppings[2:3]=new string[] {"turkey", "bacon" }; - // Now toppings={"mustard", "pepper", "turkey", "bacon", "lettuce"} -toppings[0:3]=new string[] {"tomato"}; - // Now toppings={"tomato", "bacon", "lettuce"} - - If an array is assigned to a slice of itself, a copy of the original -array is assigned to the slice. That is, code such as `x[m:n]=x' is -equivalent to `x[m:n]=copy(x)'. One can use the shorthand `x[m:m]=y' -to insert the contents of the array `y' into the array `x' starting at -the location just before `x[m]'. - - For a cyclic array, a slice is bridging if it addresses cells up to -the end of the array and then continues on to address cells at the -start of the array. For instance, if `A' is a cyclic array of length -10, `A[8:12]', `A[-3:1]', and `A[5:25]' are bridging slices whereas -`A[3:7]', `A[7:10]', `A[-3:0]' and `A[103:107]' are not. Bridging -slices can only be assigned to if the number of elements in the slice -is exactly equal to the number of elements we are assigning to it. -Otherwise, there is no clear way to decide which of the new entries -should be `A[0]' and an error is reported. Non-bridging slices may be -assigned an array of any length. - - For a cyclic array `A' an expression of the form -`A[A.length:A.length]' is equivalent to the expression `A[0:0]' and so -assigning to this slice will insert values at the start of the array. -`A.append()' can be used to insert values at the end of the array. - - It is illegal to assign to a slice of a cyclic array that repeats -any of the cells. - - -File: asymptote.info, Node: Casts, Next: Import, Prev: Arrays, Up: Programming - -5.13 Casts -========== - -`Asymptote' implicitly casts `int' to `real', `int' to `pair', `real' -to `pair', `pair' to `path', `pair' to `guide', `path' to `guide', -`guide' to `path', `real' to `pen', `pair[]' to `guide[]', `pair[]' to -`path[]', `path' to `path[]', and `guide' to `path[]', along with -various three-dimensional casts defined in `three.asy'. Implicit casts -are automatically attempted on assignment and when trying to match -function calls with possible function signatures. Implicit casting can -be inhibited by declaring individual arguments `explicit' in the -function signature, say to avoid an ambiguous function call in the -following example, which outputs 0: - -int f(pair a) {return 0;} -int f(explicit real x) {return 1;} - -write(f(0)); - - Other conversions, say `real' to `int' or `real' to `string', -require an explicit cast: -int i=(int) 2.5; -string s=(string) 2.5; - -real[] a={2.5,-3.5}; -int[] b=(int []) a; -write(stdout,b); // Outputs 2,-3 - - Casting to user-defined types is also possible using `operator cast': -struct rpair { - real radius; - real angle; -} - -pair operator cast(rpair x) { - return (x.radius*cos(x.angle),x.radius*sin(x.angle)); -} - -rpair x; -x.radius=1; -x.angle=pi/6; - -write(x); // Outputs (0.866025403784439,0.5) - - One must use care when defining new cast operators. Suppose that in -some code one wants all integers to represent multiples of 100. To -convert them to reals, one would first want to multiply them by 100. -However, the straightforward implementation -real operator cast(int x) {return x*100;} - is equivalent to an infinite recursion, since the result `x*100' needs -itself to be cast from an integer to a real. Instead, we want to use -the standard conversion of int to real: -real convert(int x) {return x*100;} -real operator cast(int x)=convert; - - Explicit casts are implemented similarly, with `operator ecast'. - - -File: asymptote.info, Node: Import, Next: Static, Prev: Casts, Up: Programming - -5.14 Import -=========== - -While `Asymptote' provides many features by default, some applications -require specialized features contained in external `Asymptote' modules. -For instance, the lines -access graph; -graph.axes(); - draw x and y axes on a two-dimensional graph. Here, the command looks -up the module under the name `graph' in a global dictionary of modules -and puts it in a new variable named `graph'. The module is a -structure, and we can refer to its fields as we usually would with a -structure. - - Often, one wants to use module functions without having to specify -the module name. The code -from graph access axes; - adds the `axes' field of `graph' into the local name space, so that -subsequently, one can just write `axes()'. If the given name is -overloaded, all types and variables of that name are added. To add -more than one name, just use a comma-separated list: - -from graph access axes, xaxis, yaxis; - Wild card notation can be used to add all non-private fields and types -of a module to the local name space: - -from graph access *; - - Similarly, one can add the non-private fields and types of a -structure to the local environment with the `unravel' keyword: - -struct matrix { - real a,b,c,d; -} - -real det(matrix m) { - unravel m; - return a*d-b*c; -} - Alternatively, one can unravel selective fields: -real det(matrix m) { - from m unravel a,b,c as C,d; - return a*d-b*C; -} - - The command -import graph; - is a convenient abbreviation for the commands -access graph; -unravel graph; - That is, `import graph' first loads a module into a structure called -`graph' and then adds its non-private fields and types to the local -environment. This way, if a member variable (or function) is -overwritten with a local variable (or function of the same signature), -the original one can still be accessed by qualifying it with the module -name. - - Wild card importing will work fine in most cases, but one does not -usually know all of the internal types and variables of a module, which -can also change as the module writer adds or changes features of the -module. As such, it is prudent to add `import' commands at the start -of an `Asymptote' file, so that imported names won't shadow locally -defined functions. Still, imported names may shadow other imported -names, depending on the order in which they were imported, and imported -functions may cause overloading resolution problems if they have the -same name as local functions defined later. - - To rename modules or fields when adding them to the local -environment, use `as': - -access graph as graph2d; -from graph access xaxis as xline, yaxis as yline; - - The command -import graph as graph2d; - is a convenient abbreviation for the commands -access graph as graph2d; -unravel graph2d; - - Except for a few built-in modules, such as `settings', all modules -are implemented as `Asymptote' files. When looking up a module that -has not yet been loaded, `Asymptote' searches the standard search paths -(*note Search paths::) for the matching file. The file corresponding -to that name is read and the code within it is interpreted as the body -of a structure defining the module. - - If the file name contains nonalphanumeric characters, enclose it -with quotation marks: - -`access "/usr/local/share/asymptote/graph.asy" as graph;' - -`from "/usr/local/share/asymptote/graph.asy" access axes;' - -`import "/usr/local/share/asymptote/graph.asy" as graph;' - - It is an error if modules import themselves (or each other in a -cycle). The module name to be imported must be known at compile time. - - However, you can import an `Asymptote' module determined by the -string `s' at runtime like this: -eval("import "+s,true); - - To conditionally execute an array of asy files, use -void asy(string format, bool overwrite ... string[] s); - The file will only be processed, using output format `format', if -overwrite is `true' or the output file is missing. - - One can evaluate an `Asymptote' expression (without any return -value, however) contained in the string `s' with: -void eval(string s, bool embedded=false); - It is not necessary to terminate the string `s' with a semicolon. If -`embedded' is `true', the string will be evaluated at the top level of -the current environment. If `embedded' is `false' (the default), the -string will be evaluated in an independent environment, sharing the same -`settings' module (*note settings::). - - One can evaluate arbitrary `Asymptote' code (which may contain -unescaped quotation marks) with the command -void eval(code s, bool embedded=false); - Here `code' is a special type used with `quote {}' to enclose -`Asymptote code' like this: -real a=1; -code s=quote { - write(a); -}; -eval(s,true); // Outputs 1 - - To include the contents of a file `graph' verbatim (as if the -contents of the file were inserted at that point), use one of the forms: -include graph; - -`include "/usr/local/share/asymptote/graph.asy";' - - To list all global functions and variables defined in a module named -by the contents of the string `s', use the function -void list(string s, bool imports=false); - Imported global functions and variables are also listed if `imports' -is `true'. - - -File: asymptote.info, Node: Static, Prev: Import, Up: Programming - -5.15 Static -=========== - -Static qualifiers allocate the memory address of a variable in a higher -enclosing level. - - For a function body, the variable is allocated in the block where the -function is defined; so in the code -struct s { - int count() { - static int c=0; - ++c; - return c; - } -} - -there is one instance of the variable `c' for each object `s' (as -opposed to each call of `count'). - - Similarly, in -int factorial(int n) { - int helper(int k) { - static int x=1; - x *= k; - return k == 1 ? x : helper(k-1); - } - return helper(n); -} - -there is one instance of `x' for every call to `factorial' (and not for -every call to `helper'), so this is a correct, but ugly, implementation -of factorial. - - Similarly, a static variable declared within a structure is -allocated in the block where the structure is defined. Thus, -struct A { - struct B { - static pair z; - } -} - -creates one object `z' for each object of type `A' created. - - In this example, -int pow(int n, int k) { - struct A { - static int x=1; - void helper() { - x *= n; - } - } - for(int i=0; i < k; ++i) { - A a; - a.helper(); - } - return A.x; -} - -there is one instance of `x' for each call to `pow', so this is an ugly -implementation of exponentiation. - - Loop constructs allocate a new frame in every iteration. This is so -that higher-order functions can refer to variables of a specific -iteration of a loop: - -void f(); -for(int i=0; i < 10; ++i) { - int x=i; - if(x==5) { - f=new void () { write(x); } - } -} -f(); - - Here, every iteration of the loop has its own variable `x', so `f()' -will write `5'. If a variable in a loop is declared static, it will be -allocated where the enclosing function or structure was defined (just -as if it were declared static outside of the loop). For instance, in: - -void f() { - static int x; - for(int i=0; i < 10; ++i) { - static int y; - } -} - both `x' and `y' will be allocated in the same place, which is also -where `f' is also allocated. - - Statements may also be declared static, in which case they are run -at the place where the enclosing function or structure is defined. -Declarations or statements not enclosed in a function or structure -definition are already at the top level, so static modifiers are -meaningless. A warning is given in such a case. - - Since structures can have static fields, it is not always clear for -a qualified name whether the qualifier is a variable or a type. For -instance, in: - -struct A { - static int x; -} -pair A; - -int y=A.x; - does the `A' in `A.x' refer to the structure or to the pair variable. -It is the convention in Asymptote that, if there is a non-function -variable with the same name as the qualifier, the qualifier refers to -that variable, and not to the type. This is regardless of what fields -the variable actually possesses. - - -File: asymptote.info, Node: LaTeX usage, Next: Base modules, Prev: Programming, Up: Top - -6 `LaTeX' usage -*************** - -`Asymptote' comes with a convenient `LaTeX' style file `asymptote.sty' -that makes `LaTeX' `Asymptote'-aware. Entering `Asymptote' code -directly into the `LaTeX' source file, at the point where it is needed, -keeps figures organized and avoids the need to invent new file names -for each figure. Simply add the line `\usepackage{asymptote}' at the -beginning of your file and enclose your `Asymptote' code within a -`\begin{asy}...\end{asy}' environment. As with the `LaTeX' `comment' -environment, the `\end{asy}' command must appear on a line by itself, -with no leading spaces or trailing commands/comments. - - The sample `LaTeX' file below, named `latexusage.tex', can be run as -follows: -latex latexusage -asy latexusage -latex latexusage - -or - -pdflatex latexusage -asy latexusage -pdflatex latexusage - - To switch between using `latex' and `pdflatex' you may first need to -remove the files `latexusage-*', `latexusage_.pre', and -`latexusage.aux'. - - One can specify `width', `height', `viewportwidth', -`viewportheight', and `attach' `keyval'-style options to the `asy' -environment. The current version (1.07) of `asymptote.sty' supports the -embedding of 3D PRC files, either inline or, using the `attach' option -with the `attachfile2' (or older `attachfile') `LaTeX' package, as -annotated (but printable) attachments. For many applications, the -annotated attachment method tends to be more convenient. The default -value of `viewportwidth' is `\the\linewidth' for inline 3D figures and -`0' for attachments. - - If the `inline' option is given to the `asymptote.sty' package, -inline `LaTeX' code is generated instead of EPS or PDF files. This -makes 2D LaTeX symbols visible to the `\begin{asy}...\end{asy}' -environment. In this mode, Asymptote correctly aligns 2D LaTeX symbols -defined outside of `\begin{asy}...\end{asy}', but treats their size as -zero; an optional second string can be given to `Label' to provide an -estimate of the unknown label size. - - Note that if `latex' is used with the `inline' option, the labels -might not show up in DVI viewers that cannot handle raw `PostScript' -code. One can use `dvips'/`dvipdf' to produce `PostScript'/PDF output -(we recommend using the modified version of `dvipdf' in the `Asymptote' -patches directory, which accepts the `dvips -z' hyperdvi option). - - An excellent tutorial by Dario Teixeira on integrating `Asymptote' -and `LaTeX' is available at `http://dario.dse.nl/projects/asylatex/'. - - Here now is `latexusage.tex': - -\documentclass[12pt]{article} - -% Use this form to include EPS (latex) or PDF (pdflatex) files: -\usepackage{asymptote} - -% Use this form with latex or pdflatex to include inline LaTeX code: -%\usepackage[inline]{asymptote} - -% Enable this line to support PDF hyperlinks: -%\usepackage[setpagesize=false]{hyperref} - -% Enable this line for PDF attachments with asy environment option attach=true: -%\usepackage[dvips]{attachfile2} - -\begin{document} - -\begin{asydef} -// Global Asymptote definitions can be put here. -usepackage("bm"); -texpreamble("\def\V#1{\bm{#1}}"); -// One can globally override the default toolbar settings here: -// settings.toolbar=true; -\end{asydef} - -Here is a venn diagram produced with Asymptote, drawn to width 4cm: - -\def\A{A} -\def\B{\V{B}} - -%\begin{figure} -\begin{center} -\begin{asy} -size(4cm,0); -pen colour1=red; -pen colour2=green; - -pair z0=(0,0); -pair z1=(-1,0); -pair z2=(1,0); -real r=1.5; -path c1=circle(z1,r); -path c2=circle(z2,r); -fill(c1,colour1); -fill(c2,colour2); - -picture intersection=new picture; -fill(intersection,c1,colour1+colour2); -clip(intersection,c2); - -add(intersection); - -draw(c1); -draw(c2); - -//draw("$\A$",box,z1); // Requires [inline] package option. -//draw(Label("$\B$","$B$"),box,z2); // Requires [inline] package option. -draw("$A$",box,z1); -draw("$\V{B}$",box,z2); - -pair z=(0,-2); -real m=3; -margin BigMargin=Margin(0,m*dot(unit(z1-z),unit(z0-z))); - -draw(Label("$A\cap B$",0),conj(z)--z0,Arrow,BigMargin); -draw(Label("$A\cup B$",0),z--z0,Arrow,BigMargin); -draw(z--z1,Arrow,Margin(0,m)); -draw(z--z2,Arrow,Margin(0,m)); - -shipout(bbox(0.25cm)); -\end{asy} -%\caption{Venn diagram}\label{venn} -\end{center} -%\end{figure} - -Each graph is drawn in its own environment. One can specify the width -and height to \LaTeX\ explicitly. This 3D example can be viewed -interactively either with Adobe Reader or Asymptote's fast OpenGL-based -renderer. It is often desirable to embed such files as annotated attachments; -this requires the optional \verb+\usepackage{attachfile2}+ package and -the \verb+{attach=true}+ option: -\begin{center} -\begin{asy}[height=4cm,attach=false] -import three; -currentprojection=orthographic(5,4,2); -draw(unitcube,blue); -label("$V-E+F=2$",(0,1,0.5),3Y,blue+fontsize(17)); -\end{asy} -\end{center} - -One can also scale the figure to the full line width: -\begin{center} -\begin{asy}[width=\the\linewidth] -pair z0=(0,0); -pair z1=(2,0); -pair z2=(5,0); -pair zf=z1+0.75*(z2-z1); - -draw(z1--z2); -dot(z1,red+0.15cm); -dot(z2,darkgreen+0.3cm); -label("$m$",z1,1.2N,red); -label("$M$",z2,1.5N,darkgreen); -label("$\hat{\ }$",zf,0.2*S,fontsize(24)+blue); - -pair s=-0.2*I; -draw("$x$",z0+s--z1+s,N,red,Arrows,Bars,PenMargins); -s=-0.5*I; -draw("$\bar{x}$",z0+s--zf+s,blue,Arrows,Bars,PenMargins); -s=-0.95*I; -draw("$X$",z0+s--z2+s,darkgreen,Arrows,Bars,PenMargins); -\end{asy} -\end{center} -\end{document} - - -File: asymptote.info, Node: Base modules, Next: Options, Prev: LaTeX usage, Up: Top - -7 Base modules -************** - -`Asymptote' currently ships with the following base modules: - -* Menu: - -* plain:: Default `Asymptote' base file -* simplex:: Linear programming: simplex method -* math:: Extend `Asymptote''s math capabilities -* interpolate:: Interpolation routines -* geometry:: Geometry routines -* trembling:: Wavy lines -* stats:: Statistics routines and histograms -* patterns:: Custom fill and draw patterns -* markers:: Custom path marker routines -* tree:: Dynamic binary search tree -* binarytree:: Binary tree drawing module -* drawtree:: Tree drawing module -* syzygy:: Syzygy and braid drawing module -* feynman:: Feynman diagrams -* roundedpath:: Round the sharp corners of paths -* animation:: Embedded PDF and MPEG movies -* embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with `Asymptote' -* MetaPost:: `MetaPost' compatibility routines -* unicode:: Accept `unicode' (UTF-8) characters -* latin1:: Accept `ISO 8859-1' characters -* babel:: Interface to `LaTeX' `babel' package -* labelpath:: Drawing curved labels -* labelpath3:: Drawing curved labels in 3D -* annotate:: Annotate your PDF files -* CAD:: 2D CAD pen and measurement functions (DIN 15) -* graph:: 2D linear & logarithmic graphs -* palette:: Color density images and palettes -* three:: 3D vector graphics -* obj:: 3D obj files -* graph3:: 3D linear & logarithmic graphs -* grid3:: 3D grids -* solids:: 3D solid geometry -* tube:: 3D rotation minimizing tubes -* flowchart:: Flowchart drawing routines -* contour:: Contour lines -* contour3:: Contour surfaces -* slopefield:: Slope fields -* ode:: Ordinary differential equations - - -File: asymptote.info, Node: plain, Next: simplex, Up: Base modules - -7.1 `plain' -=========== - -This is the default `Asymptote' base file, which defines key parts of -the drawing language (such as the `picture' structure). - - By default, an implicit `private import plain;' occurs before -translating a file and before the first command given in interactive -mode. This also applies when translating files for module definitions -(except when translating `plain', of course). This means that the -types and functions defined in `plain' are accessible in almost all -`Asymptote' code. Use the `-noautoplain' command-line option to disable -this feature. - - -File: asymptote.info, Node: simplex, Next: math, Prev: plain, Up: Base modules - -7.2 `simplex' -============= - -This package solves the two-variable linear programming problem using -the simplex method. It is used by the module `plain' for automatic -sizing of pictures. - - -File: asymptote.info, Node: math, Next: interpolate, Prev: simplex, Up: Base modules - -7.3 `math' -========== - -This package extends `Asymptote''s mathematical capabilities with -intersection algorithms and matrix arithmetic: - -`void drawline(picture pic=currentpicture, pair P, pair Q, pen p=currentpen);' - draw the visible portion of the (infinite) line going through `P' - and `Q', without altering the size of picture `pic', using pen `p'. - -`real intersect(triple P, triple Q, triple n, triple Z);' - returns the intersection time of the extension of the line segment - `PQ' with the plane perpendicular to `n' and passing through `Z'. - -`triple intersectionpoint(triple n0, triple P0, triple n1, triple P1);' - Return any point on the intersection of the two planes with normals - `n0' and `n1' passing through points `P0' and `P1', respectively. - If the planes are parallel, return `(infinity,infinity,infinity)'. - -``pair[] quarticroots(real a, real b, real c, real d, real e);'' - returns the four complex roots of the quartic equation - ax^4+bx^3+cx^2+dx+e=0. - - - -File: asymptote.info, Node: interpolate, Next: geometry, Prev: math, Up: Base modules - -7.4 `interpolate' -================= - -This module implements Lagrange, Hermite, and standard cubic spline -interpolation in `Asymptote', as illustrated in the example -`interpolate1.asy'. - - -File: asymptote.info, Node: geometry, Next: trembling, Prev: interpolate, Up: Base modules - -7.5 `geometry' -============== - -This module, written by Philippe Ivaldi, provides an extensive set of -geometry routines, including `perpendicular' symbols and a `triangle' -structure. Link to the documentation for the `geometry' module are -posted here: `http://asymptote.sourceforge.net/links.html', including -an extensive set of examples, -`http://piprim.tuxfamily.org/asymptote/geometry/index.html', and an -index: - - `http://piprim.tuxfamily.org/asymptote/geometry/modules/geometry.asy.index.type.html' - - -File: asymptote.info, Node: trembling, Next: stats, Prev: geometry, Up: Base modules - -7.6 `trembling' -=============== - -This module, written by Philippe Ivaldi and illustrated in the example -`floatingdisk.asy', allows one to draw wavy lines, as if drawn by hand. -Further examples are posted at -`http://piprim.tuxfamily.org/asymptote/trembling/index.html' - - -File: asymptote.info, Node: stats, Next: patterns, Prev: trembling, Up: Base modules - -7.7 `stats' -=========== - -This package implements a Gaussian random number generator and a -collection of statistics routines, including `histogram' and -`leastsquares'. - - -File: asymptote.info, Node: patterns, Next: markers, Prev: stats, Up: Base modules - -7.8 `patterns' -============== - -This package implements `Postscript' tiling patterns and includes -several convenient pattern generation routines. - - -File: asymptote.info, Node: markers, Next: tree, Prev: patterns, Up: Base modules - -7.9 `markers' -============= - -This package implements specialized routines for marking paths and -angles. The principal mark routine provided by this package is -markroutine markinterval(int n=1, frame f, bool rotated=false); - which centers `n' copies of frame `f' within uniformly space intervals -in arclength along the path, optionally rotated by the angle of the -local tangent. - - The `marker' (*note marker::) routine can be used to construct new -markers from these predefined frames: - -frame stickframe(int n=1, real size=0, pair space=0, real angle=0, - pair offset=0, pen p=currentpen); - -frame circlebarframe(int n=1, real barsize=0, - real radius=0,real angle=0, - pair offset=0, pen p=currentpen, - filltype filltype=NoFill, bool above=false); - -frame crossframe(int n=3, real size=0, pair space=0, - real angle=0, pair offset=0, pen p=currentpen); - -frame tildeframe(int n=1, real size=0, pair space=0, - real angle=0, pair offset=0, pen p=currentpen); - - For convenience, this module also constructs the markers -`StickIntervalMarker', `CrossIntervalMarker', -`CircleBarIntervalMarker', and `TildeIntervalMarker' from the above -frames. The example `markers1.asy' illustrates the use of these markers: - - - - -This package also provides a routine for marking an angle AOB: -void markangle(picture pic=currentpicture, Label L="", - int n=1, real radius=0, real space=0, - pair A, pair O, pair B, arrowbar arrow=None, - pen p=currentpen, margin margin=NoMargin, - marker marker=nomarker); - as illustrated in the example `markers2.asy'. - - - - - -File: asymptote.info, Node: tree, Next: binarytree, Prev: markers, Up: Base modules - -7.10 `tree' -=========== - -This package implements an example of a dynamic binary search tree. - - -File: asymptote.info, Node: binarytree, Next: drawtree, Prev: tree, Up: Base modules - -7.11 `binarytree' -================= - -This module can be used to draw an arbitrary binary tree and includes an -input routine for the special case of a binary search tree, as -illustrated in the example `binarytreetest.asy': - -import binarytree; - -picture pic,pic2; - -binarytree bt=binarytree(1,2,4,nil,5,nil,nil,0,nil,nil,3,6,nil,nil,7); -draw(pic,bt); - -binarytree st=searchtree(10,5,2,1,3,4,7,6,8,9,15,13,12,11,14,17,16,18,19); -draw(pic2,st,blue); - -add(pic.fit(),(0,0),10N); -add(pic2.fit(),(0,0),10S); - - - - -File: asymptote.info, Node: drawtree, Next: syzygy, Prev: binarytree, Up: Base modules - -7.12 `drawtree' -=============== - -This is a simple tree drawing module used by the example `treetest.asy'. - - -File: asymptote.info, Node: syzygy, Next: feynman, Prev: drawtree, Up: Base modules - -7.13 `syzygy' -============= - -This module automates the drawing of braids, relations, and syzygies, -along with the corresponding equations, as illustrated in the example -`knots.asy'. - - -File: asymptote.info, Node: feynman, Next: roundedpath, Prev: syzygy, Up: Base modules - -7.14 `feynman' -============== - -This package, contributed by Martin Wiebusch, is useful for drawing -Feynman diagrams, as illustrated by the examples `eetomumu.asy' and -`fermi.asy'. - - -File: asymptote.info, Node: roundedpath, Next: animation, Prev: feynman, Up: Base modules - -7.15 `roundedpath' -================== - -This package, contributed by Stefan Knorr, is useful for rounding the -sharp corners of paths, as illustrated in the example file -`roundpath.asy'. - - -File: asymptote.info, Node: animation, Next: embed, Prev: roundedpath, Up: Base modules - -7.16 `animation' -================ - -This module allows one to generate animations, as illustrated by the -files `wheel.asy', `wavelet.asy', and `cube.asy' in the `animations' -subdirectory of the examples directory. These animations use the -`ImageMagick' `convert' program to `merge' multiple images into a GIF -or MPEG movie. - - The related `animate' module, derived from the `animation' module, -generates higher-quality portable clickable PDF movies, with optional -controls. This requires installing the package - - `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/animate.sty' - (version 2007/11/30 or later) in a new directory `animate' in the -local `LaTeX' directory (for example, in -`/usr/local/share/texmf/tex/latex/animate'). On `UNIX' systems, one -must then execute the command `texhash'. - - The example `pdfmovie.asy' in the `animations' directory, along with -the slide presentations `slidemovies.asy' and `intro.asy', illustrate -the use of embedded PDF movies. The examples `inlinemovie.tex' and -`inlinemovie3.tex' show how to generate and embed PDF movies directly -within a `LaTeX' file (*note LaTeX usage::). The member function -string pdf(fit fit=NoBox, real delay=animationdelay, string options="", - bool keep=settings.keep, bool multipage=true); - of the `animate' structure accepts any of the `animate.sty' options, -as described here: - - `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/doc/animate.pdf' - - -File: asymptote.info, Node: embed, Next: slide, Prev: animation, Up: Base modules - -7.17 `embed' -============ - -This module provides an interface to the `LaTeX' package (included with -`MikTeX') - - `http://www.ctan.org/tex-archive/macros/latex/contrib/movie15' - for embedding movies, sounds, and 3D objects into a PDF document. However, -`XeLaTeX' users need to rename the modified version -`movie15_dvipdfmx.sty' from - - `http://asymptote.svn.sourceforge.net/viewvc/asymptote/trunk/asymptote/patches/' - to `movie15.sty' and place it in their `LaTeX' path. - - The latest version of the `movie15' package requires both `pdflatex' -version 1.20 or later and the file - - `http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/ifdraft.dtx' - which can be installed by placing it in a directory `ifdraft' in the -local `LaTeX' directory (e.g. -`/usr/local/share/texmf/tex/latex/ifdraft') and executing in that -directory the commands: -tex ifdraft.dtx -texhash - - An example of embedding `U3D' code is provided in the file -`embeddedu3d.asy'. As of version 7.0.8, `Adobe Reader' supports the -`U3D' format under Linux. - - Unfortunately, Adobe has not yet made available an embedded movie -plugin for the Linux version of `Adobe Reader'. A portable method for -embedding movie files, which should work on any platform and does not -require the `movie15' or `ifdraft' packages, is provided by using the -`external' module instead of `embed'. An example of these interfaces is -provided in the file `embeddedmovie.asy' and `externalmovie.asy' in the -`animations' subdirectory of the examples directory. For a higher -quality movie generated directly by `Asymptote', use the `animate' -module along with the `animate.sty' package to embed a portable PDF -animation (*note animate::). - - -File: asymptote.info, Node: slide, Next: MetaPost, Prev: embed, Up: Base modules - -7.18 `slide' -============ - -This package provides a simple yet high-quality facility for making -presentation slides, including portable embedded PDF animations (see -the file `slidemovies.asy'). A simple example is provided in the file -`slidedemo.asy'. - - -File: asymptote.info, Node: MetaPost, Next: unicode, Prev: slide, Up: Base modules - -7.19 `MetaPost' -=============== - -This package provides some useful routines to help `MetaPost' users -migrate old `MetaPost' code to `Asymptote'. Further contributions here -are welcome. - - Unlike `MetaPost', `Asymptote' does not implicitly solve linear -equations and therefore does not have the notion of a `whatever' -unknown. The routine `extension' (*note extension::) provides a useful -replacement for a common use of `whatever': finding the intersection -point of the lines through `P', `Q' and `p', `q'. For less common -occurrences of `whatever', one can use the built-in explicit linear -equation solver `solve' instead. - - -File: asymptote.info, Node: unicode, Next: latin1, Prev: MetaPost, Up: Base modules - -7.20 `unicode' -============== - -Import this package at the beginning of the file to instruct `LaTeX' to -accept `unicode' (UTF-8) standardized international characters. To use -Cyrillic fonts, you will need to change the font encoding: -import unicode; -texpreamble("\usepackage{mathtext}\usepackage[russian]{babel}"); -defaultpen(font("T2A","cmr","m","n")); - Support for Chinese, Japanese, and Korean fonts is provided by the CJK -package: - - `http://www.ctan.org/tex-archive/languages/chinese/CJK/' - The following commands enable the CJK song family (within a label, -you can also temporarily switch to another family, say kai, by -prepending `"\CJKfamily{kai}"' to the label string): -texpreamble("\usepackage{CJK} -\AtBeginDocument{\begin{CJK*}{GBK}{song}} -\AtEndDocument{\clearpage\end{CJK*}}"); - - -File: asymptote.info, Node: latin1, Next: babel, Prev: unicode, Up: Base modules - -7.21 `latin1' -============= - -If you don't have `LaTeX' support for `unicode' installed, you can -enable support for Western European languages (ISO 8859-1) by importing -the module `latin1'. This module can be used as a template for -providing support for other ISO 8859 alphabets. - - -File: asymptote.info, Node: babel, Next: labelpath, Prev: latin1, Up: Base modules - -7.22 `babel' -============ - -This module implements the `LaTeX' `babel' package in `Asymptote'. For -example: -import babel; -babel("german"); - - -File: asymptote.info, Node: labelpath, Next: labelpath3, Prev: babel, Up: Base modules - -7.23 `labelpath' -================ - -This module uses the `PSTricks' `pstextpath' macro to fit labels along -a path (properly kerned, as illustrated in the example file -`curvedlabel.asy'), using the command -void labelpath(picture pic=currentpicture, Label L, path g, - string justify=Centered, pen p=currentpen); - Here `justify' is one of `LeftJustified', `Centered', or -`RightJustified'. The x component of a shift transform applied to the -Label is interpreted as a shift along the curve, whereas the y -component is interpreted as a shift away from the curve. All other -Label transforms are ignored. This package requires the `latex' tex -engine and inherits the limitations of the `PSTricks' `\pstextpath' -macro. - - -File: asymptote.info, Node: labelpath3, Next: annotate, Prev: labelpath, Up: Base modules - -7.24 `labelpath3' -================= - -This module, contributed by Jens Schwaiger, implements a 3D version of -`labelpath' that does not require the `PSTricks' package. An example -is provided in `curvedlabel3.asy'. - - -File: asymptote.info, Node: annotate, Next: CAD, Prev: labelpath3, Up: Base modules - -7.25 `annotate' -=============== - -This module supports PDF annotations for viewing with `Adobe Reader', -via the function -void annotate(picture pic=currentpicture, string title, string text, - pair position); - Annotations are illustrated in the example file `annotation.asy'. -Currently, annotations are only implemented for the `latex' (default) -and `tex' TeX engines. - - -File: asymptote.info, Node: CAD, Next: graph, Prev: annotate, Up: Base modules - -7.26 `CAD' -========== - -This package, contributed by Mark Henning, provides basic pen -definitions and measurement functions for simple 2D CAD drawings -according to DIN 15. It is documented separately, in the file `CAD.pdf'. - - -File: asymptote.info, Node: graph, Next: palette, Prev: CAD, Up: Base modules - -7.27 `graph' -============ - -This package implements two-dimensional linear and logarithmic graphs, -including automatic scale and tick selection (with the ability to -override manually). A graph is a `guide' (that can be drawn with the -draw command, with an optional legend) constructed with one of the -following routines: - - * guide graph(picture pic=currentpicture, real f(real), real a, real b, - int n=ngraph, real T(real)=identity, - interpolate join=operator --); - guide[] graph(picture pic=currentpicture, real f(real), real a, real b, - int n=ngraph, real T(real)=identity, bool3 cond(real), - interpolate join=operator --); - - Returns a graph using the scaling information for picture `pic' - (*note automatic scaling::) of the function `f' on the interval - [`T'(`a'),`T'(`b')], sampling at `n' points evenly spaced in - [`a',`b'], optionally restricted by the bool3 function `cond' on - [`a',`b']. If `cond' is: - * `true', the point is added to the existing guide; - - * `default', the point is added to a new guide; - - * `false', the point is omitted and a new guide is begun. - Th points are connected using the interpolation specified by - `join': - * `operator --' (linear interpolation; the abbreviation - `Straight' is also accepted); - - * `operator ..' (piecewise Bezier cubic spline interpolation; - the abbreviation `Spline' is also accepted); - - * `Hermite' (standard cubic spline interpolation using boundary - condition `notaknot', `natural', `periodic', `clamped(real - slopea, real slopeb)'), or `monotonic'. The abbreviation - `Hermite' is equivalent to `Hermite(notaknot)' for - nonperiodic data and `Hermite(periodic)' for periodic data). - - - * guide graph(picture pic=currentpicture, real x(real), real y(real), - real a, real b, int n=ngraph, real T(real)=identity, - interpolate join=operator --); - guide[] graph(picture pic=currentpicture, real x(real), real y(real), - real a, real b, int n=ngraph, real T(real)=identity, - bool3 cond(real), interpolate join=operator --); - - Returns a graph using the scaling information for picture `pic' of - the parametrized function (`x'(t),`y'(t)) for t in the interval - [`T'(`a'),`T'(`b')], sampling at `n' points evenly spaced in - [`a',`b'], optionally restricted by the bool3 function `cond' on - [`a',`b'], using the given interpolation type. - - * guide graph(picture pic=currentpicture, pair z(real), real a, real b, - int n=ngraph, real T(real)=identity, - interpolate join=operator --); - guide[] graph(picture pic=currentpicture, pair z(real), real a, real b, - int n=ngraph, real T(real)=identity, bool3 cond(real), - interpolate join=operator --); - - Returns a graph using the scaling information for picture `pic' of - the parametrized function `z'(t) for t in the interval - [`T'(`a'),`T'(`b')], sampling at `n' points evenly spaced in - [`a',`b'], optionally restricted by the bool3 function `cond' on - [`a',`b'], using the given interpolation type. - - * guide graph(picture pic=currentpicture, pair[] z, - interpolate join=operator --); - guide[] graph(picture pic=currentpicture, pair[] z, bool3[] cond, - interpolate join=operator --); - - Returns a graph using the scaling information for picture `pic' of - the elements of the array `z', optionally restricted to those - indices for which the elements of the boolean array `cond' are - `true', using the given interpolation type. - - * guide graph(picture pic=currentpicture, real[] x, real[] y, - interpolate join=operator --); - guide[] graph(picture pic=currentpicture, real[] x, real[] y, - bool3[] cond, interpolate join=operator --); - - Returns a graph using the scaling information for picture `pic' of - the elements of the arrays (`x',`y'), optionally restricted to - those indices for which the elements of the boolean array `cond' - are `true', using the given interpolation type. - - * guide polargraph(picture pic=currentpicture, real f(real), real a, - real b, int n=ngraph, interpolate join=operator --); - - Returns a polar-coordinate graph using the scaling information for - picture `pic' of the function `f' on the interval [`a',`b'], - sampling at `n' evenly spaced points, with the given interpolation - type. - - - - - An axis can be drawn on a picture with one of the following commands: - - * void xaxis(picture pic=currentpicture, Label L="", axis axis=YZero, - real xmin=-infinity, real xmax=infinity, pen p=currentpen, - ticks ticks=NoTicks, arrowbar arrow=None, bool above=false); - - Draw an x axis on picture `pic' from x=`xmin' to x=`xmax' using - pen `p', optionally labelling it with Label `L'. The relative - label location along the axis (a real number from [0,1]) defaults - to 1 (*note Label::), so that the label is drawn at the end of the - axis. An infinite value of `xmin' or `xmax' specifies that the - corresponding axis limit will be automatically determined from the - picture limits. The optional `arrow' argument takes the same - values as in the `draw' command (*note arrows::). The axis is - drawn before any existing objects in the current picture unless - `above=true'. The axis placement is determined by one of the - following `axis' types: - - `YZero(bool extend=true)' - Request an x axis at y=0 (or y=1 on a logarithmic axis) - extending to the full dimensions of the picture, unless - `extend'=false. - - `YEquals(real Y, bool extend=true)' - Request an x axis at y=`Y' extending to the full dimensions - of the picture, unless `extend'=false. - - `Bottom(bool extend=false)' - Request a bottom axis. - - `Top(bool extend=false)' - Request a top axis. - - `BottomTop(bool extend=false)' - Request a bottom and top axis. - - - Custom axis types can be created by following the examples in - `graph.asy'. One can easily override the default values for the - standard axis types: import graph; - - YZero=new axis(bool extend=true) { - return new void(picture pic, axisT axis) { - real y=pic.scale.x.scale.logarithmic ? 1 : 0; - axis.value=I*pic.scale.y.T(y); - axis.position=1; - axis.side=right; - axis.align=2.5E; - axis.value2=Infinity; - axis.extend=extend; - }; - }; - YZero=YZero(); - - The default tick option is `NoTicks'. The options `LeftTicks', - `RightTicks', or `Ticks' can be used to draw ticks on the left, - right, or both sides of the path, relative to the direction in - which the path is drawn. These tick routines accept a number of - optional arguments: ticks LeftTicks(Label format="", ticklabel ticklabel=null, - bool beginlabel=true, bool endlabel=true, - int N=0, int n=0, real Step=0, real step=0, - bool begin=true, bool end=true, tickmodifier modify=None, - real Size=0, real size=0, bool extend=false, - pen pTick=nullpen, pen ptick=nullpen); - - If any of these parameters are omitted, reasonable defaults will - be chosen: - `Label format' - override the default tick label format (`defaultformat', - initially "$%.4g$"), rotation, pen, and alignment (for - example, `LeftSide', `Center', or `RightSide') relative to - the axis. To enable `LaTeX' math mode fonts, the format - string should begin and end with `$' *note format::. If the - format string is `trailingzero', trailing zeros will be added - to the tick labels; if the format string is `"%"', the tick - label will be suppressed; - - `ticklabel' - is a function `string(real x)' returning the label (by - default, format(format.s,x)) for each major tick value `x'; - - `bool beginlabel' - include the first label; - - `bool endlabel' - include the last label; - - `int N' - when automatic scaling is enabled (the default; *note - automatic scaling::), divide a linear axis evenly into this - many intervals, separated by major ticks; for a logarithmic - axis, this is the number of decades between labelled ticks; - - `int n' - divide each interval into this many subintervals, separated - by minor ticks; - - `real Step' - the tick value spacing between major ticks (if `N'=`0'); - - `real step' - the tick value spacing between minor ticks (if `n'=`0'); - - `bool begin' - include the first major tick; - - `bool end' - include the last major tick; - - `tickmodifier modify;' - an optional function that takes and returns a `tickvalue' - structure having real[] members `major' and `minor' - consisting of the tick values (to allow modification of the - automatically generated tick values); - - `real Size' - the size of the major ticks (in `PostScript' coordinates); - - `real size' - the size of the minor ticks (in `PostScript' coordinates); - - `bool extend;' - extend the ticks between two axes (useful for drawing a grid - on the graph); - - `pen pTick' - an optional pen used to draw the major ticks; - - `pen ptick' - an optional pen used to draw the minor ticks. - - - For convenience, the predefined tickmodifier `OmitTick(... real[] - x)' tickmodifier can be used to remove specific auto-generated - ticks and their labels. The `OmitFormat(string s=defaultformat ... - real[] x)' ticklabel can be used to remove specific tick labels - but not the corresponding ticks. The tickmodifier `NoZero' is an - abbreviation for `OmitTick(0)' and the ticklabel `NoZeroFormat' is - an abbrevation for `OmitFormat(0)'. - - It is also possible to specify custom tick locations with - `LeftTicks', `RightTicks', and `Ticks' by passing explicit real - arrays `Ticks' and (optionally) `ticks' containing the locations - of the major and minor ticks, respectively: ticks LeftTicks(Label format="", ticklabel ticklabel=null, - bool beginlabel=true, bool endlabel=true, - real[] Ticks, real[] ticks=new real[], - real Size=0, real size=0, bool extend=false, - pen pTick=nullpen, pen ptick=nullpen) - - * void yaxis(picture pic=currentpicture, Label L="", axis axis=XZero, - real ymin=-infinity, real ymax=infinity, pen p=currentpen, - ticks ticks=NoTicks, arrowbar arrow=None, bool above=false); - - Draw a y axis on picture `pic' from y=`ymin' to y=`ymax' using pen - `p', optionally labelling it with Label `L'. The relative location - of the label (a real number from [0,1]) defaults to 1 (*note - Label::). An infinite value of `ymin' or `ymax' specifies that the - corresponding axis limit will be automatically determined from the - picture limits. The optional `arrow' argument takes the same - values as in the `draw' command (*note arrows::). The axis is - drawn before any existing objects in the current picture unless - `above=true'. The tick type is specified by `ticks' and the axis - placement is determined by one of the following `axis' types: - - `XZero(bool extend=true)' - Request a y axis at x=0 (or x=1 on a logarithmic axis) - extending to the full dimensions of the picture, unless - `extend'=false. - - `XEquals(real X, bool extend=true)' - Request a y axis at x=`X' extending to the full dimensions of - the picture, unless `extend'=false. - - `Left(bool extend=false)' - Request a left axis. - - `Right(bool extend=false)' - Request a right axis. - - `LeftRight(bool extend=false)' - Request a left and right axis. - - - * For convenience, the functions void xequals(picture pic=currentpicture, Label L="", real x, - bool extend=false, real ymin=-infinity, real ymax=infinity, - pen p=currentpen, ticks ticks=NoTicks, bool above=true, - arrowbar arrow=None); - and void yequals(picture pic=currentpicture, Label L="", real y, - bool extend=false, real xmin=-infinity, real xmax=infinity, - pen p=currentpen, ticks ticks=NoTicks, bool above=true, - arrowbar arrow=None); - can be respectively used to call `yaxis' and `xaxis' with the - appropriate axis types `XEquals(x,extend)' and - `YEquals(y,extend)'. This is the recommended way of drawing - vertical or horizontal lines and axes at arbitrary locations. - - * void axes(picture pic=currentpicture, Label xlabel="", Label ylabel="", - pair min=(-infinity,-infinity), pair max=(infinity,infinity), - pen p=currentpen, arrowbar arrow=None, bool above=false); - This convenience routine draws both x and y axes on picture `pic' - from `min' to `max', with optional labels `xlabel' and `ylabel' - and any arrows specified by `arrow'. The axes are drawn on top of - existing objects in the current picture only if `above=true'. - - * void axis(picture pic=currentpicture, Label L="", path g, - pen p=currentpen, ticks ticks, ticklocate locate, - arrowbar arrow=None, int[] divisor=new int[], - bool above=false, bool opposite=false); - - This routine can be used to draw on picture `pic' a general axis - based on an arbitrary path `g', using pen `p'. One can optionally - label the axis with Label `L' and add an arrow `arrow'. The tick - type is given by `ticks'. The optional integer array `divisor' - specifies what tick divisors to try in the attempt to produce - uncrowded tick labels. A `true' value for the flag `opposite' - identifies an unlabelled secondary axis (typically drawn opposite - a primary axis). The axis is drawn before any existing objects in - the current picture unless `above=true'. The tick locator - `ticklocate' is constructed by the routine ticklocate ticklocate(real a, real b, autoscaleT S=defaultS, - real tickmin=-infinity, real tickmax=infinity, - real time(real)=null, pair dir(real)=zero); - where `a' and `b' specify the respective tick values at - `point(g,0)' and `point(g,length(g))', `S' specifies the - autoscaling transformation, the function `real time(real v)' - returns the time corresponding to the value `v', and `pair - dir(real t)' returns the absolute tick direction as a function of - `t' (zero means draw the tick perpendicular to the axis). - - * These routines are useful for manually putting ticks and labels on - axes (if the variable `Label' is given as the `Label' argument, - the `format' argument will be used to format a string based on the - tick location): void xtick(picture pic=currentpicture, Label L="", explicit pair z, - pair dir=N, string format="", - real size=Ticksize, pen p=currentpen); - void xtick(picture pic=currentpicture, Label L="", real x, - pair dir=N, string format="", - real size=Ticksize, pen p=currentpen); - void ytick(picture pic=currentpicture, Label L="", explicit pair z, - pair dir=E, string format="", - real size=Ticksize, pen p=currentpen); - void ytick(picture pic=currentpicture, Label L="", real y, - pair dir=E, string format="", - real size=Ticksize, pen p=currentpen); - void tick(picture pic=currentpicture, pair z, - pair dir, real size=Ticksize, pen p=currentpen); - void labelx(picture pic=currentpicture, Label L="", explicit pair z, - align align=S, string format="", pen p=nullpen); - void labelx(picture pic=currentpicture, Label L="", real x, - align align=S, string format="", pen p=nullpen); - void labelx(picture pic=currentpicture, Label L, - string format="", explicit pen p=currentpen); - void labely(picture pic=currentpicture, Label L="", explicit pair z, - align align=W, string format="", pen p=nullpen); - void labely(picture pic=currentpicture, Label L="", real y, - align align=W, string format="", pen p=nullpen); - void labely(picture pic=currentpicture, Label L, - string format="", explicit pen p=nullpen); - - Here are some simple examples of two-dimensional graphs: - - 1. This example draws a textbook-style graph of y= exp(x), with the y - axis starting at y=0: import graph; - size(150,0); - - real f(real x) {return exp(x);} - pair F(real x) {return (x,f(x));} - - xaxis("$x$"); - yaxis("$y$",0); - - draw(graph(f,-4,2,operator ..),red); - - labely(1,E); - label("$e^x$",F(1),SE); - - - - 2. The next example draws a scientific-style graph with a legend. - The position of the legend can be adjusted either explicitly or by - using the graphical user interface `xasy' (*note GUI::). If an - `UnFill(real xmargin=0, real ymargin=xmargin)' or `Fill(pen)' - option is specified to `add', the legend will obscure any - underlying objects. Here we illustrate how to clip the portion of - the picture covered by a label: - - import graph; - - size(400,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\sin(2\pi x)$"); - draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$"); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - label("LABEL",point(0),UnFill(1mm)); - - add(legend(),point(E),20E,UnFill); - - - - To specify a fixed size for the graph proper, use `attach': import graph; - - size(250,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\sin(2\pi x)$"); - draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$"); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - label("LABEL",point(0),UnFill(1mm)); - - attach(legend(),truepoint(E),20E,UnFill); - A legend can have multiple entries per line: import graph; - size(8cm,6cm,IgnoreAspect); - - typedef real realfcn(real); - realfcn F(real p) { - return new real(real x) {return sin(p*x);}; - }; - - for(int i=1; i < 5; ++i) - draw(graph(F(i*pi),0,1),Pen(i), - "$\sin("+(i == 1 ? "" : (string) i)+"\pi x)$"); - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - attach(legend(2),(point(S).x,truepoint(S).y),10S,UnFill); - - - - 3. This example draws a graph of one array versus another (both of - the same size) using custom tick locations and a smaller font size - for the tick labels on the y axis. import graph; - - size(200,150,IgnoreAspect); - - real[] x={0,1,2,3}; - real[] y=x^2; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight, - RightTicks(Label(fontsize(8)),new real[]{0,4,9})); - - - - 4. This example shows how to graph columns of data read from a file. import graph; - - size(200,150,IgnoreAspect); - - file in=line(input("filegraph.dat")); - real[][] a=dimension(in,0,0); - a=transpose(a); - - real[] x=a[0]; - real[] y=a[1]; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - 5. The next example draws two graphs of an array of coordinate pairs, - using frame alignment and data markers. In the left-hand graph, the - markers, constructed with marker marker(path g, markroutine markroutine=marknodes, - pen p=currentpen, filltype filltype=NoFill, - bool above=true); - using the path `unitcircle' (*note filltype::), are drawn below - each node. Any frame can be converted to a marker, using marker marker(frame f, markroutine markroutine=marknodes, - bool above=true); - In the right-hand graph, the unit n-sided regular polygon - `polygon(int n)' and the unit n-point cyclic cross `cross(int n, - bool round=true, real r=0)' (where `r' is an optional "inner" - radius) are used to build a custom marker frame. Here - `markuniform(bool centered=false, int n, bool rotated=false)' adds - this frame at `n' uniformly spaced points along the arclength of - the path, optionally rotated by the angle of the local tangent to - the path (if centered is true, the frames will be centered within - `n' evenly spaced arclength intervals). Alternatively, one can use - markroutine `marknodes' to request that the marks be placed at each - Bezier node of the path, or markroutine `markuniform(pair z(real - t), real a, real b, int n)' to place marks at points `z(t)' for n - evenly spaced values of `t' in `[a,b]'. - - These markers are predefined: marker[] Mark={ - marker(scale(circlescale)*unitcircle), - marker(polygon(3)),marker(polygon(4)), - marker(polygon(5)),marker(invert*polygon(3)), - marker(cross(4)),marker(cross(6)) - }; - - marker[] MarkFill={ - marker(scale(circlescale)*unitcircle,Fill),marker(polygon(3),Fill), - marker(polygon(4),Fill),marker(polygon(5),Fill), - marker(invert*polygon(3),Fill) - }; - - The example also illustrates the `errorbar' routines: - - void errorbars(picture pic=currentpicture, pair[] z, pair[] dp, - pair[] dm={}, bool[] cond={}, pen p=currentpen, - real size=0); - - void errorbars(picture pic=currentpicture, real[] x, real[] y, - real[] dpx, real[] dpy, real[] dmx={}, real[] dmy={}, - bool[] cond={}, pen p=currentpen, real size=0); - - Here, the positive and negative extents of the error are given by - the absolute values of the elements of the pair array `dp' and the - optional pair array `dm'. If `dm' is not specified, the positive - and negative extents of the error are assumed to be equal. import graph; - - picture pic; - real xsize=200, ysize=140; - size(pic,xsize,ysize,IgnoreAspect); - - pair[] f={(5,5),(50,20),(90,90)}; - pair[] df={(0,0),(5,7),(0,5)}; - - errorbars(pic,f,df,red); - draw(pic,graph(pic,f),"legend", - marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false)); - - scale(pic,true); - - xaxis(pic,"$x$",BottomTop,LeftTicks); - yaxis(pic,"$y$",LeftRight,RightTicks); - add(pic,legend(pic),point(pic,NW),20SE,UnFill); - - picture pic2; - size(pic2,xsize,ysize,IgnoreAspect); - - frame mark; - filldraw(mark,scale(0.8mm)*polygon(6),green,green); - draw(mark,scale(0.8mm)*cross(6),blue); - - draw(pic2,graph(pic2,f),marker(mark,markuniform(5))); - - scale(pic2,true); - - xaxis(pic2,"$x$",BottomTop,LeftTicks); - yaxis(pic2,"$y$",LeftRight,RightTicks); - - yequals(pic2,55.0,red+Dotted); - xequals(pic2,70.0,red+Dotted); - - // Fit pic to W of origin: - add(pic.fit(),(0,0),W); - - // Fit pic2 to E of (5mm,0): - add(pic2.fit(),(5mm,0),E); - - - - 6. A custom mark routine can be also be specified: import graph; - - size(200,100,IgnoreAspect); - - markroutine marks() { - return new void(picture pic=currentpicture, frame f, path g) { - path p=scale(1mm)*unitcircle; - for(int i=0; i <= length(g); ++i) { - pair z=point(g,i); - frame f; - if(i % 4 == 0) { - fill(f,p); - add(pic,f,z); - } else { - if(z.y > 50) { - pic.add(new void(frame F, transform t) { - path q=shift(t*z)*p; - unfill(F,q); - draw(F,q); - }); - } else { - draw(f,p); - add(pic,f,z); - } - } - } - }; - } - - pair[] f={(5,5),(40,20),(55,51),(90,30)}; - - draw(graph(f),marker(marks())); - - scale(true); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - 7. This example shows how to label an axis with arbitrary strings. import graph; - - size(400,150,IgnoreAspect); - - real[] x=sequence(12); - real[] y=sin(2pi*x/12); - - scale(false); - - string[] month={"Jan","Feb","Mar","Apr","May","Jun", - "Jul","Aug","Sep","Oct","Nov","Dec"}; - - draw(graph(x,y),red,MarkFill[0]); - - xaxis(BottomTop,LeftTicks(new string(real x) { - return month[round(x % 12)];})); - yaxis("$y$",LeftRight,RightTicks(4)); - - - - 8. The next example draws a graph of a parametrized curve. The calls - to xlimits(picture pic=currentpicture, real min=-infinity, - real max=infinity, bool crop=NoCrop); - and the analogous function `ylimits' can be uncommented to set - the respective axes limits for picture `pic' to the specified - `min' and `max' values. Alternatively, the function void limits(picture pic=currentpicture, pair min, pair max, bool crop=NoCrop); - can be used to limit the axes to the box having opposite vertices - at the given pairs). Existing objects in picture `pic' will be - cropped to lie within the given limits if `crop'=`Crop'. The - function `crop(picture pic)' can be used to crop a graph to the - current graph limits. import graph; - - size(0,200); - - real x(real t) {return cos(2pi*t);} - real y(real t) {return sin(2pi*t);} - - draw(graph(x,y,0,1)); - - //xlimits(0,1,Crop); - //ylimits(-1,0,Crop); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - - - The next example illustrates how one can extract a common axis - scaling factor. import graph; - - axiscoverage=0.9; - size(200,IgnoreAspect); - - real[] x={-1e-11,1e-11}; - real[] y={0,1e6}; - - real xscale=round(log10(max(x))); - real yscale=round(log10(max(y)))-1; - - draw(graph(x*10^(-xscale),y*10^(-yscale)),red); - - xaxis("$x/10^{"+(string) xscale+"}$",BottomTop,LeftTicks); - yaxis("$y/10^{"+(string) yscale+"}$",LeftRight,RightTicks(trailingzero)); - - - - Axis scaling can be requested and/or automatic selection of the - axis limits can be inhibited with one of these `scale' routines: void scale(picture pic=currentpicture, scaleT x, scaleT y); - - void scale(picture pic=currentpicture, bool xautoscale=true, - bool yautoscale=xautoscale, bool zautoscale=yautoscale); - - This sets the scalings for picture `pic'. The `graph' routines - accept an optional `picture' argument for determining the - appropriate scalings to use; if none is given, it uses those set - for `currentpicture'. - - Two frequently used scaling routines `Linear' and `Log' are - predefined in `graph'. - - All picture coordinates (including those in paths and those given - to the `label' and `limits' functions) are always treated as linear - (post-scaled) coordinates. Use pair Scale(picture pic=currentpicture, pair z); - to convert a graph coordinate into a scaled picture coordinate. - - The x and y components can be individually scaled using the - analogous routines real ScaleX(picture pic=currentpicture, real x); - real ScaleY(picture pic=currentpicture, real y); - - The predefined scaling routines can be given two optional boolean - arguments: `automin=false' and `automax=automin'. These default to - `false' but can be respectively set to `true' to enable automatic - selection of "nice" axis minimum and maximum values. The `Linear' - scaling can also take as optional final arguments a multiplicative - scaling factor and intercept (e.g. for a depth axis, `Linear(-1)' - requests axis reversal). - - For example, to draw a log/log graph of a function, use - `scale(Log,Log)': import graph; - - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - - draw(graph(f,0.1,10)); - - //xlimits(1,10,Crop); - //ylimits(0.1,1,Crop); - - dot(Label("(3,5)",align=S),Scale((3,5))); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - By extending the ticks, one can easily produce a logarithmic grid: import graph; - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - draw(graph(f,0.1,10),red); - pen thin=linewidth(0.5*linewidth()); - xaxis("$x$",BottomTop,LeftTicks(begin=false,end=false,extend=true, - ptick=thin)); - yaxis("$y$",LeftRight,RightTicks(begin=false,end=false,extend=true, - ptick=thin)); - - - - One can also specify custom tick locations and formats for - logarithmic axes: import graph; - - size(300,175,IgnoreAspect); - scale(Log,Log); - draw(graph(identity,5,20)); - xlimits(5,20); - ylimits(1,100); - xaxis("$M/M_\odot$",BottomTop,LeftTicks(DefaultFormat, - new real[] {6,10,12,14,16,18})); - yaxis("$\nu_{\rm upp}$ [Hz]",LeftRight,RightTicks(DefaultFormat)); - - - - It is easy to draw logarithmic graphs with respect to other bases: import graph; - size(200,IgnoreAspect); - - // Base-2 logarithmic scale on y-axis: - - real log2(real x) {static real log2=log(2); return log(x)/log2;} - real pow2(real x) {return 2^x;} - - scaleT yscale=scaleT(log2,pow2,logarithmic=true); - scale(Linear,yscale); - - real f(real x) {return 1+x^2;} - - draw(graph(f,-4,4)); - - yaxis("$y$",ymin=1,ymax=f(5),RightTicks(Label(Fill(white))),EndArrow); - xaxis("$x$",xmin=-5,xmax=5,LeftTicks,EndArrow); - - - - Here is an example of "broken" linear x and logarithmic y axes - that omit the segments [3,8] and [100,1000], respectively. In the - case of a logarithmic axis, the break endpoints are automatically - rounded to the nearest integral power of the base. import graph; - - size(200,150,IgnoreAspect); - - // Break the x axis at 3; restart at 8: - real a=3, b=8; - - // Break the y axis at 100; restart at 1000: - real c=100, d=1000; - - scale(Broken(a,b),BrokenLog(c,d)); - - real[] x={1,2,4,6,10}; - real[] y=x^4; - - draw(graph(x,y),red,MarkFill[0]); - - xaxis("$x$",BottomTop,LeftTicks(Break(a,b))); - yaxis("$y$",LeftRight,RightTicks(Break(c,d))); - - label(rotate(90)*Break,(a,point(S).y)); - label(rotate(90)*Break,(a,point(N).y)); - label(Break,(point(W).x,ScaleY(c))); - label(Break,(point(E).x,ScaleY(c))); - - - - 9. `Asymptote' can draw secondary axes with the routines picture secondaryX(picture primary=currentpicture, void f(picture)); - picture secondaryY(picture primary=currentpicture, void f(picture)); - - In this example, `secondaryY' is used to draw a secondary linear y - axis against a primary logarithmic y axis: import graph; - texpreamble("\def\Arg{\mathop {\rm Arg}\nolimits}"); - - size(10cm,5cm,IgnoreAspect); - - real ampl(real x) {return 2.5/(1+x^2);} - real phas(real x) {return -atan(x)/pi;} - - scale(Log,Log); - draw(graph(ampl,0.01,10)); - ylimits(0.001,100); - - xaxis("$\omega\tau_0$",BottomTop,LeftTicks); - yaxis("$|G(\omega\tau_0)|$",Left,RightTicks); - - picture q=secondaryY(new void(picture pic) { - scale(pic,Log,Linear); - draw(pic,graph(pic,phas,0.01,10),red); - ylimits(pic,-1.0,1.5); - yaxis(pic,"$\Arg G/\pi$",Right,red, - LeftTicks("$% #.1f$", - begin=false,end=false)); - yequals(pic,1,Dotted); - }); - label(q,"(1,0)",Scale(q,(1,0)),red); - add(q); - - - - A secondary logarithmic y axis can be drawn like this: import graph; - - size(9cm,6cm,IgnoreAspect); - string data="secondaryaxis.csv"; - - file in=line(csv(input(data))); - - string[] titlelabel=in; - string[] columnlabel=in; - - real[][] a=dimension(in,0,0); - a=transpose(a); - real[] t=a[0], susceptible=a[1], infectious=a[2], dead=a[3], larvae=a[4]; - real[] susceptibleM=a[5], exposed=a[6],infectiousM=a[7]; - - scale(true); - - draw(graph(t,susceptible,t >= 10 & t <= 15)); - draw(graph(t,dead,t >= 10 & t <= 15),dashed); - - xaxis("Time ($\tau$)",BottomTop,LeftTicks); - yaxis(Left,RightTicks); - - picture secondary=secondaryY(new void(picture pic) { - scale(pic,Linear(true),Log(true)); - draw(pic,graph(pic,t,infectious,t >= 10 & t <= 15),red); - yaxis(pic,Right,red,LeftTicks(begin=false,end=false)); - }); - - add(secondary); - label(shift(5mm*N)*"Proportion of crows",point(NW),E); - - - - 10. Here is a histogram example, which uses the `stats' module. import graph; - import stats; - - size(400,200,IgnoreAspect); - - int n=10000; - real[] a=new real[n]; - for(int i=0; i < n; ++i) a[i]=Gaussrand(); - - draw(graph(Gaussian,min(a),max(a)),blue); - - // Optionally calculate "optimal" number of bins a la Shimazaki and Shinomoto. - int N=bins(a); - - histogram(a,min(a),max(a),N,normalize=true,low=0,lightred,black,bars=false); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$dP/dx$",LeftRight,RightTicks(trailingzero)); - - - - 11. Here is an example of reading column data in from a file and a - least-squares fit, using the `stats' module. size(400,200,IgnoreAspect); - - import graph; - import stats; - - file fin=line(input("leastsquares.dat")); - - real[][] a=dimension(fin,0,0); - a=transpose(a); - - real[] t=a[0], rho=a[1]; - - // Read in parameters from the keyboard: - //real first=getreal("first"); - //real step=getreal("step"); - //real last=getreal("last"); - - real first=100; - real step=50; - real last=700; - - // Remove negative or zero values of rho: - t=rho > 0 ? t : null; - rho=rho > 0 ? rho : null; - - scale(Log(true),Linear(true)); - - int n=step > 0 ? ceil((last-first)/step) : 0; - - real[] T,xi,dxi; - - for(int i=0; i <= n; ++i) { - real first=first+i*step; - real[] logrho=(t >= first & t <= last) ? log(rho) : null; - real[] logt=(t >= first & t <= last) ? -log(t) : null; - - if(logt.length < 2) break; - - // Fit to the line logt=L.m*logrho+L.b: - linefit L=leastsquares(logt,logrho); - - T.push(first); - xi.push(L.m); - dxi.push(L.dm); - } - - draw(graph(T,xi),blue); - errorbars(T,xi,dxi,red); - - crop(); - - ylimits(0); - - xaxis("$T$",BottomTop,LeftTicks); - yaxis("$\xi$",LeftRight,RightTicks); - - - - 12. Here is an example that illustrates the general `axis' routine. import graph; - size(0,100); - - path g=ellipse((0,0),1,2); - - scale(true); - - axis(Label("C",align=10W),g,LeftTicks(endlabel=false,8,end=false), - ticklocate(0,360,new real(real v) { - path h=(0,0)--max(abs(max(g)),abs(min(g)))*dir(v); - return intersect(g,h)[0];})); - - - - 13. To draw a vector field of `n' arrows evenly spaced along the - arclength of a path, use the routine picture vectorfield(path vector(real), path g, int n, bool truesize=false, - pen p=currentpen, arrowbar arrow=Arrow); - as illustrated in this simple example of a flow field: import graph; - defaultpen(1.0); - - size(0,150,IgnoreAspect); - - real arrowsize=4mm; - real arrowlength=2arrowsize; - - typedef path vector(real); - - // Return a vector interpolated linearly between a and b. - vector vector(pair a, pair b) { - return new path(real x) { - return (0,0)--arrowlength*interp(a,b,x); - }; - } - - real f(real x) {return 1/x;} - - real epsilon=0.5; - path g=graph(f,epsilon,1/epsilon); - - int n=3; - draw(g); - xaxis("$x$"); - yaxis("$y$"); - - add(vectorfield(vector(W,W),g,n,true)); - add(vectorfield(vector(NE,NW),(0,0)--(point(E).x,0),n,true)); - add(vectorfield(vector(NE,NE),(0,0)--(0,point(N).y),n,true)); - - - - 14. To draw a vector field of `nx'\times`ny' arrows in `box(a,b)', use - the routine picture vectorfield(path vector(pair), pair a, pair b, - int nx=nmesh, int ny=nx, bool truesize=false, - real maxlength=truesize ? 0 : maxlength(a,b,nx,ny), - bool cond(pair z)=null, pen p=currentpen, - arrowbar arrow=Arrow, margin margin=PenMargin) - as illustrated in this example: import graph; - size(100); - - pair a=(0,0); - pair b=(2pi,2pi); - - path vector(pair z) {return (0,0)--(sin(z.x),cos(z.y));} - - add(vectorfield(vector,a,b)); - - - - 15. The following scientific graphs, which illustrate many features of - `Asymptote''s graphics routines, were generated from the examples - `diatom.asy' and `westnile.asy', using the comma-separated data in - `diatom.csv' and `westnile.csv'. - - - -File: asymptote.info, Node: palette, Next: three, Prev: graph, Up: Base modules - -7.28 `palette' -============== - -`Asymptote' can also generate color density images and palettes. The -following palettes are predefined in `palette.asy': - -`pen[] Grayscale(int NColors=256)' - a grayscale palette; - -`pen[] Rainbow(int NColors=32766)' - a rainbow spectrum; - -`pen[] BWRainbow(int NColors=32761)' - a rainbow spectrum tapering off to black/white at the ends; - -`pen[] BWRainbow2(int NColors=32761)' - a double rainbow palette tapering off to black/white at the ends, - with a linearly scaled intensity. - -`pen[] Wheel(int NColors=32766)' - a full color wheel palette; - -`pen[] Gradient(int NColors=256 ... pen[] p)' - a palette varying linearly over the specified array of pens, using - NColors in each interpolation interval; - - - The function `cmyk(pen[] Palette)' may be used to convert any of -these palettes to the CMYK colorspace. - - A color density plot using palette `palette' can be generated from a -function `f'(x,y) and added to a picture `pic': -bounds image(picture pic=currentpicture, real f(real,real), - range range=Full, pair initial, pair final, - int nx=ngraph, int ny=nx, pen[] palette, bool antialias=false) - The function `f' will be sampled at `nx' and `ny' evenly spaced points -over a rectangle defined by the points `initial' and `final', -respecting the current graphical scaling of `pic'. The color space is -scaled according to the z axis scaling (*note automatic scaling::). A -bounds structure for the function values is returned: -struct bounds { - real min; - real max; - // Possible tick intervals: - int[] divisor; -} - This information can be used for generating an optional palette bar. -The palette color space corresponds to a range of values specified by -the argument `range', which can be `Full', `Automatic', or an explicit -range `Range(real min, real max)'. Here `Full' specifies a range -varying from the minimum to maximum values of the function over the -sampling interval, while `Automatic' selects "nice" limits. The -example `imagecontour.asy' illustrates how level sets (contour lines) -can be drawn on a color density plot (*note contour::). - - A color density plot can also be generated from an explicit real[][] -array `data': -bounds image(picture pic=currentpicture, real[][] f, range range=Full, - pair initial, pair final, pen[] palette, - bool transpose=(initial.x < final.x && initial.y < final.y), - bool copy=true, bool antialias=false); - If the initial point is to the left and below the final point, by -default the array indices are interpreted according to the Cartesian -convention (first index: x, second index: y) rather than the usual -matrix convention (first index: -y, second index: x). - - To construct an image from an array of irregularly spaced points and -an array of values `f' at these points, use one of the routines -bounds image(picture pic=currentpicture, pair[] z, real[] f, - range range=Full, pen[] palette) -bounds image(picture pic=currentpicture, real[] x, real[] y, real[] f, - range range=Full, pen[] palette) - - An optionally labelled palette bar may be generated with the routine -void palette(picture pic=currentpicture, Label L="", bounds bounds, - pair initial, pair final, axis axis=Right, pen[] palette, - pen p=currentpen, paletteticks ticks=PaletteTicks, - bool copy=true, bool antialias=false); - The color space of `palette' is taken to be over bounds `bounds' with -scaling given by the z scaling of `pic'. The palette orientation is -specified by `axis', which may be one of `Right', `Left', `Top', or -`Bottom'. The bar is drawn over the rectangle from `initial' to -`final'. The argument `paletteticks' is a special tick type (*note -ticks::) that takes the following arguments: -paletteticks PaletteTicks(Label format="", ticklabel ticklabel=null, - bool beginlabel=true, bool endlabel=true, - int N=0, int n=0, real Step=0, real step=0, - pen pTick=nullpen, pen ptick=nullpen); - - The image and palette bar can be fit to a frame and added and -optionally aligned to a picture at the desired location: - -size(12cm,12cm); - -import graph; -import palette; - -int n=256; -real ninv=2pi/n; -real[][] v=new real[n][n]; - -for(int i=0; i < n; ++i) - for(int j=0; j < n; ++j) - v[i][j]=sin(i*ninv)*cos(j*ninv); - -pen[] Palette=BWRainbow(); - -picture bar; - -bounds range=image(v,(0,0),(1,1),Palette); -palette(bar,"$A$",range,(0,0),(0.5cm,8cm),Right,Palette, - PaletteTicks("$%+#.1f$")); -add(bar.fit(),point(E),30E); - - - -Here is an example that uses logarithmic scaling of the function values: - -import graph; -import palette; - -size(10cm,10cm,IgnoreAspect); - -real f(real x, real y) { - return 0.9*pow10(2*sin(x/5+2*y^0.25)) + 0.1*(1+cos(10*log(y))); -} - -scale(Linear,Log,Log); - -pen[] Palette=BWRainbow(); - -bounds range=image(f,Automatic,(0,1),(100,100),nx=200,Palette); - -xaxis("$x$",BottomTop,LeftTicks,above=true); -yaxis("$y$",LeftRight,RightTicks,above=true); - -palette("$f(x,y)$",range,(0,200),(100,250),Top,Palette, - PaletteTicks(ptick=linewidth(0.5*linewidth()))); - - - -One can also draw an image directly from a two-dimensional pen array: -void image(picture pic=currentpicture, pen[][] data, - pair initial, pair final, - bool transpose=(initial.x < final.x && initial.y < final.y), - bool copy=true, bool antialias=false); - as illustrated in the following example: - -size(200); - -import palette; - -int n=256; -real ninv=2pi/n; -pen[][] v=new pen[n][n]; - -for(int i=0; i < n; ++i) - for(int j=0; j < n; ++j) - v[i][j]=rgb(0.5*(1+sin(i*ninv)),0.5*(1+cos(j*ninv)),0); - -image(v,(0,0),(1,1)); - - - -For convenience, the module `palette' also defines functions that may -be used to construct a pen array from a given function and palette: -pen[] palette(real[] f, pen[] palette); -pen[][] palette(real[][] f, pen[] palette); - - -File: asymptote.info, Node: three, Next: obj, Prev: palette, Up: Base modules - -7.29 `three' -============ - -This module fully extends the notion of guides and paths in `Asymptote' -to three dimensions. It introduces the new types guide3, path3, and -surface. Guides in three dimensions are specified with the same syntax -as in two dimensions except that triples `(x,y,z)' are used in place of -pairs `(x,y)' for the nodes and direction specifiers. This -generalization of John Hobby's spline algorithm is shape-invariant under -three-dimensional rotation, scaling, and shifting, and reduces in the -planar case to the two-dimensional algorithm used in `Asymptote', -`MetaPost', and `MetaFont' [cf. J. C. Bowman, Proceedings in Applied -Mathematics and Mechanics, 7:1, 2010021-2010022 (2007)]. - - For example, a unit circle in the XY plane may be filled and drawn -like this: - -import three; - -size(100); - -path3 g=(1,0,0)..(0,1,0)..(-1,0,0)..(0,-1,0)..cycle; -draw(g); -draw(O--Z,red+dashed,Arrow3); -draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle)); -dot(g,red); - - -and then distorted into a saddle: - -import three; - -size(100,0); -path3 g=(1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle; -draw(g); -draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle)); -dot(g,red); - - -Module `three' provides constructors for converting two-dimensional -paths to three-dimensional ones, and vice-versa: -path3 path3(path p, triple plane(pair)=XYplane); -path path(path3 p, pair P(triple)=xypart); - - A Bezier surface, the natural two-dimensional generalization of -Bezier curves, is defined in `three_surface.asy' as a structure -containing an array of Bezier patches. Surfaces may drawn with one of -the routines -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material surfacepen=currentpen, pen meshpen=nullpen, - light light=currentlight, light meshlight=light); -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material[] surfacepen, pen meshpen, - light light=currentlight, light meshlight=light); -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material[] surfacepen, pen[] meshpen=nullpens, - light light=currentlight, light meshlight=light); - The parameters `nu' and `nv' specify the number of subdivisions for -drawing optional mesh lines for each Bezier patch. Here material is a -structure defined in `three_light.asy': -struct material { - pen[] p; // diffusepen,ambientpen,emissivepen,specularpen - real opacity; - real shininess; - real granularity; -... -} - These material properties are used to implement `OpenGL'-style -lighting, based on the Phong-Blinn specular model. Sample Bezier -surfaces are contained in the example files `BezierSurface.asy', -`teapot.asy', and `parametricsurface.asy'. - - The examples `elevation.asy' and `sphericalharmonic.asy' illustrate -how to draw a surface with patch-dependent colors. The examples -`vertexshading' and `smoothelevation' illustrate vertex-dependent -colors, which is supported for both `Asymptote''s native `OpenGL' -renderer and two-dimensional projections. Since the PRC output format -does not currently support vertex shading of Bezier surfaces, PRC -patches are shaded with the mean of the four vertex colors. - - A surface can be constructed from a cyclic `path3' with the -constructor -surface surface(path3 external, triple[] internal=new triple[], - triple[] normals=new triple[], pen[] colors=new pen[], - bool3 planar=default); - and then filled: -draw(surface(path3(polygon(5))),red,nolight); -draw(surface(unitcircle3),red,nolight); -draw(surface(unitcircle3,new pen[] {red,green,blue,black}),nolight); - The last example constructs a patch with vertex-specific colors. A -three-dimensional planar surface in the plane `plane' can be -constructed from a two-dimensional cyclic path `g' with the constructor -surface surface(path p, triple plane(pair)=XYplane); - and then filled: -draw(surface((0,0)--E+2N--2E--E+N..0.2E..cycle),red); - Planar Bezier surfaces patches are constructed using Orest Shardt's -`bezulate' routine, which decomposes (possibly nonsimply connected) -regions bounded by nonselfintersecting cyclic paths (according to the -`zerowinding' fill rule) into subregions bounded by cyclic paths of -length `4' or less. - - Arbitrary thick three-dimensional curves and line caps (which the -`OpenGL' standard does not require implementations to provide) are -constructed with the routine -surface tube(path3 g, real width); - which returns a tube of diameter `width' centered on `g'. This can -make files slow to render, especially with the `Adobe Reader' renderer. -The setting `thick=false' can be used to disable this feature and force -all lines to be drawn with `linewidth(0)' (one pixel wide, regardless -of the resolution). By default mesh and contour lines in -three-dimensions are always drawn thin, unless an explicit line width -is given in the pen parameter or the setting `thin' is set to `false'. -The pens `thin()' and `thick()' defined in plain_pens.asy can also be -used to override these defaults for specific draw commands. - -There are four choices for viewing 3D `Asymptote' output: - 1. Use the native `Asymptote' adaptive `OpenGL'-based renderer (with - the command-line option `-V' and the default settings - `outformat=""' and `render=-1'). If you encounter warnings from - your graphics card driver, try specifying `-glOptions=-indirect' - on the command line. On `UNIX' systems with graphics support for - multisampling, we recommend installing the latest SVN (antialiased) - version of the `freeglut' library (*note multisampling::); the - sample width can be controlled with the setting `multisample'. An - initial screen position can be specified with the pair setting - `position', where negative values are interpreted as relative to - the corresponding maximum screen dimension. The default settings import settings; - leftbutton=new string[] {"rotate","zoom","shift",""}; - middlebutton=new string[] {"menu"}; - rightbutton=new string[] {"zoom/menu","rotateX","rotateY","rotateZ"}; - wheelup=new string[] {"zoomin"}; - wheeldown=new string[] {"zoomout"}; - bind the mouse buttons as follows: - * Left: rotate - - * Shift Left: zoom - - * Ctrl Left: shift - - * Middle: menu - - * Wheel Up: zoom in - - * Wheel Down: zoom out - - * Right: zoom - - * Right double click: menu - - * Shift Right: rotate about the X axis - - * Ctrl Right: rotate about the Y axis - - * Alt Right: rotate about the Z axis - - The keyboard shortcuts are: - * h: home - - * f: toggle fitscreen - - * x: spin about the X axis - - * y: spin about the Y axis - - * z: spin about the Z axis - - * s: stop spinning - - * m: rendering mode (solid/mesh/patch) - - * e: export - - * c: show camera parameters - - * +: expand - - * =: expand - - * -: shrink - - * _: shrink - - * q: exit - - * Ctrl-q: exit - - 2. Render the scene to a specified rasterized format `outformat' at - the resolution of `n' pixels per `bp', as specified by the setting - `render=n'. A negative value of `n' is interpreted as `|2n|' for - EPS and PDF formats and `|n|' for other formats. The default value - of `render' is -1. By default, the scene is internally rendered - at twice the specified resolution; this can be disabled by setting - `antialias=1'. High resolution rendering is done by tiling the - image. If your graphics card allows it, the rendering can be made - more efficient by increasing the maximum tile size `maxtile' - beyond the screen dimensions (indicated by `maxtile=(0,0)'. The - tile size is also limited by the setting `maxviewport', which - restricts the maximum width and height of the viewport. On `UNIX' - systems some graphics drivers support batch mode (`-noV') - rendering in an iconified window; this can be enabled with the - setting `iconify=true'. Other `UNIX' graphics drivers may require - the command line setting `-glOptions=-indirect'. - - 3. Embed the 3D PRC format in a PDF file and view the resulting PDF - file with version `8.0' or later of `Adobe Reader'. In addition - to the default `settings.prc=true', this requires - `settings.outformat="pdf"', which can be specified by the command - line option `-f pdf', put in the `Asymptote' configuration file - (*note configuration file::), or specified in the script before - `three.asy' (or `graph3.asy') is imported. Version 2008/10/08 or - later of the `movie15' package is also required (*note embed::). - The example `pdb.asy' illustrates how one can generate a list of - predefined views (see `100d.views'). A stationary preview image - with a resolution of `n' pixels per `bp' can be embedded with the - setting `render=n'; this allows the file to be viewed with other - `PDF' viewers. Alternatively, the file `externalprc.tex' - illustrates how the resulting PRC and rendered image files can be - extracted and processed in a separate `LaTeX' file. However, see - *note LaTeX usage:: for an easier way to embed three-dimensional - `Asymptote' pictures within `LaTeX'. The open-source PRC - specification is available from - `http://livedocs.adobe.com/acrobat_sdk/9/Acrobat9_HTMLHelp/API_References/PRCReference/PRC_Format_Specification/'. - - 4. Project the scene to a two-dimensional vector (EPS or PDF) format - with `render=0'. Only limited hidden surface removal facilities - are currently available with this approach (*note PostScript3D::). - - - Automatic picture sizing in three dimensions is accomplished with -double deferred drawing. The maximal desired dimensions of the scene in -each of the three dimensions can optionally be specified with the -routine -void size3(picture pic=currentpicture, real x, real y=x, real z=y, - bool keepAspect=pic.keepAspect); - The resulting simplex linear programming problem is then solved to -produce a 3D version of a frame (actually implemented as a 3D picture). -The result is then fit with another application of deferred drawing to -the viewport dimensions corresponding to the usual two-dimensional -picture `size' parameters. The global pair `viewportmargin' may be used -to add horizontal and vertical margins to the viewport dimensions. -Alternatively, a minimum `viewportsize' may be specified. - - For convenience, the `three' module defines `O=(0,0,0)', -`X=(1,0,0)', `Y=(0,1,0)', and `Z=(0,0,1)', along with a unitcircle in -the XY plane: -path3 unitcircle3=X..Y..-X..-Y..cycle; - - A general (approximate) circle can be drawn perpendicular to the -direction `normal' with the routine -path3 circle(triple c, real r, triple normal=Z); - - A circular arc centered at `c' with radius `r' from -`c+r*dir(theta1,phi1)' to `c+r*dir(theta2,phi2)', drawing -counterclockwise relative to the normal vector -`cross(dir(theta1,phi1),dir(theta2,phi2))' if `theta2 > theta1' or if -`theta2 == theta1' and `phi2 >= phi1', can be constructed with -path3 arc(triple c, real r, real theta1, real phi1, real theta2, real phi2, - triple normal=O); - The normal must be explicitly specified if `c' and the endpoints are -colinear. If `r' < 0, the complementary arc of radius `|r|' is -constructed. For convenience, an arc centered at `c' from triple `v1' -to `v2' (assuming `|v2-c|=|v1-c|') in the direction CCW -(counter-clockwise) or CW (clockwise) may also be constructed with -path3 arc(triple c, triple v1, triple v2, triple normal=O, - bool direction=CCW); - When high accuracy is needed, the routines `Circle' and `Arc' defined -in `graph3' may be used instead. See *note GaussianSurface:: for an -example of a three-dimensional circular arc. - - The representation `O--O+u--O+u+v--O+v--cycle' of the plane passing -through point `O' with normal `cross(u,v)' is returned by -path3 plane(triple u, triple v, triple O=O); - A three-dimensional box with opposite vertices at triples `v1' and -`v2' may be drawn with the function -path3[] box(triple v1, triple v2); - For example, a unit box is predefined as -path3[] unitbox=box(O,(1,1,1)); - `Asymptote' also provides optimized definitions for the -three-dimensional paths `unitsquare3' and `unitcircle3', along with the -surfaces `unitdisk', `unitplane', `unitcube', `unitcylinder', -`unitcone', `unitsolidcone', `unitfrustum(real t1, real t2)', -`unitsphere', and `unithemisphere'. - -These projections to two dimensions are predefined: -`oblique' - -`oblique(real angle);' - The point `(x,y,z)' is projected to `(x-0.5z,y-0.5z)'. If an - optional real argument is given, the negative z axis is drawn at - this angle in degrees. The projection `obliqueZ' is a synonym for - `oblique'. - -`obliqueX' - -`obliqueX(real angle)' - The point `(x,y,z)' is projected to `(y-0.5x,z-0.5x)'. If an - optional real argument is given, the negative x axis is drawn at - this angle in degrees. - -`obliqueY' - -`obliqueY(real angle)' - The point `(x,y,z)' is projected to `(x+0.5y,z+0.5y)'. If an - optional real argument is given, the positive y axis is drawn at - this angle in degrees. - -`orthographic(triple camera, triple up=Z, triple target=O, - bool showtarget=true, bool center=false)' - This projects from three to two dimensions using the view as seen - at a point infinitely far away in the direction `unit(camera)', - orienting the camera so that, if possible, the vector `up' points - upwards. Parallel lines are projected to parallel lines. The - bounding volume is expanded to include `target' if - `showtarget=true'. If `center=true', the target will be adjusted - to the center of the bounding volume. - -`orthographic(real x, real y, real z, triple up=Z, triple target=O, - bool showtarget=true, bool center=false)' - This is equivalent to - `orthographic((x,y,z),up,target,showtarget,center)'. - -`perspective(triple camera, triple up=Z, triple target=O, - bool showtarget=true, bool autoadjust=true, - bool center=autoadjust)' - This projects from three to two dimensions, taking account of - perspective, as seen from the location `camera' looking at - `target', orienting the camera so that, if possible, the vector - `up' points upwards. If `render=0', projection of - three-dimensional cubic Bezier splines is implemented by - approximating a two-dimensional nonuniform rational B-spline - (NURBS) with a two-dimensional Bezier curve containing additional - nodes and control points. If `autoadjust=true', the camera will - automatically be adjusted to lie outside the bounding volume for - all possible interactive rotations about `target'. If - `center=true', the target will be adjusted to the center of the - bounding volume. - -`perspective(real x, real y, real z, triple up=Z, triple target=O, - bool showtarget=true, bool autoadjust=true, - bool center=autoadjust)' - This is equivalent to `perspective((x,y,z),up,target,showtarget, - autoadjust,center)'. - -The default projection, `currentprojection', is initially set to -`perspective(5,4,2)'. - - We also define standard orthographic views used in technical drawing: -projection LeftView=orthographic(-X,showtarget=true); -projection RightView=orthographic(X,showtarget=true); -projection FrontView=orthographic(-Y,showtarget=true); -projection BackView=orthographic(Y,showtarget=true); -projection BottomView=orthographic(-Z,showtarget=true); -projection TopView=orthographic(Z,showtarget=true); - The function -void addViews(picture dest=currentpicture, picture src, bool group=true, - filltype filltype=NoFill); - adds picture `pic' as seen with `FrontView' aligned above the -projection `TopView' and to the right of the projection `RightView'. -Alternatively, the function -void addAllViews(picture dest=currentpicture, picture src, - real xmargin=0, real ymargin=xmargin, - bool group=true, filltype filltype=NoFill); - may be used to exhibit all six standard views, with FrontView, -TopView, RightView in the upper row and BackView, BottomView, LeftView -in the lower row. - - A triple or path3 can be projected to a pair or path, with -`project(triple, projection P=currentprojection)' or `project(path3, -projection P=currentprojection)'. - - It is occasionally useful to be able to invert a projection, sending -a pair `z' onto the plane perpendicular to `normal' and passing through -`point': -triple invert(pair z, triple normal, triple point, - projection P=currentprojection); - A pair `z' on the projection plane can be inverted to a triple with -the routine -triple invert(pair z, projection P=currentprojection); - A pair direction `dir' on the projection plane can be inverted to a -triple direction relative to a point `v' with the routine -triple invert(pair dir, triple v, projection P=currentprojection). - - Three-dimensional objects may be transformed with one of the -following built-in transform3 types: - -`shift(triple v)' - translates by the triple `v'; - -`xscale3(real x)' - scales by `x' in the x direction; - -`yscale3(real y)' - scales by `y' in the y direction; - -`zscale3(real z)' - scales by `z' in the z direction; - -`scale3(real s)' - scales by `s' in the x, y, and z directions; - -`scale(real x, real y, real z)' - scales by `x' in the x direction, by `y' in the y direction, and - by `z' in the z direction; - -`rotate(real angle, triple v)' - rotates by `angle' in degrees about an axis `v' through the origin; - -`rotate(real angle, triple u, triple v)' - rotates by `angle' in degrees about the axis `u--v'; - -`reflect(triple u, triple v, triple w)' - reflects about the plane through `u', `v', and `w'. - - Three-dimensional TeX Labels, which are by default drawn as Bezier -surfaces directly on the projection plane, can be transformed from the -`XY' plane by any of the above transforms or mapped to a specified -two-dimensional plane with the transform3 types `XY', `YZ', `ZX', `YX', -`ZY', `ZX'. There are also modified versions of these transforms that -take an optional argument `projection P=currentprojection' that rotate -and/or flip the label so that it is more readable from the initial -viewpoint. - - A transform3 that projects in the direction `dir' onto the plane -with normal `n' through point `O' is returned by -transform3 planeproject(triple n, triple O=O, triple dir=n); - One can use -triple normal(path3 p); - to find the unit normal vector to a planar three-dimensional path `p'. -As illustrated in the example `planeproject.asy', a transform3 that -projects in the direction `dir' onto the plane defined by a planar path -`p' is returned by -transform3 planeproject(path3 p, triple dir=normal(p)); - - The functions -surface extrude(path p, triple axis=Z); -surface extrude(Label L, triple axis=Z); - return the surface obtained by extruding path `p' or Label `L' along -`axis'. - - Three-dimensional versions of the path functions `length', `size', -`point', `dir', `accel', `radius', `precontrol', `postcontrol', -`arclength', `arctime', `reverse', `subpath', `intersect', -`intersections', `intersectionpoint', `intersectionpoints', `min', -`max', `cyclic', and `straight' are also defined. - - The routine -real[][] intersections(path3 p, surface s, real fuzz=-1); - returns the intersection times of a path `p' with a surface `s' as a -sorted array of real arrays of length 2, and -triple[] intersectionpoints(path3 p, surface s, real fuzz=-1); - returns the corresponding intersection points. Here, the computations -are performed to the absolute error specified by `fuzz', or if `fuzz < -0', to machine precision. - - Here is an example showing all five guide3 connectors: - -import graph3; - -size(200); - -currentprojection=orthographic(500,-500,500); - -triple[] z=new triple[10]; - -z[0]=(0,100,0); z[1]=(50,0,0); z[2]=(180,0,0); - -for(int n=3; n <= 9; ++n) - z[n]=z[n-3]+(200,0,0); - -path3 p=z[0]..z[1]---z[2]::{Y}z[3] -&z[3]..z[4]--z[5]::{Y}z[6] -&z[6]::z[7]---z[8]..{Y}z[9]; - -draw(p,grey+linewidth(4mm)+opacity(0.5)); - -xaxis3(Label(XY()*"$x$",align=-3Y),red,above=true); -yaxis3(Label(XY()*"$y$",align=-3X),red,above=true); - -dot(z); - - - -Three-dimensional versions of bars or arrows can be drawn with one of -the specifiers `None', `Blank', `BeginBar3', `EndBar3' (or equivalently -`Bar3'), `Bars3', `BeginArrow3', `MidArrow3', `EndArrow3' (or -equivalently `Arrow3'), `Arrows3', `BeginArcArrow3', `EndArcArrow3' (or -equivalently `ArcArrow3'), `MidArcArrow3', and `ArcArrows3'. -Three-dimensional bars accept the optional arguments `(real size=0, -triple dir=O)'. If `size=O', the default bar length is used; if -`dir=O', the bar is drawn perpendicular to the path and the initial -viewing direction. The predefined three-dimensional arrowhead styles -are `DefaultHead3', `HookHead3', `TeXHead3'. Versions of the -two-dimensional arrowheads lifted to three-dimensional space and -aligned according to the initial viewpoint (or an optionally specified -`normal' vector) are also defined: `DefaultHead2(triple normal=O)', -`HookHead2(triple normal=O)', `TeXHead2(triple normal=O)'. These are -illustrated in the example `arrows3.asy'. - - Module `three' also defines the three-dimensional margins -`NoMargin3', `BeginMargin3', `EndMargin3', `Margin3', `Margins3', -`BeginPenMargin2', `EndPenMargin2', `PenMargin2', `PenMargins2', -`BeginPenMargin3', `EndPenMargin3', `PenMargin3', `PenMargins3', -`BeginDotMargin3', `EndDotMargin3', `DotMargin3', `DotMargins3', -`Margin3', and `TrueMargin3'. - - Further three-dimensional examples are provided in the files -`near_earth.asy', `conicurv.asy', and (in the `animations' -subdirectory) `cube.asy'. - - Limited support for projected vector graphics (effectively -three-dimensional nonrendered `PostScript') is available with the -setting `render=0'. This currently only works for piecewise planar -surfaces, such as those produced by the parametric `surface' routines -in the `graph3' module. Surfaces produced by the `solids' package will -also be properly rendered if the parameter `nslices' is sufficiently -large. - - In the module `bsp', hidden surface removal of planar pictures is -implemented using a binary space partition and picture clipping. A -planar path is first converted to a structure `face' derived from -`picture'. A `face' may be given to a two-dimensional drawing routine -in place of any `picture' argument. An array of such faces may then be -drawn, removing hidden surfaces: -void add(picture pic=currentpicture, face[] faces, - projection P=currentprojection); - Labels may be projected to two dimensions, using projection `P', onto -the plane passing through point `O' with normal `cross(u,v)' by -multiplying it on the left by the transform -transform transform(triple u, triple v, triple O=O, - projection P=currentprojection); - - Here is an example that shows how a binary space partition may be -used to draw a two-dimensional vector graphics projection of three -orthogonal intersecting planes: - -size(6cm,0); -import bsp; - -real u=2.5; -real v=1; - -currentprojection=oblique; - -path3 y=plane((2u,0,0),(0,2v,0),(-u,-v,0)); -path3 l=rotate(90,Z)*rotate(90,Y)*y; -path3 g=rotate(90,X)*rotate(90,Y)*y; - -face[] faces; -filldraw(faces.push(y),project(y),yellow); -filldraw(faces.push(l),project(l),lightgrey); -filldraw(faces.push(g),project(g),green); - -add(faces); - - - - -File: asymptote.info, Node: obj, Next: graph3, Prev: three, Up: Base modules - -7.30 `obj' -========== - -This module allows one to construct surfaces from simple obj files, as -illustrated in the example files `galleon.asy' and `triceratops.asy'. - - -File: asymptote.info, Node: graph3, Next: grid3, Prev: obj, Up: Base modules - -7.31 `graph3' -============= - -This module implements three-dimensional versions of the functions in -`graph.asy'. To draw an x axis in three dimensions, use the routine -void xaxis3(picture pic=currentpicture, Label L="", axis axis=YZZero, - real xmin=-infinity, real xmax=infinity, pen p=currentpen, - ticks3 ticks=NoTicks3, arrowbar3 arrow=None, bool above=false); - Analogous routines `yaxis' and `zaxis' can be used to draw y and z -axes in three dimensions. There is also a routine for drawing all -three axis: -void axes3(picture pic=currentpicture, - Label xlabel="", Label ylabel="", Label zlabel="", - triple min=(-infinity,-infinity,-infinity), - triple max=(infinity,infinity,infinity), - pen p=currentpen, arrowbar3 arrow=None); - -The predefined three-dimensional axis types are -axis YZEquals(real y, real z, triple align=O, bool extend=false); -axis XZEquals(real x, real z, triple align=O, bool extend=false); -axis XYEquals(real x, real y, triple align=O, bool extend=false); -axis YZZero(triple align=O, bool extend=false); -axis XZZero(triple align=O, bool extend=false); -axis XYZero(triple align=O, bool extend=false); -axis Bounds(int type=Both, int type2=Both, triple align=O, bool extend=false); - The optional `align' parameter to these routines can be used to -specify the default axis and tick label alignments. The `Bounds' axis -accepts two type parameters, each of which must be one of `Min', `Max', -or `Both'. These parameters specify which of the four possible -three-dimensional bounding box edges should be drawn. - - The three-dimensional tick options are `NoTicks3', `InTicks', -`OutTicks', and `InOutTicks'. These specify the tick directions for the -`Bounds' axis type; other axis types inherit the direction that would -be used for the `Bounds(Min,Min)' axis. - - Here is an example of a helix and bounding box axes with ticks and -axis labels, using orthographic projection: - -import graph3; - -size(0,200); -size3(200,IgnoreAspect); - -currentprojection=orthographic(4,6,3); - -real x(real t) {return cos(2pi*t);} -real y(real t) {return sin(2pi*t);} -real z(real t) {return t;} - -path3 p=graph(x,y,z,0,2.7,operator ..); - -draw(p,Arrow3); - -scale(true); - -xaxis3(XZ()*"$x$",Bounds(),red,InTicks(Label,2,2)); -yaxis3(YZ()*"$y$",Bounds(),red,InTicks(beginlabel=false,Label,2,2)); -zaxis3(XZ()*"$z$",Bounds(),red,InTicks); - - - -The next example illustrates three-dimensional x, y, and z axes, -without autoscaling of the axis limits: - -import graph3; - -size(0,200); -size3(200,IgnoreAspect); - -currentprojection=perspective(5,2,2); - -scale(Linear,Linear,Log); - -xaxis3("$x$",0,1,red,OutTicks(2,2)); -yaxis3("$y$",0,1,red,OutTicks(2,2)); -zaxis3("$z$",1,30,red,OutTicks(beginlabel=false)); - - - -One can also place ticks along a general three-dimensional axis: - -import graph3; - -size(0,100); - -path3 g=yscale3(2)*unitcircle3; -currentprojection=perspective(10,10,10); - -axis(Label("C",position=0,align=15X),g,InTicks(endlabel=false,8,end=false), - ticklocate(0,360,new real(real v) { - path3 h=O--max(abs(max(g)),abs(min(g)))*dir(90,v); - return intersect(g,h)[0];}, - new triple(real t) {return cross(dir(g,t),Z);})); - - - -Surface plots of matrices and functions over the region `box(a,b)' in -the XY plane are also implemented: -surface surface(real[][] f, pair a, pair b, bool[][] cond={}); -surface surface(real[][] f, pair a, pair b, splinetype xsplinetype, - splinetype ysplinetype=xsplinetype, bool[][] cond={}); -surface surface(real[][] f, real[] x, real[] y, - splinetype xsplinetype=null, splinetype ysplinetype=xsplinetype, - bool[][] cond={}) -surface surface(triple[][] f, bool[][] cond={}); -surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx, - bool cond(pair z)=null); -surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx, - splinetype xsplinetype, splinetype ysplinetype=xsplinetype, - bool cond(pair z)=null); -surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu, - bool cond(pair z)=null); -surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu, - splinetype[] usplinetype, splinetype[] vsplinetype=Spline, - bool cond(pair z)=null); - The final two versions draw parametric surfaces for a function f(u,v) -over the parameter space `box(a,b)', as illustrated in the example -`parametricsurface.asy'. An optional splinetype `Spline' may be -specified. The boolean array or function `cond' can be used to control -which surface mesh cells are actually drawn (by default all mesh cells -over `box(a,b)' are drawn). Surface lighting is illustrated in the -example files `parametricsurface.asy' and `sinc.asy'. Lighting can be -disabled by setting `light=nolight', as in this example of a Gaussian -surface: - -import graph3; - -size(200,0); - -currentprojection=perspective(10,8,4); - -real f(pair z) {return 0.5+exp(-abs(z)^2);} - -draw((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle); - -draw(arc(0.12Z,0.2,90,60,90,25),ArcArrow3); - -surface s=surface(f,(-1,-1),(1,1),nx=5,Spline); - -xaxis3(Label("$x$"),red,Arrow3); -yaxis3(Label("$y$"),red,Arrow3); -zaxis3(XYZero(extend=true),red,Arrow3); - -draw(s,lightgray,meshpen=black+thick(),nolight); - -label("$O$",O,-Z+Y,red); - - -A mesh can be drawn without surface filling by specifying `nullpen' for -the surfacepen. - - A vector field of `nu'\times`nv' arrows on a parametric surface `f' -over `box(a,b)' can be drawn with the routine -picture vectorfield(path3 vector(pair v), triple f(pair z), pair a, pair b, - int nu=nmesh, int nv=nu, bool truesize=false, - real maxlength=truesize ? 0 : maxlength(f,a,b,nu,nv), - bool cond(pair z)=null, pen p=currentpen, - arrowbar3 arrow=Arrow3, margin3 margin=PenMargin3) - as illustrated in the examples `vectorfield3.asy' and -`vectorfieldsphere.asy'. - - -File: asymptote.info, Node: grid3, Next: solids, Prev: graph3, Up: Base modules - -7.32 `grid3' -============ - -This module, contributed by Philippe Ivaldi, can be used for drawing 3D -grids. Here is an example (further examples can be found in `grid3.asy' -and at `http://piprim.tuxfamily.org/asymptote/grid3/'): - -import grid3; - -size(8cm,0,IgnoreAspect); -currentprojection=orthographic(0.5,1,0.5); - -scale(Linear, Linear, Log); - -limits((-2,-2,1),(0,2,100)); - -grid3(XYZgrid); - -xaxis3(Label("$x$",position=EndPoint,align=S),Bounds(Min,Min), - OutTicks()); -yaxis3(Label("$y$",position=EndPoint,align=S),Bounds(Min,Min),OutTicks()); -zaxis3(Label("$z$",position=EndPoint,align=(-1,0.5)),Bounds(Min,Min), - OutTicks(beginlabel=false)); - - - - -File: asymptote.info, Node: solids, Next: tube, Prev: grid3, Up: Base modules - -7.33 `solids' -============= - -This solid geometry package defines a structure `revolution' that can -be used to fill and draw surfaces of revolution. The following example -uses it to display the outline of a circular cylinder of radius 1 with -axis `O--1.5unit(Y+Z)' with perspective projection: - -import solids; - -size(0,100); - -revolution r=cylinder(O,1,1.5,Y+Z); -draw(r,heavygreen); - - - -Further illustrations are provided in the example files `cylinder.asy', -`cones.asy', `hyperboloid.asy', and `torus.asy'. - - The structure `skeleton' contains the three-dimensional wireframe -used to visualize a volume of revolution: -struct skeleton { - struct curve { - path3[] front; - path3[] back; - } - // transverse skeleton (perpendicular to axis of revolution) - curve transverse; - // longitudinal skeleton (parallel to axis of revolution) - curve longitudinal; -} - - -File: asymptote.info, Node: tube, Next: flowchart, Prev: solids, Up: Base modules - -7.34 `tube' -=========== - -This package extends the routine `tube' defined in `three_arrows.asy' -to arbitrary cross sections, colors, and spine transformations. The -routine -surface tube(path3 g, coloredpath section, - transform T(real)=new transform(real t) {return identity();}, - real corner=1, real relstep=0); - draws a tube along `g' with cross section `section', after applying -the transformation `T(t)' at `relpoint(g,t)'. The parameter `corner' -controls the number of elementary tubes at the angular points of `g'. A -nonzero value of `relstep' specifies a fixed relative time step (in the -sense of `relpoint(g,t)') to use in constructing elementary tubes along -`g'. The type `coloredpath' is a generalization of `path' to which a -`path' can be cast: -struct coloredpath -{ - path p; - pen[] pens(real); - int colortype=coloredSegments; -} - Here `p' defines the cross section and the method `pens(real t)' -returns an array of pens (interpreted as a cyclic array) used for -shading the tube patches at `relpoint(g,t)'. If -`colortype=coloredSegments', the tube patches are filled as if each -segment of the section was colored with the pen returned by `pens(t)', -whereas if `colortype=coloredNodes', the tube components are vertex -shaded as if the nodes of the section were colored. - - A `coloredpath' can be constructed with one of the routines: -coloredpath coloredpath(path p, pen[] pens(real), - int colortype=coloredSegments); -coloredpath coloredpath(path p, pen[] pens=new pen[] {currentpen}, - int colortype=coloredSegments); -coloredpath coloredpath(path p, pen pen(real)); - In the second case, the pens are independent of the relative time. In -the third case, the array of pens contains only one pen, which depends -of the relative time. - - The casting of `path' to `coloredpath' allows the use of a `path' -instead of a `coloredpath'; in this case the shading behaviour is the -default shading behavior for a surface. - - An example of `tube' is provided in the file `trefoilknot.asy'. -Further examples can be found at -`http://piprim.tuxfamily.org/asymptote/tube/'. - - -File: asymptote.info, Node: flowchart, Next: contour, Prev: tube, Up: Base modules - -7.35 `flowchart' -================ - -This package provides routines for drawing flowcharts. The primary -structure is a `block', which represents a single block on the -flowchart. The following eight functions return a position on the -appropriate edge of the block, given picture transform `t': - -pair block.top(transform t=identity()); -pair block.left(transform t=identity()); -pair block.right(transform t=identity()); -pair block.bottom(transform t=identity()); -pair block.topleft(transform t=identity()); -pair block.topright(transform t=identity()); -pair block.bottomleft(transform t=identity()); -pair block.bottomright(transform t=identity()); - - -To obtain an arbitrary position along the boundary of the block in user -coordinates, use: -pair block.position(real x, transform t=identity()); - - -The center of the block in user coordinates is stored in `block.center' -and the block size in `PostScript' coordinates is given by `block.size'. - -A frame containing the block is returned by -frame block.draw(pen p=currentpen); - - - The following block generation routines accept a Label, string, or -frame for their object argument: - -"rectangular block with an optional header (and padding `dx' around header and body):" - block rectangle(object header, object body, pair center=(0,0), - pen headerpen=mediumgray, pen bodypen=invisible, - pen drawpen=currentpen, - real dx=3, real minheaderwidth=minblockwidth, - real minheaderheight=minblockwidth, - real minbodywidth=minblockheight, - real minbodyheight=minblockheight); - block rectangle(object body, pair center=(0,0), - pen fillpen=invisible, pen drawpen=currentpen, - real dx=3, real minwidth=minblockwidth, - real minheight=minblockheight); - -"diamond-shaped flowchart block:" - block diamond(object body, pair center=(0,0), - pen fillpen=invisible, pen drawpen=currentpen, - real ds=5, real dw=1, - real height=20, real minwidth=minblockwidth, - real minheight=minblockheight); - -"circular flowchart block:" - block circle(object body, pair center=(0,0), pen fillpen=invisible, - pen drawpen=currentpen, real dr=3, - real mindiameter=mincirclediameter); - -"rectangular flowchart block with rounded corners:" - block roundrectangle(object body, pair center=(0,0), - pen fillpen=invisible, pen drawpen=currentpen, - real ds=5, real dw=0, real minwidth=minblockwidth, - real minheight=minblockheight); - -"rectangular flowchart block with beveled edges:" - block bevel(object body, pair center=(0,0), pen fillpen=invisible, - pen drawpen=currentpen, real dh=5, real dw=5, - real minwidth=minblockwidth, real minheight=minblockheight); - - - To draw paths joining the pairs in `point' with right-angled lines, -use the routine: -path path(pair point[] ... flowdir dir[]); - The entries in `dir' identify whether successive segments between the -pairs specified by `point' should be drawn in the `Horizontal' or -`Vertical' direction. - - Here is a simple flowchart example: - -size(0,300); - -import flowchart; - -block block1=rectangle(Label("Example",magenta), - pack(Label("Start:",heavygreen),"",Label("$A:=0$",blue), - "$B:=1$"),(-0.5,3),palegreen,paleblue,red); -block block2=diamond(Label("Choice?",blue),(0,2),palegreen,red); -block block3=roundrectangle("Do something",(-1,1)); -block block4=bevel("Don't do something",(1,1)); -block block5=circle("End",(0,0)); - -draw(block1); -draw(block2); -draw(block3); -draw(block4); -draw(block5); - -add(new void(picture pic, transform t) { - draw(pic,path(new pair[]{block1.right(t),block2.top(t)},Horizontal), - Arrow,PenMargin); - draw(pic,Label("Yes",0.5,NW),path(new pair[]{block2.left(t),block3.top(t)}, - Horizontal),Arrow,PenMargin); - draw(pic,Label("No",0.5,NE),path(new pair[]{block2.right(t),block4.top(t)}, - Horizontal),Arrow,PenMargin); - draw(pic,path(new pair[]{block3.bottom(t),block5.left(t)},Vertical), - Arrow,PenMargin); - draw(pic,path(new pair[]{block4.bottom(t),block5.right(t)},Vertical), - Arrow,PenMargin); - }); - - - - -File: asymptote.info, Node: contour, Next: contour3, Prev: flowchart, Up: Base modules - -7.36 `contour' -============== - -This package draws contour lines. To construct contours corresponding -to the values in an array `c' for a function `f' on `box(a,b)', use -guide[][] contour(real f(real, real), pair a, pair b, - real[] c, int nx=ngraph, int ny=nx, - interpolate join=operator --); - The integers `nx' and `ny' define the resolution. The default -resolution, `ngraph x ngraph' (here `ngraph' defaults to `100'), can be -increased for greater accuracy. The default interpolation operator is -`operator --' (linear). Spline interpolation (`operator ..') may -produce smoother contours but it can also lead to overshooting. - - To construct contours for an array of data values on a uniform -two-dimensional lattice on `box(a,b)', use -guide[][] contour(real[][] f, real[][] midpoint=new real[][], - pair a, pair b, real[] c, - interpolate join=operator --); - - To construct contours for an array of data values on a nonoverlapping -regular mesh specified by the two-dimensional array `z', optionally -specifying the values of `f' at the mesh midpoints, use -guide[][] contour(pair[][] z, real[][] f, - real[][] midpoint=new real[][], real[] c, - interpolate join=operator --); - - To construct contours for an array of values `f' specified at -irregularly positioned points `z', use the routine -guide[][] contour(pair[] z, real[] f, real[] c, - interpolate join=operator --); - The contours themselves can be drawn with one of the routines -void draw(picture pic=currentpicture, Label[] L=new Label[], - guide[][] g, pen p=currentpen) - -void draw(picture pic=currentpicture, Label[] L=new Label[], - guide[][] g, pen[] p) - - The following simple example draws the contour at value `1' for the -function z=x^2+y^2, which is a unit circle: - -import contour; -size(75); - -real f(real a, real b) {return a^2+b^2;} -draw(contour(f,(-1,-1),(1,1),new real[] {1})); - - - -The next example draws and labels multiple contours for the function -z=x^2-y^2 with the resolution `100 x 100', using a dashed pen for -negative contours and a solid pen for positive (and zero) contours: - -import contour; - -size(200); - -real f(real x, real y) {return x^2-y^2;} -int n=10; -real[] c=new real[n]; -for(int i=0; i < n; ++i) c[i]=(i-n/2)/n; - -pen[] p=sequence(new pen(int i) { - return (c[i] >= 0 ? solid : dashed)+fontsize(6); - },c.length); - -Label[] Labels=sequence(new Label(int i) { - return Label(c[i] != 0 ? (string) c[i] : "",Relative(unitrand()),(0,0), - UnFill(1bp)); - },c.length); - -draw(Labels,contour(f,(-1,-1),(1,1),c),p); - - - -The next example illustrates how contour lines can be drawn on color -density images: - -import graph; -import palette; -import contour; - -size(10cm,10cm,IgnoreAspect); - -pair a=(0,0); -pair b=(2pi,2pi); - -real f(real x, real y) {return cos(x)*sin(y);} - -int N=200; -int Divs=10; -int divs=2; - -defaultpen(1bp); -pen Tickpen=black; -pen tickpen=gray+0.5*linewidth(currentpen); -pen[] Palette=BWRainbow(); - -scale(false); - -bounds range=image(f,Automatic,a,b,N,Palette); - -// Major contours - -real[] Cvals=uniform(range.min,range.max,Divs); -draw(contour(f,a,b,Cvals,N,operator --),Tickpen); - -// Minor contours -real[] cvals; -for(int i=0; i < Cvals.length-1; ++i) - cvals.append(uniform(Cvals[i],Cvals[i+1],divs)[1:divs]); -draw(contour(f,a,b,cvals,N,operator --),tickpen); - -xaxis("$x$",BottomTop,LeftTicks,above=true); -yaxis("$y$",LeftRight,RightTicks,above=true); - -palette("$f(x,y)$",range,point(NW)+(0,0.5),point(NE)+(0,1),Top,Palette, - PaletteTicks(N=Divs,n=divs,Tickpen,tickpen)); - - - -Finally, here is an example that illustrates the construction of -contours from irregularly spaced data: - -import contour; - -size(200); - -int n=100; - -pair[] points=new pair[n]; -real[] values=new real[n]; - -real f(real a, real b) {return a^2+b^2;} - -real r() {return 1.1*(rand()/randMax*2-1);} - -for(int i=0; i < n; ++i) { - points[i]=(r(),r()); - values[i]=f(points[i].x,points[i].y); -} - -draw(contour(points,values,new real[]{0.25,0.5,1},operator ..),blue); - - - -In the above example, the contours of irregularly spaced data are -constructed by first creating a triangular mesh from an array `z' of -pairs: - -int[][] triangulate(pair[] z); - -size(200); -int np=100; -pair[] points; - -real r() {return 1.2*(rand()/randMax*2-1);} - -for(int i=0; i < np; ++i) - points.push((r(),r())); - -int[][] trn=triangulate(points); - -for(int i=0; i < trn.length; ++i) { - draw(points[trn[i][0]]--points[trn[i][1]]); - draw(points[trn[i][1]]--points[trn[i][2]]); - draw(points[trn[i][2]]--points[trn[i][0]]); -} - -for(int i=0; i < np; ++i) - dot(points[i],red); - - - -The example `Gouraudcontour' illustrates how to produce color density -images over such irregular triangular meshes. `Asymptote' uses a -robust version of Paul Bourke's Delaunay triangulation algorithm based -on the public-domain exact arithmetic predicates written by Jonathan -Shewchuk. - - -File: asymptote.info, Node: contour3, Next: slopefield, Prev: contour, Up: Base modules - -7.37 `contour3' -=============== - -This package draws surfaces described as the null space of real-valued -functions of (x,y,z) or real[][][] matrices. Its usage is illustrated -in the example file `magnetic.asy'. - - -File: asymptote.info, Node: slopefield, Next: ode, Prev: contour3, Up: Base modules - -7.38 `slopefield' -================= - -To draw a slope field for the differential equation dy/dx=f(x,y) (or -dy/dx=f(x)), use: -picture slopefield(real f(real,real), pair a, pair b, - int nx=nmesh, int ny=nx, - real tickfactor=0.5, pen p=currentpen, - arrowbar arrow=None); - Here, the points `a' and `b' are the lower left and upper right -corners of the rectangle in which the slope field is to be drawn, `nx' -and `ny' are the respective number of ticks in the x and y directions, -`tickfactor' is the fraction of the minimum cell dimension to use for -drawing ticks, and `p' is the pen to use for drawing the slope fields. -The return value is a picture that can be added to `currentpicture' via -the `add(picture)' command. - - The function -path curve(pair c, real f(real,real), pair a, pair b); - takes a point (`c') and a slope field-defining function `f' and -returns, as a path, the curve passing through that point. The points -`a' and `b' represent the rectangular boundaries over which the curve -is interpolated. - - Both `slopefield' and `curve' alternatively accept a function `real -f(real)' that depends on x only, as seen in this example: - -import slopefield; - -size(200); - -real func(real x) {return 2x;} -add(slopefield(func,(-3,-3),(3,3),20,Arrow)); -draw(curve((0,0),func,(-3,-3),(3,3)),red); - - - - -File: asymptote.info, Node: ode, Prev: slopefield, Up: Base modules - -7.39 `ode' -========== - -The `ode' module, illustrated in the example `odetest.asy', implements -a number of explicit numerical integration schemes for ordinary -differential equations. - - -File: asymptote.info, Node: Options, Next: Interactive mode, Prev: Base modules, Up: Top - -8 Options -********* - -Type `asy -h' to see the full list of command-line options supported by -`Asymptote': - -Usage: ../asy [options] [file ...] - -Options (negate by replacing - with -no): - --V,-View View output; command-line only --a,-align C|B|T|Z Center, Bottom, Top, or Zero page alignment [C] --antialias n Antialiasing width for rasterized output [2] --auto3D Automatically activate 3D scene [true] --autoimport string Module to automatically import --autoplain Enable automatic importing of plain [true] --autorotate Enable automatic PDF page rotation [false] --batchMask Mask fpu exceptions in batch mode [false] --batchView View output in batch mode [false] --bw Convert all colors to black and white [false] --cd directory Set current directory; command-line only --cmyk Convert rgb colors to cmyk [false] --c,-command string Command to autoexecute --compact Conserve memory at the expense of speed [false] --d,-debug Enable debugging messages [false] --divisor n Garbage collect using purge(divisor=n) [2] --embed Embed rendered preview image [true] --exitonEOF Exit interactive mode on EOF [true] --fitscreen Fit rendered image to screen [true] --globalwrite Allow write to other directory [false] --gray Convert all colors to grayscale [false] --h,-help Show summary of options; command-line only --historylines n Retain n lines of history [1000] --iconify Iconify rendering window [false] --inlineimage Generate inline embedded image [false] --inlinetex Generate inline TeX code [false] --interactiveMask Mask fpu exceptions in interactive mode [true] --interactiveView View output in interactive mode [true] --interactiveWrite Write expressions entered at the prompt to stdout [true] --k,-keep Keep intermediate files [false] --keepaux Keep intermediate LaTeX .aux files [false] --level n Postscript level [3] --l,-listvariables List available global functions and variables [false] --localhistory Use a local interactive history file [false] --m,-mask Mask fpu exceptions; command-line only --maxtile pair Maximum rendering tile size [(0,0)] --maxviewport pair Maximum viewport size [(2048,2048)] --multiline Input code over multiple lines at the prompt [false] --multipleView View output from multiple batch-mode files [false] --multisample n Multisampling width for screen images [4] --O,-offset pair PostScript offset [(0,0)] --f,-outformat format Convert each output file to specified format --o,-outname name Alternative output directory/filename --p,-parseonly Parse file [false] --pdfreload Automatically reload document in pdfviewer [false] --pdfreloaddelay usec Delay before attempting initial pdf reload [750000] --position pair Initial 3D rendering screen position [(0,0)] --prc Embed 3D PRC graphics in PDF output [true] --prompt string Prompt [> ] --prompt2 string Continuation prompt for multiline input [..] --q,-quiet Suppress welcome message [false] --render n Render 3D graphics using n pixels per bp (-1=auto) [-1] --rgb Convert cmyk colors to rgb [false] --safe Disable system call [true] --scroll n Scroll standard output n lines at a time [0] --tabcompletion Interactive prompt auto-completion [true] --tex engine latex|pdflatex|xelatex|tex|pdftex|context|none [latex] --thick Render thick 3D lines [true] --thin Render thin 3D lines [true] --threads Use POSIX threads for 3D rendering [true] --toolbar Show 3D toolbar in PDF output [true] --s,-translate Show translated virtual machine code [false] --twice Run LaTeX twice (to resolve references) [false] --twosided Use two-sided 3D lighting model for rendering [true] --u,-user string General purpose user string --v,-verbose Increase verbosity level (can specify multiple times) [0] --version Show version; command-line only --wait Wait for child processes to finish before exiting [false] --where Show where listed variables are declared [false] --xformat format GUI deconstruction format [png] - - All boolean options can be negated by prepending `no' to the option -name. - - If no arguments are given, `Asymptote' runs in interactive mode -(*note Interactive mode::). In this case, the default output file is -`out.eps'. - - If `-' is given as the file argument, `Asymptote' reads from -standard input. - - If multiple files are specified, they are treated as separate -`Asymptote' runs. - - If the string `autoimport' is nonempty, a module with this name is -automatically imported for each run as the final step in loading module -`plain'. - - Default option values may be entered as `Asymptote' code in a -configuration file named `config.asy' (or the file specified by the -environment variable `ASYMPTOTE_CONFIG' or `-config' option). -`Asymptote' will look for this file in its usual search path. -Typically the configuration file is placed in the `.asy' directory in -the user's home directory (`%USERPROFILE%\.asy' under `MSDOS'). -Configuration variables are accessed using the long form of the option -names: -import settings; -outformat="pdf"; -batchView=false; -interactiveView=true; -batchMask=false; -interactiveMask=true; - Command-line options override these defaults. Most configuration -variables may also be changed at runtime. The advanced configuration -variables `dvipsOptions', `convertOptions', `gsOptions', -`psviewerOptions', `pdfviewerOptions', and `glOptions' allow -specialized options to be passed as a string to the respective -applications or libraries. - - If you insert -import plain; -settings.autoplain=true; - at the beginning of the configuration file, it can contain arbitrary -`Asymptote' code. - - The default output format is EPS for the (default) `latex' and `tex' -tex engine and PDF for the `pdflatex', `xelatex', and `context' tex -engines. Alternative output formats may be produced using the `-f' -option (or `outformat' setting). The optional setting `-render n' -requests an output resolution of `n' pixels per `bp'. Antialiasing is -controlled by the parameter `antialias', which by default specifies a -sampling width of 2 pixels. `Asymptote' can produce any output format -supported by the `ImageMagick' `convert' program (version 6.3.5 or -later recommended; an `Invalid Parameter' error message indicates that -the `MSDOS' utility `convert' is being used instead of the one that -comes with `ImageMagick'). To give specific options to `convert', use -the `convertOptions' setting or call convert manually. This example -emulates how `Asymptote' produces antialiased `tiff' output at one -pixel per `bp': -asy -o - venn | convert -alpha Off -density 144x144 -geometry 50%x eps:- venn.tiff - - If the option `-nosafe' is given, `Asymptote' runs in unsafe mode. -This enables the `int system(string s)' call, allowing one to execute -arbitrary shell commands. The default mode, `-safe', disables this call. - - A `PostScript' offset may be specified as a pair (in `bp' units) -with the `-O' option: -asy -O 0,0 file - The default offset is zero. The default value of the page alignment -setting `align' is `Center'. - - The `-c' (`command') option may be used to execute arbitrary -`Asymptote' code on the command line as a string. It is not necessary -to terminate the string with a semicolon. Multiple `-c' options are -executed in the order they are given. For example -asy -c 2+2 -c "sin(1)" -c "size(100); draw(unitsquare)" - produces the output -4 -0.841470984807897 - and draws a unitsquare of size `100'. - - The `-u' (`user') option may be used to specify arbitrary -`Asymptote' settings on the command line as a string. It is not -necessary to terminate the string with a semicolon. Multiple `-u' -options are executed in the order they are given. Command-line code like -`-u x=sqrt(2)' can be executed within a module like this: -real x; -usersetting(); -write(x); - - When the `-l' (`listvariables') option is used with file arguments, -only global functions and variables defined in the specified file(s) -are listed. - - Additional debugging output is produced with each additional `-v' -option: -`-v' - Display top-level module and final output file names. - -`-vv' - Also display imported and included module names and final `LaTeX' - and `dvips' processing information. - -`-vvv' - Also output `LaTeX' bidirectional pipe diagnostics. - -`-vvvv' - Also output knot guide solver diagnostics. - -`-vvvvv' - Also output `Asymptote' traceback diagnostics. - - -File: asymptote.info, Node: Interactive mode, Next: GUI, Prev: Options, Up: Top - -9 Interactive mode -****************** - -Interactive mode is entered by executing the command `asy' with no file -arguments. When the `-multiline' option is disabled (the default), each -line must be a complete `Asymptote' statement (unless explicitly -continued by a final backslash character `\'); it is not necessary to -terminate input lines with a semicolon. If one assigns -`settings.multiline=true', interactive code can be entered over -multiple lines; in this mode, the automatic termination of interactive -input lines by a semicolon is inhibited. Multiline mode is useful for -cutting and pasting `Asymptote' code directly into the interactive -input buffer. - - Interactive mode can be conveniently used as a calculator: -expressions entered at the interactive prompt (for which a -corresponding `write' function exists) are automatically evaluated and -written to `stdout'. - - The following special commands are supported only in interactive mode -and must be entered immediately after the prompt: - -`help' - view the manual; - -`reset' - reset the `Asymptote' environment to its initial state, except for - changes to the settings module (*note settings::), the current - directory (*note cd::), and breakpoints (*note Debugger::); - -`input FILE' - does an interactive reset, followed by the command `include FILE'. - If the file name `FILE' contains nonalphanumeric characters, - enclose it with quotation marks. A trailing semi-colon followed - by optional `Asymptote' commands may be entered on the same line. - -`quit' - exit interactive mode (`exit' is a synonym; the abbreviation `q' - is also accepted unless there exists a top-level variable named - `q'). A history of the most recent 1000 (this number can be - changed with the `historylines' configuration variable) previous - commands will be retained in the file `.asy/history' in the user's - home directory (unless the command-line option `-localhistory' was - specified, in which case the history will be stored in the file - `.asy_history' in the current directory). - - - Typing `ctrl-C' interrupts the execution of `Asymptote' code and -returns control to the interactive prompt. - - Interactive mode is implemented with the GNU `readline' library, -with command history and auto-completion. To customize the key -bindings, see: -`http://cnswww.cns.cwru.edu/php/chet/readline/readline.html' - - The file `asymptote.py' in the `Asymptote' system directory provides -an alternative way of entering `Asymptote' commands interactively, -coupled with the full power of `Python'. Copy this file to your `Python -path' and then execute from within `Python' the commands -from asymptote import * -g=asy() -g.size(200) -g.draw("unitcircle") -g.send("draw(unitsquare)") -g.fill("unitsquare, blue") -g.clip("unitcircle") -g.label("\"$O$\", (0,0), SW") - - -File: asymptote.info, Node: GUI, Next: PostScript to Asymptote, Prev: Interactive mode, Up: Top - -10 Graphical User Interface -*************************** - -In the event that adjustments to the final figure are required, the -preliminary Graphical User Interface (GUI) `xasy' included with -`Asymptote' allows you to move graphical objects and draw new ones. -The modified figure can then be saved as a normal `Asymptote' file. - -* Menu: - -* GUI Installation:: Installing `xasy' -* GUI Usage:: - - -File: asymptote.info, Node: GUI Installation, Next: GUI Usage, Up: GUI - -10.1 GUI Installation -===================== - -As `xasy' is written in the interactive scripting language `Python/TK', -it requires `Python' (`http://www.python.org'), the `Python Imaging -Library' (`http://www.pythonware.com/products/pil/'), and the `tkinter' -package (included with `Python' under `Microsoft Windows') be -installed. `Fedora Linux' users can either install `tkinter' with the -commands -yum install tkinter -yum install tk-devel - or manually install the `tkinter', `tix', `tk', and `tk-devel' -packages. - - Pictures are deconstructed into the PNG image format, which supports -full alpha channel transparency. Under `Microsoft Windows', this -requires `Python 2.6.2' and the `Python Imaging Library': - - `http://www.python.org/ftp/python/2.6.2/python-2.6.2.msi' - - `http://effbot.org/downloads/PIL-1.1.7b1.win32-py2.6.exe'. - On `UNIX' systems, place -`http://effbot.org/downloads/Imaging-1.1.7b1.tar.gz' in the `Asymptote' -source directory, and type (as the root user): -tar -zxf Imaging-1.1.7b1.tar.gz -cd Imaging-1.1.7b1 -python setup.py install - - Alternatively, `xasy' can deconstruct pictures into the GIF image -format (not recommended as this is very slow), using white as the -transparent color. This requires the lines -import settings; -xformat="gif"; - in the `Asymptote' configuration file (*note configuration file::), -along with the `ImageMagick' (*note convert::) program. - - -File: asymptote.info, Node: GUI Usage, Prev: GUI Installation, Up: GUI - -10.2 GUI Usage -============== - -A wheel mouse is convenient for raising and lowering objects within -`xasy', to expose the object to be moved. If a wheel mouse is not -available, mouse `Button-2' can be used to repeatedly lower an object -instead. When run from the command line, `xasy' accepts a command line -option `-x n', which sets the initial magnification to `n'. - - Deconstruction of compound objects (such as arrows) can be prevented -by enclosing them within the commands -void begingroup(picture pic=currentpicture); -void endgroup(picture pic=currentpicture); - By default, the elements of a picture or frame will be grouped -together on adding them to a picture. However, the elements of a frame -added to another frame are not grouped together by default: their -elements will be individually deconstructed (*note add::). - - -File: asymptote.info, Node: PostScript to Asymptote, Next: Help, Prev: GUI, Up: Top - -11 `PostScript' to `Asymptote' -****************************** - -The excellent `PostScript' editor `pstoedit' (version 3.45 or later; -available from `http://pstoedit.net') includes an `Asymptote' backend. -Unlike virtually all other `pstoedit' backends, this driver includes -native clipping, even-odd fill rule, `PostScript' subpath, and full -image support. - - For full functionality, the patch `pstoedit-3.45asy.patch' in the -`patches' directory should be applied. On `UNIX' systems, as the root -user, place - - `http://prdownloads.sourceforge.net/pstoedit/pstoedit-3.45.tar.gz' - in the `Asymptote' source directory, and type: - -tar -zxf pstoedit-3.45.tar.gz -cd pstoedit-3.45 -patch -p1 < ../patches/pstoedit-3.45asy.patch -autoconf -./configure --prefix=/usr -make install - -Then try: - -`asy -V /usr/local/share/doc/asymptote/examples/venn.asy' -pstoedit -f asy venn.eps test.asy -asy -V test - -If the line widths aren't quite correct, try giving `pstoedit' the -`-dis' option. If the fonts aren't typeset correctly, try giving -`pstoedit' the `-dt' option. - - -File: asymptote.info, Node: Help, Next: Debugger, Prev: PostScript to Asymptote, Up: Top - -12 Help -******* - -A list of frequently asked questions (FAQ) is maintained at - - `http://asymptote.sourceforge.net/FAQ' - Questions on installing and using `Asymptote' that are not addressed -in the FAQ should be sent to the `Asymptote' forum: - - `http://sourceforge.net/forum/forum.php?forum_id=409349' - Including an example that illustrates what you are trying to do will -help you get useful feedback. `LaTeX' problems can often be diagnosed -with the `-vv' or `-vvv' command-line options. Contributions in the -form of patches or `Asymptote' modules can be posted here: - - `http://sourceforge.net/tracker/?atid=685685&group_id=120000' - To receive announcements of upcoming releases, please subscribe to -`Asymptote' at - - `http://freshmeat.net/projects/asy' - If you find a bug in `Asymptote', please check (if possible) whether -the bug is still present in the latest `Subversion' developmental code -(*note Subversion::) before submitting a bug report. New bugs can be -submitted using the Bug Tracking System at - - `http://sourceforge.net/projects/asymptote' - To see if the bug has already been fixed, check bugs with Status -`Closed' and recent lines in - - `http://asymptote.sourceforge.net/ChangeLog' - `Asymptote' can be configured with the optional GNU library -`libsigsegv', available from `http://libsigsegv.sourceforge.net', which -allows one to distinguish user-generated `Asymptote' stack overflows -(*note stack overflow::) from true segmentation faults (due to internal -C++ programming errors; please submit the `Asymptote' code that -generates such segmentation faults along with your bug report). - - -File: asymptote.info, Node: Debugger, Next: Credits, Prev: Help, Up: Top - -13 Debugger -*********** - -Asymptote now includes a line-based (as opposed to code-based) debugger -that can assist the user in following flow control. To set a break -point in file `file' at line `line', use the command - -void stop(string file, int line, code s=quote{}); - The optional argument `s' may be used to conditionally set the variable -`ignore' in `plain_debugger.asy' to `true'. For example, the first 10 -instances of this breakpoint will be ignored (the variable `int -count=0' is defined in `plain_debugger.asy'): -stop("test",2,quote{ignore=(++count <= 10);}); - - To set a break point in file `file' at the first line containing the -string `text', use - -void stop(string file, string text, code s=quote{}); - To list all breakpoints, use: -void breakpoints(); - To clear a breakpoint, use: -void clear(string file, int line); - To clear all breakpoints, use: -void clear(); - - The following commands may be entered at the debugging prompt: - -``h'' - help; - -``c'' - continue execution; - -``i'' - step to the next instruction; - -``s'' - step to the next executable line; - -``n'' - step to the next executable line in the current file; - -``f'' - step to the next file; - -``r'' - return to the file associated with the most recent breakpoint; - -``t'' - toggle tracing (`-vvvvv') mode; - -``q'' - quit debugging and end execution; - -``x'' - exit the debugger and run to completion. - - Arbitrary `Asymptote' code may also be entered at the debugging -prompt; however, since the debugger is implemented with `eval', -currently only top-level (global) variables can be displayed or -modified. - - The debugging prompt may be entered manually with the call -void breakpoint(code s=quote{}); - - -File: asymptote.info, Node: Credits, Next: Index, Prev: Debugger, Up: Top - -14 Acknowledgments -****************** - -Financial support for the development of `Asymptote' was generously -provided by the Natural Sciences and Engineering Research Council of -Canada, the Pacific Institute for Mathematical Sciences, and the -University of Alberta Faculty of Science. - - We also would like to acknowledge the previous work of John D. Hobby, -author of the program `MetaPost' that inspired the development of -`Asymptote', and Donald E. Knuth, author of TeX and `MetaFont' (on -which `MetaPost' is based). - - The authors of `Asymptote' are Andy Hammerlindl, John Bowman, and -Tom Prince. Sean Healy designed the `Asymptote' logo. Other -contributors include Radoslav Marinov, Orest Shardt, Chris Savage, -Philippe Ivaldi, Olivier Guibe', Jacques Pienaar, Mark Henning, Steve -Melenchuk, Martin Wiebusch, and Stefan Knorr. - - -File: asymptote.info, Node: Index, Prev: Credits, Up: Top - -Index -***** - - -* Menu: - -* !: Arithmetic & logical. - (line 68) -* != <1>: Arithmetic & logical. - (line 38) -* !=: Structures. (line 54) -* %: Arithmetic & logical. - (line 23) -* %=: Self & prefix operators. - (line 6) -* & <1>: Arithmetic & logical. - (line 56) -* &: Tutorial. (line 192) -* &&: Arithmetic & logical. - (line 53) -* * <1>: Arithmetic & logical. - (line 17) -* *: Pens. (line 15) -* **: Arithmetic & logical. - (line 31) -* *=: Self & prefix operators. - (line 6) -* + <1>: Arithmetic & logical. - (line 13) -* +: Pens. (line 15) -* ++: Self & prefix operators. - (line 6) -* +=: Self & prefix operators. - (line 6) -* -: Arithmetic & logical. - (line 14) -* -- <1>: Self & prefix operators. - (line 6) -* --: Tutorial. (line 109) -* ---: Tutorial. (line 192) -* -=: Self & prefix operators. - (line 6) -* -c: Options. (line 154) -* -l: Options. (line 173) -* -u: Options. (line 164) -* -V <1>: Tutorial. (line 41) -* -V: Configuring. (line 6) -* ..: Tutorial. (line 109) -* .asy: Search paths. (line 13) -* /: Arithmetic & logical. - (line 20) -* /=: Self & prefix operators. - (line 6) -* 2D graphs: graph. (line 6) -* 3D graphs: graph3. (line 6) -* 3D grids: grid3. (line 6) -* 3D rendering: Compiling from UNIX source. - (line 16) -* :: Arithmetic & logical. - (line 73) -* ::: Tutorial. (line 176) -* <: Arithmetic & logical. - (line 41) -* <=: Arithmetic & logical. - (line 44) -* == <1>: Arithmetic & logical. - (line 37) -* ==: Structures. (line 54) -* >: Arithmetic & logical. - (line 50) -* >=: Arithmetic & logical. - (line 47) -* ?: Arithmetic & logical. - (line 73) -* ^: Arithmetic & logical. - (line 28) -* ^=: Self & prefix operators. - (line 6) -* ^^: Tutorial. (line 197) -* a4: Configuring. (line 62) -* abort: Data types. (line 321) -* abs <1>: Mathematical functions. - (line 35) -* abs: Data types. (line 60) -* accel <1>: three. (line 442) -* accel: Paths and guides. (line 110) -* access: Import. (line 6) -* acknowledgments: Credits. (line 6) -* aCos: Mathematical functions. - (line 20) -* acos: Mathematical functions. - (line 6) -* acosh: Mathematical functions. - (line 6) -* add: Frames and pictures. (line 192) -* Ai: Mathematical functions. - (line 48) -* Ai_deriv: Mathematical functions. - (line 48) -* Airy: Mathematical functions. - (line 48) -* alias <1>: Arrays. (line 187) -* alias: Structures. (line 54) -* align: Options. (line 148) -* Align: label. (line 12) -* all: Arrays. (line 331) -* Allow: Pens. (line 323) -* AND: Arithmetic & logical. - (line 80) -* and: Tutorial. (line 165) -* angle: Data types. (line 68) -* animate <1>: animation. (line 12) -* animate <2>: Files. (line 148) -* animate: Configuring. (line 68) -* animation: animation. (line 6) -* annotate: annotate. (line 6) -* antialias <1>: Options. (line 128) -* antialias: three. (line 189) -* antialiasing: Compiling from UNIX source. - (line 16) -* append <1>: Arrays. (line 39) -* append: Files. (line 36) -* arc: three. (line 254) -* Arc: Paths and guides. (line 32) -* arc: Paths and guides. (line 22) -* ArcArrow: draw. (line 26) -* ArcArrow3: three. (line 485) -* ArcArrows: draw. (line 26) -* ArcArrows3: three. (line 485) -* arclength <1>: three. (line 442) -* arclength: Paths and guides. (line 137) -* arctime <1>: three. (line 442) -* arctime: Paths and guides. (line 141) -* arguments: Default arguments. (line 6) -* arithmetic operators: Arithmetic & logical. - (line 6) -* array: Arrays. (line 125) -* array iteration: Programming. (line 33) -* arrays: Arrays. (line 6) -* arrow: label. (line 72) -* Arrow: draw. (line 26) -* arrow: Drawing commands. (line 31) -* arrow keys: Tutorial. (line 21) -* Arrow3: three. (line 485) -* Arrows: draw. (line 26) -* Arrows3: three. (line 485) -* as: Import. (line 70) -* aSin: Mathematical functions. - (line 20) -* asin: Mathematical functions. - (line 6) -* asinh: Mathematical functions. - (line 6) -* Aspect: Frames and pictures. (line 54) -* assignment: Programming. (line 8) -* asy: Import. (line 105) -* asy-mode: Editing modes. (line 6) -* asy.vim: Editing modes. (line 33) -* asymptote.sty: LaTeX usage. (line 6) -* asymptote.xml: Editing modes. (line 49) -* ASYMPTOTE_CONFIG: Options. (line 101) -* aTan: Mathematical functions. - (line 20) -* atan: Mathematical functions. - (line 6) -* atan2: Mathematical functions. - (line 6) -* atanh: Mathematical functions. - (line 6) -* atleast: Tutorial. (line 165) -* attach <1>: graph. (line 405) -* attach: LaTeX usage. (line 32) -* autoadjust: three. (line 324) -* autoimport: Options. (line 97) -* automatic scaling: graph. (line 672) -* axialshade: fill. (line 43) -* axis <1>: graph3. (line 66) -* axis: graph. (line 870) -* azimuth: Data types. (line 124) -* babel: babel. (line 6) -* background color: Frames and pictures. (line 164) -* BackView: three. (line 349) -* Bar: draw. (line 19) -* Bar3: three. (line 485) -* Bars: draw. (line 19) -* Bars3: three. (line 485) -* barsize: draw. (line 19) -* base modules: Base modules. (line 6) -* basealign: Pens. (line 164) -* baseline: label. (line 92) -* batch mode: Tutorial. (line 30) -* beep: Data types. (line 335) -* BeginArcArrow: draw. (line 26) -* BeginArcArrow3: three. (line 485) -* BeginArrow: draw. (line 26) -* BeginArrow3: three. (line 485) -* BeginBar: draw. (line 19) -* BeginBar3: three. (line 485) -* BeginDotMargin: draw. (line 42) -* BeginDotMargin3: three. (line 501) -* BeginMargin: draw. (line 42) -* BeginMargin3: three. (line 501) -* BeginPenMargin: draw. (line 42) -* BeginPenMargin2: three. (line 501) -* BeginPenMargin3: three. (line 501) -* BeginPoint: label. (line 57) -* Bessel: Mathematical functions. - (line 48) -* bevel: flowchart. (line 68) -* beveljoin: Pens. (line 134) -* bezulate: three. (line 98) -* Bi: Mathematical functions. - (line 48) -* Bi_deriv: Mathematical functions. - (line 48) -* binary format: Files. (line 71) -* binary operators: Arithmetic & logical. - (line 6) -* binarytree: binarytree. (line 6) -* binput: Files. (line 71) -* Blank: draw. (line 26) -* block.bottom: flowchart. (line 19) -* block.bottomleft: flowchart. (line 19) -* block.bottomright: flowchart. (line 19) -* block.center: flowchart. (line 26) -* block.draw: flowchart. (line 31) -* block.left: flowchart. (line 19) -* block.position: flowchart. (line 24) -* block.right: flowchart. (line 19) -* block.top: flowchart. (line 19) -* block.topleft: flowchart. (line 19) -* block.topright: flowchart. (line 19) -* bool: Data types. (line 14) -* bool3: Data types. (line 23) -* boolean operators: Arithmetic & logical. - (line 6) -* Bottom: graph. (line 128) -* BottomTop: graph. (line 134) -* BottomView: three. (line 349) -* bounding box: Frames and pictures. (line 164) -* Bounds: graph3. (line 20) -* boutput: Files. (line 71) -* box <1>: three. (line 276) -* box: Frames and pictures. (line 22) -* bp: Tutorial. (line 17) -* break: Programming. (line 29) -* breakpoints: Debugger. (line 21) -* brick: Pens. (line 247) -* broken axis: graph. (line 773) -* bug reports: Help. (line 23) -* buildcycle: Paths and guides. (line 251) -* Button-1: GUI. (line 6) -* Button-2: GUI. (line 6) -* BWRainbow: palette. (line 15) -* BWRainbow2: palette. (line 18) -* C string: Data types. (line 189) -* CAD: CAD. (line 6) -* calculateTransform: Frames and pictures. (line 107) -* casts: Casts. (line 6) -* cbrt: Mathematical functions. - (line 6) -* cd: Files. (line 24) -* ceil: Mathematical functions. - (line 26) -* center: three. (line 309) -* Center: label. (line 62) -* checker: Pens. (line 247) -* Chinese: unicode. (line 12) -* choose: Mathematical functions. - (line 39) -* Ci: Mathematical functions. - (line 48) -* circle <1>: flowchart. (line 57) -* circle: three. (line 250) -* Circle: Paths and guides. (line 17) -* circle: Paths and guides. (line 10) -* circlebarframe: markers. (line 18) -* CJK: unicode. (line 12) -* clear <1>: Debugger. (line 23) -* clear: Files. (line 86) -* clip: fill. (line 110) -* cm: Tutorial. (line 63) -* cmyk: Pens. (line 34) -* colatitude: Data types. (line 129) -* color: Pens. (line 23) -* coloredNodes: tube. (line 25) -* coloredpath: tube. (line 18) -* coloredSegments: tube. (line 25) -* colorless: Pens. (line 54) -* colors: Pens. (line 51) -* comma: Files. (line 59) -* comma-separated-value mode: Arrays. (line 362) -* command-line options <1>: Options. (line 6) -* command-line options: Configuring. (line 82) -* comment character: Files. (line 15) -* compass directions: Tutorial. (line 94) -* Compiling from UNIX source: Compiling from UNIX source. - (line 6) -* complement: Arrays. (line 153) -* concat: Arrays. (line 183) -* conditional <1>: Arithmetic & logical. - (line 73) -* conditional: Programming. (line 8) -* config: Options. (line 101) -* configuration file: Configuring. (line 21) -* configuring: Configuring. (line 6) -* conj: Data types. (line 57) -* constructors: Structures. (line 95) -* context: Options. (line 128) -* continue <1>: Debugger. (line 31) -* continue: Programming. (line 29) -* contour: contour. (line 9) -* contour3: contour3. (line 6) -* controls <1>: three. (line 6) -* controls: Tutorial. (line 154) -* controlSpecifier: Paths and guides. (line 375) -* convert <1>: Options. (line 128) -* convert <2>: animation. (line 6) -* convert <3>: Files. (line 148) -* convert: Configuring. (line 68) -* convertOptions: Options. (line 116) -* Coons shading: fill. (line 74) -* copy: Arrays. (line 174) -* Cos: Mathematical functions. - (line 20) -* cos: Mathematical functions. - (line 6) -* cosh: Mathematical functions. - (line 6) -* cputime: Structures. (line 177) -* crop: graph. (line 626) -* cropping graphs: graph. (line 626) -* cross <1>: graph. (line 474) -* cross: Data types. (line 167) -* crossframe: markers. (line 23) -* crosshatch: Pens. (line 263) -* csv: Arrays. (line 362) -* cubicroots: Arrays. (line 320) -* curl <1>: three. (line 6) -* curl: Tutorial. (line 172) -* curlSpecifier: Paths and guides. (line 387) -* currentpen: Pens. (line 6) -* currentprojection: three. (line 346) -* curve: slopefield. (line 20) -* custom axis types: graph. (line 138) -* custom mark routine: graph. (line 566) -* custom tick locations: graph. (line 241) -* cut: Paths and guides. (line 233) -* cycle <1>: three. (line 6) -* cycle: Tutorial. (line 46) -* cyclic <1>: three. (line 442) -* cyclic <2>: Arrays. (line 39) -* cyclic: Paths and guides. (line 75) -* cyclicflag: Arrays. (line 39) -* Cyrillic: unicode. (line 7) -* dashdotted: Pens. (line 92) -* dashed: Pens. (line 92) -* data types: Data types. (line 6) -* date: Data types. (line 291) -* Debian: UNIX binary distributions. - (line 19) -* debugger: Debugger. (line 6) -* declaration: Programming. (line 8) -* deconstruct: GUI Usage. (line 6) -* default arguments: Default arguments. (line 6) -* defaultformat: graph. (line 169) -* DefaultHead: draw. (line 26) -* DefaultHead3: three. (line 485) -* defaultpen: Pens. (line 46) -* deferred drawing: simplex. (line 6) -* Degrees: Mathematical functions. - (line 17) -* degrees <1>: Mathematical functions. - (line 17) -* degrees: Data types. (line 73) -* delete <1>: Arrays. (line 39) -* delete: Files. (line 143) -* description: Description. (line 6) -* diagonal: Arrays. (line 305) -* diamond: flowchart. (line 50) -* dimension: Arrays. (line 368) -* dir <1>: three. (line 442) -* dir <2>: Paths and guides. (line 99) -* dir <3>: Data types. (line 85) -* dir: Search paths. (line 10) -* direction specifier: Tutorial. (line 115) -* directory: Files. (line 24) -* dirSpecifier: Paths and guides. (line 369) -* dirtime: Paths and guides. (line 147) -* display: Configuring. (line 68) -* do: Programming. (line 29) -* dot <1>: Data types. (line 98) -* dot: draw. (line 83) -* DotMargin: draw. (line 42) -* DotMargin3: three. (line 501) -* DotMargins: draw. (line 42) -* DotMargins3: three. (line 501) -* dotted: Pens. (line 92) -* double: Files. (line 71) -* double deferred drawing: three. (line 231) -* Draw: Frames and pictures. (line 147) -* draw: draw. (line 110) -* Draw: draw. (line 26) -* draw: Drawing commands. (line 31) -* drawing commands: Drawing commands. (line 6) -* drawline: math. (line 9) -* drawtree: drawtree. (line 9) -* dvips: Configuring. (line 68) -* dvipsOptions: Options. (line 116) -* E <1>: Mathematical functions. - (line 48) -* E: Tutorial. (line 94) -* Editing modes: Editing modes. (line 6) -* Ei: Mathematical functions. - (line 48) -* ellipse: Frames and pictures. (line 22) -* elliptic functions: Mathematical functions. - (line 48) -* else: Programming. (line 8) -* emacs: Editing modes. (line 6) -* embed: embed. (line 6) -* empty: Frames and pictures. (line 7) -* EndArcArrow: draw. (line 26) -* EndArcArrow3: three. (line 485) -* EndArrow: draw. (line 26) -* EndArrow3: three. (line 485) -* EndBar: draw. (line 19) -* EndBar3: three. (line 485) -* EndDotMargin: draw. (line 42) -* EndDotMargin3: three. (line 501) -* endl: Files. (line 59) -* EndMargin: draw. (line 42) -* EndMargin3: three. (line 501) -* EndPenMargin: draw. (line 42) -* EndPenMargin2: three. (line 501) -* EndPenMargin3: three. (line 501) -* EndPoint: label. (line 57) -* envelope: Frames and pictures. (line 22) -* environment variables: Configuring. (line 86) -* eof <1>: Arrays. (line 346) -* eof: Files. (line 86) -* eol <1>: Arrays. (line 346) -* eol: Files. (line 86) -* EPS: label. (line 80) -* erase <1>: Frames and pictures. (line 7) -* erase: Data types. (line 239) -* erf: Mathematical functions. - (line 6) -* erfc: Mathematical functions. - (line 6) -* error: Files. (line 15) -* errorbars: graph. (line 474) -* eval: Import. (line 101) -* evenodd <1>: Pens. (line 148) -* evenodd: Tutorial. (line 211) -* exit <1>: Debugger. (line 57) -* exit <2>: Interactive mode. (line 37) -* exit: Data types. (line 326) -* exp: Mathematical functions. - (line 6) -* expi: Data types. (line 81) -* explicit: Casts. (line 6) -* explicit casts: Casts. (line 22) -* expm1: Mathematical functions. - (line 6) -* exponential integral: Mathematical functions. - (line 48) -* extendcap: Pens. (line 125) -* extension <1>: MetaPost. (line 10) -* extension: Paths and guides. (line 228) -* external: embed. (line 28) -* extrude: three. (line 436) -* F: Mathematical functions. - (line 48) -* fabs: Mathematical functions. - (line 6) -* face: three. (line 520) -* factorial: Mathematical functions. - (line 39) -* Fedora: UNIX binary distributions. - (line 15) -* feynman: feynman. (line 6) -* fft: Arrays. (line 252) -* FFTW: Compiling from UNIX source. - (line 58) -* file <1>: Debugger. (line 45) -* file: Files. (line 6) -* Fill: Frames and pictures. (line 133) -* fill <1>: fill. (line 17) -* fill: draw. (line 116) -* Fill: draw. (line 26) -* FillDraw: Frames and pictures. (line 123) -* filldraw: fill. (line 11) -* FillDraw: draw. (line 26) -* filloutside: fill. (line 27) -* fillrule: Pens. (line 148) -* find <1>: Arrays. (line 162) -* find: Data types. (line 224) -* firstcut: Paths and guides. (line 243) -* fit: Frames and pictures. (line 103) -* fix-cm: Pens. (line 174) -* fixedscaling: Frames and pictures. (line 74) -* floor: Mathematical functions. - (line 26) -* flowchart: flowchart. (line 6) -* flush: Files. (line 59) -* fmod: Mathematical functions. - (line 6) -* font: Pens. (line 188) -* font command: Pens. (line 188) -* fontcommand: Pens. (line 203) -* fontsize: Pens. (line 174) -* for: Programming. (line 8) -* format <1>: Options. (line 128) -* format: Data types. (line 266) -* forum: Help. (line 6) -* frame: Frames and pictures. (line 7) -* freeglut: Compiling from UNIX source. - (line 16) -* from: Import. (line 17) -* FrontView: three. (line 349) -* function declarations: Functions. (line 67) -* function shading: fill. (line 95) -* Function shading: fill. (line 95) -* functions <1>: Mathematical functions. - (line 6) -* functions: Functions. (line 6) -* functionshade: fill. (line 95) -* gamma: Mathematical functions. - (line 6) -* Gaussrand: Mathematical functions. - (line 39) -* geometry: geometry. (line 6) -* getc: Files. (line 30) -* getpair: Files. (line 111) -* getreal: Files. (line 111) -* getstring: Files. (line 111) -* gettriple: Files. (line 111) -* glOptions <1>: Options. (line 116) -* glOptions: three. (line 189) -* GNU Scientific Library: Mathematical functions. - (line 48) -* gouraudshade: fill. (line 58) -* Gradient: palette. (line 25) -* gradient shading: fill. (line 32) -* graph: graph. (line 6) -* graph3: graph3. (line 6) -* graphic: label. (line 80) -* graphical user interface: GUI. (line 6) -* gray: Pens. (line 25) -* Grayscale: palette. (line 9) -* grayscale: Pens. (line 25) -* grid <1>: graph. (line 724) -* grid: Pens. (line 247) -* grid3: grid3. (line 6) -* gs: Configuring. (line 6) -* gsl: Mathematical functions. - (line 48) -* GSL: Compiling from UNIX source. - (line 58) -* gsOptions: Options. (line 116) -* GUI: GUI. (line 6) -* GUI installation: GUI Installation. (line 6) -* GUI usage: GUI Usage. (line 6) -* guide: Paths and guides. (line 296) -* guide3: three. (line 6) -* hatch: Pens. (line 263) -* height: LaTeX usage. (line 32) -* help <1>: Debugger. (line 30) -* help <2>: Help. (line 6) -* help: Interactive mode. (line 25) -* Hermite: graph. (line 37) -* Hermite(splinetype splinetype: graph. (line 37) -* hex: Data types. (line 279) -* hexidecimal <1>: Pens. (line 59) -* hexidecimal: Data types. (line 279) -* hidden surface removal: three. (line 520) -* histogram: Mathematical functions. - (line 39) -* history: Files. (line 136) -* historylines: Interactive mode. (line 42) -* HookHead: draw. (line 26) -* HookHead3: three. (line 485) -* Horizontal: flowchart. (line 74) -* hypot: Mathematical functions. - (line 6) -* I: Mathematical functions. - (line 48) -* i_scaled: Mathematical functions. - (line 48) -* iconic: three. (line 189) -* identity <1>: Arrays. (line 302) -* identity <2>: Mathematical functions. - (line 6) -* identity: Transforms. (line 24) -* if: Programming. (line 8) -* IgnoreAspect: Frames and pictures. (line 58) -* image: palette. (line 34) -* ImageMagick <1>: Options. (line 128) -* ImageMagick <2>: animation. (line 6) -* ImageMagick: Configuring. (line 68) -* implicit casts: Casts. (line 6) -* implicit linear solver: MetaPost. (line 10) -* implicit scaling: Implicit scaling. (line 6) -* import: Import. (line 48) -* inches: Tutorial. (line 63) -* including images: label. (line 80) -* inheritance: Structures. (line 189) -* initialized: Arrays. (line 39) -* initializers: Variable initializers. - (line 6) -* InOutTicks: graph3. (line 34) -* input <1>: Interactive mode. (line 31) -* input: Files. (line 11) -* insert <1>: Arrays. (line 39) -* insert: Data types. (line 235) -* inside: Paths and guides. (line 275) -* inst: Debugger. (line 36) -* installation: Installation. (line 6) -* int: Data types. (line 28) -* integer division: Arithmetic & logical. - (line 6) -* interactive mode: Interactive mode. (line 6) -* interior: Paths and guides. (line 271) -* international characters: unicode. (line 6) -* interp: Arithmetic & logical. - (line 76) -* interpolate: interpolate. (line 6) -* intersect <1>: three. (line 442) -* intersect <2>: math. (line 13) -* intersect: Paths and guides. (line 176) -* intersectionpoint <1>: three. (line 442) -* intersectionpoint <2>: math. (line 17) -* intersectionpoint: Paths and guides. (line 220) -* intersectionpoints <1>: three. (line 442) -* intersectionpoints: Paths and guides. (line 224) -* intersections <1>: three. (line 442) -* intersections: Paths and guides. (line 187) -* InTicks: graph3. (line 34) -* intMax: Data types. (line 28) -* intMin: Data types. (line 28) -* inverse <1>: Arrays. (line 308) -* inverse: Transforms. (line 16) -* invert: three. (line 375) -* invisible: Pens. (line 39) -* J: Mathematical functions. - (line 6) -* Japanese: unicode. (line 12) -* K: Mathematical functions. - (line 48) -* k_scaled: Mathematical functions. - (line 48) -* Kate: Editing modes. (line 49) -* KDE editor: Editing modes. (line 49) -* keyboard bindings:: three. (line 158) -* keys: Arrays. (line 39) -* keywords: Named arguments. (line 6) -* Korean: unicode. (line 12) -* Label: graph. (line 332) -* label: clip. (line 16) -* Label: draw. (line 98) -* labelpath: labelpath. (line 6) -* labelpath3: labelpath3. (line 6) -* labelx: graph. (line 332) -* labely: graph. (line 332) -* Landscape: Frames and pictures. (line 95) -* lastcut: Paths and guides. (line 247) -* lasy-mode: Editing modes. (line 6) -* latex: Options. (line 128) -* LaTeX fonts: Pens. (line 188) -* LaTeX usage: LaTeX usage. (line 6) -* latin1: latin1. (line 6) -* latitude: Data types. (line 134) -* latticeshade: fill. (line 32) -* layer: Drawing commands. (line 16) -* leastsquares <1>: graph. (line 892) -* leastsquares: stats. (line 6) -* Left: graph. (line 274) -* LeftRight: graph. (line 280) -* LeftSide: label. (line 62) -* LeftTicks: graph. (line 155) -* LeftView: three. (line 349) -* legend <1>: graph. (line 421) -* legend <2>: draw. (line 64) -* legend: Drawing commands. (line 31) -* Legendre: Mathematical functions. - (line 48) -* length <1>: three. (line 442) -* length <2>: Arrays. (line 39) -* length <3>: Paths and guides. (line 66) -* length: Data types. (line 60) -* letter: Configuring. (line 62) -* libm routines: Mathematical functions. - (line 6) -* libsigsegv <1>: Help. (line 33) -* libsigsegv: Functions. (line 88) -* limits: graph. (line 626) -* line: Arrays. (line 346) -* line mode: Arrays. (line 346) -* Linear: graph. (line 672) -* linecap: Pens. (line 125) -* linejoin: Pens. (line 134) -* lineskip: Pens. (line 174) -* linewidth: Pens. (line 115) -* locale: Data types. (line 286) -* Log: graph. (line 672) -* log: Mathematical functions. - (line 6) -* log-log graph: graph. (line 703) -* log10: Mathematical functions. - (line 6) -* log1p: Mathematical functions. - (line 6) -* log2 graph: graph. (line 753) -* logarithmic graph: graph. (line 703) -* logical operators: Arithmetic & logical. - (line 6) -* longdashdotted: Pens. (line 92) -* longdashed: Pens. (line 92) -* longitude: Data types. (line 139) -* loop: Programming. (line 8) -* MacOS X binary distributions: MacOS X binary distributions. - (line 6) -* makepen: Pens. (line 296) -* map: Arrays. (line 144) -* Margin: draw. (line 42) -* Margin3: three. (line 501) -* margins: three. (line 237) -* Margins: draw. (line 42) -* Margins3: three. (line 501) -* mark: graph. (line 474) -* markangle: markers. (line 38) -* marker: graph. (line 474) -* markers: markers. (line 6) -* marknodes: graph. (line 474) -* markuniform: graph. (line 474) -* math: math. (line 6) -* mathematical functions: Mathematical functions. - (line 6) -* max <1>: three. (line 442) -* max <2>: Arrays. (line 231) -* max <3>: Frames and pictures. (line 7) -* max: Paths and guides. (line 260) -* maxbound: Data types. (line 104) -* maxtile: three. (line 189) -* maxtimes: Paths and guides. (line 215) -* maxviewport: three. (line 189) -* merge: animation. (line 6) -* MetaPost: MetaPost. (line 6) -* MetaPost ... : Tutorial. (line 176) -* MetaPost cutafter: Paths and guides. (line 248) -* MetaPost cutbefore: Paths and guides. (line 244) -* MetaPost pickup: Pens. (line 6) -* MetaPost whatever: MetaPost. (line 10) -* Microsoft Windows: Microsoft Windows. (line 6) -* MidArcArrow: draw. (line 26) -* MidArcArrow3: three. (line 485) -* MidArrow: draw. (line 26) -* MidArrow3: three. (line 485) -* midpoint: Paths and guides. (line 161) -* MidPoint: label. (line 57) -* min <1>: three. (line 442) -* min <2>: Arrays. (line 224) -* min <3>: Frames and pictures. (line 7) -* min: Paths and guides. (line 256) -* minbound: Data types. (line 101) -* minipage: label. (line 119) -* mintimes: Paths and guides. (line 210) -* miterjoin: Pens. (line 134) -* miterlimit: Pens. (line 143) -* mm: Tutorial. (line 63) -* mouse: GUI. (line 6) -* mouse bindings: three. (line 129) -* Move: Pens. (line 335) -* MoveQuiet: Pens. (line 341) -* multisample: three. (line 119) -* multisampling: Compiling from UNIX source. - (line 16) -* N: Tutorial. (line 94) -* named arguments: Named arguments. (line 6) -* new <1>: Arrays. (line 112) -* new: Structures. (line 6) -* newframe: Frames and pictures. (line 7) -* newl: Files. (line 59) -* newton: Mathematical functions. - (line 65) -* next: Debugger. (line 42) -* NFSS: Pens. (line 188) -* nobasealign: Pens. (line 164) -* NoFill <1>: Frames and pictures. (line 141) -* NoFill: draw. (line 26) -* NoMargin: draw. (line 42) -* NoMargin3: three. (line 501) -* none: Files. (line 59) -* None: draw. (line 19) -* normal: three. (line 428) -* nosafe: Options. (line 144) -* NOT: Arithmetic & logical. - (line 80) -* NoTicks: graph. (line 155) -* NoTicks3: graph3. (line 34) -* null: Structures. (line 6) -* nullpen <1>: Frames and pictures. (line 127) -* nullpen: label. (line 14) -* NURBS: three. (line 327) -* O: three. (line 245) -* obj: obj. (line 9) -* oblique: three. (line 290) -* obliqueX: three. (line 298) -* obliqueY: three. (line 305) -* obliqueZ: three. (line 290) -* ode: ode. (line 9) -* offset: Options. (line 148) -* opacity: Pens. (line 218) -* open: Files. (line 11) -* OpenGL: three. (line 119) -* operator: User-defined operators. - (line 6) -* operator --: graph. (line 31) -* operator ..: graph. (line 34) -* operator cast: Casts. (line 31) -* operator ecast: Casts. (line 58) -* operator init <1>: Structures. (line 141) -* operator init: Variable initializers. - (line 6) -* operators: Operators. (line 6) -* options: Options. (line 6) -* OR: Arithmetic & logical. - (line 80) -* orientation: Frames and pictures. (line 95) -* orthographic: three. (line 309) -* outformat: three. (line 119) -* outprefix: Frames and pictures. (line 83) -* output <1>: Options. (line 128) -* output: Files. (line 36) -* OutTicks: graph3. (line 34) -* overloading functions: Functions. (line 44) -* overwrite: Pens. (line 320) -* P: Mathematical functions. - (line 48) -* pack: label. (line 102) -* packing: Rest arguments. (line 30) -* pair <1>: Data types. (line 41) -* pair: Tutorial. (line 17) -* pairs: Arrays. (line 248) -* paperheight: Configuring. (line 62) -* papertype: Configuring. (line 62) -* paperwidth: Configuring. (line 62) -* parametric surface: graph3. (line 100) -* parametrized curve: graph. (line 626) -* patch-dependent colors: three. (line 75) -* path <1>: flowchart. (line 74) -* path <2>: three. (line 43) -* path: Paths and guides. (line 7) -* path3: three. (line 6) -* path[]: Tutorial. (line 197) -* patterns <1>: patterns. (line 6) -* patterns: Pens. (line 234) -* pdflatex: Options. (line 128) -* pdfviewer: Configuring. (line 6) -* pdfviewerOptions: Options. (line 116) -* pen: Pens. (line 6) -* PenMargin: draw. (line 42) -* PenMargin2: three. (line 501) -* PenMargin3: three. (line 501) -* PenMargins: draw. (line 42) -* PenMargins2: three. (line 501) -* PenMargins3: three. (line 501) -* perpendicular: geometry. (line 6) -* perspective: three. (line 327) -* picture: Frames and pictures. (line 35) -* picture alignment: Frames and pictures. (line 205) -* piecewisestraight: Paths and guides. (line 82) -* Pl: Mathematical functions. - (line 48) -* plain: plain. (line 6) -* planar: three. (line 83) -* plane: three. (line 272) -* planeproject: three. (line 425) -* point <1>: three. (line 442) -* point: Paths and guides. (line 85) -* polar: Data types. (line 119) -* polargraph: graph. (line 90) -* polygon: graph. (line 474) -* pop: Arrays. (line 39) -* Portrait: Frames and pictures. (line 95) -* postcontrol <1>: three. (line 442) -* postcontrol: Paths and guides. (line 130) -* postfix operators: Self & prefix operators. - (line 19) -* postscript: Frames and pictures. (line 267) -* PostScript fonts: Pens. (line 206) -* PostScript subpath: Tutorial. (line 197) -* pow10: Mathematical functions. - (line 6) -* prc: three. (line 206) -* precision: Files. (line 86) -* precontrol <1>: three. (line 442) -* precontrol: Paths and guides. (line 123) -* prefix operators: Self & prefix operators. - (line 6) -* private: Structures. (line 6) -* programming: Programming. (line 6) -* pstoedit: PostScript to Asymptote. - (line 6) -* psviewer: Configuring. (line 6) -* psviewerOptions: Options. (line 116) -* pt: Tutorial. (line 63) -* public: Structures. (line 6) -* push: Arrays. (line 39) -* python: Configuring. (line 27) -* Python usage: Interactive mode. (line 58) -* quadraticroots: Arrays. (line 311) -* quarticroots: math. (line 22) -* quit <1>: Debugger. (line 54) -* quit: Interactive mode. (line 37) -* quote: Import. (line 119) -* quotient: Arithmetic & logical. - (line 6) -* RadialShade: Frames and pictures. (line 159) -* radialshade: fill. (line 49) -* radians: Mathematical functions. - (line 17) -* radius <1>: three. (line 442) -* radius: Paths and guides. (line 119) -* Rainbow: palette. (line 12) -* rand: Mathematical functions. - (line 39) -* randMax: Mathematical functions. - (line 39) -* read1: Arrays. (line 386) -* read2: Arrays. (line 386) -* read3: Arrays. (line 386) -* reading: Files. (line 11) -* reading string arrays: Arrays. (line 353) -* readline: Files. (line 128) -* real: Data types. (line 33) -* realDigits: Data types. (line 33) -* realEpsilon: Data types. (line 33) -* realMax: Data types. (line 33) -* realMin: Data types. (line 33) -* realmult: Data types. (line 95) -* rectangle: flowchart. (line 37) -* recursion: Functions. (line 88) -* reflect: Transforms. (line 51) -* Relative: label. (line 52) -* relpoint: Paths and guides. (line 157) -* reltime: Paths and guides. (line 153) -* remainder: Mathematical functions. - (line 6) -* rename: Files. (line 145) -* render <1>: Options. (line 128) -* render: three. (line 119) -* replace: Data types. (line 252) -* resetdefaultpen: Pens. (line 349) -* rest arguments: Rest arguments. (line 6) -* restore: Frames and pictures. (line 261) -* restricted: Structures. (line 6) -* return: Debugger. (line 48) -* reverse <1>: three. (line 442) -* reverse <2>: Arrays. (line 149) -* reverse <3>: Paths and guides. (line 164) -* reverse: Data types. (line 248) -* rewind: Files. (line 86) -* rfind: Data types. (line 229) -* rgb: Pens. (line 30) -* Riemann zeta function: Mathematical functions. - (line 48) -* Right: graph. (line 277) -* RightSide: label. (line 62) -* RightTicks: graph. (line 155) -* RightView: three. (line 349) -* Rotate: label. (line 37) -* Rotate(pair z): label. (line 40) -* round: Mathematical functions. - (line 26) -* roundcap: Pens. (line 125) -* roundedpath: roundedpath. (line 6) -* roundjoin: Pens. (line 134) -* roundrectangle: flowchart. (line 62) -* RPM: UNIX binary distributions. - (line 6) -* runtime imports: Import. (line 101) -* Russian: unicode. (line 7) -* S: Tutorial. (line 94) -* safe: Options. (line 144) -* save: Frames and pictures. (line 258) -* saveline: Files. (line 128) -* scale: three. (line 404) -* Scale: graph. (line 688) -* scale <1>: graph. (line 672) -* scale: Transforms. (line 39) -* Scale: label. (line 46) -* scale3: three. (line 401) -* scaled graph: graph. (line 653) -* scientific graph: graph. (line 386) -* scroll: Files. (line 102) -* search: Arrays. (line 167) -* search paths: Search paths. (line 6) -* Seascape: Frames and pictures. (line 100) -* secondary axis: graph. (line 803) -* secondaryX: graph. (line 803) -* secondaryY: graph. (line 803) -* seconds: Data types. (line 299) -* seek: Files. (line 86) -* seekeof: Files. (line 86) -* segmentation fault: Help. (line 33) -* self operators: Self & prefix operators. - (line 6) -* sequence: Arrays. (line 131) -* settings <1>: Options. (line 101) -* settings: Configuring. (line 21) -* sgn: Mathematical functions. - (line 26) -* shading: fill. (line 32) -* shift <1>: three. (line 389) -* shift: Transforms. (line 27) -* Shift: label. (line 34) -* shiftless: Transforms. (line 53) -* shipout: Frames and pictures. (line 83) -* showtarget: three. (line 309) -* Si: Mathematical functions. - (line 48) -* SimpleHead: draw. (line 26) -* simplex: simplex. (line 6) -* simpson: Mathematical functions. - (line 81) -* Sin: Mathematical functions. - (line 20) -* sin: Mathematical functions. - (line 6) -* single: Files. (line 71) -* sinh: Mathematical functions. - (line 6) -* size <1>: Options. (line 128) -* size <2>: three. (line 442) -* size <3>: Frames and pictures. (line 43) -* size: Paths and guides. (line 71) -* size3: three. (line 234) -* slant: Transforms. (line 45) -* Slant: label. (line 43) -* sleep: Data types. (line 329) -* slice: Paths and guides. (line 233) -* slices: Slices. (line 6) -* slide: slide. (line 6) -* slopefield: slopefield. (line 6) -* solid: Pens. (line 92) -* solids: solids. (line 9) -* solve: Arrays. (line 265) -* sort: Arrays. (line 190) -* Spline <1>: graph3. (line 100) -* Spline: graph. (line 34) -* split: Data types. (line 261) -* sqrt: Mathematical functions. - (line 6) -* squarecap: Pens. (line 125) -* srand: Mathematical functions. - (line 39) -* stack overflow <1>: Help. (line 33) -* stack overflow: Functions. (line 88) -* static: Static. (line 6) -* stats: stats. (line 6) -* stdin: Files. (line 46) -* stdout: Files. (line 46) -* step: Debugger. (line 39) -* stickframe: markers. (line 16) -* stop: Debugger. (line 10) -* straight: three. (line 442) -* Straight: graph. (line 31) -* straight: Paths and guides. (line 78) -* strftime: Data types. (line 291) -* string: Data types. (line 179) -* stroke: fill. (line 36) -* strokepath: Paths and guides. (line 290) -* strptime: Data types. (line 299) -* struct: Structures. (line 6) -* structures: Structures. (line 6) -* subpath <1>: three. (line 442) -* subpath: Paths and guides. (line 167) -* subpictures: Frames and pictures. (line 103) -* substr: Data types. (line 244) -* Subversion: Subversion. (line 6) -* sum: Arrays. (line 219) -* superpath: Tutorial. (line 197) -* Suppress: Pens. (line 327) -* SuppressQuiet: Pens. (line 331) -* surface <1>: graph3. (line 100) -* surface: three. (line 47) -* SVN: Subversion. (line 6) -* system <1>: Options. (line 144) -* system: Files. (line 153) -* syzygy: syzygy. (line 6) -* tab: Files. (line 59) -* tab completion: Tutorial. (line 21) -* Tan: Mathematical functions. - (line 20) -* tan: Mathematical functions. - (line 6) -* tanh: Mathematical functions. - (line 6) -* target: three. (line 309) -* tell: Files. (line 86) -* tension <1>: three. (line 6) -* tension: Tutorial. (line 165) -* tensionSpecifier: Paths and guides. (line 381) -* tensor product shading: fill. (line 74) -* tensorshade: fill. (line 74) -* tex <1>: Options. (line 128) -* tex: Frames and pictures. (line 274) -* TeX fonts: Pens. (line 197) -* TeX string: Data types. (line 179) -* texcommand: Configuring. (line 68) -* texdvicommand: Configuring. (line 68) -* TeXHead: draw. (line 26) -* TeXHead3: three. (line 485) -* texpath <1>: label. (line 116) -* texpath: Configuring. (line 68) -* texpreamble: Frames and pictures. (line 282) -* texreset: Frames and pictures. (line 285) -* textbook graph: graph. (line 361) -* tgz: UNIX binary distributions. - (line 6) -* thick: three. (line 104) -* thin: three. (line 104) -* this: Structures. (line 6) -* three: three. (line 6) -* tick: graph. (line 332) -* Ticks: graph. (line 155) -* ticks: graph. (line 155) -* tildeframe: markers. (line 26) -* tile: Pens. (line 247) -* tilings: Pens. (line 234) -* time: Data types. (line 291) -* times: Paths and guides. (line 202) -* Top: graph. (line 131) -* TopView: three. (line 349) -* trace: Debugger. (line 51) -* trailingzero: graph. (line 169) -* transform <1>: three. (line 416) -* transform: Transforms. (line 6) -* transform3: three. (line 385) -* transparency: Pens. (line 218) -* transpose: Arrays. (line 211) -* tree: tree. (line 9) -* trembling: trembling. (line 6) -* triangle: geometry. (line 6) -* triangulate: contour. (line 156) -* tridiagonal: Arrays. (line 268) -* trigonometric integrals: Mathematical functions. - (line 48) -* triple: Data types. (line 108) -* TrueMargin: draw. (line 42) -* TrueMargin3: three. (line 501) -* tube <1>: tube. (line 6) -* tube: three. (line 104) -* tutorial: Tutorial. (line 6) -* typedef <1>: Functions. (line 36) -* typedef: Data types. (line 339) -* undefined: Paths and guides. (line 264) -* UnFill: Frames and pictures. (line 152) -* unfill: fill. (line 105) -* UnFill: draw. (line 26) -* unicode: unicode. (line 6) -* uniform: Arrays. (line 158) -* Uninstall: Uninstall. (line 6) -* unit: Data types. (line 78) -* unitbox <1>: three. (line 278) -* unitbox: Tutorial. (line 218) -* unitcircle <1>: three. (line 245) -* unitcircle: Tutorial. (line 110) -* unitrand: Mathematical functions. - (line 39) -* unitsize <1>: Frames and pictures. (line 64) -* unitsize: Tutorial. (line 73) -* UNIX binary distributions: UNIX binary distributions. - (line 6) -* unpacking: Rest arguments. (line 39) -* unravel: Import. (line 31) -* up: three. (line 309) -* update: Files. (line 36) -* UpsideDown: Frames and pictures. (line 95) -* usepackage: Frames and pictures. (line 287) -* user coordinates: Tutorial. (line 73) -* user-defined operators: User-defined operators. - (line 6) -* usleep: Data types. (line 332) -* variable initializers: Variable initializers. - (line 6) -* vectorfield: graph. (line 965) -* vectorfield3: graph3. (line 156) -* vectorization: Arrays. (line 325) -* verbatim: Frames and pictures. (line 267) -* vertex-dependent colors: three. (line 75) -* Vertical: flowchart. (line 74) -* viewportheight: LaTeX usage. (line 32) -* viewportmargin: three. (line 237) -* viewportsize: three. (line 237) -* viewportwidth: LaTeX usage. (line 32) -* views: three. (line 206) -* vim: Editing modes. (line 33) -* virtual functions: Structures. (line 189) -* void: Data types. (line 10) -* W: Tutorial. (line 94) -* whatever: Paths and guides. (line 228) -* Wheel: palette. (line 22) -* wheel mouse: GUI. (line 6) -* while: Programming. (line 29) -* white-space string delimiter mode: Arrays. (line 353) -* width: LaTeX usage. (line 32) -* windingnumber: Paths and guides. (line 264) -* word: Arrays. (line 353) -* write <1>: Arrays. (line 394) -* write: Files. (line 51) -* X: three. (line 245) -* xasy <1>: GUI. (line 6) -* xasy: Configuring. (line 68) -* xaxis3: graph3. (line 7) -* xelatex <1>: Options. (line 128) -* xelatex: embed. (line 10) -* xequals: graph. (line 284) -* XEquals: graph. (line 270) -* xinput: Files. (line 71) -* xlimits: graph. (line 626) -* XOR: Arithmetic & logical. - (line 80) -* xoutput: Files. (line 71) -* xpart: Data types. (line 89) -* xscale: Transforms. (line 33) -* xscale3: three. (line 392) -* xtick: graph. (line 332) -* XYEquals: graph3. (line 20) -* XYZero: graph3. (line 20) -* XZEquals: graph3. (line 20) -* XZero: graph. (line 265) -* XZZero: graph3. (line 20) -* Y <1>: three. (line 245) -* Y: Mathematical functions. - (line 6) -* yaxis3: graph3. (line 7) -* yequals: graph. (line 284) -* YEquals: graph. (line 124) -* ylimits: graph. (line 626) -* ypart: Data types. (line 92) -* yscale: Transforms. (line 36) -* yscale3: three. (line 395) -* ytick: graph. (line 332) -* YZEquals: graph3. (line 20) -* YZero: graph. (line 119) -* YZZero: graph3. (line 20) -* Z: three. (line 245) -* zaxis3: graph3. (line 7) -* zero_Ai: Mathematical functions. - (line 48) -* zero_Ai_deriv: Mathematical functions. - (line 48) -* zero_Bi: Mathematical functions. - (line 48) -* zero_Bi_deriv: Mathematical functions. - (line 48) -* zero_J: Mathematical functions. - (line 48) -* zerowinding: Pens. (line 148) -* zeta: Mathematical functions. - (line 48) -* zpart: Data types. (line 161) -* zscale3: three. 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