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@setfilename asy-faq.info
@settitle Asymptote Frequently Asked Questions
@documentencoding US-ASCII
@c %**end of header

@copying
Asymptote Frequently Asked Questions

@today{}
@end copying

@dircategory Languages
@direntry
* asymptote FAQ: (asy-faq).    Asymptote Frequently Asked Questions.
@end direntry

@node Top
@top Asymptote Frequently Asked Questions

This is the list of Frequently Asked Questions about Asymptote (asy).

@center @today{}

@menu
* About Asymptote::
* Questions about installation and setup::
* Questions about paths::
* Questions about labels::
* Questions about arrows::
* Questions about 2D graphs::
* Questions about programming::
* Questions about differences between Asymptote and MetaPost::
* Questions about output::
@end menu

@node About Asymptote
@chapter About Asymptote

@menu
* whatisasy:: Question 1.1. What is Asymptote?
* whereisasy:: Question 1.2. How do I obtain Asymptote?
* beforeasking:: Question 1.3. Where can I ask questions about Asymptote?
* whyasy:: Question 1.4. Why was the name Asymptote chosen?
* whycamp:: Question 1.5. In the internal Asymptote source code, what does the name camp refer to?
@end menu

@node whatisasy
@section What is Asymptote?

Asymptote is a vector graphics language designed for technical graphics, inspired by MetaPost but with IEEE floating-point numerics, native three-dimensional graphics, Grayscale/RGB/CMYK colourspaces, and a C++-like syntax. Unlike MetaPost, it natively supports multiple-segment paths (and hence regions other than simply connected ones), tiling patterns, Gouraud  shading, tensor patch shading, and PostScript images.

@node whereisasy
@section How do I obtain Asymptote?

Binary releases are available for Linux, MacOS X, and Microsoft Windows platforms, in addition to full source code, from the website @uref{https://asymptote.sourceforge.io/}.  Many Linux distributions (such as RedHat and Debian) now include an Asymptote package (check your distribution's documentation for further information about this).

@node beforeasking
@section Where can I ask questions about Asymptote?

If you have a question, please try to find an answer in this FAQ, in the  extensive Asymptote documentation at @uref{https://asymptote.sourceforge.io/doc/}, or search the forum: @uref{http://sourceforge.net/forum/forum.php?forum_id=409349}.

@node whyasy
@section Why was the name Asymptote chosen?

Well, it isn't the perfect graphics package, but we do think it is getting there asymptotically...

@node whycamp
@section In the internal Asymptote source code, what does the name @code{camp} refer to?

That was our original tentative name for this project, which stood for  "C's Answer to MetaPost" (the language that inspired Asymptote).  However, we eventually decided that the name @code{Asymptote} better emphasizes the mathematical and graphical nature of this language.

@node Questions about installation and setup
@chapter Questions about installation and setup

@menu
* osx:: Question 2.1. Is it possible to install Asymptote on Mac OS X?
* osxbadCPU:: Question 2.2. Why do I get the error Bad CPU type in executable on installing Asymptote from the MAC OS binary?
* brokenpdftex:: Question 2.3. What do I do if I get the error: Error: pdfetex (file pdftex.cfg): cannot open config file...texinfo.tex appears to be broken?
* brokentexinfo:: Question 2.4. What do I do if I get the error: ! Undefined control sequence. l.6 @@copying?
* latexintegration:: Question 2.5. Is it possible to integrate Asymptote into LaTeX?
* pdflatex:: Question 2.6. Is it possible to integrate Asymptote into latex or pdflatex?
* tkinterdepend:: Question 2.7. Do I need the tkinter package to install an Asymptote rpm binary?
* windir:: Question 2.8. What does the path %USERPROFILE%\.asy\config.asy mean?
* escapechar:: Question 2.9. Why do I get the error "string not terminated" when I try to set settings.dir="C:\asymptote\";?
* winglobal:: Question 2.10. How do I change environment variables in Microsoft Windows, for example, in order to change the default PostScript viewer?
* convert:: Question 2.11. Under Microsoft Windows XP, why do I get an error like "Invalid Parameter - 432x432"?
* miktex:: Question 2.12. Why does Asymptote freeze upon trying to draw a label with my MikTex installation under Microsoft Windows?
@end menu

@node osx
@section Is it possible to install Asymptote on Mac OS X?

It is easy to compile Asymptote directly from the source code at @uref{http://sourceforge.net/project/showfiles.php?group_id=120000} We recommend first upgrading to the latest GNU readline library, unless you don't care about interactive readline support (in which case configure will automatically detect and disable obsolete versions of the readline library).  Marius Schamschula also maintains a binary package for various MacOS X platforms  @uref{http://www.hmug.org/pub/MacOS_X/X/Applications/Publishing/asymptote}.

@node osxbadCPU
@section Why do I get the error @code{Bad CPU type in executable} on installing Asymptote from the MAC OS binary?

This means either that you have a binary distribution for another MAC architecture, or (according to Marius Schamschula) that you may have a missing library. The simplest solution is to compile Asymptote directly from the official source: @uref{http://sourceforge.net/project/showfiles.php?group_id=120000}.

@node brokenpdftex
@section What do I do if I get the error: @code{Error: pdfetex (file pdftex.cfg): cannot open config file...texinfo.tex appears to be broken}?

Simply put @uref{https://asymptote.sourceforge.io/asymptote.pdf} in the directory @code{doc} and repeat the command @code{make all}.  Or, if you don't want to build a local copy of the documentation, simply proceed with @code{make install-asy}.

@node brokentexinfo
@section What do I do if I get the error: @code{! Undefined control sequence. l.6 @@copying}?

Either upgrade your @code{texinfo} package or follow one of the easy work arounds in @ref{brokenpdftex,,Question 2.3}.

@node latexintegration
@section Is it possible to integrate Asymptote into LaTeX?

Yes, see the example latexusage.tex. Dario Teixeira has also written a detailed guide on the topic. You can download it from @uref{http://dario.dse.nl/projects/asylatex/}.  

Philippe Ivaldi has contributed an Asymptote mode for Emacs users @uref{https://asymptote.sourceforge.io/doc/Editing-modes.html}, which includes a @code{lasy-mode} that allows one to compile and view the output of one \begin@{asy@}...\end@{asy@} section at a time.

@node pdflatex
@section Is it possible to integrate Asymptote into latex or pdflatex?

Yes, as of version 1.14, Asymptote supports latex and pdflatex (both in EPS/PDF and inline mode), as illustrated by the example @code{latexusage.tex}: 

@verbatim
pdflatex latexusage
asy latexusage
pdflatex latexusage
@end verbatim

@node tkinterdepend
@section Do I need the @code{tkinter} package to install an Asymptote rpm binary?

No, you don't need @code{tkinter} unless you want to try out the GUI @code{xasy}. Try 

@verbatim
rpm -Uvh --nodeps asymptote-x.xx-1.i386.rpm
@end verbatim

where @code{x.xx} represents the version number.

@node windir
@section What does the path @code{%USERPROFILE%\.asy\config.asy} mean?

That is the way that Microsoft Windows refers to the user profile directory.  There's nothing really to understand here, just put your configuration commands in the file @code{config.asy} in a new folder @code{%USERPROFILE%\.asy}.

@node escapechar
@section Why do I get the error "string not terminated" when I try to set @code{settings.dir="C:\asymptote\";}?

The backslash is an escape character here, so @code{\"} is interpreted as a verbatim quotation mark, leaving the string without a terminating quotation mark. Fortunately, this is the only escaped character in double-quoted strings. A final backslash isn't needed here anyway, but should you really want one somewhere, you can say: @code{settings.dir="C:\asymptote"+'\\';}.

@node winglobal
@section How do I change environment variables in Microsoft Windows, for example, in order to change the default PostScript viewer?

While it is easier to set the corresponding Asymptote configuration variable in your @code{config.asy} file, here is the procedure for changing Microsoft Windows environment variables: 

Click on the [Start] button  

* RIGHT-click on 'My Computer'  

* Choose 'Properties' from the popup menu  

* Click the 'Advanced' tab  

* Click the 'Environment Variables' button.

@node convert
@section Under Microsoft Windows XP, why do I get an error like "Invalid Parameter - 432x432"?

This means that ImageMagick wasn't properly installed and you are using the MSDOS convert program rather than the ImageMagick one. Or you may have installed ImageMagick but ran Asymptote from an existing MSDOS window.  In that case, simply open a new window and try again. If that doesn't work, check that  

@verbatim
convert --version 
@end verbatim

returns something like 

@verbatim
Version: ImageMagick 6.2.8 06/27/06 Q16 http://www.imagemagick.org
@end verbatim

@node miktex
@section Why does Asymptote freeze upon trying to draw a label with my MikTex installation under Microsoft Windows?

Likely, this means that latex and dvips are not in your default path.  Try adding the appropriate paths in your @code{config.asy} file,  for example: 

@verbatim
import settings;
latex="C:\Program Files\MiKTeX 2.7\miktex\bin\latex.exe";
dvips="C:\Program Files\MiKTeX 2.7\miktex\bin\dvips.exe";
@end verbatim

@node Questions about paths
@chapter Questions about paths

@menu
* tensionsyntax:: Question 3.1. Why do I get a syntax error message when I specify an integer value for the path tension?
* dots:: Question 3.2. Shouldn't dots always be the same size?
@end menu

@node tensionsyntax
@section Why do I get a syntax error message when I specify an integer value for the path tension?

What is happening here is that 

@verbatim
draw((0,0)..tension 2..(0,50)..(100,100));
@end verbatim

is read as  

@verbatim
draw((0,0)..tension 2. .(0,50)..(100,100));
@end verbatim

So the first . after the two is treated as a decimal point.  Just put a space after the integer tension value: 

@verbatim
draw((0,0)..tension 2 ..(0,50)..(100,100));
@end verbatim

@node dots
@section Shouldn't dots always be the same size?

From the documentation:  

"The dot command defined in the module plain draws a dot having a diameter  equal to an explicit pen linewidth or the default linewidth magnified by  dotfactor (6 by default)." 

Thus, when you use the default pen, the dot will have size 6*linewidth, but when you give a pen with an explicit width specified, you will  have a dot of size linewidth. If you want the first case to behave like the second, you may set dotfactor=1.

@node Questions about labels
@chapter Questions about labels

@menu
* greek:: Question 4.1. How do I get Greek letters like omega to show up in my labels?
* matlabels:: Question 4.2. Can Asymptote use matrices as labels?
* latexpackage:: Question 4.3. How do I tell Asymptote to load a particular LaTeX package, like mathptmx?
* internatfonts:: Question 4.4. How can I use international fonts in Asymptote labels?
* Fourier:: Question 4.5. How can I use Fourier fonts?
* decsep:: Question 4.6. Is there any way to change the default appearance of the decimal separator, using a comma instead of a dot?
* rotatelabel:: Question 4.7. How can I get a rotated label with the filled box rotated as well so that it fits the text?
* rotatelabel3D:: Question 4.8. How can I rotate labels in a 3D figure?
* fixedsize:: Question 4.9. How can I draw some squares and circles of a fixed size and put a label in the middle of them?
* colorssaturation:: Question 4.10. The binary operator * can be used to scale the color of a pen by a real number. Does this scaling factor have to be less than 1?
* commadecimalseparator:: Question 4.11. Why is the space after the comma decimal separator in my locale so large?
* hyperref:: Question 4.12. How can I prevent texpreamble("\usepackage[pdftex]@{hyperref@}") from changing the page size?
@end menu

@node greek
@section How do I get Greek letters like omega to show up in my labels?

In (La)TeX, Greek letters can be obtained in math mode by prepending a  backslash to the letter name. So for a omega symbol, use "$\omega$". Everything between the dollar signs is considered to be a math formula. Uppercase Greek letters can be used by capitalizing the first letter of the name: 

@verbatim
label("$\omega$",(0,0));
label("$\Omega$",(20,0));
@end verbatim

@node matlabels
@section Can Asymptote use matrices as labels?

Yes:  
@verbatim
usepackage("amsmath");
label("$\begin{matrix} 1 & 2 \\\ 1 & 1 \end{matrix}$",(0,0));
@end verbatim

@node latexpackage
@section How do I tell Asymptote to load a particular LaTeX package, like @code{mathptmx}?

Put  

@verbatim
usepackage("mathptmx");
@end verbatim

at the beginning of your file. Note: to enable the Adobe Times Roman font for text, you will also need to say: 
@verbatim
defaultpen(TimesRoman());
@end verbatim

@node internatfonts
@section How can I use international fonts in Asymptote labels?

See @uref{https://asymptote.sourceforge.io/doc/Pens.html}.

@node Fourier
@section How can I use Fourier fonts?

@verbatim
usepackage("fourier");
defaultpen(font("T1","fut\textfamilyextension","m","n"));
@end verbatim

@node decsep
@section Is there any way to change the default appearance of the decimal separator, using a comma instead of a dot?

Just set your locale appropriately: 

@verbatim
locale("it_IT");
usepackage("icomma");
label(format(0.5));
@end verbatim

@node rotatelabel
@section How can I get a rotated label with the filled box rotated as well so that it fits the text?

@verbatim
frame f;
label(f,"This is some text",white,Fill(blue));
add(rotate(65)*f);
@end verbatim

@node rotatelabel3D
@section How can I rotate labels in a 3D figure?

You need to first project the triple to a pair like this:  

@verbatim
import three;
size(100,100);

draw(rotate(90,project(Z))*"A",O--X);
@end verbatim

@node fixedsize
@section How can I draw some squares and circles of a fixed size and put a label in the middle of them?

Fixed-size objects should be drawn on a separate picture and then added to  currentpicture. Here is one way (see also @uref{https://asymptote.sourceforge.io/gallery/subpictures.asy} and @uref{https://asymptote.sourceforge.io/gallery/mosquito.asy}):  

@verbatim
real u=2cm;
 
picture square;
draw(square,scale(u)*shift(-0.5,-0.5)*unitsquare);
 
picture circle;
draw(circle,scale(0.5u)*unitcircle);
 
void add(picture pic=currentpicture, Label L, picture object, pair z) { 
add(pic,object,z);
label(pic,L,z);
} 
 
add("square",square,(0,0));
add("circle",circle,(5cm,0));
@end verbatim

@node colorssaturation
@section The binary operator * can be used to scale the color of a pen by a real number. Does this scaling factor have to be less than 1?

The scaling factor can be greater than 1. But keep in mind that the rgb color  components saturate at 1.  

Try   
@verbatim
write(cyan); write(0.8*cyan); write(1.5*cyan);
@end verbatim
and you will quickly see what is going on.  

To get a lighter cyan you can say white+cyan,  which yields rgb(0.5,1,1). If you want something even lighter specify the  rgb colors directly,  for example, rgb(0.9,1,1).  

Alternatively, work in cmyk colour space, which is nicer in that it handles  saturation separately from hue:  

0.1*Cyan is light and 0.9*Cyan is dark.  You can also say 0.1*cmyk(red).

@node commadecimalseparator
@section Why is the space after the comma decimal separator in my locale so large?

LaTeX is treating the comma as punctuation and not as a decimal separator.  The solution is to load the @code{icomma} package near the beginning of your file: 
@verbatim
usepackage("icomma");
@end verbatim

@node hyperref
@section How can I prevent @code{texpreamble("\usepackage[pdftex]@{hyperref@}")} from changing the page size?

@verbatim
texpreamble("\usepackage[pdftex,setpagesize=false]{hyperref}");
@end verbatim

@node Questions about arrows
@chapter Questions about arrows

@menu
* doublearrows:: Question 5.1. How do I draw two arrows at arbitrary positions along a path?
* reversearrow:: Question 5.2. How do I reverse the direction of an arrowhead?
* reversearrow_2:: Question 5.3. How do I change the size of all arrows?
* arrowhead:: Question 5.4. Can I create other arrowhead styles?
@end menu

@node doublearrows
@section How do I draw two arrows at arbitrary positions along a path?

Assuming that at least one of the arrowheads is to be filled, you can do this: 

@verbatim
size(200); 
path g = (0,0)..(1,3)..(3,0); 
draw(g,Arrow(Relative(0.9))); 
add(arrow(g,invisible,FillDraw(black),Relative(0.5))); 
add(arrow(reverse(g),invisible,FillDraw(white,black),Relative(0.9))); 
@end verbatim

If both of the arrowheads are to be drawn with filltype NoFill, one will need to create a specialized version of the arrow routine in  @code{plain_arrows.asy}: 

@verbatim
void arrow(frame f, arrowhead arrowhead=DefaultHead,
           path g, pen p=currentpen, real size=0,
           real angle=arrowangle, filltype filltype=arrowhead.defaultfilltype,
           position position=EndPoint, bool forwards=true,
           margin margin=NoMargin, bool center=false);
@end verbatim

@node reversearrow
@section How do I reverse the direction of an arrowhead?

Simply reverse the direction of the path.  

@verbatim
path g=((0,0)--(5cm,0));
draw(reverse(g),Arrow(Relative(0.55)));
@end verbatim

@node reversearrow_2
@section How do I change the size of all arrows?

To override the arrowsize you can give every Arrow drawing attribute a real size argument. If you want to do this globally, you can override the pen-dependent arrowsize function like this: 

@verbatim
DefaultHead.size=new real(pen p=currentpen) {return 2mm;};
@end verbatim

@node arrowhead
@section Can I create other arrowhead styles?

Yes, you can build custom arrowheads like this (see the predefined arrowhead styles in @code{plain_arrows.asy} for further examples):  

@verbatim
arrowhead DotHead;
DotHead.head=new path(path g, position position=EndPoint, pen p=currentpen,
                      real size=0, real angle=arrowangle) {
  if(size == 0) size=DotHead.size(p);
  bool relative=position.relative;
  real position=position.position.x;
  if(relative) position=reltime(g,position);
  path r=subpath(g,position,0);
  pair x=point(r,0);
  real t=arctime(r,size);
  pair y=point(r,t);
  return circle(0.5(x+y),0.5size);
};

size(100);
draw((0,0)..(1,1)..(2,0),Arrow(DotHead));
dot((2,0),red);
@end verbatim

If you submit your alternate arrowheads to the Forum or the Patch  Tracking System, we'll consider including them in a future release.

@node Questions about 2D graphs
@chapter Questions about 2D graphs

@menu
* axisticks:: Question 6.1. How can I draw x axis ticks on the right side, with the tick labels on the left side (relative to the axis path)?
* axislabel:: Question 6.2. How can I reposition the x axis label to three-quarters along the axis length?
* axislabeldown:: Question 6.3. How can I move the x axis label down 10bp?
* threeaxispens:: Question 6.4. Can I use different pens for the axis, the axis label, and the tick labels?
* axislabelfont:: Question 6.5. How can I change the font type of the axes label?
* axisticklabelfont:: Question 6.6. How can I change the font type of the tick labels on an axis?
* overlappingticklabels:: Question 6.7. How can I prevent axes tick labels from rendering on top of each other?
* fixedsizegraphs:: Question 6.8. How do I make the plot region of a graph, ignoring labels and legends, have a fixed size?
* graphlimits:: Question 6.9. How can I plot a function f(x) within [0,1]x[0,2] without explicitly calculating the x values for which f(x) hits the boundary?
* custompalettes:: Question 6.10. Is it possible to define customized palettes?
* factorial:: Question 6.11. Is there an easy way to graph factorial functions nicely?
* length:: Question 6.12. How do I indicate that a certain length should be exactly the size I prescribe with no rescaling, within a picture which has its own size?
* log2:: Question 6.13. How can I make the y axis display base-2 logarithmic values?
* align:: Question 6.14. How can I align the x axes of two graphs on the same figure?
* changeaxis:: Question 6.15. How can I change the direction of the y-axis, such that negatives values are on the upper y-axis?
* functioncolor:: Question 6.16. How can I fill a path with a function that defines the color of each location?
* nonexplicitfun:: Question 6.17. Is there a way to draw a function that is not explicitly given, such as (y - 2)^2 = x - 1 ?
* scalesecondaryaxis:: Question 6.18. Is it possible to reverse or stretch an axis?
* emptymarkers:: Question 6.19. Why can't I use the UnFill option to draw graphs with empty markers?
* paletterange:: Question 6.20. How can I force several images to use the same palette range (e.g. the entire 0-255 grayscale range)?
@end menu

@node axisticks
@section How can I draw x axis ticks on the right side, with the tick labels on the left side (relative to the axis path)?

@verbatim
import graph;

size(250,200,IgnoreAspect);

draw(graph(exp,-1,1),red);

xaxis("$x$",RightTicks(Label(align=left)));
yaxis("$y$",RightTicks);
@end verbatim

@node axislabel
@section How can I reposition the x axis label to three-quarters along the axis length?

@verbatim
import graph;

size(250,200,IgnoreAspect);

draw(graph(exp,-1,1),red);

xaxis(Label("$x$",0.75),LeftTicks);
yaxis("$y$",RightTicks);
@end verbatim

@node axislabeldown
@section How can I move the x axis label down 10bp?

@verbatim
import graph;
size(250,200,IgnoreAspect);

draw(graph(exp,-1,1),red);

xaxis(shift(0,-10)*"$x$",LeftTicks);
yaxis("$y$",RightTicks);
@end verbatim

@node threeaxispens
@section Can I use different pens for the axis, the axis label, and the tick labels?

Yes: 

@verbatim
import graph;
size(300,200,IgnoreAspect);

xlimits(-50,50);
ylimits(0,100);

xaxis(Label("$x$",MidPoint,red),Bottom,blue,LeftTicks(green));
yaxis("$y$",Left,RightTicks);
@end verbatim

@node axislabelfont
@section How can I change the font type of the axes label?

@verbatim
import graph;
size(300,200,IgnoreAspect);

xlimits(-50,50);
ylimits(0,100);

xaxis("x",Bottom,Courier("m","n"),LeftTicks);
yaxis("$y$",Left,RightTicks);
@end verbatim

@node axisticklabelfont
@section How can I change the font type of the tick labels on an axis?

Tick labels are by default typeset in (TeX) math mode, so to use other fonts you need to override the default tick format: 

@verbatim
import graph;
size(300,200,IgnoreAspect);

xlimits(-50,50);
ylimits(0,100);

xaxis("$x$",Bottom,LeftTicks("%.4g",Courier("m","n")+fontsize(12)));
yaxis("$y$",Left,RightTicks);
@end verbatim

@node overlappingticklabels
@section How can I prevent axes tick labels from rendering on top of each other?

Either: 

(i) give LeftTicks/RightTicks/Ticks the arguments beginlabel=false and/or endlabel=false; 

(ii) explicitly remove specific ticks and their labels (drawing them manually; see @uref{http://www.github.com/vectorgraphics/asymptote/base/graph.asy} for the definition of NoZero): 

@verbatim
import graph;

size(10cm);

real f(real x) {return x^2;}
 
draw(graph(f,-2,2));

xaxis(Ticks(NoZero));
yaxis(Ticks(NoZero));

label("$0$",(0,0),SW);
@end verbatim

(iii) explicitly remove specific tick labels and draw them manually (see @uref{http://www.github.com/vectorgraphics/asymptote/base/graph.asy} for the definition of NoZeroFormat): 

@verbatim
import graph;

size(10cm);

real f(real x) {return x^2;}
 
draw(graph(f,-2,2));

xaxis(Ticks(NoZeroFormat));
yaxis(Ticks(NoZeroFormat));

label("$0$",(0,0),SW);
@end verbatim

(iv) use the xasy GUI to move overlapping labels; 

(v) change the Label argument of LeftTicks, RightTicks, or Ticks to: 

@verbatim
Label(currentpen+overwrite(Move))
@end verbatim

Solution (v) will move labels that might otherwise overwrite a previous label. Other possible overwrite arguments are Allow (allows overlapping labels; the default), Suppress (an overlapping label will not be written at all), SuppressQuiet, and MoveQuiet. The last two achieve the same result as the non-quiet types, but will not notify you which labels are overlapping. See:  @uref{https://asymptote.sourceforge.io/doc/Pens.html}.  

In the case of a user-specified tick array, you can change which labels get suppressed/moved by changing the order of array entries.

@node fixedsizegraphs
@section How do I make the plot region of a graph, ignoring labels and legends, have a fixed size?

Either: 

i) Specify an explicit unitsize, which overrides any call to @code{size}: 
@verbatim
unitsize(x=1cm,y=2cm);
@end verbatim

ii) Explicitly tell Asymptote to map the plot region to a specific size: 
@verbatim
import graph;
real[] x={0,1,2,3};
real[] y=x^2;
draw(graph(x,y),red);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);

size(5cm,5cm,point(SW),point(NE));

label("$f_\mathrm{T}$",point(N),2N);
@end verbatim

iii) Specify the points in user coordinates that should correspond to a given picture size: 

@verbatim
import graph;

size(250,200,IgnoreAspect);

draw(graph(exp,-1,1),red);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);

fixedscaling((-1.5,-0.5),(1.5,3.5));
@end verbatim

In this example, the user coordinate @code{(-1.5,-0.5)} will end up being the lower left corner of the figure and @code{(1.5,3.5)} will be the upper right corner. You can use this option to ensure multiple figures have the same scaling and same resulting figure size (just ensure the two coordinates given to @code{fixedscaling()} leaves room for any labels).  

See also @uref{https://asymptote.sourceforge.io/doc/Frames-and-pictures.html}.

@node graphlimits
@section How can I plot a function f(x) within [0,1]x[0,2] without explicitly calculating the x values for which f(x) hits the boundary?

Call @code{limits} with the @code{Crop} option before drawing the graph: 
@verbatim
import graph;

size(250,200,IgnoreAspect);

draw(graph(exp,-1,1),red);

limits((0,0),(1,2),Crop);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
@end verbatim

See also @uref{https://asymptote.sourceforge.io/doc/graph.html}.

@node custompalettes
@section Is it possible to define customized palettes?

Yes, you may generate your own pen[] array. For example:  

@verbatim
int NColors=32768;
pen[] MyPalette=new pen[NColors];
real step=1/(NColors-1.0);
// Start at black: rgb(0,0,0) 
// End at yellow: rgb(1,1,0) 
for(int i=0; i < NColors; ++i) { 
  real rgval=i*step;
  MyPalette[i]=rgb(rgval,rgval,0.0);
} 
@end verbatim

@node factorial
@section Is there an easy way to graph factorial functions nicely?

The example below shows a continuous function and two methods for placing  markers at integer values of x:  

@verbatim
import graph;
 
size(200,200,IgnoreAspect);
 
real factorial(real t) {return gamma(t+1);} 
 
scale(Linear,Log);
 
// Graph the factorial function.
draw(graph(factorial,0,10));
 
// Method 1: Draw nodes, but hide line
pair F(int t) {return (t,factorial(t));} 
// Graph of factorial function from 0 to 10
pair[] z=sequence(F,11);
draw(graph(z),invisible,marker(scale(0.8mm)*unitcircle,blue,Fill));
 
// Method 2: Nongraphing routines require explicit scaling:
pair dotloc(int t) {return Scale(F(t));} 
pair[] dotlocs=sequence(dotloc,11);
dot(dotlocs);
 
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
@end verbatim

@node length
@section How do I indicate that a certain length should be exactly the size I prescribe with no rescaling, within a picture which has its own size?

Here's an easy way to do this.  

@verbatim
size(12cm,0);
 
void distance(picture pic=currentpicture, pair A, pair B, Label L="", real n=0,
              pen p=currentpen) 
{
  real d=3mm;
  path g=A--B;
  transform T=shift(-n*d*unit(B-A)*I);
  pic.add(new void(frame f, transform t) {
    picture opic;
    path G=T*t*g;
    draw(opic,Label(L,Center,UnFill(1)),G,p,Arrows(NoFill),Bars,PenMargins);
    add(f,opic.fit());
  });
  pic.addBox(min(g),max(g),T*min(p),T*max(p));
} 
 
pair A=(0,0), B=(3,3);
 
dot(A);
dot(B);
 
distance(A,B,"$\ell$",1);
@end verbatim

@node log2
@section How can I make the y axis display base-2 logarithmic values?

See the example @uref{https://asymptote.sourceforge.io/gallery/2D graphs/log2graph.asy}.

@node align
@section How can I align the x axes of two graphs on the same figure?

An easy way to do this, if the axes to be aligned have the same scaling and size, is illustrated in the example @uref{https://asymptote.sourceforge.io/gallery/2D graphs/alignedaxis.asy}.  

Here is a more general solution to the problem of aligning two arbitrary axes.  One fits the second picture to a frame based on the horizontal scaling for the first picture: 

@verbatim
import graph;

real width=15cm;
real aspect=0.3;

picture pic1,pic2;

size(pic1,width,aspect*width,IgnoreAspect);
size(pic2,width,aspect*width,IgnoreAspect);

scale(pic1,false);
scale(pic2,false);

real xmin1=6;
real xmax1=9;
real xmin2=8;
real xmax2=16;

real a1=1;
real a2=0.001;

real f1(real x) {return a1*sin(x/2*pi);}
real f2(real x) {return a2*sin(x/4*pi);}

draw(pic1,graph(pic1,f1,xmin1,xmax1));
draw(pic2,graph(pic2,f2,xmin2,xmax2));

xaxis(pic1,Bottom,LeftTicks());
yaxis(pic1,"$f_1(x)$",Left,RightTicks);

xaxis(pic2,"$x$",Bottom,LeftTicks(Step=4));
yaxis(pic2,"$f_2(x)$",Left,RightTicks);

yequals(pic1,0,Dotted);
yequals(pic2,0,Dotted);

pair min1=point(pic1,SW);
pair max1=point(pic1,NE);

pair min2=point(pic2,SW);
pair max2=point(pic2,NE);

real scale=(max1.x-min1.x)/(max2.x-min2.x);
real shift=min1.x/scale-min2.x;

transform t1=pic1.calculateTransform();
transform t2=pic2.calculateTransform();
transform T=xscale(scale*t1.xx)*yscale(t2.yy);

add(pic1.fit());
real height=truepoint(N,user=false).y-truepoint(S,user=false).y;
add(shift(0,-height)*(shift(shift)*pic2).fit(T));
@end verbatim

@node changeaxis
@section How can I change the direction of the y-axis, such that negatives values are on the upper y-axis?

Here is a simple example (see also the example @uref{https://asymptote.sourceforge.io/gallery/2D graphs/diatom.asy} or the discussion of Linear(-1) in the documentation): 

@verbatim
import graph;
size(250,200,IgnoreAspect);

scale(Linear,Linear(-1));

draw(graph(log,0.1,10),red);

xaxis("$x$",LeftTicks);
yaxis("$y$",RightTicks);
@end verbatim

@node functioncolor
@section How can I fill a path with a function that defines the color of each location?

Use @code{functionshade} with a PDF tex engine, as illustrated by the example @{functionshading.asy@}.  

If you want to produce PostScript output, an approximate solution for now would be to superimpose a fine grid and specify colors to  @code{latticeshade} that depend on position as a single pen[][] lattice. Alternatively, it may be more efficient to use @code{tensorshade}.

@node nonexplicitfun
@section Is there a way to draw a function that is not explicitly given, such as (y - 2)^2 = x - 1 ?

Yes, use the parametric form  

@verbatim
y=t 
x=(t-2)^2+1 
@end verbatim

See the example @uref{https://asymptote.sourceforge.io/gallery/2D graphs/parametricgraph.asy}.

@node scalesecondaryaxis
@section Is it possible to reverse or stretch an axis?

The real scaling argument to Linear is used to stretch (or reverse) the axis.  To see the effect of axis stretching, be sure not to specify IgnoreAspect in  the picture size command.  

A secondary axis has the same length as the primary axis, so stretching cannot  have any effect. But one can still reverse the axis, with Linear(-1).

@node emptymarkers
@section Why can't I use the UnFill option to draw graphs with empty markers?

UnFill won't work here because it only affects the local frame the markers are initially drawn on, before being added to currentpicture.  Here is a way of achieving the desired effect (assuming a white background): 

@verbatim
import graph;
size(10cm,0);
pair[] z={(0,0),(0.5,0.5),(1,1)};
path g=graph(z);
 
draw(shift(0,.5)*g,marker(scale(5)*unitcircle,FillDraw(white)));
 
xaxis(BottomTop,LeftTicks);
yaxis(LeftRight,RightTicks);
@end verbatim

@node paletterange
@section How can I force several images to use the same palette range (e.g. the entire 0-255 grayscale range)?

The palette color space corresponds to a range of values specified by the argument range, which can be @code{Full}, @code{Automatic} or an explicit range @code{Range(pair min, pair max)}. Here @code{Full} specifies a range varying from the minimum to maximum values of the function over the sampling interval, while @code{Automatic} selects "nice" limits.

@node Questions about programming
@chapter Questions about programming

@menu
* comporint:: Question 7.1. Is Asymptote an interpreter or a compiler?
* framepicture:: Question 7.2. What is the difference between a frame and a picture?
* pathguide:: Question 7.3. What is the difference between a path and a guide?
* picarray:: Question 7.4. What is a convenient way to declare and initialize an array of pictures?
* genarrays:: Question 7.5. Is there a way to define functions that act on arrays in general (i.e. work for arrays of any type)?
* cirdep:: Question 7.6. Is there any way to declare structures ahead of their definition, e.g. where struct A performs some operation on struct B, but B contains an A member?
* static:: Question 7.7. Where are static variables in for loops allocated?
* debug:: Question 7.8. Is there a debugger for asy?
* patches:: Question 7.9. Do you accept patches for Asymptote?
@end menu

@node comporint
@section Is Asymptote an interpreter or a compiler?

Asymptote compiles Asymptote commands into its own virtual machine code. It  then runs this pseudocode on a virtual machine to produce PostScript code.

@node framepicture
@section What is the difference between a frame and a picture?

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.  See @ref{unitsizes,,Question 8.8}.

@node pathguide
@section What is the difference between a path and a guide?

A path is a cubic spline with fixed endpoint conditions.  

A guide is an unresolved cubic spline (list of cubic-spline nodes and control points). A guide is like 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.

@node picarray
@section What is a convenient way to declare and initialize an array of pictures?

You could write yourself a routine such as: 
@verbatim
picture[] picture(int n) { 
  picture[] pic;
  for(int i=0; i < n; ++i) { 
    pic[i]=new picture;
    size(pic[i],19cm,0);
  } 
  return pic;
} 
 
picture[] pic=picture(6);
@end verbatim

@node genarrays
@section Is there a way to define functions that act on arrays in general (i.e. work for arrays of any type)?

Generic types aren't yet implemented.  

But for now you can at least say  
@verbatim
typedef string T;
include F;
 
typedef real T;
include F;
@end verbatim

where @code{F.asy} contains some type-dependent code like 
@verbatim
T[] operator $(T A, T B) {return new T[] {A,B};}
@end verbatim

@node cirdep
@section Is there any way to declare structures ahead of their definition, e.g. where struct A performs some operation on struct B, but B contains an A member?

Asymptote does not support forward declaration of types. You can, however,  nest structures, so that both types are visible for parts of the bodies of  both structure definitions. For example:  

@verbatim
struct B { 
  typedef void someroutine(B b);
 
  static struct A { 
    someroutine routine;
    void operator init(someroutine routine) { 
      this.routine=routine;
    } 
  } 
 
  string test="Testing";
} 
 
typedef B.A A;
 
A a=B.A(new void(B b){write(b.test);});
 
B b;
a.routine(b);
@end verbatim

@node static
@section Where are static variables in for loops allocated?

In the example  

@verbatim
void f() { 
  for(int i=0; i < 3; ++i) { 
    static int n;
    ++n;
    write(n);
  }
} 

f(); // Writes 1, 2, 3
@end verbatim

the static qualifier means that @code{n} is allocated not just outside of the for loop, but also outside the function. This is clear if you call  @code{f} multiple times; there is still only one instance of @code{n}.  

The "level" of a variable (where it is allocated) has nothing to do with the "scope" of a variable (how long it can be referred to by name).  The curly braces enclosing a block affect only a variable's scope, not its level.  

Static modifiers are meaningless at the top level; they generate a warning and are simply ignored: 

@verbatim
for(int i=0; i < 3; ++i) { 
  static int n;
  ++n;
  write(n);
}
// Writes warning about top-level static modifier and then 1, 1, 1
@end verbatim

Since version 1.22, non-static variables allocated in a loop body are allocated anew every iteration.  This is only noticable in obscure cases where a variable in a loop is accessed in the closure of a function defined in the loop: 

@verbatim
int f();
 
for(int i=0; i < 10; ++i) { 
  int j=10*i;
  if(i == 5)
    f=new int() {return j;};
} 
 
write(f()); // Writes 50
@end verbatim

Variables in the body of a loop last as long as that iteration of the loop, unless they are kept alive by a function closure as in the example above.  In a function body, variables will last at least as long as the function call, though because of closures and garbage collection, they may last longer than that.  If defined at the top level of a file or at the interactive prompt, they will last at least until the end of the file or prompt's run.

@node debug
@section Is there a debugger for asy?

Yes, Asymptote includes a line-based debugger: 

@uref{https://asymptote.sourceforge.io/doc/Debugger.html}

@node patches
@section Do you accept patches for Asymptote?

Yes, in fact we would prefer that users submit patches for customized features (to @uref{http://sourceforge.net/tracker/?atid=685685&group_id=120000}) instead of relying on us to do all of the coding. Development will proceed  faster that way.

@node Questions about differences between Asymptote and MetaPost
@chapter Questions about differences between Asymptote and MetaPost

@menu
* interp:: Question 8.1. What is the equivalent of the MetaPost c[a,b] interpolation operator?
* automaticscaling:: Question 8.2. How does picture scaling differ in Asymptote and MetaPost?
* manualscaling:: Question 8.3. How can I avoid automatic scaling of a picture?
* mp3dots:: Question 8.4. What is the equivalent of MetaPost ... command?
* mppickup:: Question 8.5. What is the equivalent of the MetaPost pickup command?
* whatever:: Question 8.6. What is the equivalent of the MetaPost whatever command?
* lray:: Question 8.7. What is the equivalent for the MetaPost command for lray - horiz*v - verti*u = whatever*(LightSource - R), a system of three linear equations for three unknowns: horiz, verti, whatever?
* unitsizes:: Question 8.8. In MetaPost, it is possible to have a drawing remain the same size in different pictures by defining a unit u and explicitly multiply all the coordinates by u. Is there a better way to do this in Asymptote?
* tiles:: Question 8.9. In MetaPost, one could produce tiling pictures by generating a picture, and then clipping the picture to a rectangle of fixed dimensions around the center of the picture. How is that done in Asymptote?
@end menu

@node interp
@section What is the equivalent of the MetaPost c[a,b] interpolation operator?

@verbatim
interp(a,b,c);
@end verbatim

@node automaticscaling
@section How does picture scaling differ in Asymptote and MetaPost?

Asymptote includes an optional facility to do automatic scaling of pictures to achieve a given overall picture size, whereas Metapost only supports manual scaling. Asymptote defers drawing of objects drawn to pictures and distinguishes between true-size objects and objects that should scale with the picture size. The resulting linear programming problem is solved via the Simplex method.  

See the @uref{https://asymptote.sourceforge.io/gallery/dimension.asy} example for an example of how deferred drawing is used to accomodate both user and true-size (PostScript) coordinates.

@node manualscaling
@section How can I avoid automatic scaling of a picture?

If you really like Metapost-style manual (hard-wired) scaling either:  

(i) use the default size(0,0) for the entire picture and do all of the  scaling by hand, just like in MetaPost; 

(ii) draw to a separate picture pic and add(pic.fit()); 

(iii) use frames.

@node mp3dots
@section What is the equivalent of MetaPost ... command?

The connector @code{::} is a macro for tension atleast 1: 

@verbatim
size(100);
pair z0=(0,0);
pair z1=(1,0.25);
pair z2=(2,0);
draw(z0{up}::z1{right}::z2{down});
@end verbatim

@node mppickup
@section What is the equivalent of the MetaPost pickup command?

Just say, for example: 

@verbatim
currentpen=red;
@end verbatim

@node whatever
@section What is the equivalent of the MetaPost whatever command?

Asymptote does not implicitly solve linear equations and therefore does not have the notion of a @code{whatever} unknown. Such a facility could certainly be added (perhaps using the notation @code{?=} since @code{=} means assignment).  However, the most common uses of @code{whatever} in MetaPost are covered by functions like @code{extension} in @code{math.asy}:  
@verbatim
pair extension(pair P, pair Q, pair p, pair q);
@end verbatim
this returns the intersection point of the extensions of the line segments  @code{PQ} and @code{pq}. We find using routines like @code{extension} more explicit and less confusing to new users. But we could be persuaded to add something similar if someone can justify the need. In the meantime, one can always use the explicit built-in linear solver @code{solve} (see @uref{https://asymptote.sourceforge.io/doc/solve.html}), which uses LU decomposition.

@node lray
@section What is the equivalent for the MetaPost command for @code{lray - horiz*v - verti*u = whatever*(LightSource - R)}, a system of three linear equations for three unknowns: @code{horiz, verti, whatever}?

Since @code{horiz*v+verti*u} spans a plane, you could use 
@verbatim
real intersect(vector P, vector Q, vector n, vector Z);
@end verbatim

to find the intersection time for the line  @code{lray-whatever*(LightSource - R)} and then extract the three desired values from there. (You'll still need to use the built-in explicit linear solver to solve a 2x2 system to get  @code{horiz} and @code{verti}.)

@node unitsizes
@section In MetaPost, it is possible to have a drawing remain the same size in different pictures by defining a unit @code{u} and explicitly multiply all the coordinates by @code{u}. Is there a better way to do this in Asymptote?

Yes, Asymptote has a better way: you definitely don't want to manually scale  all of your coordinates. To make the user coordinates represent multiples of exactly @code{1cm}: 

@verbatim
unitsize(1cm);
draw(unitsquare);
@end verbatim

One can also specify different x and y unit sizes: 

@verbatim
unitsize(x=1cm,y=2cm);
draw(unitsquare);
@end verbatim

Another way is to draw your fixed size object to a frame and add it to currentpicture like this: 

@verbatim
path p=(0,0)--(1,0);
frame object;
draw(object,scale(100)*p);
 
add(object);
add(object,(0,-10));
@end verbatim

To understand the difference between frames and pictures, try this:  

@verbatim
size(300,300);
 
path p=(0,0)--(1,0);
picture object;
draw(object,scale(100)*p);
 
add(object);
add(object,(0,-10)); // Adds truesize object to currentpicture 
@end verbatim

@node tiles
@section In MetaPost, one could produce tiling pictures by generating a picture, and then clipping the picture to a rectangle of fixed dimensions around the center of the picture. How is that done in Asymptote?

If you are using currentpicture the way one would in MetaPost (drawing in  raw PostScript coordinates), you can simply do something like:  

@verbatim
fill((0,0)--(100,100)--(200,0)--cycle);
 
pair center(picture pic=currentpicture) {return 0.5*(pic.min()+pic.max());} 
 
real height=100;
real width=100;
pair delta=0.5(width,height);
pair c=center();
clip(box(c-delta,c+delta));
@end verbatim

However, drawing in PostScript coordinates is often inconvenient. Here's the  Asymptote way of doing the same thing, using deferred drawing:  

@verbatim
size(200,100);
fill((0,0)--(1,1)--(2,0)--cycle);
 
void clip(picture pic=currentpicture, real width, real height) 
{
  pic.clip(new void (frame f, transform) { 
    pair center=0.5(min(f)+max(f));
    pair delta=0.5(width,height);
    clip(f,box(center-delta,center+delta));
  });
} 
 
clip(100,100);
@end verbatim

See also the discussion of tilings in the documentation:  @uref{https://asymptote.sourceforge.io/doc/Pens.html}.

@node Questions about output
@chapter Questions about output

@menu
* psviewer:: Question 9.1. How can I disable automatic invocation of the PS viewer after an asy file is done processing?
* jpeg:: Question 9.2. How do I output jpeg images?
* embedbitmaps:: Question 9.3. Can I embed bitmaps (photos) into my drawings and position and scale them?
* directpdf:: Question 9.4. Does Asymptote support direct PDF output?
* bigpictures:: Question 9.5. How to I produce large pictures of high quality in raster format (e.g. png, giff etc).
* multipage:: Question 9.6. Is it possible to produce multi-page documents with asymptote?
@end menu

@node psviewer
@section How can I disable automatic invocation of the PS viewer after an asy file is done processing?

It's actually not on by default, unless you happen to be using Microsoft Windows (because that is what most Microsoft Windows users expect). Microsoft Windows users can turn this feature off with the command-line option -noV or by putting   

@verbatim
import settings;
interactiveView=false;
batchView=false;
@end verbatim

in their @code{config.asy} file. See @uref{https://asymptote.sourceforge.io/doc/Options.html}.

@node jpeg
@section How do I output jpeg images?

If you have the ImageMagick convert program installed, simply type 

@verbatim
asy -f jpg test.asy 
@end verbatim

@node embedbitmaps
@section Can I embed bitmaps (photos) into my drawings and position and scale them?

Convert them to eps format and use the graphic(string) function just like a Label: 

@verbatim
label(graphic("file"),(0,0));
@end verbatim

See the example @uref{https://asymptote.sourceforge.io/gallery/orthocenter.asy} and @uref{https://asymptote.sourceforge.io/doc/label.html}.

@node directpdf
@section Does Asymptote support direct PDF output?

Yes, PDF output can be produced by the -f pdf option or -tex pdflatex option.  This supports transparency, annotations, embedded movies, and U3D/PRC content.

@node bigpictures
@section How to I produce large pictures of high quality in raster format (e.g. png, giff etc).

Try using some of the options to convert, mainly -geometry and -density. For example:  
@verbatim
convert -geometry 1000x3000 example.eps example.png 
@end verbatim

You can also change the default resolution of the image with:  
@verbatim
convert -geometry 1000x3000 -density 300 -units PixelsPerInch example.eps example.png 
@end verbatim
This does not change the number of pixels in the image, but just gives a hint  as to how large each pixel should be displayed.  

If you include the -density option without the -geometry option, convert will  keep the image size constant (so a 4cm x 3cm eps figure will generate a 4cm x 3cm png  image).

@node multipage
@section Is it possible to produce multi-page documents with asymptote?

Yes, simply call the newpage() function. This is used by the @code{slide.asy} package to produce high-quality slide presentations (easier to use than Prosper).

@bye
