            ASYMPTOTE FREQUENTLY ASKED QUESTIONS
                            2024-05-01
                           
This is the list of Frequently Asked Questions about Asymptote (asy).

===============================================================================

Index

 Section 1.  About Asymptote
 Q1.1        What is Asymptote?
 Q1.2        How do I obtain Asymptote?
 Q1.3        Where can I ask questions about Asymptote? 
 Q1.4        Why was the name Asymptote chosen?
 Q1.5        In the internal Asymptote source code, what does the name camp ref

 Section 2.  Questions about installation and setup
 Q2.1        Is it possible to install Asymptote on Mac OS X?
 Q2.2        Why do I get the error Bad CPU type in executable on installing As
 Q2.3        What do I do if I get the error: Error: pdfetex (file pdftex.cfg):
 Q2.4        What do I do if I get the error: ! Undefined control sequence. l.6
 Q2.5        Is it possible to integrate Asymptote into LaTeX?
 Q2.6        Is it possible to integrate Asymptote into latex or pdflatex?
 Q2.7        Do I need the tkinter package to install an Asymptote rpm binary?
 Q2.8        What does the path %USERPROFILE%\.asy\config.asy mean?
 Q2.9        Why do I get the error "string not terminated" when I try to set s
 Q2.10       How do I change environment variables in Microsoft Windows, for ex
 Q2.11       Under Microsoft Windows XP, why do I get an error like "Invalid Pa
 Q2.12       Why does Asymptote freeze upon trying to draw a label with my MikT

 Section 3.  Questions about paths
 Q3.1        Why do I get a syntax error message when I specify an integer valu
 Q3.2        Shouldn't dots always be the same size?

 Section 4.  Questions about labels
 Q4.1        How do I get Greek letters like omega to show up in my labels?
 Q4.2        Can Asymptote use matrices as labels?
 Q4.3        How do I tell Asymptote to load a particular LaTeX package, like m
 Q4.4        How can I use international fonts in Asymptote labels?
 Q4.5        How can I use Fourier fonts? 
 Q4.6        Is there any way to change the default appearance of the decimal s
 Q4.7        How can I get a rotated label with the filled box rotated as well 
 Q4.8        How can I rotate labels in a 3D figure?
 Q4.9        How can I draw some squares and circles of a fixed size and put a 
 Q4.10       The binary operator * can be used to scale the color of a pen by a
 Q4.11       Why is the space after the comma decimal separator in my locale so
 Q4.12       How can I prevent texpreamble("\usepackage[pdftex]{hyperref}") fro

 Section 5.  Questions about arrows
 Q5.1        How do I draw two arrows at arbitrary positions along a path?
 Q5.2        How do I reverse the direction of an arrowhead?
 Q5.3        How do I change the size of all arrows?
 Q5.4        Can I create other arrowhead styles?

 Section 6.  Questions about 2D graphs
 Q6.1        How can I draw x axis ticks on the right side, with the tick label
 Q6.2        How can I reposition the x axis label to three-quarters along the 
 Q6.3        How can I move the x axis label down 10bp?
 Q6.4        Can I use different pens for the axis, the axis label, and the tic
 Q6.5        How can I change the font type of the axes label?
 Q6.6        How can I change the font type of the tick labels on an axis?
 Q6.7        How can I prevent axes tick labels from rendering on top of each o
 Q6.8        How do I make the plot region of a graph, ignoring labels and lege
 Q6.9        How can I plot a function f(x) within [0,1]x[0,2] without explicit
 Q6.10       Is it possible to define customized palettes?
 Q6.11       Is there an easy way to graph factorial functions nicely?
 Q6.12       How do I indicate that a certain length should be exactly the size
 Q6.13       How can I make the y axis display base-2 logarithmic values?
 Q6.14       How can I align the x axes of two graphs on the same figure?
 Q6.15       How can I change the direction of the y-axis, such that negatives 
 Q6.16       How can I fill a path with a function that defines the color of ea
 Q6.17       Is there a way to draw a function that is not explicitly given, su
 Q6.18       Is it possible to reverse or stretch an axis?
 Q6.19       Why can't I use the UnFill option to draw graphs with empty marker
 Q6.20       How can I force several images to use the same palette range (e.g.

 Section 7.  Questions about programming
 Q7.1        Is Asymptote an interpreter or a compiler?  
 Q7.2        What is the difference between a frame and a picture? 
 Q7.3        What is the difference between a path and a guide? 
 Q7.4        What is a convenient way to declare and initialize an array of pic
 Q7.5        Is there a way to define functions that act on arrays in general (
 Q7.6        Is there any way to declare structures ahead of their definition, 
 Q7.7        Where are static variables in for loops allocated?
 Q7.8        Is there a debugger for asy?
 Q7.9        Do you accept patches for Asymptote?

 Section 8.  Questions about differences between Asymptote and MetaPost
 Q8.1        What is the equivalent of the MetaPost c[a,b] interpolation operat
 Q8.2        How does picture scaling differ in Asymptote and MetaPost?
 Q8.3        How can I avoid automatic scaling of a picture?
 Q8.4        What is the equivalent of MetaPost ... command?
 Q8.5        What is the equivalent of the MetaPost pickup command?
 Q8.6        What is the equivalent of the MetaPost whatever command?
 Q8.7        What is the equivalent for the MetaPost command for lray - horiz*v
 Q8.8        In MetaPost, it is possible to have a drawing remain the same size
 Q8.9        In MetaPost, one could produce tiling pictures by generating a pic

 Section 9.  Questions about output
 Q9.1        How can I disable automatic invocation of the PS viewer after an a
 Q9.2        How do I output jpeg images?
 Q9.3        Can I embed bitmaps (photos) into my drawings and position and sca
 Q9.4        Does Asymptote support direct PDF output?
 Q9.5        How to I produce large pictures of high quality in raster format (
 Q9.6        Is it possible to produce multi-page documents with asymptote? 

===============================================================================

Section 1.  About Asymptote

 Q1.1        What is Asymptote?
 Q1.2        How do I obtain Asymptote?
 Q1.3        Where can I ask questions about Asymptote? 
 Q1.4        Why was the name Asymptote chosen?
 Q1.5        In the internal Asymptote source code, what does the name camp ref

-------------------------------------------------------------------------------

Question 1.1.  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.

-------------------------------------------------------------------------------

Question 1.2.  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
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).

-------------------------------------------------------------------------------

Question 1.3.  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
https://asymptote.sourceforge.io/doc/, or search the forum:
http://sourceforge.net/forum/forum.php?forum_id=409349.

-------------------------------------------------------------------------------

Question 1.4.  Why was the name Asymptote chosen?

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

-------------------------------------------------------------------------------

Question 1.5.  In the internal Asymptote source code, what does the name 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 Asymptote better emphasizes the
mathematical and graphical nature of this language.

===============================================================================

Section 2.  Questions about installation and setup

 Q2.1        Is it possible to install Asymptote on Mac OS X?
 Q2.2        Why do I get the error Bad CPU type in executable on installing As
 Q2.3        What do I do if I get the error: Error: pdfetex (file pdftex.cfg):
 Q2.4        What do I do if I get the error: ! Undefined control sequence. l.6
 Q2.5        Is it possible to integrate Asymptote into LaTeX?
 Q2.6        Is it possible to integrate Asymptote into latex or pdflatex?
 Q2.7        Do I need the tkinter package to install an Asymptote rpm binary?
 Q2.8        What does the path %USERPROFILE%\.asy\config.asy mean?
 Q2.9        Why do I get the error "string not terminated" when I try to set s
 Q2.10       How do I change environment variables in Microsoft Windows, for ex
 Q2.11       Under Microsoft Windows XP, why do I get an error like "Invalid Pa
 Q2.12       Why does Asymptote freeze upon trying to draw a label with my MikT

-------------------------------------------------------------------------------

Question 2.1.  Is it possible to install Asymptote on Mac OS X?

It is easy to compile Asymptote directly from the source code at
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
http://www.hmug.org/pub/MacOS_X/X/Applications/Publishing/asymptote.

-------------------------------------------------------------------------------

Question 2.2.  Why do I get the error 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:
http://sourceforge.net/project/showfiles.php?group_id=120000.

-------------------------------------------------------------------------------

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?

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

-------------------------------------------------------------------------------

Question 2.4.  What do I do if I get the error: ! Undefined control sequence. l.6 @copying?

Either upgrade your texinfo package or follow one of the easy work arounds
in Q2.3 `What do I do if I get the error: Error: pdfetex (file
pdftex.cfg): cannot open config file...texinfo.tex appears to be broken?'.

-------------------------------------------------------------------------------

Question 2.5.  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
http://dario.dse.nl/projects/asylatex/.

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

-------------------------------------------------------------------------------

Question 2.6.  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 latexusage.tex:

pdflatex latexusage
asy latexusage
pdflatex latexusage
-------------------------------------------------------------------------------

Question 2.7.  Do I need the tkinter package to install an Asymptote rpm binary?

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

rpm -Uvh --nodeps asymptote-x.xx-1.i386.rpm
where x.xx represents the version number.

-------------------------------------------------------------------------------

Question 2.8.  What does the path %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 config.asy in a new folder
%USERPROFILE%\.asy.

-------------------------------------------------------------------------------

Question 2.9.  Why do I get the error "string not terminated" when I try to set settings.dir="C:\asymptote\";?

The backslash is an escape character here, so \" 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:
settings.dir="C:\asymptote"+'\\';.

-------------------------------------------------------------------------------

Question 2.10.  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 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.

-------------------------------------------------------------------------------

Question 2.11.  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

convert --version 
returns something like

Version: ImageMagick 6.2.8 06/27/06 Q16 http://www.imagemagick.org
-------------------------------------------------------------------------------

Question 2.12.  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 config.asy file,  for example:

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

Section 3.  Questions about paths

 Q3.1        Why do I get a syntax error message when I specify an integer valu
 Q3.2        Shouldn't dots always be the same size?

-------------------------------------------------------------------------------

Question 3.1.  Why do I get a syntax error message when I specify an integer value for the path tension?

What is happening here is that

draw((0,0)..tension 2..(0,50)..(100,100));
is read as

draw((0,0)..tension 2. .(0,50)..(100,100));
So the first . after the two is treated as a decimal point.  Just put a
space after the integer tension value:

draw((0,0)..tension 2 ..(0,50)..(100,100));
-------------------------------------------------------------------------------

Question 3.2.  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.

===============================================================================

Section 4.  Questions about labels

 Q4.1        How do I get Greek letters like omega to show up in my labels?
 Q4.2        Can Asymptote use matrices as labels?
 Q4.3        How do I tell Asymptote to load a particular LaTeX package, like m
 Q4.4        How can I use international fonts in Asymptote labels?
 Q4.5        How can I use Fourier fonts? 
 Q4.6        Is there any way to change the default appearance of the decimal s
 Q4.7        How can I get a rotated label with the filled box rotated as well 
 Q4.8        How can I rotate labels in a 3D figure?
 Q4.9        How can I draw some squares and circles of a fixed size and put a 
 Q4.10       The binary operator * can be used to scale the color of a pen by a
 Q4.11       Why is the space after the comma decimal separator in my locale so
 Q4.12       How can I prevent texpreamble("\usepackage[pdftex]{hyperref}") fro

-------------------------------------------------------------------------------

Question 4.1.  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:

label("$\omega$",(0,0));
label("$\Omega$",(20,0));
-------------------------------------------------------------------------------

Question 4.2.  Can Asymptote use matrices as labels?

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

-------------------------------------------------------------------------------

Question 4.3.  How do I tell Asymptote to load a particular LaTeX package, like mathptmx?

Put

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

-------------------------------------------------------------------------------

Question 4.4.  How can I use international fonts in Asymptote labels?

See https://asymptote.sourceforge.io/doc/Pens.html.

-------------------------------------------------------------------------------

Question 4.5.  How can I use Fourier fonts?

usepackage("fourier");
defaultpen(font("T1","fut\textfamilyextension","m","n"));
-------------------------------------------------------------------------------

Question 4.6.  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:

locale("it_IT");
usepackage("icomma");
label(format(0.5));
-------------------------------------------------------------------------------

Question 4.7.  How can I get a rotated label with the filled box rotated as well so that it fits the text?

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

Question 4.8.  How can I rotate labels in a 3D figure?

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

import three;
size(100,100);

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

Question 4.9.  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
https://asymptote.sourceforge.io/gallery/subpictures.asy and
https://asymptote.sourceforge.io/gallery/mosquito.asy):

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));
-------------------------------------------------------------------------------

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?

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

Try
write(cyan); write(0.8*cyan); write(1.5*cyan);
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).

-------------------------------------------------------------------------------

Question 4.11.  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 icomma package near the beginning of your
file:
usepackage("icomma");

-------------------------------------------------------------------------------

Question 4.12.  How can I prevent texpreamble("\usepackage[pdftex]{hyperref}") from changing the page size?

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

Section 5.  Questions about arrows

 Q5.1        How do I draw two arrows at arbitrary positions along a path?
 Q5.2        How do I reverse the direction of an arrowhead?
 Q5.3        How do I change the size of all arrows?
 Q5.4        Can I create other arrowhead styles?

-------------------------------------------------------------------------------

Question 5.1.  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:

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))); 
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
plain_arrows.asy:

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);
-------------------------------------------------------------------------------

Question 5.2.  How do I reverse the direction of an arrowhead?

Simply reverse the direction of the path.

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

Question 5.3.  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:

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

Question 5.4.  Can I create other arrowhead styles?

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

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

===============================================================================

Section 6.  Questions about 2D graphs

 Q6.1        How can I draw x axis ticks on the right side, with the tick label
 Q6.2        How can I reposition the x axis label to three-quarters along the 
 Q6.3        How can I move the x axis label down 10bp?
 Q6.4        Can I use different pens for the axis, the axis label, and the tic
 Q6.5        How can I change the font type of the axes label?
 Q6.6        How can I change the font type of the tick labels on an axis?
 Q6.7        How can I prevent axes tick labels from rendering on top of each o
 Q6.8        How do I make the plot region of a graph, ignoring labels and lege
 Q6.9        How can I plot a function f(x) within [0,1]x[0,2] without explicit
 Q6.10       Is it possible to define customized palettes?
 Q6.11       Is there an easy way to graph factorial functions nicely?
 Q6.12       How do I indicate that a certain length should be exactly the size
 Q6.13       How can I make the y axis display base-2 logarithmic values?
 Q6.14       How can I align the x axes of two graphs on the same figure?
 Q6.15       How can I change the direction of the y-axis, such that negatives 
 Q6.16       How can I fill a path with a function that defines the color of ea
 Q6.17       Is there a way to draw a function that is not explicitly given, su
 Q6.18       Is it possible to reverse or stretch an axis?
 Q6.19       Why can't I use the UnFill option to draw graphs with empty marker
 Q6.20       How can I force several images to use the same palette range (e.g.

-------------------------------------------------------------------------------

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)?

import graph;

size(250,200,IgnoreAspect);

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

xaxis("$x$",RightTicks(Label(align=left)));
yaxis("$y$",RightTicks);
-------------------------------------------------------------------------------

Question 6.2.  How can I reposition the x axis label to three-quarters along the axis length?

import graph;

size(250,200,IgnoreAspect);

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

xaxis(Label("$x$",0.75),LeftTicks);
yaxis("$y$",RightTicks);
-------------------------------------------------------------------------------

Question 6.3.  How can I move the x axis label down 10bp?

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

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

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

Question 6.4.  Can I use different pens for the axis, the axis label, and the tick labels?

Yes:

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);
-------------------------------------------------------------------------------

Question 6.5.  How can I change the font type of the axes label?

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

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

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

Question 6.6.  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:

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);
-------------------------------------------------------------------------------

Question 6.7.  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
http://www.github.com/vectorgraphics/asymptote/base/graph.asy for the
definition of NoZero):

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

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

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

Label(currentpen+overwrite(Move))
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:  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.

-------------------------------------------------------------------------------

Question 6.8.  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 size:
unitsize(x=1cm,y=2cm);

ii) Explicitly tell Asymptote to map the plot region to a specific size:
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);

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

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));
In this example, the user coordinate (-1.5,-0.5) will end up being the
lower left corner of the figure and (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 fixedscaling() leaves room for any labels).

See also https://asymptote.sourceforge.io/doc/Frames-and-pictures.html.

-------------------------------------------------------------------------------

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?

Call limits with the Crop option before drawing the graph:
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);

See also https://asymptote.sourceforge.io/doc/graph.html.

-------------------------------------------------------------------------------

Question 6.10.  Is it possible to define customized palettes?

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

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);
} 
-------------------------------------------------------------------------------

Question 6.11.  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:

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);
-------------------------------------------------------------------------------

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?

Here's an easy way to do this.

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);
-------------------------------------------------------------------------------

Question 6.13.  How can I make the y axis display base-2 logarithmic values?

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

-------------------------------------------------------------------------------

Question 6.14.  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
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:

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));
-------------------------------------------------------------------------------

Question 6.15.  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
https://asymptote.sourceforge.io/gallery/2D graphs/diatom.asy or the
discussion of Linear(-1) in the documentation):

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

scale(Linear,Linear(-1));

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

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

Question 6.16.  How can I fill a path with a function that defines the color of each location?

Use 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  latticeshade
that depend on position as a single pen[][] lattice. Alternatively, it may
be more efficient to use tensorshade}.

-------------------------------------------------------------------------------

Question 6.17.  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

y=t 
x=(t-2)^2+1 
See the example https://asymptote.sourceforge.io/gallery/2D
graphs/parametricgraph.asy.

-------------------------------------------------------------------------------

Question 6.18.  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).

-------------------------------------------------------------------------------

Question 6.19.  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):

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);
-------------------------------------------------------------------------------

Question 6.20.  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 Full, Automatic or an explicit range
Range(pair min, pair 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.

===============================================================================

Section 7.  Questions about programming

 Q7.1        Is Asymptote an interpreter or a compiler?  
 Q7.2        What is the difference between a frame and a picture? 
 Q7.3        What is the difference between a path and a guide? 
 Q7.4        What is a convenient way to declare and initialize an array of pic
 Q7.5        Is there a way to define functions that act on arrays in general (
 Q7.6        Is there any way to declare structures ahead of their definition, 
 Q7.7        Where are static variables in for loops allocated?
 Q7.8        Is there a debugger for asy?
 Q7.9        Do you accept patches for Asymptote?

-------------------------------------------------------------------------------

Question 7.1.  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.

-------------------------------------------------------------------------------

Question 7.2.  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
Q8.8 `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?'.

-------------------------------------------------------------------------------

Question 7.3.  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.

-------------------------------------------------------------------------------

Question 7.4.  What is a convenient way to declare and initialize an array of pictures?

You could write yourself a routine such as:
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);

-------------------------------------------------------------------------------

Question 7.5.  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
typedef string T;
include F;
 
typedef real T;
include F;

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

-------------------------------------------------------------------------------

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?

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:

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);
-------------------------------------------------------------------------------

Question 7.7.  Where are static variables in for loops allocated?

In the example

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

f(); // Writes 1, 2, 3
the static qualifier means that n is allocated not just outside of the for
loop, but also outside the function. This is clear if you call  f multiple
times; there is still only one instance of 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:

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
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:

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
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.

-------------------------------------------------------------------------------

Question 7.8.  Is there a debugger for asy?

Yes, Asymptote includes a line-based debugger:

https://asymptote.sourceforge.io/doc/Debugger.html

-------------------------------------------------------------------------------

Question 7.9.  Do you accept patches for Asymptote?

Yes, in fact we would prefer that users submit patches for customized
features (to 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.

===============================================================================

Section 8.  Questions about differences between Asymptote and MetaPost

 Q8.1        What is the equivalent of the MetaPost c[a,b] interpolation operat
 Q8.2        How does picture scaling differ in Asymptote and MetaPost?
 Q8.3        How can I avoid automatic scaling of a picture?
 Q8.4        What is the equivalent of MetaPost ... command?
 Q8.5        What is the equivalent of the MetaPost pickup command?
 Q8.6        What is the equivalent of the MetaPost whatever command?
 Q8.7        What is the equivalent for the MetaPost command for lray - horiz*v
 Q8.8        In MetaPost, it is possible to have a drawing remain the same size
 Q8.9        In MetaPost, one could produce tiling pictures by generating a pic

-------------------------------------------------------------------------------

Question 8.1.  What is the equivalent of the MetaPost c[a,b] interpolation operator?

interp(a,b,c);
-------------------------------------------------------------------------------

Question 8.2.  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 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.

-------------------------------------------------------------------------------

Question 8.3.  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.

-------------------------------------------------------------------------------

Question 8.4.  What is the equivalent of MetaPost ... command?

The connector :: is a macro for tension atleast 1:

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

Question 8.5.  What is the equivalent of the MetaPost pickup command?

Just say, for example:

currentpen=red;
-------------------------------------------------------------------------------

Question 8.6.  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 whatever unknown. Such a facility could certainly
be added (perhaps using the notation ?= since = means assignment).
However, the most common uses of whatever in MetaPost are covered by
functions like extension in math.asy:
pair extension(pair P, pair Q, pair p, pair q);
this returns the intersection point of the extensions of the line segments
PQ and pq. We find using routines like 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 solve (see
https://asymptote.sourceforge.io/doc/solve.html), which uses LU
decomposition.

-------------------------------------------------------------------------------

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?

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

to find the intersection time for the line  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  horiz and verti.)

-------------------------------------------------------------------------------

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?

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 1cm:

unitsize(1cm);
draw(unitsquare);
One can also specify different x and y unit sizes:

unitsize(x=1cm,y=2cm);
draw(unitsquare);
Another way is to draw your fixed size object to a frame and add it to
currentpicture like this:

path p=(0,0)--(1,0);
frame object;
draw(object,scale(100)*p);
 
add(object);
add(object,(0,-10));
To understand the difference between frames and pictures, try this:

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 
-------------------------------------------------------------------------------

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?

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

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

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);
See also the discussion of tilings in the documentation:
https://asymptote.sourceforge.io/doc/Pens.html.

===============================================================================

Section 9.  Questions about output

 Q9.1        How can I disable automatic invocation of the PS viewer after an a
 Q9.2        How do I output jpeg images?
 Q9.3        Can I embed bitmaps (photos) into my drawings and position and sca
 Q9.4        Does Asymptote support direct PDF output?
 Q9.5        How to I produce large pictures of high quality in raster format (
 Q9.6        Is it possible to produce multi-page documents with asymptote? 

-------------------------------------------------------------------------------

Question 9.1.  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

import settings;
interactiveView=false;
batchView=false;
in their config.asy file. See
https://asymptote.sourceforge.io/doc/Options.html.

-------------------------------------------------------------------------------

Question 9.2.  How do I output jpeg images?

If you have the ImageMagick convert program installed, simply type

asy -f jpg test.asy 
-------------------------------------------------------------------------------

Question 9.3.  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:

label(graphic("file"),(0,0));
See the example https://asymptote.sourceforge.io/gallery/orthocenter.asy
and https://asymptote.sourceforge.io/doc/label.html.

-------------------------------------------------------------------------------

Question 9.4.  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.

-------------------------------------------------------------------------------

Question 9.5.  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:
convert -geometry 1000x3000 example.eps example.png 

You can also change the default resolution of the image with:
convert -geometry 1000x3000 -density 300 -units PixelsPerInch example.eps example.png 
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).

-------------------------------------------------------------------------------

Question 9.6.  Is it possible to produce multi-page documents with asymptote?

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

