asy 2.25 sources again, this time from CTAN

git-svn-id: svn://tug.org/texlive/trunk@33603 c570f23f-e606-0410-a88d-b1316a301751

11 files changed, 11999 insertions, 99 deletions

diff --git a/Build/source/utils/asymptote/doc/.cvsignore b/Build/source/utils/asymptote/doc/.cvsignore
deleted file mode 100644
index bd8d0a3caf6..00000000000
--- a/Build/source/utils/asymptote/doc/.cvsignore
+++ /dev/null
@@ -1,18 +0,0 @@
-*.png
-*.jpg
-*.eps
-*.aux
-*.log
-*.dvi
-*.cp
-*.cps
-*.fn
-*.info
-*.ky
-*.pg
-*.toc
-*.tp
-*.vr
-asymptote
-latexusage.asy
-version.texi
diff --git a/Build/source/utils/asymptote/doc/CAD.pdf b/Build/source/utils/asymptote/doc/CAD.pdf
new file mode 100644
index 00000000000..2eeebe293a4
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/CAD.pdf
diff --git a/Build/source/utils/asymptote/doc/CAD1.asy b/Build/source/utils/asymptote/doc/CAD1.asy
index 4602e73b709..26184aaad2c 100644
--- a/Build/source/utils/asymptote/doc/CAD1.asy
+++ b/Build/source/utils/asymptote/doc/CAD1.asy
@@ -1,43 +1,43 @@
-import CAD;

-

-sCAD cad=sCAD.Create();

-

-// Freehand line

-draw(g=cad.MakeFreehand(pFrom=(3,-1)*cm,(6,-1)*cm),

-     p=cad.pFreehand);

-

-// Standard measurement lines

-draw(g=box((0,0)*cm,(1,1)*cm),p=cad.pVisibleEdge);

-cad.MeasureParallel(L="$\sqrt{2}$",

-                    pFrom=(0,1)*cm,

-                    pTo=(1,0)*cm,

-                    dblDistance=-15mm);

-

-// Label inside,shifted to the right; arrows outside

-draw(g=box((2,0)*cm,(3,1)*cm),p=cad.pVisibleEdge);

-cad.MeasureParallel(L="1",

-                    pFrom=(2,1)*cm,

-                    pTo=(3,1)*cm,

-                    dblDistance=5mm,

-                    dblLeft=5mm,

-                    dblRelPosition=0.75);

-

-// Label and arrows outside

-draw(g=box((5,0)*cm,(5.5,1)*cm),p=cad.pVisibleEdge);

-cad.MeasureParallel(L="0.5",

-                    pFrom=(5,1)*cm,

-                    pTo=(5.5,1)*cm,

-                    dblDistance=5mm,

-                    dblLeft=10mm,

-                    dblRelPosition=-1);

-

-// Small bounds,asymmetric measurement line

-draw(g=box((7,0)*cm,(7.5,1)*cm),p=cad.pVisibleEdge);

-cad.MeasureParallel(L="0.5",

-                    pFrom=(7,1)*cm,

-                    pTo=(7.5,1)*cm,

-                    dblDistance=5mm,

-                    dblLeft=2*cad.GetMeasurementBoundSize(bSmallBound=true),

-                    dblRight=10mm,

-                    dblRelPosition=2,

-                    bSmallBound=true);

+import CAD;
+
+sCAD cad=sCAD.Create();
+
+// Freehand line
+draw(g=cad.MakeFreehand(pFrom=(3,-1)*cm,(6,-1)*cm),
+     p=cad.pFreehand);
+
+// Standard measurement lines
+draw(g=box((0,0)*cm,(1,1)*cm),p=cad.pVisibleEdge);
+cad.MeasureParallel(L="$\sqrt{2}$",
+                    pFrom=(0,1)*cm,
+                    pTo=(1,0)*cm,
+                    dblDistance=-15mm);
+
+// Label inside,shifted to the right; arrows outside
+draw(g=box((2,0)*cm,(3,1)*cm),p=cad.pVisibleEdge);
+cad.MeasureParallel(L="1",
+                    pFrom=(2,1)*cm,
+                    pTo=(3,1)*cm,
+                    dblDistance=5mm,
+                    dblLeft=5mm,
+                    dblRelPosition=0.75);
+
+// Label and arrows outside
+draw(g=box((5,0)*cm,(5.5,1)*cm),p=cad.pVisibleEdge);
+cad.MeasureParallel(L="0.5",
+                    pFrom=(5,1)*cm,
+                    pTo=(5.5,1)*cm,
+                    dblDistance=5mm,
+                    dblLeft=10mm,
+                    dblRelPosition=-1);
+
+// Small bounds,asymmetric measurement line
+draw(g=box((7,0)*cm,(7.5,1)*cm),p=cad.pVisibleEdge);
+cad.MeasureParallel(L="0.5",
+                    pFrom=(7,1)*cm,
+                    pTo=(7.5,1)*cm,
+                    dblDistance=5mm,
+                    dblLeft=2*cad.GetMeasurementBoundSize(bSmallBound=true),
+                    dblRight=10mm,
+                    dblRelPosition=2,
+                    bSmallBound=true);
diff --git a/Build/source/utils/asymptote/doc/FAQ/asy-faq.info b/Build/source/utils/asymptote/doc/FAQ/asy-faq.info
new file mode 100644
index 00000000000..30134dc77d7
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/FAQ/asy-faq.info
@@ -0,0 +1,1671 @@
+Info file: asy-faq.info,    -*-Text-*-
+produced by bfnnconv.pl from the Bizarre Format With No Name.
+
+INFO-DIR-SECTION Languages
+START-INFO-DIR-ENTRY
+* asymptote FAQ: (asy-faq).    Asymptote Frequently Asked Questions.
+END-INFO-DIR-ENTRY
+
+
+File: asy-faq.info, Node: Top, Next: Question 1.1, Up: (dir)
+
+            ASYMPTOTE FREQUENTLY ASKED QUESTIONS
+                            20 Apr 2014
+                          
+This is the list of Frequently Asked Questions about Asymptote (asy).
+
+Index
+
+* Menu:
+* Section 1::       About Asymptote
+* Section 2::       Questions about installation and setup
+* Section 3::       Questions about paths
+* Section 4::       Questions about labels
+* Section 5::       Questions about arrows
+* Section 6::       Questions about 2D graphs
+* Section 7::       Questions about programming
+* Section 8::       Questions about differences between Asymptote and
+                    MetaPost
+* Section 9::       Questions about output
+
+Section 1, About Asymptote
+* Question 1.1::    What is Asymptote?
+* Question 1.2::    How do I obtain Asymptote?
+* Question 1.3::    Where can I ask questions about Asymptote?
+* Question 1.4::    Why was the name Asymptote chosen?
+* Question 1.5::    In the internal Asymptote source code, what does the
+                    name camp refer to?
+
+Section 2, Questions about installation and setup
+* Question 2.1::    Is it possible to install Asymptote on Mac OS X?
+* Question 2.2::    Why do I get the error Bad CPU type in executable on
+                    installing Asymptote from the MAC OS binary?
+* 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?
+* Question 2.4::    What do I do if I get the error: ! Undefined control
+                    sequence. l.6 @copying?
+* Question 2.5::    Is it possible to integrate Asymptote into LaTeX?
+* Question 2.6::    Is it possible to integrate Asymptote into latex or
+                    pdflatex?
+* Question 2.7::    Do I need the tkinter package to install an Asymptote
+                    rpm binary?
+* Question 2.8::    What does the path %USERPROFILE%\.asy\config.asy mean?
+* Question 2.9::    Why do I get the error "string not terminated" when I
+                    try to set 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?
+* Question 2.11::   Under Microsoft Windows XP, why do I get an error like
+                    "Invalid Parameter - 432x432"?
+* Question 2.12::   Why does Asymptote freeze upon trying to draw a label
+                    with my MikTex installation under Microsoft Windows?
+
+Section 3, Questions about paths
+* Question 3.1::    Why do I get a syntax error message when I specify an
+                    integer value for the path tension?
+* Question 3.2::    Shouldn't dots always be the same size?
+
+Section 4, Questions about labels
+* Question 4.1::    How do I get Greek letters like omega to show up in my
+                    labels?
+* Question 4.2::    Can Asymptote use matrices as labels?
+* Question 4.3::    How do I tell Asymptote to load a particular LaTeX
+                    package, like mathptmx?
+* Question 4.4::    How can I use international fonts in Asymptote labels?
+* Question 4.5::    How can I use Fourier fonts?
+* Question 4.6::    Is there any way to change the default appearance of
+                    the decimal separator, using a comma instead of a dot?
+* Question 4.7::    How can I get a rotated label with the filled box
+                    rotated as well so that it fits the text?
+* Question 4.8::    How can I rotate labels in a 3D figure?
+* Question 4.9::    How can I draw some squares and circles of a fixed
+                    size and put a label in the middle of them?
+* 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?
+* Question 4.11::   Why is the space after the comma decimal separator in
+                    my locale so large?
+* Question 4.12::   How can I prevent
+                    texpreamble("\usepackage[pdftex]{hyperref}") from
+                    changing the page size?
+
+Section 5, Questions about arrows
+* Question 5.1::    How do I draw two arrows at arbitrary positions along
+                    a path?
+* Question 5.2::    How do I reverse the direction of an arrowhead?
+* Question 5.3::    How do I change the size of all arrows?
+* Question 5.4::    Can I create other arrowhead styles?
+
+Section 6, Questions about 2D graphs
+* 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)?
+* Question 6.2::    How can I reposition the x axis label to
+                    three-quarters along the axis length?
+* Question 6.3::    How can I move the x axis label down 10bp?
+* Question 6.4::    Can I use different pens for the axis, the axis label,
+                    and the tick labels?
+* Question 6.5::    How can I change the font type of the axes label?
+* Question 6.6::    How can I change the font type of the tick labels on
+                    an axis?
+* Question 6.7::    How can I prevent axes tick labels from rendering on
+                    top of each other?
+* Question 6.8::    How do I make the plot region of a graph, ignoring
+                    labels and legends, have a fixed size?
+* 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?
+* Question 6.10::   Is it possible to define customized palettes?
+* Question 6.11::   Is there an easy way to graph factorial functions
+                    nicely?
+* 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?
+* Question 6.13::   How can I make the y axis display base-2 logarithmic
+                    values?
+* Question 6.14::   How can I align the x axes of two graphs on the same
+                    figure?
+* Question 6.15::   How can I change the direction of the y-axis, such
+                    that negatives values are on the upper y-axis?
+* Question 6.16::   How can I fill a path with a function that defines the
+                    color of each location?
+* Question 6.17::   Is there a way to draw a function that is not
+                    explicitly given, such as (y - 2)^2 = x - 1 ?
+* Question 6.18::   Is it possible to reverse or stretch an axis?
+* Question 6.19::   Why can't I use the UnFill option to draw graphs with
+                    empty markers?
+* Question 6.20::   How can I force several images to use the same palette
+                    range (e.g. the entire 0-255 grayscale range)?
+
+Section 7, Questions about programming
+* Question 7.1::    Is Asymptote an interpreter or a compiler?
+* Question 7.2::    What is the difference between a frame and a picture?
+* Question 7.3::    What is the difference between a path and a guide?
+* Question 7.4::    What is a convenient way to declare and initialize an
+                    array of pictures?
+* Question 7.5::    Is there a way to define functions that act on arrays
+                    in general (i.e. work for arrays of any type)?
+* 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?
+* Question 7.7::    Where are static variables in for loops allocated?
+* Question 7.8::    Is there a debugger for asy?
+* Question 7.9::    Do you accept patches for Asymptote?
+
+Section 8, Questions about differences between Asymptote and
+                    MetaPost
+* Question 8.1::    What is the equivalent of the MetaPost c[a,b]
+                    interpolation operator?
+* Question 8.2::    How does picture scaling differ in Asymptote and
+                    MetaPost?
+* Question 8.3::    How can I avoid automatic scaling of a picture?
+* Question 8.4::    What is the equivalent of MetaPost ... command?
+* Question 8.5::    What is the equivalent of the MetaPost pickup command?
+* Question 8.6::    What is the equivalent of the MetaPost whatever
+                    command?
+* 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?
+* 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?
+* 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?
+
+Section 9, Questions about output
+* Question 9.1::    How can I disable automatic invocation of the PS
+                    viewer after an asy file is done processing?
+* Question 9.2::    How do I output jpeg images?
+* Question 9.3::    Can I embed bitmaps (photos) into my drawings and
+                    position and scale them?
+* Question 9.4::    Does Asymptote support direct PDF output?
+* Question 9.5::    How to I produce large pictures of high quality in
+                    raster format (e.g. png, giff etc).
+* Question 9.6::    Is it possible to produce multi-page documents with
+                    asymptote?
+
+
+
+File: asy-faq.info, Node: Section 1, Next: Section 2, Previous: Top, Up: Top
+
+About Asymptote
+
+* Menu:
+* Question 1.1::    What is Asymptote?
+* Question 1.2::    How do I obtain Asymptote?
+* Question 1.3::    Where can I ask questions about Asymptote?
+* Question 1.4::    Why was the name Asymptote chosen?
+* Question 1.5::    In the internal Asymptote source code, what does the
+                    name camp refer to?
+
+
+
+File: asy-faq.info, Node: Question 1.1, Next: Question 1.2, Previous: Top, Up: Section 1
+
+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.
+
+
+File: asy-faq.info, Node: Question 1.2, Next: Question 1.3, Previous: Question 1.1, Up: Section 1
+
+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
+http://asymptote.sourceforge.net/.  Many Linux distributions (such as
+RedHat and Debian) now include an Asymptote package (check your
+distribution's documentation for further information about this).
+
+
+File: asy-faq.info, Node: Question 1.3, Next: Question 1.4, Previous: Question 1.2, Up: Section 1
+
+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
+http://asymptote.sourceforge.net/doc/, or search the forum:
+http://sourceforge.net/forum/forum.php?forum_id=409349.
+
+
+File: asy-faq.info, Node: Question 1.4, Next: Question 1.5, Previous: Question 1.3, Up: Section 1
+
+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...
+
+
+File: asy-faq.info, Node: Question 1.5, Next: Question 2.1, Previous: Question 1.4, Up: Section 1
+
+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.
+
+
+File: asy-faq.info, Node: Section 2, Next: Section 3, Previous: Section 1, Up: Top
+
+Questions about installation and setup
+
+* Menu:
+* Question 2.1::    Is it possible to install Asymptote on Mac OS X?
+* Question 2.2::    Why do I get the error Bad CPU type in executable on
+                    installing Asymptote from the MAC OS binary?
+* 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?
+* Question 2.4::    What do I do if I get the error: ! Undefined control
+                    sequence. l.6 @copying?
+* Question 2.5::    Is it possible to integrate Asymptote into LaTeX?
+* Question 2.6::    Is it possible to integrate Asymptote into latex or
+                    pdflatex?
+* Question 2.7::    Do I need the tkinter package to install an Asymptote
+                    rpm binary?
+* Question 2.8::    What does the path %USERPROFILE%\.asy\config.asy mean?
+* Question 2.9::    Why do I get the error "string not terminated" when I
+                    try to set 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?
+* Question 2.11::   Under Microsoft Windows XP, why do I get an error like
+                    "Invalid Parameter - 432x432"?
+* Question 2.12::   Why does Asymptote freeze upon trying to draw a label
+                    with my MikTex installation under Microsoft Windows?
+
+
+
+File: asy-faq.info, Node: Question 2.1, Next: Question 2.2, Previous: Question 1.5, Up: Section 2
+
+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.
+
+
+File: asy-faq.info, Node: Question 2.2, Next: Question 2.3, Previous: Question 2.1, Up: Section 2
+
+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.
+
+
+File: asy-faq.info, Node: Question 2.3, Next: Question 2.4, Previous: Question 2.2, Up: Section 2
+
+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 http://asymptote.sourceforge.net/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.
+
+
+File: asy-faq.info, Node: Question 2.4, Next: Question 2.5, Previous: Question 2.3, Up: Section 2
+
+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 *Note 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?'.
+
+
+File: asy-faq.info, Node: Question 2.5, Next: Question 2.6, Previous: Question 2.4, Up: Section 2
+
+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
+http://asymptote.sourceforge.net/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.
+
+
+File: asy-faq.info, Node: Question 2.6, Next: Question 2.7, Previous: Question 2.5, Up: Section 2
+
+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
+
+File: asy-faq.info, Node: Question 2.7, Next: Question 2.8, Previous: Question 2.6, Up: Section 2
+
+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.
+
+
+File: asy-faq.info, Node: Question 2.8, Next: Question 2.9, Previous: Question 2.7, Up: Section 2
+
+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.
+
+
+File: asy-faq.info, Node: Question 2.9, Next: Question 2.10, Previous: Question 2.8, Up: Section 2
+
+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"+'\\';.
+
+
+File: asy-faq.info, Node: Question 2.10, Next: Question 2.11, Previous: Question 2.9, Up: Section 2
+
+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.
+
+
+File: asy-faq.info, Node: Question 2.11, Next: Question 2.12, Previous: Question 2.10, Up: Section 2
+
+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
+
+File: asy-faq.info, Node: Question 2.12, Next: Question 3.1, Previous: Question 2.11, Up: Section 2
+
+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";
+
+File: asy-faq.info, Node: Section 3, Next: Section 4, Previous: Section 2, Up: Top
+
+Questions about paths
+
+* Menu:
+* Question 3.1::    Why do I get a syntax error message when I specify an
+                    integer value for the path tension?
+* Question 3.2::    Shouldn't dots always be the same size?
+
+
+
+File: asy-faq.info, Node: Question 3.1, Next: Question 3.2, Previous: Question 2.12, Up: Section 3
+
+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));
+
+File: asy-faq.info, Node: Question 3.2, Next: Question 4.1, Previous: Question 3.1, Up: Section 3
+
+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.
+
+
+File: asy-faq.info, Node: Section 4, Next: Section 5, Previous: Section 3, Up: Top
+
+Questions about labels
+
+* Menu:
+* Question 4.1::    How do I get Greek letters like omega to show up in my
+                    labels?
+* Question 4.2::    Can Asymptote use matrices as labels?
+* Question 4.3::    How do I tell Asymptote to load a particular LaTeX
+                    package, like mathptmx?
+* Question 4.4::    How can I use international fonts in Asymptote labels?
+* Question 4.5::    How can I use Fourier fonts?
+* Question 4.6::    Is there any way to change the default appearance of
+                    the decimal separator, using a comma instead of a dot?
+* Question 4.7::    How can I get a rotated label with the filled box
+                    rotated as well so that it fits the text?
+* Question 4.8::    How can I rotate labels in a 3D figure?
+* Question 4.9::    How can I draw some squares and circles of a fixed
+                    size and put a label in the middle of them?
+* 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?
+* Question 4.11::   Why is the space after the comma decimal separator in
+                    my locale so large?
+* Question 4.12::   How can I prevent
+                    texpreamble("\usepackage[pdftex]{hyperref}") from
+                    changing the page size?
+
+
+
+File: asy-faq.info, Node: Question 4.1, Next: Question 4.2, Previous: Question 3.2, Up: Section 4
+
+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));
+
+File: asy-faq.info, Node: Question 4.2, Next: Question 4.3, Previous: Question 4.1, Up: Section 4
+
+Question 4.2.  Can Asymptote use matrices as labels?
+
+Yes:
+usepackage("amsmath");
+label("$\begin{matrix} 1 & 2 \\\ 1 & 1 \end{matrix}$",(0,0));
+
+File: asy-faq.info, Node: Question 4.3, Next: Question 4.4, Previous: Question 4.2, Up: Section 4
+
+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());
+
+File: asy-faq.info, Node: Question 4.4, Next: Question 4.5, Previous: Question 4.3, Up: Section 4
+
+Question 4.4.  How can I use international fonts in Asymptote labels?
+
+See http://asymptote.sourceforge.net/doc/unicode.html.
+
+
+File: asy-faq.info, Node: Question 4.5, Next: Question 4.6, Previous: Question 4.4, Up: Section 4
+
+Question 4.5.  How can I use Fourier fonts?
+
+usepackage("fourier");
+defaultpen(font("T1","fut\textfamilyextension","m","n"));
+
+File: asy-faq.info, Node: Question 4.6, Next: Question 4.7, Previous: Question 4.5, Up: Section 4
+
+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));
+
+File: asy-faq.info, Node: Question 4.7, Next: Question 4.8, Previous: Question 4.6, Up: Section 4
+
+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);
+
+File: asy-faq.info, Node: Question 4.8, Next: Question 4.9, Previous: Question 4.7, Up: Section 4
+
+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);
+
+File: asy-faq.info, Node: Question 4.9, Next: Question 4.10, Previous: Question 4.8, Up: Section 4
+
+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
+http://asymptote.sourceforge.net/gallery/subpictures.asy and
+http://asymptote.sourceforge.net/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));
+
+File: asy-faq.info, Node: Question 4.10, Next: Question 4.11, Previous: Question 4.9, Up: Section 4
+
+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).
+
+
+File: asy-faq.info, Node: Question 4.11, Next: Question 4.12, Previous: Question 4.10, Up: Section 4
+
+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");
+
+File: asy-faq.info, Node: Question 4.12, Next: Question 5.1, Previous: Question 4.11, Up: Section 4
+
+Question 4.12.  How can I prevent texpreamble("\usepackage[pdftex]{hyperref}") from changing the page size?
+
+texpreamble("\usepackage[pdftex,setpagesize=false]{hyperref}");
+
+File: asy-faq.info, Node: Section 5, Next: Section 6, Previous: Section 4, Up: Top
+
+Questions about arrows
+
+* Menu:
+* Question 5.1::    How do I draw two arrows at arbitrary positions along
+                    a path?
+* Question 5.2::    How do I reverse the direction of an arrowhead?
+* Question 5.3::    How do I change the size of all arrows?
+* Question 5.4::    Can I create other arrowhead styles?
+
+
+
+File: asy-faq.info, Node: Question 5.1, Next: Question 5.2, Previous: Question 4.12, Up: Section 5
+
+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);
+
+File: asy-faq.info, Node: Question 5.2, Next: Question 5.3, Previous: Question 5.1, Up: Section 5
+
+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)));
+
+File: asy-faq.info, Node: Question 5.3, Next: Question 5.4, Previous: Question 5.2, Up: Section 5
+
+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;};
+
+File: asy-faq.info, Node: Question 5.4, Next: Question 6.1, Previous: Question 5.3, Up: Section 5
+
+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.
+
+
+File: asy-faq.info, Node: Section 6, Next: Section 7, Previous: Section 5, Up: Top
+
+Questions about 2D graphs
+
+* Menu:
+* 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)?
+* Question 6.2::    How can I reposition the x axis label to
+                    three-quarters along the axis length?
+* Question 6.3::    How can I move the x axis label down 10bp?
+* Question 6.4::    Can I use different pens for the axis, the axis label,
+                    and the tick labels?
+* Question 6.5::    How can I change the font type of the axes label?
+* Question 6.6::    How can I change the font type of the tick labels on
+                    an axis?
+* Question 6.7::    How can I prevent axes tick labels from rendering on
+                    top of each other?
+* Question 6.8::    How do I make the plot region of a graph, ignoring
+                    labels and legends, have a fixed size?
+* 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?
+* Question 6.10::   Is it possible to define customized palettes?
+* Question 6.11::   Is there an easy way to graph factorial functions
+                    nicely?
+* 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?
+* Question 6.13::   How can I make the y axis display base-2 logarithmic
+                    values?
+* Question 6.14::   How can I align the x axes of two graphs on the same
+                    figure?
+* Question 6.15::   How can I change the direction of the y-axis, such
+                    that negatives values are on the upper y-axis?
+* Question 6.16::   How can I fill a path with a function that defines the
+                    color of each location?
+* Question 6.17::   Is there a way to draw a function that is not
+                    explicitly given, such as (y - 2)^2 = x - 1 ?
+* Question 6.18::   Is it possible to reverse or stretch an axis?
+* Question 6.19::   Why can't I use the UnFill option to draw graphs with
+                    empty markers?
+* Question 6.20::   How can I force several images to use the same palette
+                    range (e.g. the entire 0-255 grayscale range)?
+
+
+
+File: asy-faq.info, Node: Question 6.1, Next: Question 6.2, Previous: Question 5.4, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.2, Next: Question 6.3, Previous: Question 6.1, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.3, Next: Question 6.4, Previous: Question 6.2, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.4, Next: Question 6.5, Previous: Question 6.3, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.5, Next: Question 6.6, Previous: Question 6.4, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.6, Next: Question 6.7, Previous: Question 6.5, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.7, Next: Question 6.8, Previous: Question 6.6, Up: Section 6
+
+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://asymptote.svn.sourceforge.net/viewvc/asymptote/trunk/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://asymptote.svn.sourceforge.net/viewvc/asymptote/trunk/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:  http://asymptote.sourceforge.net/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.
+
+
+File: asy-faq.info, Node: Question 6.8, Next: Question 6.9, Previous: Question 6.7, Up: Section 6
+
+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 http://asymptote.sourceforge.net/doc/Frames-and-pictures.html.
+
+
+File: asy-faq.info, Node: Question 6.9, Next: Question 6.10, Previous: Question 6.8, Up: Section 6
+
+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 http://asymptote.sourceforge.net/doc/graph.html.
+
+
+File: asy-faq.info, Node: Question 6.10, Next: Question 6.11, Previous: Question 6.9, Up: Section 6
+
+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);
+} 
+
+File: asy-faq.info, Node: Question 6.11, Next: Question 6.12, Previous: Question 6.10, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.12, Next: Question 6.13, Previous: Question 6.11, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.13, Next: Question 6.14, Previous: Question 6.12, Up: Section 6
+
+Question 6.13.  How can I make the y axis display base-2 logarithmic values?
+
+See the example http://asymptote.sourceforge.net/gallery/2D
+graphs/log2graph.asy.
+
+
+File: asy-faq.info, Node: Question 6.14, Next: Question 6.15, Previous: Question 6.13, Up: Section 6
+
+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
+http://asymptote.sourceforge.net/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));
+
+File: asy-faq.info, Node: Question 6.15, Next: Question 6.16, Previous: Question 6.14, Up: Section 6
+
+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
+http://asymptote.sourceforge.net/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);
+
+File: asy-faq.info, Node: Question 6.16, Next: Question 6.17, Previous: Question 6.15, Up: Section 6
+
+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}.
+
+
+File: asy-faq.info, Node: Question 6.17, Next: Question 6.18, Previous: Question 6.16, Up: Section 6
+
+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 http://asymptote.sourceforge.net/gallery/2D
+graphs/parametricgraph.asy.
+
+
+File: asy-faq.info, Node: Question 6.18, Next: Question 6.19, Previous: Question 6.17, Up: Section 6
+
+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).
+
+
+File: asy-faq.info, Node: Question 6.19, Next: Question 6.20, Previous: Question 6.18, Up: Section 6
+
+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);
+
+File: asy-faq.info, Node: Question 6.20, Next: Question 7.1, Previous: Question 6.19, Up: Section 6
+
+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.
+
+
+File: asy-faq.info, Node: Section 7, Next: Section 8, Previous: Section 6, Up: Top
+
+Questions about programming
+
+* Menu:
+* Question 7.1::    Is Asymptote an interpreter or a compiler?
+* Question 7.2::    What is the difference between a frame and a picture?
+* Question 7.3::    What is the difference between a path and a guide?
+* Question 7.4::    What is a convenient way to declare and initialize an
+                    array of pictures?
+* Question 7.5::    Is there a way to define functions that act on arrays
+                    in general (i.e. work for arrays of any type)?
+* 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?
+* Question 7.7::    Where are static variables in for loops allocated?
+* Question 7.8::    Is there a debugger for asy?
+* Question 7.9::    Do you accept patches for Asymptote?
+
+
+
+File: asy-faq.info, Node: Question 7.1, Next: Question 7.2, Previous: Question 6.20, Up: Section 7
+
+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.
+
+
+File: asy-faq.info, Node: Question 7.2, Next: Question 7.3, Previous: Question 7.1, Up: Section 7
+
+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
+*Note 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?'.
+
+
+File: asy-faq.info, Node: Question 7.3, Next: Question 7.4, Previous: Question 7.2, Up: Section 7
+
+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.
+
+
+File: asy-faq.info, Node: Question 7.4, Next: Question 7.5, Previous: Question 7.3, Up: Section 7
+
+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);
+
+File: asy-faq.info, Node: Question 7.5, Next: Question 7.6, Previous: Question 7.4, Up: Section 7
+
+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};}
+
+File: asy-faq.info, Node: Question 7.6, Next: Question 7.7, Previous: Question 7.5, Up: Section 7
+
+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);
+
+File: asy-faq.info, Node: Question 7.7, Next: Question 7.8, Previous: Question 7.6, Up: Section 7
+
+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.
+
+
+File: asy-faq.info, Node: Question 7.8, Next: Question 7.9, Previous: Question 7.7, Up: Section 7
+
+Question 7.8.  Is there a debugger for asy?
+
+Yes, Asymptote includes a line-based debugger:
+
+http://asymptote.sourceforge.net/doc/Debugger.html
+
+
+File: asy-faq.info, Node: Question 7.9, Next: Question 8.1, Previous: Question 7.8, Up: Section 7
+
+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.
+
+
+File: asy-faq.info, Node: Section 8, Next: Section 9, Previous: Section 7, Up: Top
+
+Questions about differences between Asymptote and MetaPost
+
+* Menu:
+* Question 8.1::    What is the equivalent of the MetaPost c[a,b]
+                    interpolation operator?
+* Question 8.2::    How does picture scaling differ in Asymptote and
+                    MetaPost?
+* Question 8.3::    How can I avoid automatic scaling of a picture?
+* Question 8.4::    What is the equivalent of MetaPost ... command?
+* Question 8.5::    What is the equivalent of the MetaPost pickup command?
+* Question 8.6::    What is the equivalent of the MetaPost whatever
+                    command?
+* 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?
+* 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?
+* 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?
+
+
+
+File: asy-faq.info, Node: Question 8.1, Next: Question 8.2, Previous: Question 7.9, Up: Section 8
+
+Question 8.1.  What is the equivalent of the MetaPost c[a,b] interpolation operator?
+
+interp(a,b,c);
+
+File: asy-faq.info, Node: Question 8.2, Next: Question 8.3, Previous: Question 8.1, Up: Section 8
+
+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 http://asymptote.sourceforge.net/gallery/dimension.asy example for
+an example of how deferred drawing is used to accomodate both user and
+true-size (PostScript) coordinates.
+
+
+File: asy-faq.info, Node: Question 8.3, Next: Question 8.4, Previous: Question 8.2, Up: Section 8
+
+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.
+
+
+File: asy-faq.info, Node: Question 8.4, Next: Question 8.5, Previous: Question 8.3, Up: Section 8
+
+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});
+
+File: asy-faq.info, Node: Question 8.5, Next: Question 8.6, Previous: Question 8.4, Up: Section 8
+
+Question 8.5.  What is the equivalent of the MetaPost pickup command?
+
+Just say, for example:
+
+currentpen=red;
+
+File: asy-faq.info, Node: Question 8.6, Next: Question 8.7, Previous: Question 8.5, Up: Section 8
+
+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
+http://asymptote.sourceforge.net/doc/solve.html), which uses LU
+decomposition.
+
+
+File: asy-faq.info, Node: Question 8.7, Next: Question 8.8, Previous: Question 8.6, Up: Section 8
+
+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.)
+
+
+File: asy-faq.info, Node: Question 8.8, Next: Question 8.9, Previous: Question 8.7, Up: Section 8
+
+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 
+
+File: asy-faq.info, Node: Question 8.9, Next: Question 9.1, Previous: Question 8.8, Up: Section 8
+
+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:
+http://asymptote.sourceforge.net/doc/Pens.html.
+
+
+File: asy-faq.info, Node: Section 9, Previous: Section 8, Up: Top
+
+Questions about output
+
+* Menu:
+* Question 9.1::    How can I disable automatic invocation of the PS
+                    viewer after an asy file is done processing?
+* Question 9.2::    How do I output jpeg images?
+* Question 9.3::    Can I embed bitmaps (photos) into my drawings and
+                    position and scale them?
+* Question 9.4::    Does Asymptote support direct PDF output?
+* Question 9.5::    How to I produce large pictures of high quality in
+                    raster format (e.g. png, giff etc).
+* Question 9.6::    Is it possible to produce multi-page documents with
+                    asymptote?
+
+
+
+File: asy-faq.info, Node: Question 9.1, Next: Question 9.2, Previous: Question 8.9, Up: Section 9
+
+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
+http://asymptote.sourceforge.net/doc/Options.html.
+
+
+File: asy-faq.info, Node: Question 9.2, Next: Question 9.3, Previous: Question 9.1, Up: Section 9
+
+Question 9.2.  How do I output jpeg images?
+
+If you have the ImageMagick convert program installed, simply type
+
+asy -f jpg test.asy 
+
+File: asy-faq.info, Node: Question 9.3, Next: Question 9.4, Previous: Question 9.2, Up: Section 9
+
+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 http://asymptote.sourceforge.net/gallery/orthocenter.asy
+and http://asymptote.sourceforge.net/doc/label.html.
+
+
+File: asy-faq.info, Node: Question 9.4, Next: Question 9.5, Previous: Question 9.3, Up: Section 9
+
+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.
+
+
+File: asy-faq.info, Node: Question 9.5, Next: Question 9.6, Previous: Question 9.4, Up: Section 9
+
+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).
+
+
+File: asy-faq.info, Node: Question 9.6, Previous: Question 9.5, Up: Section 9
+
+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).
+
diff --git a/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf b/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf
new file mode 100644
index 00000000000..e956672af0d
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf
diff --git a/Build/source/utils/asymptote/doc/asy-latex.pdf b/Build/source/utils/asymptote/doc/asy-latex.pdf
new file mode 100644
index 00000000000..bb3e9426e26
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/asy-latex.pdf
diff --git a/Build/source/utils/asymptote/doc/asy.1 b/Build/source/utils/asymptote/doc/asy.1
new file mode 100644
index 00000000000..979fd50ee38
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/asy.1
@@ -0,0 +1,297 @@
+.\"                                      Hey, EMACS: -*- nroff -*-
+.TH ASY 1 "1 Dec 2004"
+.SH NAME
+asy \- Asymptote: a script-based vector graphics language
+.SH SYNOPSIS
+.B asy
+.RI [ options ]
+.RI [ file \ ...]
+.SH DESCRIPTION
+\fBAsymptote\fP is a powerful descriptive vector graphics language for
+technical drawings, inspired by MetaPost but with an improved C++-like syntax.
+Asymptote provides for figures the same high-quality level of typesetting that
+LaTeX does for scientific text.
+.SH OPTIONS
+If no arguments are given, Asymptote runs in interactive mode.
+.PP
+If "\-" is given as the file argument, Asymptote reads from standard input.
+.PP
+A summary of options is included below. The effect of most options
+can be negated by prepending 
+.B no
+to the option name. 
+Default values for most options may also be entered in the 
+file 
+.B .asy/config.asy
+in the user's home directory using the long form:
+.PP
+     import settings;
+     batchView=true;
+.PP
+For a complete
+description, see the Info files.
+.TP
+.B \-V,\-View             
+View output; command-line only.
+.TP
+.B \-a,\-align C|B|T|Z    
+Center, Bottom, Top, or Zero page alignment [C].
+.TP
+.B \-antialias n         
+Antialiasing width for rasterized output [2].
+.TP
+.B \-arcballradius pixels
+Arcball radius [750].
+.TP
+.B \-auto3D              
+Automatically activate 3D scene [true].
+.TP
+.B \-autobillboard       
+3D labels always face viewer by default [true].
+.TP
+.B \-autoimport string   
+Module to automatically import.
+.TP
+.B \-autoplain           
+Enable automatic importing of plain [true].
+.TP
+.B \-autoplay            
+Autoplay 3D animations [false].
+.TP
+.B \-autorotate          
+Enable automatic PDF page rotation [false].
+.TP
+.B \-axes3               
+Show 3D axes in PDF output [true].
+.TP
+.B \-batchMask           
+Mask fpu exceptions in batch mode [false].
+.TP
+.B \-batchView           
+View output in batch mode [false].
+.TP
+.B \-bw                  
+Convert all colors to black and white [false].
+.TP
+.B \-cd directory        
+Set current directory; command-line only.
+.TP
+.B \-cmyk                
+Convert rgb colors to cmyk [false].
+.TP
+.B \-c,\-command string   
+Command to autoexecute.
+.TP
+.B \-compact             
+Conserve memory at the expense of speed [false].
+.TP
+.B \-d,\-debug            
+Enable debugging messages [false].
+.TP
+.B \-divisor n           
+Garbage collect using purge(divisor=n) [2].
+.TP
+.B \-doubleclick ms      
+Emulated double-click timeout [200].
+.TP
+.B \-embed               
+Embed rendered preview image [true].
+.TP
+.B \-exitonEOF           
+Exit interactive mode on EOF [true].
+.TP
+.B \-fitscreen           
+Fit rendered image to screen [true].
+.TP
+.B \-framedelay ms       
+Additional frame delay [0].
+.TP
+.B \-framerate frames/s  
+Animation speed [30].
+.TP
+.B \-globalwrite         
+Allow write to other directory [false].
+.TP
+.B \-gray                
+Convert all colors to grayscale [false].
+.TP
+.B \-h,\-help             
+Show summary of options; command-line only.
+.TP
+.B \-historylines n      
+Retain n lines of history [1000].
+.TP
+.B \-iconify             
+Iconify rendering window [false].
+.TP
+.B \-inlineimage         
+Generate inline embedded image [false].
+.TP
+.B \-inlinetex           
+Generate inline TeX code [false].
+.TP
+.B \-interactiveMask     
+Mask fpu exceptions in interactive mode [true].
+.TP
+.B \-interactiveView     
+View output in interactive mode [true].
+.TP
+.B \-interactiveWrite    
+Write expressions entered at the prompt to stdout [true].
+.TP
+.B \-k,\-keep             
+Keep intermediate files [false].
+.TP
+.B \-keepaux             
+Keep intermediate LaTeX .aux files [false].
+.TP
+.B \-level n             
+Postscript level [3].
+.TP
+.B \-l,\-listvariables    
+List available global functions and variables [false].
+.TP
+.B \-localhistory        
+Use a local interactive history file [false].
+.TP
+.B \-loop                
+Loop 3D animations [false].
+.TP
+.B \-m,\-mask             
+Mask fpu exceptions; command-line only.
+.TP
+.B \-maxtile pair        
+Maximum rendering tile size [(1024,768)].
+.TP
+.B \-maxviewport pair    
+Maximum viewport size [(2048,2048)].
+.TP
+.B \-multiline           
+Input code over multiple lines at the prompt [false].
+.TP
+.B \-multipleView        
+View output from multiple batch-mode files [false].
+.TP
+.B \-multisample n       
+Multisampling width for screen images [4].
+.TP
+.B \-offscreen           
+Use offscreen rendering [false].
+.TP
+.B \-O,\-offset pair      
+PostScript offset [(0,0)].
+.TP
+.B \-f,\-outformat format 
+Convert each output file to specified format.
+.TP
+.B \-o,\-outname name     
+Alternative output directory/filename.
+.TP
+.B \-p,\-parseonly        
+Parse file [false].
+.TP
+.B \-pdfreload           
+Automatically reload document in pdfviewer [false].
+.TP
+.B \-pdfreloaddelay usec 
+Delay before attempting initial pdf reload [750000].
+.TP
+.B \-position pair       
+Initial 3D rendering screen position [(0,0)].
+.TP
+.B \-prc                 
+Embed 3D PRC graphics in PDF output [true].
+.TP
+.B \-prompt string       
+Prompt [> ].
+.TP
+.B \-prompt2 string      
+Continuation prompt for multiline input  [..].
+.TP
+.B \-q,\-quiet            
+Suppress welcome message [false].
+.TP
+.B \-render n            
+Render 3D graphics using n pixels per bp (-1=auto) [-1].
+.TP
+.B \-resizestep step     
+Resize step [1.2].
+.TP
+.B \-reverse             
+reverse 3D animations [false].
+.TP
+.B \-rgb                 
+Convert cmyk colors to rgb [false].
+.TP
+.B \-safe                
+Disable system call [true].
+.TP
+.B \-scroll n            
+Scroll standard output n lines at a time [0].
+.TP
+.B \-spinstep deg/s      
+Spin speed [60].
+.TP
+.B \-svgemulation        
+Emulate unimplemented SVG shading [false].
+.TP
+.B \-tabcompletion       
+Interactive prompt auto-completion [true].
+.TP
+.B \-tex engine          
+latex|pdflatex|xelatex|tex|pdftex|context|none [latex].
+.TP
+.B \-thick               
+Render thick 3D lines [true].
+.TP
+.B \-thin                
+Render thin 3D lines [true].
+.TP
+.B \-threads             
+Use POSIX threads for 3D rendering [true].
+.TP
+.B \-toolbar             
+Show 3D toolbar in PDF output [true].
+.TP
+.B \-s,\-translate        
+Show translated virtual machine code [false].
+.TP
+.B \-twice               
+Run LaTeX twice (to resolve references) [false].
+.TP
+.B \-twosided            
+Use two-sided 3D lighting model for rendering [true].
+.TP
+.B \-u,\-user string      
+General purpose user string.
+.TP
+.B \-v,\-verbose          
+Increase verbosity level (can specify multiple times) [0].
+.TP
+.B \-version             
+Show version; command-line only.
+.TP
+.B \-wait                
+Wait for child processes to finish before exiting [false].
+.TP
+.B \-warn string         
+Enable warning; command-line only.
+.TP
+.B \-where               
+Show where listed variables are declared [false].
+.TP
+.B \-zoomfactor factor   
+Zoom step factor [1.05].
+.TP
+.B \-zoomstep step       
+Mouse motion zoom step [0.1].
+
+.SH SEE ALSO
+Asymptote is documented fully in the asymptote Info page.
+The manual can also be accessed in interactive mode with the "help" command.
+
+.SH AUTHOR
+Asymptote was written by Andy Hammerlindl, John Bowman, and Tom Prince.
+.PP
+This manual page was written by Hubert Chan for the Debian project (but may
+be used by others).
diff --git a/Build/source/utils/asymptote/doc/asyRefCard.pdf b/Build/source/utils/asymptote/doc/asyRefCard.pdf
new file mode 100644
index 00000000000..c65e097e700
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/asyRefCard.pdf
diff --git a/Build/source/utils/asymptote/doc/asymptote.pdf b/Build/source/utils/asymptote/doc/asymptote.pdf
new file mode 100644
index 00000000000..8dd542c1c2f
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/asymptote.pdf
diff --git a/Build/source/utils/asymptote/doc/extra/intro_.bbl b/Build/source/utils/asymptote/doc/extra/intro_.bbl
deleted file mode 100644
index cf591457f05..00000000000
--- a/Build/source/utils/asymptote/doc/extra/intro_.bbl
+++ /dev/null
@@ -1,38 +0,0 @@
-\begin{thebibliography}{Bow07}
-
-\bibitem[BH08]{Bowman08}
-John~C. Bowman and Andy Hammerlindl.
-\newblock Asymptote: A vector graphics language.
-\newblock {\em TUGboat: The Communications of the \TeX\ Users Group},
-  29(2):288--294, 2008.
-
-\bibitem[Bow07]{Bowman07}
-John~C. Bowman.
-\newblock {The 3D {A}symptote generalization of MetaPost B\'ezier
-  interpolation}.
-\newblock {\em Proceedings in Applied Mathematics and Mechanics},
-  7(1):2010021--2010022, 2007.
-
-\bibitem[BS09]{Bowman09}
-John~C. Bowman and Orest Shardt.
-\newblock Asymptote: Lifting {\TeX} to three dimensions.
-\newblock {\em TUGboat: The Communications of the \TeX\ Users Group},
-  30(1):58--63, 2009.
-
-\bibitem[Hob86]{Hobby86}
-John~D. Hobby.
-\newblock Smooth, easy to compute interpolating splines.
-\newblock {\em Discrete Comput. Geom.}, 1:123--140, 1986.
-
-\bibitem[Knu86]{Knuth86b}
-Donald~E. Knuth.
-\newblock {\em The \MF{}book}.
-\newblock Addison-Wesley, Reading, Massachusetts, 1986.
-
-\bibitem[SB10]{Shardt10}
-Orest Shardt and John~C. Bowman.
-\newblock Surface parametrization of nonsimply connected planar {B\'ezier}
-  regions.
-\newblock {\em Submitted to Computer Aided Design}, 2010.
-
-\end{thebibliography}
diff --git a/Build/source/utils/asymptote/doc/png/asymptote.info b/Build/source/utils/asymptote/doc/png/asymptote.info
new file mode 100644
index 00000000000..d9bfe6891e3
--- /dev/null
+++ b/Build/source/utils/asymptote/doc/png/asymptote.info
@@ -0,0 +1,9988 @@
+This is asymptote.info, produced by makeinfo version 4.13 from
+../asymptote.texi.
+
+This file documents `Asymptote', version 2.25.
+
+   `http://asymptote.sourceforge.net'
+
+   Copyright (C) 2004-14 Andy Hammerlindl, John Bowman, and Tom Prince.
+
+     Permission is granted to copy, distribute and/or modify this
+     document under the terms of the GNU Lesser General Public License
+     (see the file LICENSE in the top-level source directory).
+
+
+INFO-DIR-SECTION Languages
+START-INFO-DIR-ENTRY
+* asymptote: (asymptote/asymptote). Vector graphics language.
+END-INFO-DIR-ENTRY
+
+
+File: asymptote.info,  Node: Top,  Next: Description,  Up: (dir)
+
+Asymptote
+*********
+
+This file documents `Asymptote', version 2.25.
+
+   `http://asymptote.sourceforge.net'
+
+   Copyright (C) 2004-14 Andy Hammerlindl, John Bowman, and Tom Prince.
+
+     Permission is granted to copy, distribute and/or modify this
+     document under the terms of the GNU Lesser General Public License
+     (see the file LICENSE in the top-level source directory).
+
+
+* Menu:
+
+* Description::                 What is `Asymptote'?
+* Installation::                Downloading and installing
+* Tutorial::                    Getting started
+* Drawing commands::            Four primitive graphics commands
+* Bezier curves::               Path connectors and direction specifiers
+* Programming::                 The `Asymptote' vector graphics language
+* LaTeX usage::                 Embedding `Asymptote' commands within `LaTeX'
+* Base modules::                Base modules shipped with `Asymptote'
+* Options::                     Command-line options
+* Interactive mode::            Typing `Asymptote' commands interactively
+* GUI::                         Graphical user interface
+* PostScript to Asymptote::     `Asymptote' backend to `pstoedit'
+* Help::                        Where to get help and submit bug reports
+* Debugger::                    Squish those bugs!
+* Credits::                     Contributions and acknowledgments
+* Index::                       General index
+
+ --- The Detailed Node Listing ---
+
+Installation
+
+* UNIX binary distributions::   Prebuilt `UNIX' binaries
+* MacOS X binary distributions::  Prebuilt `MacOS X' binaries
+* Microsoft Windows::           Prebuilt `Microsoft Windows' binary
+* Configuring::                 Configuring `Asymptote' for your system
+* Search paths::                Where `Asymptote' looks for your files
+* Compiling from UNIX source::  Building `Asymptote' from scratch
+* Editing modes::               Convenient `emacs' and `vim' modes
+* Subversion::                  Getting the latest development source
+* Uninstall::                   Goodbye, `Asymptote'!
+
+Drawing commands
+
+* draw::                        Draw a path on a picture or frame
+* fill::                        Fill a cyclic path on a picture or frame
+* clip::                        Clip a picture or frame to a cyclic path
+* label::                       Label a point on a picture
+
+Programming
+
+* Data types::                  void, bool, int, real, pair, triple, string
+* Paths and guides::            Bezier curves
+* Pens::                        Colors, line types, line widths, font sizes
+* Transforms::                  Affine transforms
+* Frames and pictures::         Canvases for immediate and deferred drawing
+* Files::                       Reading and writing your data
+* Variable initializers::       Initialize your variables
+* Structures::                  Organize your data
+* Operators::                   Arithmetic and logical operators
+* Implicit scaling::            Avoiding those ugly *s
+* Functions::                   Traditional and high-order functions
+* Arrays::                      Dynamic vectors
+* Casts::                       Implicit and explicit casts
+* Import::                      Importing external `Asymptote' modules
+* Static::                      Where to allocate your variable?
+
+Operators
+
+* Arithmetic & logical::        Basic mathematical operators
+* Self & prefix operators::     Increment and decrement
+* User-defined operators::      Overloading operators
+
+Functions
+
+* Default arguments::           Default values can appear anywhere
+* Named arguments::             Assigning function arguments by keyword
+* Rest arguments::              Functions with a variable number of arguments
+* Mathematical functions::      Standard libm functions
+
+
+Arrays
+
+* Slices::                      Python-style array slices
+
+Base modules
+
+* plain::                       Default `Asymptote' base file
+* simplex::                     Linear programming: simplex method
+* math::                        Extend `Asymptote''s math capabilities
+* interpolate::                 Interpolation routines
+* geometry::                    Geometry routines
+* trembling::                   Wavy lines
+* stats::                       Statistics routines and histograms
+* patterns::                    Custom fill and draw patterns
+* markers::                     Custom path marker routines
+* tree::                        Dynamic binary search tree
+* binarytree::                  Binary tree drawing module
+* drawtree::                    Tree drawing module
+* syzygy::                      Syzygy and braid drawing module
+* feynman::                     Feynman diagrams
+* roundedpath::                 Round the sharp corners of paths
+* animation::                   Embedded PDF and MPEG movies
+* embed::                       Embedding movies, sounds, and 3D objects
+* slide::                       Making presentations with `Asymptote'
+* MetaPost::                    `MetaPost' compatibility routines
+* unicode::                     Accept `unicode' (UTF-8) characters
+* latin1::                      Accept `ISO 8859-1' characters
+* babel::                       Interface to `LaTeX' `babel' package
+* labelpath::                   Drawing curved labels
+* labelpath3::                  Drawing curved labels in 3D
+* annotate::                    Annotate your PDF files
+* CAD::                         2D CAD pen and measurement functions (DIN 15)
+* graph::                       2D linear & logarithmic graphs
+* palette::                     Color density images and palettes
+* three::                       3D vector graphics
+* obj::                         3D obj files
+* graph3::                      3D linear & logarithmic graphs
+* grid3::                       3D grids
+* solids::                      3D solid geometry
+* tube::                        3D rotation minimizing tubes
+* flowchart::                   Flowchart drawing routines
+* contour::                     Contour lines
+* contour3::                    Contour surfaces
+* slopefield::                  Slope fields
+* ode::                         Ordinary differential equations
+
+Graphical User Interface
+
+* GUI installation::            Installing `xasy'
+* GUI usage::
+
+
+File: asymptote.info,  Node: Description,  Next: Installation,  Prev: Top,  Up: Top
+
+1 Description
+*************
+
+`Asymptote' is a powerful descriptive vector graphics language that
+provides a mathematical coordinate-based framework for technical
+drawings.  Labels and equations are typeset with `LaTeX', for overall
+document consistency, yielding the same high-quality level of
+typesetting that `LaTeX' provides for scientific text. By default it
+produces `PostScript' output, but it can also generate any format that
+the `ImageMagick' package can produce.
+
+   A major advantage of `Asymptote' over other graphics packages is
+that it is a high-level programming language, as opposed to just a
+graphics program: it can therefore exploit the best features of the
+script (command-driven) and graphical-user-interface (GUI) methods for
+producing figures. The rudimentary GUI `xasy' included with the package
+allows one to move script-generated objects around. To make `Asymptote'
+accessible to the average user, this GUI is currently being developed
+into a full-fledged interface that can generate objects directly.
+However, the script portion of the language is now ready for general
+use by users who are willing to learn a few simple `Asymptote' graphics
+commands (*note Drawing commands::).
+
+   `Asymptote' is mathematically oriented (e.g. one can use complex
+multiplication to rotate a vector) and uses `LaTeX' to do the
+typesetting of labels. This is an important feature for scientific
+applications. It was inspired by an earlier drawing program (with a
+weaker syntax and capabilities) called `MetaPost'.
+
+   The `Asymptote' vector graphics language provides:
+
+   * a standard for typesetting mathematical figures, just as
+     TeX/`LaTeX' is the de-facto standard for typesetting equations.
+
+   * `LaTeX' typesetting of labels, for overall document consistency;
+
+   * the ability to generate and embed 3D vector PRC graphics within
+     PDF files;
+
+   * a natural coordinate-based framework for technical drawings,
+     inspired by `MetaPost', with a much cleaner, powerful C++-like
+     programming syntax;
+
+   * compilation of figures into virtual machine code for speed, without
+     sacrificing portability;
+
+   * the power of a script-based language coupled to the convenience of
+     a GUI;
+
+   * customization using its own C++-like graphics programming language;
+
+   * sensible defaults for graphical features, with the ability to
+     override;
+
+   * a high-level mathematically oriented interface to the `PostScript'
+     language for vector graphics, including affine transforms and
+     complex variables;
+
+   * functions that can create new (anonymous) functions;
+
+   * deferred drawing that uses the simplex method to solve overall size
+     constraint issues between fixed-sized objects (labels and
+     arrowheads) and objects that should scale with figure size;
+
+
+   Many of the features of `Asymptote' are written in the `Asymptote'
+language itself. While the stock version of `Asymptote' is designed for
+mathematics typesetting needs, one can write `Asymptote' modules that
+tailor it to specific applications. A scientific graphing module has
+already been written (*note graph::). Examples of `Asymptote' code and
+output, including animations, are available at
+
+     `http://asymptote.sourceforge.net/gallery/'.
+   Links to many external resources, including an excellent user-written
+`Asymptote' tutorial can be found at
+
+     `http://asymptote.sourceforge.net/links.html'.
+   A quick reference card for `Asymptote' is available at
+
+     `http://asymptote.sourceforge.net/asyRefCard.pdf'.
+
+
+File: asymptote.info,  Node: Installation,  Next: Tutorial,  Prev: Description,  Up: Top
+
+2 Installation
+**************
+
+* Menu:
+
+* UNIX binary distributions::   Prebuilt `UNIX' binaries
+* MacOS X binary distributions::  Prebuilt `MacOS X' binaries
+* Microsoft Windows::           Prebuilt `Microsoft Windows' binary
+* Configuring::                 Configuring `Asymptote' for your system
+* Search paths::                Where `Asymptote' looks for your files
+* Compiling from UNIX source::  Building `Asymptote' from scratch
+* Editing modes::               Convenient `emacs' and `vim' modes
+* Subversion::                  Getting the latest development source
+* Uninstall::                   Goodbye, `Asymptote'!
+
+   After following the instructions for your specific distribution,
+please see also *note Configuring::.
+
+We recommend subscribing to new release announcements at
+
+     `http://freshmeat.net/projects/asy'
+   Users may also wish to monitor the `Asymptote' forum:
+
+     `http://sourceforge.net/p/asymptote/discussion/409349'
+
+
+File: asymptote.info,  Node: UNIX binary distributions,  Next: MacOS X binary distributions,  Up: Installation
+
+2.1 UNIX binary distributions
+=============================
+
+We release both `tgz' and RPM binary distributions of `Asymptote'. The
+root user can install the `Linux i386' `tgz' distribution of version
+`x.xx' of `Asymptote' with the commands:
+tar -C / -zxf asymptote-x.xx.i386.tgz
+texhash
+ The `texhash' command, which installs LaTeX style files, is optional.
+The executable file will be `/usr/local/bin/asy') and example code will
+be installed by default in `/usr/local/share/doc/asymptote/examples'.
+
+Fedora users can easily install the most recent version of `Asymptote'
+with the command
+yum --enablerepo=rawhide install asymptote
+
+To install the latest version of `Asymptote' on a Debian-based
+distribution (e.g. Ubuntu, Mepis, Linspire) follow the instructions for
+compiling from `UNIX' source (*note Compiling from UNIX source::).
+Alternatively, Debian users can install one of Hubert Chan's prebuilt
+`Asymptote' binaries from
+
+     `http://ftp.debian.org/debian/pool/main/a/asymptote'
+
+
+File: asymptote.info,  Node: MacOS X binary distributions,  Next: Microsoft Windows,  Prev: UNIX binary distributions,  Up: Installation
+
+2.2 MacOS X binary distributions
+================================
+
+`MacOS X' users can either compile the `UNIX' source code (*note
+Compiling from UNIX source::) or install the contributed `Asymptote'
+binary available at
+
+`http://www.hmug.org/pub/MacOS_X/X/Applications/Publishing/asymptote/'
+
+Because these preconfigured binary distributions have strict
+architecture and library dependencies that many installations do not
+satisfy, we recommend installing `Asymptote' directly from the official
+source:
+
+   `http://sourceforge.net/project/showfiles.php?group_id=120000'
+
+Note that many `MacOS X' (and FreeBSD) systems lack the GNU `readline'
+library. For full interactive functionality, GNU `readline' version 4.3
+or later must be installed.
+
+
+File: asymptote.info,  Node: Microsoft Windows,  Next: Configuring,  Prev: MacOS X binary distributions,  Up: Installation
+
+2.3 Microsoft Windows
+=====================
+
+Users of the `Microsoft Windows' operating system can install the
+self-extracting `Asymptote' executable `asymptote-x.xx-setup.exe',
+where `x.xx' denotes the latest version.
+
+   A working TeX implementation (such as the one available at
+`http://www.miktex.org') will be required to typeset labels.  You will
+also need to install `GPL Ghostscript' from
+`http://sourceforge.net/projects/ghostscript/'.
+
+   To view the default `PostScript' output, you can install the program
+`gsview' available from `http://www.cs.wisc.edu/~ghost/gsview/'.  A
+better (and free) `PostScript' viewer available at
+`http://psview.sourceforge.net/' (which in particular works properly in
+interactive mode) unfortunately currently requires some manual
+configuration. Specifically, if version `x.xx' of `psview' is extracted
+to the directory `c:\Program Files' one needs to put
+import settings;
+psviewer="c:\Program Files\psview-x.xx\psv.exe";
+ in the optional `Asymptote' configuration file; *note configuration
+file::).
+
+   The `ImageMagick' package from
+
+   `http://www.imagemagick.org/script/binary-releases.php'
+
+is required to support output formats other than EPS, PDF, SVG, and PNG
+(*note convert::).  The `Python 2' interpreter from
+`http://www.python.org' is only required if you wish to try out the
+graphical user interface (*note GUI::).
+
+Example code will be installed by default in the `examples'
+subdirectory of the installation directory (by default, `C:\Program
+Files\Asymptote').
+
+
+File: asymptote.info,  Node: Configuring,  Next: Search paths,  Prev: Microsoft Windows,  Up: Installation
+
+2.4 Configuring
+===============
+
+In interactive mode, or when given the `-V' option (the default when
+running `Asymptote' on a single file under `MSDOS'), `Asymptote' will
+automatically invoke the `PostScript' viewer `gv' (under `UNIX') or
+`gsview' (under `MSDOS' to display graphical output. These defaults may
+be overridden with the configuration variable `psviewer'.  The
+`PostScript' viewer should be capable of automatically redrawing
+whenever the output file is updated. The default `UNIX' `PostScript'
+viewer `gv' supports this (via a `SIGHUP' signal). Version `gv-3.6.3'
+or later (from `http://ftp.gnu.org/gnu/gv/') is required for
+interactive mode to work properly.  Users of `ggv' will need to enable
+`Watch file' under `Edit/Postscript Viewer Preferences'.  Users of
+`gsview' will need to enable `Options/Auto Redisplay' (however, under
+`MSDOS' it is still necessary to click on the `gsview' window; under
+`UNIX' one must manually redisplay by pressing the `r' key). A better
+(and free) multiplatform alternative to `gsview' is `psview' (*note
+psview::).
+
+   Configuration variables are most easily set as `Asymptote' variables
+in an optional configuration file `config.asy' *note configuration
+file::).  Here are the default values of several important configuration
+variables under `UNIX':
+
+
+import settings;
+psviewer="gv";
+pdfviewer="acroread";
+gs="gs";
+
+Under `MSDOS', the (installation-dependent) default values of these
+configuration variables are determined automatically from the
+`Microsoft Windows' registry. Viewer settings (such as `psviewer' and
+`pdfviewer') can be set to the string `cmd' to request the application
+normally associated with the corresponding file type.
+
+   For PDF format output, the `gs' setting specifies the location of
+the `PostScript'-to-PDF processor `Ghostscript', available from
+`http://sourceforge.net/projects/ghostscript/'.
+
+   The setting `pdfviewer' specifies the location of the PDF viewer. On
+`UNIX' systems, to support automatic document reloading in `Adobe
+Reader', we recommend copying the file `reload.js' from the `Asymptote'
+system directory (by default, `/usr/local/share/asymptote' under `UNIX'
+to `~/.adobe/Acrobat/x.x/JavaScripts/', where `x.x' represents the
+appropriate `Adobe Reader' version number. The automatic document
+reload feature must then be explicitly enabled by putting
+import settings;
+pdfreload=true;
+pdfreloadOptions="-tempFile";
+ in the `Asymptote' configuration file. This reload feature is not
+useful under `MSDOS' since the document cannot be updated anyway on
+that operating system until it is first closed by `Adobe Reader'.
+
+   The configuration variable `dir' can be used to adjust the search
+path (*note Search paths::).
+
+   By default, `Asymptote' attempts to center the figure on the page,
+assuming that the paper type is `letter'. The default paper type may be
+changed to `a4' with the configuration variable `papertype'. Alignment
+to other paper sizes can be obtained by setting the configuration
+variables `paperwidth' and `paperheight'.
+
+   The following configuration variables normally do not require
+adjustment:
+texpath
+texcommand
+dvips
+dvisvgm
+libgs
+convert
+display
+animate
+ Warnings (such as "writeoverloaded") may be enabled or disabled with
+the functions
+warn(string s);
+nowarn(string s);
+ or by directly modifying the string array `settings.suppress', which
+lists all disabled warnings.
+
+   Configuration variables may also be set or overwritten with a
+command-line option:
+asy -psviewer=gsview -V venn
+
+   Alternatively, system environment versions of the above configuration
+variables may be set in the conventional way. The corresponding
+environment variable name is obtained by converting the configuration
+variable name to upper case  and prepending `ASYMPTOTE_': for example,
+to set the environment variable
+ASYMPTOTE_PSVIEWER="C:\Program Files\Ghostgum\gsview\gsview32.exe";
+ under `Microsoft Windows XP':
+  1. Click on the `Start' button;
+
+  2. Right-click on `My Computer';
+
+  3. Choose `View system information';
+
+  4. Click the `Advanced' tab;
+
+  5. Click the `Environment Variables' button.
+
+
+File: asymptote.info,  Node: Search paths,  Next: Compiling from UNIX source,  Prev: Configuring,  Up: Installation
+
+2.5 Search paths
+================
+
+In looking for `Asymptote' system files, `asy' will search the
+following paths, in the order listed:
+  1. The current directory;
+
+  2. A list of one or more directories specified by the configuration
+     variable `dir' or environment variable `ASYMPTOTE_DIR' (separated
+     by `:' under UNIX and `;' under `MSDOS');
+
+  3. The directory specified by the environment variable
+     `ASYMPTOTE_HOME'; if this variable is not set, the directory
+     `.asy' in the user's home directory (`%USERPROFILE%\.asy' under
+     `MSDOS') is used;
+
+  4. The `Asymptote' system directory (by default,
+     `/usr/local/share/asymptote' under `UNIX' and `C:\Program
+     Files\Asymptote' under `MSDOS').
+
+
+File: asymptote.info,  Node: Compiling from UNIX source,  Next: Editing modes,  Prev: Search paths,  Up: Installation
+
+2.6 Compiling from UNIX source
+==============================
+
+To compile and install a `UNIX' executable from a source release
+`x.xx', first execute the commands:
+gunzip asymptote-x.xx.src.tgz
+tar -xf asymptote-x.xx.src.tar
+cd asymptote-x.xx
+ By default the system version of the Boehm garbage collector will be
+used; if it is old we recommend first putting
+`http://hboehm.info/gc/gc_source/gc-7.4.0.tar.gz'
+`http://hboehm.info/gc/gc_source/libatomic_ops-7.4.0.tar.gz' in the
+`Asymptote' source directory.
+
+   On `UNIX' platforms (other than `MacOS X'), we recommend using
+version `2.8.1' of the `freeglut' library. To compile `freeglut',
+download
+
+     `http://prdownloads.sourceforge.net/freeglut/freeglut-2.8.1.tar.gz'
+   and type (as the root user):
+gunzip freeglut-2.8.1.tar.gz
+tar -xf freeglut-2.8.1.tar
+cd freeglut-2.8.1
+./configure --prefix=/usr
+make install
+cd ..
+ Then compile `Asymptote' with the commands
+./configure
+make all
+make install
+ Be sure to use GNU `make' (on non-GNU systems this command may be
+called `gmake').  To build the documentation, you may need to install
+the `texinfo-tex' package. If you get errors from a broken `texinfo' or
+`pdftex' installation, simply put
+
+     `http://asymptote.sourceforge.net/asymptote.pdf'
+   in the directory `doc' and repeat the command `make all'.
+
+For a (default) system-wide installation, the last command should be
+done as the root user. To install without root privileges, change the
+`./configure' command to
+./configure --prefix=$HOME/asymptote
+ One can disable use of the Boehm garbage collector by configuring with
+`./configure --disable-gc'. For a list of other configuration options,
+say `./configure --help'. For example, one can tell configure to look
+for header files and libraries in nonstandard locations:
+./configure CFLAGS=-I/opt/usr/include LDFLAGS=-L/opt/usr/lib
+
+   If you are compiling `Asymptote' with `gcc', you will need a
+relatively recent version (e.g. 3.4.4 or later).  For full interactive
+functionality, you will need version 4.3 or later of the GNU `readline'
+library.  The file `gcc3.3.2curses.patch' in the `patches' directory can
+be used to patch the broken curses.h header file (or a local copy
+thereof in the current directory) on some `AIX' and `IRIX' systems.
+
+   The `FFTW' library is only required if you want `Asymptote' to be
+able to take Fourier transforms of data (say, to compute an audio power
+spectrum). The `GSL' library is only required if you require the
+special functions that it supports.
+
+   If you don't want to install `Asymptote' system wide, just make sure
+the compiled binary `asy' and GUI script `xasy' are in your path and
+set the configuration variable `dir' to point to the directory `base'
+(in the top level directory of the `Asymptote' source code).
+
+
+File: asymptote.info,  Node: Editing modes,  Next: Subversion,  Prev: Compiling from UNIX source,  Up: Installation
+
+2.7 Editing modes
+=================
+
+Users of `emacs' can edit `Asymptote' code with the mode `asy-mode',
+after enabling it by putting the following lines in their `.emacs'
+initialization file, replacing `ASYDIR' with the location of the
+`Asymptote' system directory (by default, `/usr/local/share/asymptote'
+or `C:\Program Files\Asymptote' under `MSDOS'):
+(add-to-list 'load-path "ASYDIR")
+(autoload 'asy-mode "asy-mode.el" "Asymptote major mode." t)
+(autoload 'lasy-mode "asy-mode.el" "hybrid Asymptote/Latex major mode." t)
+(autoload 'asy-insinuate-latex "asy-mode.el" "Asymptote insinuate LaTeX." t)
+(add-to-list 'auto-mode-alist '("\\.asy$" . asy-mode))
+
+ Particularly useful key bindings in this mode are `C-c C-c', which
+compiles and displays the current buffer, and the key binding `C-c ?',
+which shows the available function prototypes for the command at the
+cursor.  For full functionality you should also install the Apache
+Software Foundation package `two-mode-mode':
+
+     `http://www.dedasys.com/freesoftware/files/two-mode-mode.el'
+   Once installed, you can use the hybrid mode `lasy-mode' to edit a
+LaTeX file containing embedded `Asymptote' code (*note LaTeX usage::).
+This mode can be enabled within `latex-mode' with the key sequence `M-x
+lasy-mode <RET>'.  On `UNIX' systems, additional keywords will be
+generated from all `asy' files in the space-separated list of
+directories specified by the environment variable `ASYMPTOTE_SITEDIR'.
+Further documentation of `asy-mode' is available within `emacs' by
+pressing the sequence keys `C-h f asy-mode <RET>'.
+
+   Fans of `vim' can customize `vim' for `Asymptote' with
+
+`cp /usr/local/share/asymptote/asy.vim ~/.vim/syntax/asy.vim'
+
+and add the following to their `~/.vimrc' file:
+augroup filetypedetect
+au BufNewFile,BufRead *.asy     setf asy
+augroup END
+filetype plugin on
+
+   If any of these directories or files don't exist, just create them.
+To set `vim' up to run the current asymptote script using `:make' just
+add to `~/.vim/ftplugin/asy.vim':
+setlocal makeprg=asy\ %
+setlocal errorformat=%f:\ %l.%c:\ %m
+
+   Syntax highlighting support for the KDE editor `Kate' can be enabled
+by running `asy-kate.sh' in the `/usr/local/share/asymptote' directory
+and putting the generated `asymptote.xml' file in
+`~/.kde/share/apps/katepart/syntax/'.
+
+
+File: asymptote.info,  Node: Subversion,  Next: Uninstall,  Prev: Editing modes,  Up: Installation
+
+2.8 Subversion (SVN)
+====================
+
+The following commands are needed to install the latest development
+version of `Asymptote' using `Subversion':
+svn co http://svn.code.sf.net/p/asymptote/code/trunk/asymptote
+cd asymptote
+./autogen.sh
+./configure
+make all
+make install
+
+To compile without optimization, use the command `make CFLAGS=-g'.
+
+
+File: asymptote.info,  Node: Uninstall,  Prev: Subversion,  Up: Installation
+
+2.9 Uninstall
+=============
+
+To uninstall an `Linux i386' binary distribution, use the commands
+tar -zxvf asymptote-x.xx.i386.tgz | xargs --replace=% rm /%
+texhash
+
+To uninstall all `Asymptote' files installed from a source
+distribution, use the command
+make uninstall
+
+
+File: asymptote.info,  Node: Tutorial,  Next: Drawing commands,  Prev: Installation,  Up: Top
+
+3 Tutorial
+**********
+
+3.1 Drawing in batch mode
+=========================
+
+To draw a line from coordinate (0,0) to coordinate (100,100), create a
+text file `test.asy' containing
+
+draw((0,0)--(100,100));
+ Then execute the command
+asy -V test
+ Alternatively, `MSDOS' users can drag and drop `test.asy' onto the
+Desktop `asy' icon (or make `Asymptote' the default application for the
+extension `asy').
+
+This method, known as _batch mode_, outputs a `PostScript' file
+`test.eps'. If you prefer PDF output, use the command line
+asy -V -f pdf test
+ In either case, the `-V' option opens up a viewer window so you can
+immediately view the result:
+
+
+Here, the `--' connector joins the two points `(0,0)' and `(100,100)'
+with a line segment.
+
+3.2 Drawing in interactive mode
+===============================
+
+Another method is _interactive mode_, where `Asymptote' reads
+individual commands as they are entered by the user. To try this out,
+enter `Asymptote''s interactive mode by clicking on the `Asymptote'
+icon or typing the command `asy'.  Then type
+draw((0,0)--(100,100));
+ followed by `Enter', to obtain the above image.  At this point you can
+type further `draw' commands, which will be added to the displayed
+figure, `erase' to clear the canvas,
+input test;
+ to execute all of the commands contained in the file `test.asy', or
+`quit' to exit interactive mode.  You can use the arrow keys in
+interactive mode to edit previous lines.  The tab key will
+automatically complete unambiguous words; otherwise, hitting tab again
+will show the possible choices. Further commands specific to
+interactive mode are described in *note Interactive mode::.
+
+3.3 Figure size
+===============
+
+In `Asymptote', coordinates like `(0,0)' and `(100,100)', called
+_pairs_, are expressed in `PostScript' "big points" (1 `bp' = 1/72
+`inch') and the default line width is `0.5bp'.  However, it is often
+inconvenient to work directly in `PostScript' coordinates.  The next
+example produces identical output to the previous example, by scaling
+the line `(0,0)--(1,1)' to fit a rectangle of width `100.5 bp' and
+height `100.5 bp' (the extra `0.5bp' accounts for the line width):
+size(100.5,100.5);
+draw((0,0)--(1,1));
+
+
+
+One can also specify the size in `pt' (1 `pt' = 1/72.27 `inch'), `cm',
+`mm', or `inches'.  Two nonzero size arguments (or a single size
+argument) restrict the size in both directions, preserving the aspect
+ratio.  If 0 is given as a size argument, no restriction is made in
+that direction; the overall scaling will be determined by the other
+direction (*note size::):
+
+size(0,100.5);
+draw((0,0)--(2,1),Arrow);
+
+
+
+To connect several points and create a cyclic path, use the `cycle'
+keyword:
+
+size(3cm);
+draw((0,0)--(1,0)--(1,1)--(0,1)--cycle);
+
+
+For convenience, the path `(0,0)--(1,0)--(1,1)--(0,1)--cycle' may be
+replaced with the predefined variable `unitsquare', or equivalently,
+`box((0,0),(1,1))'.
+
+   To make the user coordinates represent multiples of exactly `1cm':
+unitsize(1cm);
+draw(unitsquare);
+
+3.4 Labels
+==========
+
+Adding labels is easy in `Asymptote'; one specifies the label as a
+double-quoted `LaTeX' string, a coordinate, and an optional alignment
+direction:
+
+size(3cm);
+draw(unitsquare);
+label("$A$",(0,0),SW);
+label("$B$",(1,0),SE);
+label("$C$",(1,1),NE);
+label("$D$",(0,1),NW);
+
+
+
+`Asymptote' uses the standard compass directions `E=(1,0)', `N=(0,1)',
+`NE=unit(N+E)', and `ENE=unit(E+NE)', etc., which along with the
+directions `up', `down', `right', and `left' are defined as pairs in
+the `Asymptote' base module `plain' (a user who has a local variable
+named `E' may access the compass direction `E' by prefixing it with the
+name of the module where it is defined: `plain.E').
+
+3.5 Paths
+=========
+
+This example draws a path that approximates a quarter circle,
+terminated with an arrowhead:
+
+size(100,0);
+draw((1,0){up}..{left}(0,1),Arrow);
+
+
+Here the directions `up' and `left' in braces specify the incoming and
+outgoing directions at the points `(1,0)' and `(0,1)', respectively.
+
+   In general, a path is specified as a list of points (or other paths)
+interconnected with `--', which denotes a straight line segment, or
+`..', which denotes a cubic spline (*note Bezier curves::).  Specifying
+a final `..cycle' creates a cyclic path that connects smoothly back to
+the initial node, as in this approximation (accurate to within 0.06%)
+of a unit circle:
+path unitcircle=E..N..W..S..cycle;
+
+An `Asymptote' path, being connected, is equivalent to a `Postscript
+subpath'. The `^^' binary operator, which requests that the pen be
+moved (without drawing or affecting endpoint curvatures) from the final
+point of the left-hand path to the initial point of the right-hand
+path, may be used to group several `Asymptote' paths into a `path[]'
+array (equivalent to a `PostScript' path):
+
+size(0,100);
+path unitcircle=E..N..W..S..cycle;
+path g=scale(2)*unitcircle;
+filldraw(unitcircle^^g,evenodd+yellow,black);
+
+
+
+The `PostScript' even-odd fill rule here specifies that only the region
+bounded between the two unit circles is filled (*note fillrule::).  In
+this example, the same effect can be achieved by using the default zero
+winding number fill rule, if one is careful to alternate the
+orientation of the paths:
+filldraw(unitcircle^^reverse(g),yellow,black);
+
+   The `^^' operator is used by the `box(triple, triple)' function in
+the module `three.asy' to construct the edges of a cube `unitbox'
+without retracing steps (*note three::):
+
+import three;
+
+currentprojection=orthographic(5,4,2,center=true);
+
+size(5cm);
+size3(3cm,5cm,8cm);
+
+draw(unitbox);
+
+dot(unitbox,red);
+
+label("$O$",(0,0,0),NW);
+label("(1,0,0)",(1,0,0),S);
+label("(0,1,0)",(0,1,0),E);
+label("(0,0,1)",(0,0,1),Z);
+
+
+
+See section *note graph:: (or the online `Asymptote' gallery and
+external links posted at `http://asymptote.sourceforge.net') for
+further examples, including two-dimensional and interactive
+three-dimensional scientific graphs. Additional examples have been
+posted by Philippe Ivaldi at `http://www.piprime.fr/asymptote'.
+Excellent user-written `Asymptote' tutorials are also available:
+
+   `http://www.artofproblemsolving.com/Wiki/index.php/Asymptote:_Basics'
+
+`http://math.uchicago.edu/~cstaats/Charles_Staats_III/Notes_and_papers_files/asymptote_tutorial.pdf'
+
+
+File: asymptote.info,  Node: Drawing commands,  Next: Bezier curves,  Prev: Tutorial,  Up: Top
+
+4 Drawing commands
+******************
+
+All of `Asymptote''s graphical capabilities are based on four primitive
+commands. The three `PostScript' drawing commands `draw', `fill', and
+`clip' add objects to a picture in the order in which they are
+executed, with the most recently drawn object appearing on top.  The
+labeling command `label' can be used to add text labels and external
+EPS images, which will appear on top of the `PostScript' objects (since
+this is normally what one wants), but again in the relative order in
+which they were executed. After drawing objects on a picture, the
+picture can be output with the `shipout' function (*note shipout::).
+
+   If you wish to draw `PostScript' objects on top of labels (or
+verbatim `tex' commands; *note tex::), the `layer' command may be used
+to start a new `PostScript/LaTeX' layer:
+void layer(picture pic=currentpicture);
+
+   The `layer' function gives one full control over the order in which
+objects are drawn. Layers are drawn sequentially, with the most recent
+layer appearing on top. Within each layer, labels, images, and verbatim
+`tex' commands are always drawn after the `PostScript' objects in that
+layer.
+
+   While some of these drawing commands take many options, they all
+have sensible default values (for example, the picture argument
+defaults to currentpicture).
+
+* Menu:
+
+* draw::                        Draw a path on a picture or frame
+* fill::                        Fill a cyclic path on a picture or frame
+* clip::                        Clip a picture or frame to a cyclic path
+* label::                       Label a point on a picture
+
+
+File: asymptote.info,  Node: draw,  Next: fill,  Up: Drawing commands
+
+4.1 draw
+========
+
+void draw(picture pic=currentpicture, Label L="", path g,
+          align align=NoAlign, pen p=currentpen,
+          arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin,
+          Label legend="", marker marker=nomarker);
+
+Draw the path `g' on the picture `pic' using pen `p' for drawing, with
+optional drawing attributes (Label `L', explicit label alignment
+`align', arrows and bars `arrow' and `bar', margins `margin', legend,
+and markers `marker'). Only one parameter, the path, is required. For
+convenience, the arguments `arrow' and `bar' may be specified in either
+order. The argument `legend' is a Label to use in constructing an
+optional legend entry.
+
+   Bars are useful for indicating dimensions. The possible values of
+`bar' are `None', `BeginBar', `EndBar' (or equivalently `Bar'), and
+`Bars' (which draws a bar at both ends of the path). Each of these bar
+specifiers (except for `None') will accept an optional real argument
+that denotes the length of the bar in `PostScript' coordinates. The
+default bar length is `barsize(pen)'.
+
+   The possible values of `arrow' are `None', `Blank' (which draws no
+arrows or path), `BeginArrow', `MidArrow', `EndArrow' (or equivalently
+`Arrow'), and `Arrows' (which draws an arrow at both ends of the path).
+All of the arrow specifiers except for `None' and `Blank' may be given
+the optional arguments arrowhead `arrowhead' (one of the predefined
+arrowhead styles `DefaultHead', `SimpleHead', `HookHead', `TeXHead'),
+real `size' (arrowhead size in `PostScript' coordinates), real `angle'
+(arrowhead angle in degrees), filltype `filltype' (one of `FillDraw',
+`Fill', `NoFill', `UnFill', `Draw') and (except for `MidArrow' and
+`Arrows') a real `position' (in the sense of `point(path p, real t)')
+along the path where the tip of the arrow should be placed. The default
+arrowhead size when drawn with a pen `p' is `arrowsize(p)'. There are
+also arrow versions with slightly modified default values of `size' and
+`angle' suitable for curved arrows: `BeginArcArrow', `EndArcArrow' (or
+equivalently `ArcArrow'), `MidArcArrow', and `ArcArrows'.
+
+   Margins can be used to shrink the visible portion of a path by
+`labelmargin(p)' to avoid overlap with other drawn objects.  Typical
+values of `margin' are `NoMargin', `BeginMargin', `EndMargin' (or
+equivalently `Margin'), and `Margins' (which leaves a margin at both
+ends of the path). One may use `Margin(real begin, real end)' to
+specify the size of the beginning and ending margin, respectively, in
+multiples of the units `labelmargin(p)' used for aligning labels.
+Alternatively, `BeginPenMargin', `EndPenMargin' (or equivalently
+`PenMargin'), `PenMargins', `PenMargin(real begin, real end)' specify a
+margin in units of the pen line width, taking account of the pen line
+width when drawing the path or arrow. For example, use `DotMargin', an
+abbreviation for `PenMargin(-0.5*dotfactor,0.5*dotfactor)', to draw
+from the usual beginning point just up to the boundary of an end dot of
+width `dotfactor*linewidth(p)'.  The qualifiers `BeginDotMargin',
+`EndDotMargin', and `DotMargins' work similarly. The qualifier
+`TrueMargin(real begin, real end)' allows one to specify a margin
+directly in `PostScript' units, independent of the pen line width.
+
+   The use of arrows, bars, and margins is illustrated by the examples
+`Pythagoras.asy', `sqrtx01.asy', and `triads.asy'.
+
+   The legend for a picture `pic' can be fit and aligned to a frame
+with the routine: 
+frame legend(picture pic=currentpicture, int perline=1,
+             real xmargin=legendmargin, real ymargin=xmargin,
+             real linelength=legendlinelength,
+             real hskip=legendhskip, real vskip=legendvskip,
+             real maxwidth=0, real maxheight=0,
+             bool hstretch=false, bool vstretch=false, pen p=currentpen);
+ Here `xmargin' and `ymargin' specify the surrounding x and y margins,
+`perline' specifies the number of entries per line (default 1; 0 means
+choose this number automatically), `linelength' specifies the length of
+the path lines, `hskip' and `vskip' specify the line skip (as a
+multiple of the legend entry size), `maxwidth' and `maxheight' specify
+optional upper limits on the width and height of the resulting legend
+(0 means unlimited), `hstretch' and `vstretch' allow the legend to
+stretch horizontally or vertically, and `p' specifies the pen used to
+draw the bounding box. The legend frame can then be added and aligned
+about a point on a picture `dest' using `add' or `attach' (*note add
+about::).
+
+   To draw a dot, simply draw a path containing a single point.  The
+`dot' command defined in the module `plain' draws a dot having a
+diameter equal to an explicit pen line width or the default line width
+magnified by `dotfactor' (6 by default), using the specified filltype
+(*note filltype::):
+void dot(picture pic=currentpicture, pair z, pen p=currentpen,
+         filltype filltype=Fill);
+void dot(picture pic=currentpicture, Label L, pair z, align align=NoAlign,
+         string format=defaultformat, pen p=currentpen, filltype filltype=Fill);
+void dot(picture pic=currentpicture, Label[] L=new Label[], pair[] z,
+         align align=NoAlign, string format=defaultformat, pen p=currentpen,
+         filltype filltype=Fill)
+void dot(picture pic=currentpicture, Label L, pen p=currentpen,
+         filltype filltype=Fill);
+
+   If the variable `Label' is given as the `Label' argument to the
+second routine, the `format' argument will be used to format a string
+based on the dot location (here `defaultformat' is `"$%.4g$"').  The
+third routine draws a dot at every point of a pair array `z'.  One can
+also draw a dot at every node of a path:
+void dot(picture pic=currentpicture, Label[] L=new Label[],
+         path g, align align=RightSide, string format=defaultformat,
+         pen p=currentpen, filltype filltype=Fill);
+ See *note pathmarkers:: and *note markers:: for more general methods
+for marking path nodes.
+
+   To draw a fixed-sized object (in `PostScript' coordinates) about the
+user coordinate `origin', use the routine 
+void draw(pair origin, picture pic=currentpicture, Label L="", path g,
+          align align=NoAlign, pen p=currentpen, arrowbar arrow=None,
+          arrowbar bar=None, margin margin=NoMargin, Label legend="",
+          marker marker=nomarker);
+
+
+File: asymptote.info,  Node: fill,  Next: clip,  Prev: draw,  Up: Drawing commands
+
+4.2 fill
+========
+
+void fill(picture pic=currentpicture, path g, pen p=currentpen);
+
+Fill the interior region bounded by the cyclic path `g' on the picture
+`pic', using the pen `p'.
+
+   There is also a convenient `filldraw' command, which fills the path
+and then draws in the boundary. One can specify separate pens for each
+operation:
+void filldraw(picture pic=currentpicture, path g, pen fillpen=currentpen,
+              pen drawpen=currentpen);
+
+   This fixed-size version of `fill' allows one to fill an object
+described in `PostScript' coordinates about the user coordinate
+`origin':
+void fill(pair origin, picture pic=currentpicture, path g, pen p=currentpen);
+
+This is just a convenient abbreviation for the commands:
+picture opic;
+fill(opic,g,p);
+add(pic,opic,origin);
+
+   The routine 
+void filloutside(picture pic=currentpicture, path g, pen p=currentpen);
+ fills the region exterior to the path `g', out to the current boundary
+of picture `pic'.
+
+   Lattice gradient shading varying smoothly over a two-dimensional
+array of pens `p', using fill rule `fillrule', can be produced with
+void latticeshade(picture pic=currentpicture, path g, bool stroke=false,
+                  pen fillrule=currentpen, pen[][] p)
+ If `stroke=true', the region filled is the same as the region that
+would be drawn by `draw(pic,g,fillrule+zerowinding)'; in this case the
+path `g' need not be cyclic.  The pens in `p' must belong to the same
+color space. One can use the functions `rgb(pen)' or `cmyk(pen)' to
+promote pens to a higher color space, as illustrated in the example file
+`latticeshading.asy'.
+
+   Axial gradient shading varying smoothly from `pena' to `penb' in the
+direction of the line segment `a--b' can be achieved with
+void axialshade(picture pic=currentpicture, path g, bool stroke=false,
+                pen pena, pair a, bool extenda=true,
+                pen penb, pair b, bool extendb=true);
+ The boolean parameters `extenda' and `extendb' indicate whether the
+shading should extend beyond the axis endpoints `a' and `b'.
+
+   Radial gradient shading varying smoothly from `pena' on the circle
+with center `a' and radius `ra' to `penb' on the circle with center `b'
+and radius `rb' is similar:
+void radialshade(picture pic=currentpicture, path g, bool stroke=false,
+                 pen pena, pair a, real ra, bool extenda=true,
+                 pen penb, pair b, real rb, bool extendb=true);
+ The boolean parameters `extenda' and `extendb' indicate whether the
+shading should extend beyond the radii `a' and `b'.  Illustrations of
+radial shading are provided in the example files `shade.asy',
+`ring.asy', and `shadestroke.asy'.
+
+   Gouraud shading using fill rule `fillrule' and the vertex colors in
+the pen array `p' on a triangular lattice defined by the vertices `z'
+and edge flags `edges' is implemented with
+void gouraudshade(picture pic=currentpicture, path g, bool stroke=false,
+                  pen fillrule=currentpen, pen[] p, pair[] z,
+                  int[] edges);
+void gouraudshade(picture pic=currentpicture, path g, bool stroke=false,
+                  pen fillrule=currentpen, pen[] p, int[] edges);
+ In the second form, the elements of `z' are taken to be successive
+nodes of path `g'. The pens in `p' must belong to the same color space.
+Illustrations of Gouraud shading are provided in the example file
+`Gouraud.asy' and in the solid geometry module `solids.asy'.  The edge
+flags used in Gouraud shading are documented here:
+
+     `http://partners.adobe.com/public/developer/en/ps/sdk/TN5600.SmoothShading.pdf'.
+
+   Tensor product shading using fill rule `fillrule' on patches bounded
+by the n cyclic paths of length 4 in path array `b', using the vertex
+colors specified in the n \times 4 pen array `p' and internal control
+points in the n \times 4 array `z', is implemented with
+void tensorshade(picture pic=currentpicture, path[] g, bool stroke=false,
+                 pen fillrule=currentpen, pen[][] p, path[] b=g,
+                 pair[][] z=new pair[][]);
+ If the array `z' is empty, Coons shading, in which the color control
+points are calculated automatically, is used.  The pens in `p' must
+belong to the same color space.  A simpler interface for the case of a
+single patch (n=1) is also available:
+void tensorshade(picture pic=currentpicture, path g, bool stroke=false,
+                 pen fillrule=currentpen, pen[] p, path b=g,
+                 pair[] z=new pair[]);
+ One can also smoothly shade the regions between consecutive paths of a
+sequence using a given array of pens:
+void draw(picture pic=currentpicture, pen fillrule=currentpen, path[] g,
+          pen[] p);
+ Illustrations of tensor product and Coons shading are provided in the
+example files `tensor.asy', `Coons.asy', `BezierSurface.asy', and
+`rainbow.asy'.
+
+   More general shading possibilities are available with the `pdflatex',
+`context', and `pdftex' TeX engines: the routine
+void functionshade(picture pic=currentpicture, path[] g, bool stroke=false,
+                   pen fillrule=currentpen, string shader);
+ shades on picture `pic' the interior of path `g' according to fill
+rule `fillrule' using the `PostScript' calculator routine specified by
+the string `shader'; this routine takes 2 arguments, each in [0,1], and
+returns `colors(fillrule).length' color components.  Function shading
+is illustrated in the example `functionshading.asy'.
+
+   The following routine uses `evenodd' clipping together with the `^^'
+operator to unfill a region:
+
+void unfill(picture pic=currentpicture, path g);
+
+
+File: asymptote.info,  Node: clip,  Next: label,  Prev: fill,  Up: Drawing commands
+
+4.3 clip
+========
+
+void clip(picture pic=currentpicture, path g, stroke=false,
+          pen fillrule=currentpen);
+
+Clip the current contents of picture `pic' to the region bounded by the
+path `g', using fill rule `fillrule' (*note fillrule::).  If
+`stroke=true', the clipped portion is the same as the region that would
+be drawn with `draw(pic,g,fillrule+zerowinding)'; in this case the path
+`g' need not be cyclic. For an illustration of picture clipping, see
+the first example in *note LaTeX usage::.
+
+
+File: asymptote.info,  Node: label,  Prev: clip,  Up: Drawing commands
+
+4.4 label
+=========
+
+void label(picture pic=currentpicture, Label L, pair position,
+           align align=NoAlign, pen p=currentpen, filltype filltype=NoFill)
+
+Draw Label `L' on picture `pic' using pen `p'. If `align' is `NoAlign',
+the label will be centered at user coordinate `position'; otherwise it
+will be aligned in the direction of `align' and displaced from
+`position' by the `PostScript' offset `align*labelmargin(p)'.  The
+constant `Align' can be used to align the bottom-left corner of the
+label at `position'.  The Label `L' can either be a string or the
+structure obtained by calling one of the functions
+Label Label(string s="", pair position, align align=NoAlign,
+            pen p=nullpen, embed embed=Rotate, filltype filltype=NoFill);
+Label Label(string s="", align align=NoAlign,
+            pen p=nullpen, embed embed=Rotate, filltype filltype=NoFill);
+Label Label(Label L, pair position, align align=NoAlign,
+            pen p=nullpen, embed embed=L.embed, filltype filltype=NoFill);
+Label Label(Label L, align align=NoAlign,
+            pen p=nullpen, embed embed=L.embed, filltype filltype=NoFill);
+ The text of a Label can be scaled, slanted, rotated, or shifted by
+multiplying it on the left by an affine transform (*note Transforms::).
+For example, `rotate(45)*xscale(2)*L' first scales `L' in the x
+direction and then rotates it counterclockwise by 45 degrees. The final
+position of a Label can also be shifted by a `PostScript' coordinate
+translation: `shift(10,0)*L'.  An explicit pen specified within the
+Label overrides other pen arguments.  The `embed' argument determines
+how the Label should transform with the embedding picture:
+`Shift'
+     only shift with embedding picture;
+
+`Rotate'
+     only shift and rotate with embedding picture (default);
+
+`Rotate(pair z)'
+     rotate with (picture-transformed) vector `z'.
+
+`Slant'
+     only shift, rotate, slant, and reflect with embedding picture;
+
+`Scale'
+     shift, rotate, slant, reflect, and scale with embedding picture.
+
+
+   To add a label to a path, use
+void label(picture pic=currentpicture, Label L, path g, align align=NoAlign,
+           pen p=currentpen, filltype filltype=NoFill);
+ By default the label will be positioned at the midpoint of the path.
+An alternative label position (in the sense of `point(path p, real t)')
+may be specified as a real value for `position' in constructing the
+Label. The position `Relative(real)' specifies a location relative to
+the total arclength of the path. These convenient abbreviations are
+predefined: 
+position BeginPoint=Relative(0);
+position MidPoint=Relative(0.5);
+position EndPoint=Relative(1);
+
+   Path labels are aligned in the direction `align', which may be
+specified as an absolute compass direction (pair) or a direction
+`Relative(pair)' measured relative to a north axis in the local
+direction of the path. For convenience `LeftSide', `Center', and
+`RightSide' are defined as `Relative(W)', `Relative((0,0))', and
+`Relative(E)', respectively.  Multiplying `LeftSide', `Center',
+`RightSide' on the left by a real scaling factor will move the label
+further away from or closer to the path.
+
+   A label with a fixed-size arrow of length `arrowlength' pointing to
+`b' from direction `dir' can be produced with the routine 
+void arrow(picture pic=currentpicture, Label L="", pair b, pair dir,
+           real length=arrowlength, align align=NoAlign,
+           pen p=currentpen, arrowbar arrow=Arrow, margin margin=EndMargin);
+ If no alignment is specified (either in the Label or as an explicit
+argument), the optional Label will be aligned in the direction `dir',
+using margin `margin'.
+
+   The function `string graphic(string name, string options="")'
+returns a string that can be used to include an encapsulated
+`PostScript' (EPS) file. Here, `name' is the name of the file to
+include and `options' is a string containing a comma-separated list of
+optional bounding box (`bb=llx lly urx ury'), width (`width=value'),
+height (`height=value'), rotation (`angle=value'), scaling
+(`scale=factor'), clipping (`clip=bool'), and draft mode (`draft=bool')
+parameters. The `layer()' function can be used to force future objects
+to be drawn on top of the included image:
+label(graphic("file.eps","width=1cm"),(0,0),NE);
+layer();
+
+   The `string baseline(string s, string template="\strut")' function
+can be used to enlarge the bounding box of labels to match a given
+template, so that their baselines will be typeset on a horizontal line.
+See `Pythagoras.asy' for an example.
+
+   One can prevent labels from overwriting one another with the
+`overwrite' pen attribute (*note overwrite::).
+
+   The structure `object' defined in `plain_Label.asy' allows Labels
+and frames to be treated in a uniform manner.  A group of objects may
+be packed together into single frame with the routine 
+frame pack(pair align=2S ... object inset[]);
+ To draw or fill a box (or ellipse or other path) around a Label and
+return the bounding object, use one of the routines
+object draw(picture pic=currentpicture, Label L, envelope e,
+            real xmargin=0, real ymargin=xmargin, pen p=currentpen,
+            filltype filltype=NoFill, bool above=true);
+object draw(picture pic=currentpicture, Label L, envelope e, pair position,
+            real xmargin=0, real ymargin=xmargin, pen p=currentpen,
+            filltype filltype=NoFill, bool above=true);
+ Here `envelope' is a boundary-drawing routine such as `box',
+`roundbox', or `ellipse' defined in `plain_boxes.asy' (*note
+envelope::).
+
+   The function `path[] texpath(Label L)' returns the path array that
+TeX would fill to draw the Label `L'.
+
+   The `string minipage(string s, width=100pt)' function can be used to
+format string `s' into a paragraph of width `width'.  This example uses
+`minipage', `clip', and `graphic' to produce a CD label:
+
+
+size(11.7cm,11.7cm);
+asy(nativeformat(),"logo");
+fill(unitcircle^^(scale(2/11.7)*unitcircle),
+     evenodd+rgb(124/255,205/255,124/255));
+label(scale(1.1)*minipage(
+"\centering\scriptsize \textbf{\LARGE {\tt Asymptote}\\
+\smallskip
+\small The Vector Graphics Language}\\
+\smallskip
+\textsc{Andy Hammerlindl, John Bowman, and Tom Prince}
+http://asymptote.sourceforge.net\\
+",8cm),(0,0.6));
+label(graphic("logo."+nativeformat(),"height=7cm"),(0,-0.22));
+clip(unitcircle^^(scale(2/11.7)*unitcircle),evenodd);
+
+
+File: asymptote.info,  Node: Bezier curves,  Next: Programming,  Prev: Drawing commands,  Up: Top
+
+5 Bezier curves
+***************
+
+Each interior node of a cubic spline may be given a direction prefix or
+suffix `{dir}': the direction of the pair `dir' specifies the direction
+of the incoming or outgoing tangent, respectively, to the curve at that
+node. Exterior nodes may be given direction specifiers only on their
+interior side.
+
+   A cubic spline between the node z_0, with postcontrol point c_0, and
+the node z_1, with precontrol point c_1, is computed as the Bezier curve
+
+
+
+As illustrated in the diagram below, the third-order midpoint (m_5)
+constructed from two endpoints z_0 and z_1 and two control points c_0
+and c_1, is the point corresponding to t=1/2 on the Bezier curve formed
+by the quadruple (z_0, c_0, c_1, z_1). This allows one to recursively
+construct the desired curve, by using the newly extracted third-order
+midpoint as an endpoint and the respective second- and first-order
+midpoints as control points:
+
+
+
+Here m_0, m_1 and m_2 are the first-order midpoints, m_3 and m_4 are
+the second-order midpoints, and m_5 is the third-order midpoint.  The
+curve is then constructed by recursively applying the algorithm to
+(z_0, m_0, m_3, m_5) and (m_5, m_4, m_2, z_1).
+
+   In fact, an analogous property holds for points located at any
+fraction t in [0,1] of each segment, not just for midpoints (t=1/2).
+
+   The Bezier curve constructed in this manner has the following
+properties:
+   * It is entirely contained in the convex hull of the given four
+     points.
+
+   * It starts heading from the first endpoint to the first control
+     point and finishes heading from the second control point to the
+     second endpoint.
+
+
+   The user can specify explicit control points between two nodes like
+this:
+draw((0,0)..controls (0,100) and (100,100)..(100,0));
+
+   However, it is usually more convenient to just use the `..'
+operator, which tells `Asymptote' to choose its own control points
+using the algorithms described in Donald Knuth's monograph, The
+MetaFontbook, Chapter 14.  The user can still customize the guide (or
+path) by specifying direction, tension, and curl values.
+
+   The higher the tension, the straighter the curve is, and the more it
+approximates a straight line.  One can change the spline tension from
+its default value of 1 to any real value greater than or equal to 0.75
+(cf. John D. Hobby, Discrete and Computational Geometry 1, 1986):
+draw((100,0)..tension 2 ..(100,100)..(0,100));
+draw((100,0)..tension 3 and 2 ..(100,100)..(0,100));
+draw((100,0)..tension atleast 2 ..(100,100)..(0,100));
+
+   In these examples there is a space between `2' and `..'.  This is
+needed as `2.' is interpreted as a numerical constant.
+
+   The curl parameter specifies the curvature at the endpoints of a path
+(0 means straight; the default value of 1 means approximately circular):
+draw((100,0){curl 0}..(100,100)..{curl 0}(0,100));
+
+   The `MetaPost ...' path connector, which requests, when possible, an
+inflection-free curve confined to a triangle defined by the endpoints
+and directions, is implemented in `Asymptote' as the convenient
+abbreviation `::' for `..tension atleast 1 ..' (the ellipsis `...' is
+used in `Asymptote' to indicate a variable number of arguments; *note
+Rest arguments::).  For example, compare
+
+draw((0,0){up}..(100,25){right}..(200,0){down});
+
+
+with
+
+draw((0,0){up}::(100,25){right}::(200,0){down});
+
+
+
+The `---' connector is an abbreviation for `..tension atleast
+infinity..' and the `&' connector concatenates two paths, after first
+stripping off the last node of the first path (which normally should
+coincide with the first node of the second path).
+
+
+File: asymptote.info,  Node: Programming,  Next: LaTeX usage,  Prev: Bezier curves,  Up: Top
+
+6 Programming
+*************
+
+Here is a short introductory example to the `Asymptote' programming
+language that highlights the similarity of its control structures with
+those of C, C++, and Java: 
+// This is a comment.
+
+// Declaration: Declare x to be a real variable;
+real x;
+
+// Assignment: Assign the real variable x the value 1.
+x=1.0;
+
+// Conditional: Test if x equals 1 or not.
+if(x == 1.0) {
+  write("x equals 1.0");
+} else {
+  write("x is not equal to 1.0");
+}
+
+// Loop: iterate 10 times
+for(int i=0; i < 10; ++i) {
+  write(i);
+}
+
+   `Asymptote' supports `while', `do', `break', and `continue'
+statements just as in C/C++. It also supports the Java-style shorthand
+for iterating over all elements of an array:
+
+// Iterate over an array
+int[] array={1,1,2,3,5};
+for(int k : array) {
+  write(k);
+}
+ In addition, it supports many features beyond the ones found in those
+languages.
+
+* Menu:
+
+* Data types::                  void, bool, int, real, pair, triple, string
+* Paths and guides::            Bezier curves
+* Pens::                        Colors, line types, line widths, font sizes
+* Transforms::                  Affine transforms
+* Frames and pictures::         Canvases for immediate and deferred drawing
+* Files::                       Reading and writing your data
+* Variable initializers::       Initialize your variables
+* Structures::                  Organize your data
+* Operators::                   Arithmetic and logical operators
+* Implicit scaling::            Avoiding those ugly *s
+* Functions::                   Traditional and high-order functions
+* Arrays::                      Dynamic vectors
+* Casts::                       Implicit and explicit casts
+* Import::                      Importing external `Asymptote' modules
+* Static::                      Where to allocate your variable?
+
+
+File: asymptote.info,  Node: Data types,  Next: Paths and guides,  Up: Programming
+
+6.1 Data types
+==============
+
+`Asymptote' supports the following data types (in addition to
+user-defined types):
+
+`void'
+     The void type is used only by functions that take or return no
+     arguments.
+
+`bool'
+     a boolean type that can only take on the values `true' or `false'.
+     For example: bool b=true;
+
+     defines a boolean variable `b' and initializes it to the value
+     `true'. If no initializer is given: bool b;
+
+     the value `false' is assumed.
+
+`bool3'
+     an extended boolean type that can take on the values `true',
+     `default', or `false'. A bool3 type can be cast to or from a bool.
+     The default initializer for bool3 is `default'.
+
+`int'
+     an integer type; if no initializer is given, the implicit value `0'
+     is assumed. The minimum allowed value of an integer is `intMin'
+     and the maximum value is `intMax'.
+
+`real'
+     a real number; this should be set to the highest-precision native
+     floating-point type on the architecture. The implicit initializer
+     for reals is `0.0'. Real numbers have precision `realEpsilon',
+     with `realDigits' significant digits.  The smallest positive real
+     number is `realMin' and the largest positive real number is
+     `realMax'.  The variable `inf' and function `bool isnan(real x)'
+     are useful when floating-point exceptions are masked with the
+     `-mask' command-line option (the default in interactive mode).
+
+`pair'
+     complex number, that is, an ordered pair of real components
+     `(x,y)'.  The real and imaginary parts of a pair `z' can read as
+     `z.x' and `z.y'. We say that `x' and `y' are virtual members of
+     the data element pair; they cannot be directly modified, however.
+     The implicit initializer for pairs is `(0.0,0.0)'.
+
+     There are a number of ways to take the complex conjugate of a pair:
+          pair z=(3,4);
+          z=(z.x,-z.y);
+          z=z.x-I*z.y;
+          z=conj(z);
+
+     Here `I' is the pair `(0,1)'.  A number of built-in functions are
+     defined for pairs:
+
+    `pair conj(pair z)'
+          returns the conjugate of `z';
+
+    `real length(pair z)'
+          returns the complex modulus `|z|' of its argument `z'.  For
+          example,
+               pair z=(3,4);
+               length(z);
+          returns the result 5. A synonym for `length(pair)' is
+          `abs(pair)';
+
+    `real angle(pair z, bool warn=true)'
+          returns the angle of `z' in radians in the interval
+          [-`pi',`pi'] or `0' if `warn' is `false' and `z=(0,0)'
+          (rather than producing an error);
+
+    `real degrees(pair z, bool warn=true)'
+          returns the angle of `z' in degrees in the interval [0,360)
+          or `0' if `warn' is `false' and `z=(0,0)' (rather than
+          producing an error);
+
+    `pair unit(pair z)'
+          returns a unit vector in the direction of the pair `z';
+
+    `pair expi(real angle)'
+          returns a unit vector in the direction `angle' measured in
+          radians;
+
+    `pair dir(real degrees)'
+          returns a unit vector in the direction `degrees' measured in
+          degrees;
+
+    `real xpart(pair z)'
+          returns `z.x';
+
+    `real ypart(pair z)'
+          returns `z.y';
+
+    `pair realmult(pair z, pair w)'
+          returns the element-by-element product `(z.x*w.x,z.y*w.y)';
+
+    `real dot(explicit pair z, explicit pair w)'
+          returns the dot product `z.x*w.x+z.y*w.y';
+
+    `pair minbound(pair z, pair w)'
+          returns `(min(z.x,w.x),min(z.y,w.y))';
+
+    `pair maxbound(pair z, pair w)'
+          returns `(max(z.x,w.x),max(z.y,w.y))'.
+
+
+`triple'
+     an ordered triple of real components `(x,y,z)' used for
+     three-dimensional drawings. The respective components of a triple
+     `v' can read as `v.x', `v.y', and `v.z'.  The implicit initializer
+     for triples is `(0.0,0.0,0.0)'.
+
+     Here are the built-in functions for triples:
+    `real length(triple v)'
+          returns the length `|v|' of the vector `v'.  A synonym for
+          `length(triple)' is `abs(triple)';
+
+    `real polar(triple v, bool warn=true)'
+          returns the colatitude of `v' measured from the z axis in
+          radians or `0' if `warn' is `false' and `v=O' (rather than
+          producing an error);
+
+    `real azimuth(triple v, bool warn=true)'
+          returns the longitude of `v' measured from the x axis in
+          radians or `0' if `warn' is `false' and `v.x=v.y=0' (rather
+          than producing an error);
+
+    `real colatitude(triple v, bool warn=true)'
+          returns the colatitude of `v' measured from the z axis in
+          degrees or `0' if `warn' is `false' and `v=O' (rather than
+          producing an error);
+
+    `real latitude(triple v, bool warn=true)'
+          returns the latitude of `v' measured from the xy plane in
+          degrees or `0' if `warn' is `false' and `v=O' (rather than
+          producing an error);
+
+    `real longitude(triple v, bool warn=true)'
+          returns the longitude of `v' measured from the x axis in
+          degrees or `0' if `warn' is `false' and `v.x=v.y=0' (rather
+          than producing an error);
+
+    `triple unit(triple v)'
+          returns a unit triple in the direction of the triple `v';
+
+    `triple expi(real polar, real azimuth)'
+          returns a unit triple in the direction `(polar,azimuth)'
+          measured in radians;
+
+    `triple dir(real colatitude, real longitude)'
+          returns a unit triple in the direction
+          `(colatitude,longitude)' measured in degrees;
+
+    `real xpart(triple v)'
+          returns `v.x';
+
+    `real ypart(triple v)'
+          returns `v.y';
+
+    `real zpart(triple v)'
+          returns `v.z';
+
+    `real dot(triple u, triple v)'
+          returns the dot product `u.x*v.x+u.y*v.y+u.z*v.z';
+
+    `triple cross(triple u, triple v)'
+          returns the cross product
+
+          `(u.y*v.z-u.z*v.y,u.z*v.x-u.x*v.z,u.x*v.y-v.x*u.y)';
+
+    `triple minbound(triple u, triple v)'
+          returns `(min(u.x,v.x),min(u.y,v.y),min(u.z,v.z))';
+
+    `triple maxbound(triple u, triple v)'
+          returns `(max(u.x,v.x),max(u.y,v.y),max(u.z,v.z)').
+
+
+`string'
+     a character string, implemented using the STL `string' class.
+
+     Strings delimited by double quotes (`"') are subject to the
+     following mappings to allow the use of double quotes in TeX (e.g.
+     for using the `babel' package, *note babel::):
+
+        * \" maps to "
+
+        * \\ maps to \\
+
+     Strings delimited by single quotes (`'') have the same mappings as
+     character strings in ANSI `C':
+
+        * \' maps to '
+
+        * \" maps to "
+
+        * \? maps to ?
+
+        * \\ maps to backslash
+
+        * \a maps to alert
+
+        * \b maps to backspace
+
+        * \f maps to form feed
+
+        * \n maps to newline
+
+        * \r maps to carriage return
+
+        * \t maps to tab
+
+        * \v maps to vertical tab
+
+        * \0-\377 map to corresponding octal byte
+
+        * \x0-\xFF map to corresponding hexadecimal byte
+
+     The implicit initializer for strings is the empty string `""'.
+     Strings may be concatenated with the `+' operator. In the following
+     string functions, position `0' denotes the start of the string:
+    `int length(string s)'
+          returns the length of the string `s';
+
+    `int find(string s, string t, int pos=0)'
+          returns the position of the first occurrence of string `t' in
+          string `s' at or after position `pos', or -1 if `t' is not a
+          substring of `s';
+
+    `int rfind(string s, string t, int pos=-1)'
+          returns the position of the last occurrence of string `t' in
+          string `s' at or before position `pos' (if `pos'=-1, at the
+          end of the string `s'), or -1 if `t' is not a substring of
+          `s';
+
+    `string insert(string s, int pos, string t)'
+          returns the string formed by inserting string `t' at position
+          `pos' in `s';
+
+    `string erase(string s, int pos, int n)'
+          returns the string formed by erasing the string of length `n'
+          (if `n'=-1, to the end of the string `s') at position `pos'
+          in `s';
+
+    `string substr(string s, int pos, int n=-1)'
+          returns the substring of `s' starting at position `pos' and
+          of length `n' (if `n'=-1, until the end of the string `s');
+
+    `string reverse(string s)'
+          returns the string formed by reversing string `s';
+
+    `string replace(string s, string before, string after)'
+          returns a string with all occurrences of the string `before'
+          in the string `s' changed to the string `after';
+
+    `string replace(string s, string[][] table)'
+          returns a string constructed by translating in string `s' all
+          occurrences of the string `before' in an array `table' of
+          string pairs {`before',`after'} to the corresponding string
+          `after';
+
+    `string[] split(string s, string delimiter="")'
+          returns an array of strings obtained by splitting `s' into
+          substrings delimited by `delimiter' (an empty delimiter
+          signifies a space, but with duplicate delimiters discarded);
+
+    `string format(string s, int n, string locale="")'
+          returns a string containing `n' formatted according to the
+          C-style format string `s' using locale `locale' (or the
+          current locale if an empty string is specified);
+
+    `string format(string s=defaultformat, string s=defaultseparator, real x, string locale="")'
+          returns a string containing `x' formatted according to the
+          C-style format string `s' using locale `locale' (or the
+          current locale if an empty string is specified), following
+          the behaviour of the C function `fprintf'), except that only
+          one data field is allowed, trailing zeros are removed by
+          default (unless `#' is specified), and (if the format string
+          specifies math mode) TeX is used to typeset scientific
+          notation using the `defaultseparator="\!\times\!";';
+
+    `int hex(string s);'
+          casts a hexidecimal string `s' to an integer;
+
+    `int ascii(string s);'
+          returns the ASCII code for the first character of string `s';
+
+    `string string(real x, int digits=realDigits)'
+          casts `x' to a string using precision `digits' and the C
+          locale;
+
+    `string locale(string s="")'
+          sets the locale to the given string, if nonempty, and returns
+          the current locale;
+
+    `string time(string format="%a %b %d %T %Z %Y")'
+          returns the current time formatted by the ANSI C routine
+          `strftime' according to the string `format' using the current
+          locale. Thus time();
+          time("%a %b %d %H:%M:%S %Z %Y");
+
+          are equivalent ways of returning the current time in the
+          default format used by the `UNIX' `date' command;
+
+    `int seconds(string t="", string format="")'
+          returns the time measured in seconds after the Epoch (Thu Jan
+          01 00:00:00 UTC 1970) as determined by the ANSI C routine
+          `strptime' according to the string `format' using the current
+          locale, or the current time if `t' is the empty string.  Note
+          that the `"%Z"' extension to the POSIX `strptime'
+          specification is ignored by the current GNU C Library. If an
+          error occurs, the value -1 is returned. Here are some
+          examples: seconds("Mar 02 11:12:36 AM PST 2007","%b %d %r PST %Y");
+          seconds(time("%b %d %r %z %Y"),"%b %d %r %z %Y");
+          seconds(time("%b %d %r %Z %Y"),"%b %d %r "+time("%Z")+" %Y");
+          1+(seconds()-seconds("Jan 1","%b %d"))/(24*60*60);
+           The last example returns today's ordinal date, measured from
+          the beginning of the year.
+
+    `string time(int seconds, string format="%a %b %d %T %Z %Y")'
+          returns the time corresponding to `seconds' seconds after the
+          Epoch (Thu Jan 01 00:00:00 UTC 1970) formatted by the ANSI C
+          routine `strftime' according to the string `format' using the
+          current locale. For example, to return the date corresponding
+          to 24 hours ago: time(seconds()-24*60*60);
+
+    `int system(string s)'
+
+    `int system(string[] s)'
+          if the setting `safe' is false, call the arbitrary system
+          command `s';
+
+    `void asy(string format, bool overwrite=false ... string[] s)'
+          conditionally process each file name in array `s' in a new
+          environment, using format `format', overwriting the output
+          file only if `overwrite' is true;
+
+    `void abort(string s="")'
+          aborts execution (with a non-zero return code in batch mode);
+          if string `s' is nonempty, a diagnostic message constructed
+          from the source file, line number, and `s' is printed;
+
+    `void assert(bool b, string s="")'
+          aborts execution with an error message constructed from `s' if
+          `b=false';
+
+    `void exit()'
+          exits (with a zero error return code in batch mode);
+
+    `void sleep(int seconds)'
+          pauses for the given number of seconds;
+
+    `void usleep(int microseconds)'
+          pauses for the given number of microseconds;
+
+    `void beep()'
+          produces a beep on the console;
+
+
+
+   As in C/C++, complicated types may be abbreviated with `typedef'
+(see the example in *note Functions::).
+
+
+File: asymptote.info,  Node: Paths and guides,  Next: Pens,  Prev: Data types,  Up: Programming
+
+6.2 Paths and guides
+====================
+
+`path'
+     a cubic spline resolved into a fixed path.  The implicit
+     initializer for paths is `nullpath'.
+
+     For example, the routine `circle(pair c, real r)', which returns a
+     Bezier curve approximating a circle of radius `r' centered on `c',
+     is based on `unitcircle' (*note unitcircle::): path circle(pair c, real r)
+     {
+       return shift(c)*scale(r)*unitcircle;
+     }
+      If high accuracy is needed, a true circle may be produced with the
+     routine `Circle' defined in the module `graph.asy': import graph;
+     path Circle(pair c, real r, int n=nCircle);
+
+     A circular arc consistent with `circle' centered on `c' with
+     radius `r' from `angle1' to `angle2' degrees, drawing
+     counterclockwise if `angle2 >= angle1', can be constructed with path arc(pair c, real r, real angle1, real angle2);
+      One may also specify the direction explicitly: path arc(pair c, real r, real angle1, real angle2, bool direction);
+      Here the direction can be specified as CCW (counter-clockwise) or
+     CW (clockwise). For convenience, an arc centered at `c' from pair
+     `z1' to `z2' (assuming `|z2-c|=|z1-c|') in the may also be
+     constructed with path arc(pair c, explicit pair z1, explicit pair z2,
+              bool direction=CCW)
+
+     If high accuracy is needed, true arcs may be produced with routines
+     in the module `graph.asy' that produce Bezier curves with `n'
+     control points: import graph;
+     path Arc(pair c, real r, real angle1, real angle2, bool direction,
+              int n=nCircle);
+     path Arc(pair c, real r, real angle1, real angle2, int n=nCircle);
+     path Arc(pair c, explicit pair z1, explicit pair z2,
+              bool direction=CCW, int n=nCircle);
+
+     An ellipse can be drawn with the routine path ellipse(pair c, real a, real b)
+     {
+       return shift(c)*scale(a,b)*unitcircle;
+     }
+
+     A brace can be constructed between pairs `a' and `b' with path brace(pair a, pair b, real amplitude=bracedefaultratio*length(b-a));
+
+     This example illustrates the use of all five guide connectors
+     discussed in *note Tutorial:: and *note Bezier curves::: size(300,0);
+     pair[] z=new pair[10];
+
+     z[0]=(0,100); z[1]=(50,0); z[2]=(180,0);
+
+     for(int n=3; n <= 9; ++n)
+       z[n]=z[n-3]+(200,0);
+
+     path p=z[0]..z[1]---z[2]::{up}z[3]
+     &z[3]..z[4]--z[5]::{up}z[6]
+     &z[6]::z[7]---z[8]..{up}z[9];
+
+     draw(p,grey+linewidth(4mm));
+
+     dot(z);
+
+
+
+     Here are some useful functions for paths:
+
+    `int length(path p);'
+          This is the number of (linear or cubic) segments in path `p'.
+          If `p' is cyclic, this is the same as the number of nodes in
+          `p'.
+
+    `int size(path p);'
+          This is the number of nodes in the path `p'.  If `p' is
+          cyclic, this is the same as `length(p)'.
+
+    `bool cyclic(path p);'
+          returns `true' iff path `p' is cyclic.
+
+    `bool straight(path p, int i);'
+          returns `true' iff the segment of path `p' between node `i'
+          and node `i+1' is straight.
+
+    `bool piecewisestraight(path p)'
+          returns `true' iff the path `p' is piecewise straight.
+
+    `pair point(path p, int t);'
+          If `p' is cyclic, return the coordinates of node `t' mod
+          `length(p)'. Otherwise, return the coordinates of node `t',
+          unless `t' < 0 (in which case `point(0)' is returned) or `t'
+          > `length(p)' (in which case `point(length(p))' is returned).
+
+    `pair point(path p, real t);'
+          This returns the coordinates of the point between node
+          `floor(t)' and `floor(t)+1' corresponding to the cubic spline
+          parameter `t-floor(t)' (*note Bezier curves::). If `t' lies
+          outside the range [0,`length(p)'], it is first reduced modulo
+          `length(p)' in the case where `p' is cyclic or else converted
+          to the corresponding endpoint of `p'.
+
+    `pair dir(path p, int t, int sign=0, bool normalize=true);'
+          If `sign < 0', return the direction (as a pair) of the
+          incoming tangent to path `p' at node `t'; if `sign > 0',
+          return the direction of the outgoing tangent. If `sign=0',
+          the mean of these two directions is returned.
+
+    `pair dir(path p, real t, bool normalize=true);'
+          returns the direction of the tangent to path `p' at the point
+          between node `floor(t)' and `floor(t)+1' corresponding to the
+          cubic spline parameter `t-floor(t)' (*note Bezier curves::).
+
+    `pair dir(path p)'
+          returns dir(p,length(p)).
+
+    `pair dir(path p, path q)'
+          returns unit(dir(p)+dir(q)).
+
+    `pair accel(path p, int t, int sign=0);'
+          If `sign < 0', return the acceleration of the incoming path
+          `p' at node `t'; if `sign > 0', return the acceleration of
+          the outgoing path. If `sign=0', the mean of these two
+          accelerations is returned.
+
+    `pair accel(path p, real t);'
+          returns the acceleration of the path `p' at the point `t'.
+
+    `real radius(path p, real t);'
+          returns the radius of curvature of the path `p' at the point
+          `t'.
+
+    `pair precontrol(path p, int t);'
+          returns the precontrol point of `p' at node `t'.
+
+    `pair precontrol(path p, real t);'
+          returns the effective precontrol point of `p' at parameter
+          `t'.
+
+    `pair postcontrol(path p, int t);'
+          returns the postcontrol point of `p' at node `t'.
+
+    `pair postcontrol(path p, real t);'
+          returns the effective postcontrol point  of `p' at parameter
+          `t'.
+
+    `real arclength(path p);'
+          returns the length (in user coordinates) of the piecewise
+          linear or cubic curve that path `p' represents.
+
+    `real arctime(path p, real L);'
+          returns the path "time", a real number between 0 and the
+          length of the path in the sense of `point(path p, real t)',
+          at which the cumulative arclength (measured from the
+          beginning of the path) equals `L'.
+
+    `real arcpoint(path p, real L);'
+          returns `point(p,arctime(p,L))'.
+
+    `real dirtime(path p, pair z);'
+          returns the first "time", a real number between 0 and the
+          length of the path in the sense of `point(path, real)', at
+          which the tangent to the path has the direction of pair `z',
+          or -1 if this never happens.
+
+    `real reltime(path p, real l);'
+          returns the time on path `p' at the relative fraction `l' of
+          its arclength.
+
+    `pair relpoint(path p, real l);'
+          returns the point on path `p' at the relative fraction `l' of
+          its arclength.
+
+    `pair midpoint(path p);'
+          returns the point on path `p' at half of its arclength.
+
+    `path reverse(path p);'
+          returns a path running backwards along `p'.
+
+    `path subpath(path p, int a, int b);'
+          returns the subpath of `p' running from node `a' to node `b'.
+          If `a' < `b', the direction of the subpath is reversed.
+
+    `path subpath(path p, real a, real b);'
+          returns the subpath  of `p' running from path time `a' to path
+          time `b', in the sense of `point(path, real)'. If `a' < `b',
+          the direction of the subpath is reversed.
+
+    `real[] intersect(path p, path q, real fuzz=-1);'
+          If `p' and `q' have at least one intersection point, return a
+          real array of length 2 containing the times representing the
+          respective path times along `p' and `q', in the sense of
+          `point(path, real)', for one such intersection point (as
+          chosen by the algorithm described on page 137 of `The
+          MetaFontbook').  The computations are performed to the
+          absolute error specified by `fuzz', or if `fuzz < 0', to
+          machine precision. If the paths do not intersect, return a
+          real array of length 0.
+
+    `real[][] intersections(path p, path q, real fuzz=-1);'
+          Return all (unless there are infinitely many) intersection
+          times of paths `p' and `q' as a sorted array of real arrays
+          of length 2 (*note sort::). The computations are performed to
+          the absolute error specified by `fuzz', or if `fuzz < 0', to
+          machine precision.
+
+    `real[] intersections(path p, explicit pair a, explicit pair b, real fuzz=-1);'
+          Return all (unless there are infinitely many) intersection
+          times of path `p' with the (infinite) line through points `a'
+          and `b' as a sorted array. The intersections returned are
+          guaranteed to be correct to within the absolute error
+          specified by `fuzz', or if `fuzz < 0', to machine precision.
+
+    `real[] times(path p, real x)'
+          returns all intersection times of path `p' with the vertical
+          line through `(x,0)'.
+
+    `real[] times(path p, explicit pair z)'
+          returns all intersection times of path `p' with the
+          horizontal line through `(0,z.y)'.
+
+    `real[] mintimes(path p)'
+          returns an array of length 2 containing times at which path
+          `p' reaches its minimal horizontal and vertical extents,
+          respectively.
+
+    `real[] maxtimes(path p)'
+          returns an array of length 2 containing times at which path
+          `p' reaches its maximal horizontal and vertical extents,
+          respectively.
+
+    `pair intersectionpoint(path p, path q, real fuzz=-1);'
+          returns the intersection point
+          `point(p,intersect(p,q,fuzz)[0])'.
+
+    `pair[] intersectionpoints(path p, path q, real fuzz=-1);'
+          returns an array containing all intersection points of the
+          paths `p' and `q'.
+
+    `pair extension(pair P, pair Q, pair p, pair q);'
+          returns the intersection point of the extensions of the line
+          segments `P--Q' and `p--q', or if the lines are parallel,
+          `(infinity,infinity)'.
+
+    `slice cut(path p, path knife, int n);'
+          returns the portions of path `p' before and after the `n'th
+          intersection of `p' with path `knife' as a structure `slice'
+          (if no intersection exist is found, the entire path is
+          considered to be `before' the intersection): struct slice {
+            path before,after;
+          }
+           The argument `n' is treated as modulo the number of
+          intersections.
+
+    `slice firstcut(path p, path knife);'
+          equivalent to `cut(p,knife,0);' Note that `firstcut.after'
+          plays the role of the `MetaPost cutbefore' command.
+
+    `slice lastcut(path p, path knife);'
+          equivalent to `cut(p,knife,-1);' Note that `lastcut.before'
+          plays the role of the `MetaPost cutafter' command.
+
+    `path buildcycle(... path[] p);'
+          This returns the path surrounding a region bounded by a list
+          of two or more consecutively intersecting paths, following
+          the behaviour of the `MetaPost buildcycle' command.
+
+    `pair min(path p);'
+          returns the pair (left,bottom) for the path bounding box of
+          path `p'.
+
+    `pair max(path p);'
+          returns the pair (right,top) for the path bounding box of
+          path `p'.
+
+    `int windingnumber(path p, pair z);'
+          returns the winding number of the cyclic path `p' relative to
+          the point `z'. The winding number is positive if the path
+          encircles `z' in the counterclockwise direction. If `z' lies
+          on `p' the constant `undefined' (defined to be the largest
+          odd integer) is returned.
+
+    `bool interior(int windingnumber, pen fillrule)'
+          returns true if `windingnumber' corresponds to an interior
+          point according to `fillrule'.
+
+    `bool inside(path p, pair z, pen fillrule=currentpen);'
+          returns `true' iff the point `z' lies inside or on the edge of
+          the region bounded by the cyclic path `p' according to the
+          fill rule `fillrule' (*note fillrule::).
+
+    `int inside(path p, path q, pen fillrule=currentpen);'
+          returns `1' if the cyclic path `p' strictly contains `q'
+          according to the fill rule `fillrule' (*note fillrule::), `-1'
+          if the cyclic path `q' strictly contains `p', and `0'
+          otherwise.
+
+    `pair inside(path p, pen fillrule=currentpen);'
+          returns an arbitrary point strictly inside a cyclic path `p'
+          according to the fill rule `fillrule' (*note fillrule::).
+
+    `real side(pair a, pair b, pair c);'
+          determines the side of `a--b' that c lies on (negative=left,
+          zero=on `a--b', positive=right).
+
+    `real incircle(pair a, pair b, pair c, pair d);'
+          determines the side of the counterclockwise circle through
+          `a,b,c' that `d' lies on (negative=inside, 0=on circle,
+          positive=right).
+
+    `path[] strokepath(path g, pen p=currentpen);'
+          returns the path array that `PostScript' would fill in
+          drawing path `g' with pen `p'.
+
+
+`guide'
+     an unresolved cubic spline (list of cubic-spline nodes and control
+     points).  The implicit initializer for a guide is `nullpath'; this
+     is useful for building up a guide within a loop.
+
+     A guide is similar to a path except that the computation of the
+     cubic spline is deferred until drawing time (when it is resolved
+     into a path); this allows two guides with free endpoint conditions
+     to be joined together smoothly.  The solid curve in the following
+     example is built up incrementally as a guide, but only resolved at
+     drawing time; the dashed curve is incrementally resolved at each
+     iteration, before the entire set of nodes (shown in red) is known:
+
+     size(200);
+
+     real mexican(real x) {return (1-8x^2)*exp(-(4x^2));}
+
+     int n=30;
+     real a=1.5;
+     real width=2a/n;
+
+     guide hat;
+     path solved;
+
+     for(int i=0; i < n; ++i) {
+       real t=-a+i*width;
+       pair z=(t,mexican(t));
+       hat=hat..z;
+       solved=solved..z;
+     }
+
+     draw(hat);
+     dot(hat,red);
+     draw(solved,dashed);
+
+
+
+     We point out an efficiency distinction in the use of guides and
+     paths: guide g;
+     for(int i=0; i < 10; ++i)
+       g=g--(i,i);
+     path p=g;
+
+     runs in linear time, whereas path p;
+     for(int i=0; i < 10; ++i)
+       p=p--(i,i);
+
+     runs in quadratic time, as the entire path up to that point is
+     copied at each step of the iteration.
+
+     The following routines can be used to examine the individual
+     elements of a guide without actually resolving the guide to a
+     fixed path (except for internal cycles, which are resolved):
+
+    `int size(guide g);'
+          Analogous to `size(path p)'.
+
+    `int length(guide g);'
+          Analogous to `length(path p)'.
+
+    `bool cyclic(path p);'
+          Analogous to `cyclic(path p)'.
+
+    `pair point(guide g, int t);'
+          Analogous to `point(path p, int t)'.
+
+    `guide reverse(guide g);'
+          Analogous to `reverse(path p)'. If `g' is cyclic and also
+          contains a secondary cycle, it is first solved to a path,
+          then reversed. If `g' is not cyclic but contains an internal
+          cycle, only the internal cycle is solved before reversal. If
+          there are no internal cycles, the guide is reversed but not
+          solved to a path.
+
+    `pair[] dirSpecifier(guide g, int i);'
+          This returns a pair array of length 2 containing the outgoing
+          (in element 0) and incoming (in element 1) direction
+          specifiers (or `(0,0)' if none specified) for the segment of
+          guide `g' between nodes `i' and `i+1'.
+
+    `pair[] controlSpecifier(guide g, int i);'
+          If the segment of guide `g' between nodes `i' and `i+1' has
+          explicit outgoing and incoming control points, they are
+          returned as elements 0 and 1, respectively, of a two-element
+          array. Otherwise, an empty array is returned.
+
+    `tensionSpecifier tensionSpecifier(guide g, int i);'
+          This returns the tension specifier for the segment of guide
+          `g' between nodes `i' and `i+1'. The individual components of
+          the `tensionSpecifier' type can be accessed as the virtual
+          members `in', `out', and `atLeast'.
+
+    `real[] curlSpecifier(guide g);'
+          This returns an array containing the initial curl specifier
+          (in element 0) and final curl specifier (in element 1) for
+          guide `g'.
+
+
+     As a technical detail we note that a direction specifier given to
+     `nullpath' modifies the node on the other side: the guides a..{up}nullpath..b;
+     c..nullpath{up}..d;
+     e..{up}nullpath{down}..f;
+      are respectively equivalent to a..nullpath..{up}b;
+     c{up}..nullpath..d;
+     e{down}..nullpath..{up}f;
+
+
+
+File: asymptote.info,  Node: Pens,  Next: Transforms,  Prev: Paths and guides,  Up: Programming
+
+6.3 Pens
+========
+
+In `Asymptote', pens provide a context for the four basic drawing
+commands (*note Drawing commands::). They are used to specify the
+following drawing attributes: color, line type, line width, line cap,
+line join, fill rule, text alignment, font, font size, pattern,
+overwrite mode, and calligraphic transforms on the pen nib. The default
+pen used by the drawing routines is called `currentpen'. This provides
+the same functionality as the `MetaPost' command `pickup'.  The
+implicit initializer for pens is `defaultpen'.
+
+   Pens may be added together with the nonassociative binary operator
+`+'. This will add the colors of the two pens.  All other non-default
+attributes of the rightmost pen will override those of the leftmost
+pen. Thus, one can obtain a yellow dashed pen by saying
+`dashed+red+green' or `red+green+dashed' or `red+dashed+green'. The
+binary operator `*' can be used to scale the color of a pen by a real
+number, until it saturates with one or more color components equal to 1.
+
+   * Colors are specified using one of the following colorspaces: 
+    `pen gray(real g);'
+          This produces a grayscale color, where the intensity `g' lies
+          in the interval [0,1], with 0.0 denoting black and 1.0
+          denoting white.
+
+    `pen rgb(real r, real g, real b);'
+          This produces an RGB color, where each of the red, green, and
+          blue intensities `r', `g', `b', lies in the interval [0,1].
+
+    `pen cmyk(real c, real m, real y, real k);'
+          This produces a CMYK color, where each of the cyan, magenta,
+          yellow, and black intensities `c', `m', `y', `k', lies in the
+          interval [0,1].
+
+    `pen invisible;'
+          This special pen writes in invisible ink, but adjusts the
+          bounding box as if something had been drawn (like the
+          `\phantom' command in TeX). The function `bool
+          invisible(pen)' can be used to test whether a pen is
+          invisible.
+
+
+     The default color is `black'; this may be changed with the routine
+     `defaultpen(pen)'. The function `colorspace(pen p)' returns the
+     colorspace of pen `p' as a string (`"gray"', `"rgb"', `"cmyk"', or
+     `""').
+
+     The function `real[] colors(pen)' returns the color components of
+     a pen.  The functions `pen gray(pen)', `pen rgb(pen)',  and `pen
+     cmyk(pen)' return new pens obtained by converting their arguments
+     to the respective color spaces.  The function
+     `colorless(pen=currentpen)' returns a copy of its argument with
+     the color attributes stripped (to avoid color mixing).
+
+     A 6-character RGB hexidecimal string can be converted to a pen with
+     the routine pen rgb(string s);
+      A pen can be converted to a hexidecimal string with 
+
+   * string hex(pen p);
+
+     Various shades and mixtures of the grayscale primary colors
+     `black' and `white', RGB primary colors `red', `green', and
+     `blue', and RGB secondary colors `cyan', `magenta', and `yellow'
+     are defined as named colors, along with the CMYK primary colors
+     `Cyan', `Magenta', `Yellow', and `Black', in the module `plain':
+
+
+
+     The standard 140 RGB `X11' colors can be imported with the command import x11colors;
+      and the standard 68 CMYK TeX colors can be imported with the
+     command import texcolors;
+      Note that there is some overlap between these two standards and
+     the definitions of some colors (e.g. `Green') actually disagree.
+
+     `Asymptote' also comes with a `asycolors.sty' `LaTeX' package that
+     defines to `LaTeX' CMYK versions of `Asymptote''s predefined
+     colors, so that they can be used directly within `LaTeX' strings.
+     Normally, such colors are passed to `LaTeX' via a pen argument;
+     however, to change the color of only a portion of a string, say
+     for a slide presentation, (*note slide::) it may be desirable to
+     specify the color directly to `LaTeX'. This file can be passed to
+     `LaTeX' with the `Asymptote' command usepackage("asycolors");
+
+     The structure `hsv' defined in `plain_pens.asy' may be used to
+     convert between HSV and RGB spaces, where the hue `h' is an angle
+     in [0,360) and the saturation `s' and value `v' lie in `[0,1]': pen p=hsv(180,0.5,0.75);
+     write(p);           // ([default], red=0.375, green=0.75, blue=0.75)
+     hsv q=p;
+     write(q.h,q.s,q.v); // 180     0.5     0.75
+
+   * Line types are specified with the function `pen linetype(real[] a,
+     real offset=0, bool scale=true, bool adjust=true)', where `a' is
+     an array of real array numbers.  The optional parameter `offset'
+     specifies where in the pattern to begin. The first number
+     specifies how far (if `scale' is `true', in units of the pen line
+     width; otherwise in `PostScript' units) to draw with the pen on,
+     the second number specifies how far to draw with the pen off, and
+     so on. If `adjust' is `true', these spacings are automatically
+     adjusted by `Asymptote' to fit the arclength of the path. Here are
+     the predefined line types: pen solid=linetype(new real[]);
+     pen dotted=linetype(new real[] {0,4});
+     pen dashed=linetype(new real[] {8,8});
+     pen longdashed=linetype(new real[] {24,8});
+     pen dashdotted=linetype(new real[] {8,8,0,8});
+     pen longdashdotted=linetype(new real[] {24,8,0,8});
+     pen Dotted(pen p=currentpen) {return linetype(new real[] {0,3})+2*linewidth(p);}
+     pen Dotted=Dotted();
+
+
+
+     The default line type is `solid'; this may be changed with
+     `defaultpen(pen)'.  The line type of a pen can be determined with
+     the functions `real[] linetype(pen p=currentpen)', `real
+     offset(pen p)', `bool scale(pen p)', and `bool adjust(pen p)'.
+
+   * The pen line width is specified in `PostScript' units with `pen
+     linewidth(real)'. The default line width is 0.5 bp; this value may
+     be changed with `defaultpen(pen)'. The line width of a pen is
+     returned by `real linewidth(pen p=currentpen)'.  For convenience,
+     in the module `plain_pens' we define void defaultpen(real w) {defaultpen(linewidth(w));}
+     pen operator +(pen p, real w) {return p+linewidth(w);}
+     pen operator +(real w, pen p) {return linewidth(w)+p;}
+      so that one may set the line width like this: defaultpen(2);
+     pen p=red+0.5;
+
+   * A pen with a specific `PostScript' line cap is returned on calling
+     `linecap' with an integer argument: pen squarecap=linecap(0);
+     pen roundcap=linecap(1);
+     pen extendcap=linecap(2);
+
+     The default line cap, `roundcap', may be changed with
+     `defaultpen(pen)'. The line cap of a pen is returned by `int
+     linecap(pen p=currentpen)'.
+
+   * A pen with a specific `PostScript' join style is returned on
+     calling `linejoin' with an integer argument: pen miterjoin=linejoin(0);
+     pen roundjoin=linejoin(1);
+     pen beveljoin=linejoin(2);
+
+     The default join style, `roundjoin', may be changed with
+     `defaultpen(pen)'.The join style of a pen is returned by `int
+     linejoin(pen p=currentpen)'.
+
+   * A pen with a specific `PostScript' miter limit is returned by
+     calling `miterlimit(real)'.  The default miterlimit, `10.0', may
+     be changed with `defaultpen(pen)'. The miter limit of a pen is
+     returned by `real miterlimit(pen p=currentpen)'.
+
+   * A pen with a specific `PostScript' fill rule is returned on
+     calling `fillrule' with an integer argument: pen zerowinding=fillrule(0);
+     pen evenodd=fillrule(1);
+
+     The fill rule, which identifies the algorithm used to determine the
+     insideness of a path or array of paths, only affects the `clip',
+     `fill', and `inside' functions. For the `zerowinding' fill rule, a
+     point `z' is outside the region bounded by a path if the number of
+     upward intersections of the path with the horizontal line
+     `z--z+infinity' minus the number of downward intersections is
+     zero. For the `evenodd' fill rule, `z' is considered to be outside
+     the region if the total number of such intersections is even.  The
+     default fill rule, `zerowinding', may be changed with
+     `defaultpen(pen)'. The fill rule of a pen is returned by `int
+     fillrule(pen p=currentpen)'.
+
+   * A pen with a specific text alignment setting is returned on
+     calling `basealign' with an integer argument: pen nobasealign=basealign(0);
+     pen basealign=basealign(1);
+
+     The default setting, `nobasealign',which may be changed with
+     `defaultpen(pen)', causes the label alignment routines to use the
+     full label bounding box for alignment. In contrast, `basealign'
+     requests that the TeX baseline be respected.  The base align
+     setting of a pen is returned by `int basealigin(pen p=currentpen)'.
+
+   * The font size is specified in TeX points (1 pt = 1/72.27 inches)
+     with the function `pen fontsize(real size, real
+     lineskip=1.2*size)'.  The default font size, 12pt, may be changed
+     with `defaultpen(pen)'.  Nonstandard font sizes may require
+     inserting import fontsize;
+      at the beginning of the file (this requires the `type1cm' package
+     available from
+
+          `http://www.ctan.org/tex-archive/macros/latex/contrib/type1cm/'
+     and included in recent `LaTeX' distributions). The font size and
+     line skip of a pen can be examined with the routines `real
+     fontsize(pen p=currentpen)' and `real lineskip(pen p=currentpen)',
+     respectively.
+
+   * A pen using a specific `LaTeX' `NFSS' font is returned by calling
+     the function `pen font(string encoding, string family, string
+     series, string shape)'. The default setting,
+     `font("OT1","cmr","m","n")', corresponds to 12pt Computer Modern
+     Roman; this may be changed with `defaultpen(pen)'.  The font
+     setting of a pen is returned by `string font(pen p=currentpen)'.
+     Support for standardized international characters is provided by
+     the `unicode' package (*note unicode::).
+
+     Alternatively, one may select a fixed-size TeX font (on which
+     `fontsize' has no effect) like `"cmr12"' (12pt Computer Modern
+     Roman) or `"pcrr"' (Courier) using the function `pen font(string
+     name)'. An optional size argument can also be given to scale the
+     font to the requested size: `pen font(string name, real size)'.
+
+     A nonstandard font command can be generated with `pen
+     fontcommand(string)'.
+
+     A convenient interface to the following standard `PostScript'
+     fonts is also provided: pen AvantGarde(string series="m", string shape="n");
+     pen Bookman(string series="m", string shape="n");
+     pen Courier(string series="m", string shape="n");
+     pen Helvetica(string series="m", string shape="n");
+     pen NewCenturySchoolBook(string series="m", string shape="n");
+     pen Palatino(string series="m", string shape="n");
+     pen TimesRoman(string series="m", string shape="n");
+     pen ZapfChancery(string series="m", string shape="n");
+     pen Symbol(string series="m", string shape="n");
+     pen ZapfDingbats(string series="m", string shape="n");
+
+   * The transparency of a pen can be changed with the command: pen opacity(real opacity=1, string blend="Compatible");
+      The opacity can be varied from `0' (fully transparent) to the
+     default value of `1' (opaque), and `blend' specifies one of the
+     following foreground-background blending operations: "Compatible","Normal","Multiply","Screen","Overlay","SoftLight",
+     "HardLight","ColorDodge","ColorBurn","Darken","Lighten","Difference",
+     "Exclusion","Hue","Saturation","Color","Luminosity",
+      as described in
+
+     `http://partners.adobe.com/public/developer/en/pdf/PDFReference16.pdf'.
+     Since `PostScript' does not support transparency, this feature is
+     only effective with the `-f pdf' output format option; other
+     formats can be produced from the resulting PDF file with the
+     `ImageMagick' `convert' program.  Labels are always drawn with an
+     `opacity' of 1.  A simple example of transparent filling is
+     provided in the example file `transparency.asy'.
+
+   * `PostScript' commands within a `picture' may be used to create a
+     tiling pattern, identified by the string `name', for `fill' and
+     `draw' operations by adding it to the global `PostScript' frame
+     `currentpatterns', with optional left-bottom margin `lb' and
+     right-top margin `rt'.  import patterns;
+     void add(string name, picture pic, pair lb=0, pair rt=0);
+
+     To `fill' or `draw' using pattern `name', use the pen
+     `pattern("name")'. For example, rectangular tilings can be
+     constructed using the routines `picture tile(real Hx=5mm, real
+     Hy=0, pen p=currentpen, filltype filltype=NoFill)', `picture
+     checker(real Hx=5mm, real Hy=0, pen p=currentpen)', and `picture
+     brick(real Hx=5mm, real Hy=0, pen p=currentpen)' defined in
+     `patterns.asy': size(0,90);
+     import patterns;
+
+     add("tile",tile());
+     add("filledtilewithmargin",tile(6mm,4mm,red,Fill),(1mm,1mm),(1mm,1mm));
+     add("checker",checker());
+     add("brick",brick());
+
+     real s=2.5;
+     filldraw(unitcircle,pattern("tile"));
+     filldraw(shift(s,0)*unitcircle,pattern("filledtilewithmargin"));
+     filldraw(shift(2s,0)*unitcircle,pattern("checker"));
+     filldraw(shift(3s,0)*unitcircle,pattern("brick"));
+
+
+
+     Hatch patterns can be generated with the routines `picture
+     hatch(real H=5mm, pair dir=NE, pen p=currentpen)', `picture
+     crosshatch(real H=5mm, pen p=currentpen)': size(0,100);
+     import patterns;
+
+     add("hatch",hatch());
+     add("hatchback",hatch(NW));
+     add("crosshatch",crosshatch(3mm));
+
+     real s=1.25;
+     filldraw(unitsquare,pattern("hatch"));
+     filldraw(shift(s,0)*unitsquare,pattern("hatchback"));
+     filldraw(shift(2s,0)*unitsquare,pattern("crosshatch"));
+
+
+
+     You may need to turn off aliasing in your `PostScript' viewer for
+     patterns to appear correctly. Custom patterns can easily be
+     constructed, following the examples in `patterns.asy'. The tiled
+     pattern can even incorporate shading (*note gradient shading::),
+     as illustrated in this example (not included in the manual because
+     not all printers support `PostScript' 3): size(0,100);
+     import patterns;
+
+     real d=4mm;
+     picture tiling;
+     path square=scale(d)*unitsquare;
+     axialshade(tiling,square,white,(0,0),black,(d,d));
+     fill(tiling,shift(d,d)*square,blue);
+     add("shadedtiling",tiling);
+
+     filldraw(unitcircle,pattern("shadedtiling"));
+
+      
+
+   * One can specify a custom pen nib as an arbitrary polygonal path
+     with `pen makepen(path)'; this path represents the mark to be
+     drawn for paths containing a single point. This pen nib path can be
+     recovered from a pen with `path nib(pen)'. Unlike in `MetaPost',
+     the path need not be convex:
+
+     size(200);
+     pen convex=makepen(scale(10)*polygon(8))+grey;
+     draw((1,0.4),convex);
+     draw((0,0)---(1,1)..(2,0)--cycle,convex);
+
+     pen nonconvex=scale(10)*
+       makepen((0,0)--(0.25,-1)--(0.5,0.25)--(1,0)--(0.5,1.25)--cycle)+red;
+     draw((0.5,-1.5),nonconvex);
+     draw((0,-1.5)..(1,-0.5)..(2,-1.5),nonconvex);
+
+
+
+     The value `nullpath' represents a circular pen nib (the default);
+     an elliptical pen can be achieved simply by multiplying the pen by
+     a transform: `yscale(2)*currentpen'.
+
+   * One can prevent labels from overwriting one another by using the
+     pen attribute `overwrite', which takes a single argument:
+
+    `Allow'
+          Allow labels to overwrite one another. This is the default
+          behaviour (unless overridden with `defaultpen(pen)'.
+
+    `Suppress'
+          Suppress, with a warning, each label that would overwrite
+          another label.
+
+    `SuppressQuiet'
+          Suppress, without warning, each label that would overwrite
+          another label.
+
+    `Move'
+          Move a label that would overwrite another out of the way and
+          issue a warning.  As this adjustment is during the final
+          output phase (in `PostScript' coordinates) it could result in
+          a larger figure than requested.
+
+    `MoveQuiet'
+          Move a label that would overwrite another out of the way,
+          without warning.  As this adjustment is during the final
+          output phase (in `PostScript' coordinates) it could result in
+          a larger figure than requested.
+
+
+
+   The routine `defaultpen()' returns the current default pen
+attributes.  Calling the routine `resetdefaultpen()' resets all pen
+default attributes to their initial values.
+
+
+File: asymptote.info,  Node: Transforms,  Next: Frames and pictures,  Prev: Pens,  Up: Programming
+
+6.4 Transforms
+==============
+
+`Asymptote' makes extensive use of affine transforms. A pair `(x,y)' is
+transformed by the transform `t=(t.x,t.y,t.xx,t.xy,t.yx,t.yy)' to
+`(x',y')', where
+x' = t.x + t.xx * x + t.xy * y
+y' = t.y + t.yx * x + t.yy * y
+ This is equivalent to the `PostScript' transformation `[t.xx t.yx t.xy
+t.yy t.x t.y]'.
+
+   Transforms can be applied to pairs, guides, paths, pens, strings,
+transforms, frames, and pictures by multiplication (via the binary
+operator `*') on the left (*note circle:: for an example).  Transforms
+can be composed with one another and inverted with the function
+`transform inverse(transform t)'; they can also be raised to any
+integer power with the `^' operator.
+
+   The built-in transforms are:
+
+`transform identity();'
+     the identity transform;
+
+`transform shift(pair z);'
+     translates by the pair `z';
+
+`transform shift(real x, real y);'
+     translates by the pair `(x,y)';
+
+`transform xscale(real x);'
+     scales by `x' in the x direction;
+
+`transform yscale(real y);'
+     scales by `y' in the y direction;
+
+`transform scale(real s);'
+     scale by `s' in both x and y directions;
+
+`transform scale(real x, real y);'
+     scale by `x' in the x direction and by `y' in the y direction;
+
+`transform slant(real s);'
+     maps `(x,y)' -> `(x+s*y,y)';
+
+`transform rotate(real angle, pair z=(0,0));'
+     rotates by `angle' in degrees about `z';
+
+`transform reflect(pair a, pair b);'
+     reflects about the line `a--b'.
+
+   The implicit initializer for transforms is `identity()'.  The
+routines `shift(transform t)' and `shiftless(transform t)' return the
+transforms `(t.x,t.y,0,0,0,0)' and `(0,0,t.xx,t.xy,t.yx,t.yy)'
+respectively.
+
+
+File: asymptote.info,  Node: Frames and pictures,  Next: Files,  Prev: Transforms,  Up: Programming
+
+6.5 Frames and pictures
+=======================
+
+`frame'
+     Frames are canvases for drawing in `PostScript' coordinates. While
+     working with frames directly is occasionally necessary for
+     constructing deferred drawing routines, pictures are usually more
+     convenient to work with.  The implicit initializer for frames is
+     `newframe'. The function `bool empty(frame f)' returns `true' only
+     if the frame `f' is empty. A frame may be erased with the
+     `erase(frame)' routine.  The functions `pair min(frame)' and `pair
+     max(frame)' return the (left,bottom) and (right,top) coordinates
+     of the frame bounding box, respectively. The contents of frame
+     `src' may be appended to frame `dest' with the command void add(frame dest, frame src);
+      or prepended with void prepend(frame dest, frame src);
+      A frame obtained by aligning frame `f' in the direction `align',
+     in a manner analogous to the `align' argument of `label' (*note
+     label::), is returned by frame align(frame f, pair align);
+
+     To draw or fill a box or ellipse around a label or frame and
+     return the boundary as a path, use one of the predefined
+     `envelope' routines path box(frame f, Label L="", real xmargin=0,
+              real ymargin=xmargin, pen p=currentpen,
+              filltype filltype=NoFill, bool above=true);
+     path roundbox(frame f, Label L="", real xmargin=0,
+                   real ymargin=xmargin, pen p=currentpen,
+                   filltype filltype=NoFill, bool above=true);
+     path ellipse(frame f, Label L="", real xmargin=0,
+                  real ymargin=xmargin, pen p=currentpen,
+                  filltype filltype=NoFill, bool above=true);
+
+`picture'
+     Pictures are high-level structures (*note Structures::) defined in
+     the module `plain' that provide canvases for drawing in user
+     coordinates.  The default picture is called `currentpicture'. A
+     new picture can be created like this: picture pic;
+      Anonymous pictures can be made by the expression `new picture'.
+
+     The `size' routine specifies the dimensions of the desired picture:
+
+     void size(picture pic=currentpicture, real x, real y=x,
+               bool keepAspect=Aspect);
+
+     If the `x' and `y' sizes are both 0, user coordinates will be
+     interpreted as `PostScript' coordinates. In this case, the
+     transform mapping `pic' to the final output frame is `identity()'.
+
+     If exactly one of `x' or `y' is 0, no size restriction is imposed
+     in that direction; it will be scaled the same as the other
+     direction.
+
+     If `keepAspect' is set to `Aspect' or `true', the picture will be
+     scaled with its aspect ratio preserved such that the final width
+     is no more than `x' and the final height is no more than `y'.
+
+     If `keepAspect' is set to `IgnoreAspect' or `false', the picture
+     will be scaled in both directions so that the final width is `x'
+     and the height is `y'.
+
+     To make the user coordinates of picture `pic' represent multiples
+     of `x' units in the x direction and `y' units in the y direction,
+     use void unitsize(picture pic=currentpicture, real x, real y=x);
+      When nonzero, these `x' and `y' values override the corresponding
+     size parameters of picture `pic'.
+
+     The routine void size(picture pic=currentpicture, real xsize, real ysize,
+               pair min, pair max);
+      forces the final picture scaling to map the user coordinates
+     `box(min,max)' to a region of width `xsize' and height `ysize'
+     (when these parameters are nonzero).
+
+     Alternatively, calling the routine transform fixedscaling(picture pic=currentpicture, pair min,
+                            pair max, pen p=nullpen, bool warn=false);
+      will cause picture `pic' to use a fixed scaling to map user
+     coordinates in `box(min,max)' to the (already specified) picture
+     size, taking account of the width of pen `p'. A warning will be
+     issued if the final picture exceeds the specified size.
+
+     A picture `pic' can be fit to a frame and output to a file
+     `prefix'.`format' using image format `format' by calling the
+     `shipout' function: void shipout(string prefix=defaultfilename, picture pic=currentpicture,
+                  orientation orientation=orientation,
+                  string format="", bool wait=false, bool view=true,
+                  string options="", string script="",
+                  light light=currentlight, projection P=currentprojection)
+      The default output format, `PostScript', may be changed with the
+     `-f' or `-tex' command-line options.  The `options', `script', and
+     `projection' parameters are only relevant for 3D pictures. If
+     `defaultfilename' is an empty string, the prefix `outprefix()'
+     will be used.
+
+     A `shipout()' command is added implicitly at file exit if no
+     previous `shipout' commands have been executed.  The default page
+     orientation is `Portrait'; this may be modified by changing the
+     variable `orientation'. To output in landscape mode, simply set
+     the variable `orientation=Landscape' or issue the command shipout(Landscape);
+
+     To rotate the page by -90 degrees, use the orientation `Seascape'.  The
+     orientation `UpsideDown' rotates the page by 180 degrees.
+
+     A picture `pic' can be explicitly fit to a frame by calling frame pic.fit(real xsize=pic.xsize, real ysize=pic.ysize,
+                   bool keepAspect=pic.keepAspect);
+      The default size and aspect ratio settings are those given to the
+     `size' command (which default to `0', `0', and `true',
+     respectively).  The transformation that would currently be used to
+     fit a picture `pic' to a frame is returned by the member function
+     `pic.calculateTransform()'.
+
+     In certain cases (e.g. 2D graphs) where only an approximate size
+     estimate for `pic' is available, the picture fitting routine frame pic.scale(real xsize=this.xsize, real ysize=this.ysize,
+                     bool keepAspect=this.keepAspect);
+      (which scales the resulting frame, including labels and fixed-size
+     objects) will enforce perfect compliance with the requested size
+     specification, but should not normally be required.
+
+     To draw a bounding box with margins around a picture, fit the
+     picture to a frame using the function frame bbox(picture pic=currentpicture, real xmargin=0,
+                real ymargin=xmargin, pen p=currentpen,
+                filltype filltype=NoFill);
+      Here `filltype' specifies one of the following fill types:
+    `FillDraw'
+          Fill the interior and draw the boundary.
+
+    `FillDraw(real xmargin=0, real ymargin=xmargin, pen fillpen=nullpen,'
+          `pen drawpen=nullpen)' If `fillpen' is `nullpen', fill with
+          the drawing pen; otherwise fill with pen `fillpen'.  If
+          `drawpen' is `nullpen', draw the boundary with `fillpen';
+          otherwise with `drawpen'. An optional margin of `xmargin' and
+          `ymargin' can be specified.
+
+    `Fill'
+          Fill the interior.
+
+    `Fill(real xmargin=0, real ymargin=xmargin, pen p=nullpen)'
+          If `p' is `nullpen', fill with the drawing pen; otherwise
+          fill with pen `p'. An optional margin of `xmargin' and
+          `ymargin' can be specified.
+
+    `NoFill'
+          Do not fill.
+
+    `Draw'
+          Draw only the boundary.
+
+    `Draw(real xmargin=0, real ymargin=xmargin, pen p=nullpen)'
+          If `p' is `nullpen', draw the boundary with the drawing pen;
+          otherwise draw with pen `p'. An optional margin of `xmargin'
+          and `ymargin' can be specified.
+
+    `UnFill'
+          Clip the region.
+
+    `UnFill(real xmargin=0, real ymargin=xmargin)'
+          Clip the region and surrounding margins `xmargin' and
+          `ymargin'.
+
+    `RadialShade(pen penc, pen penr)'
+          Fill varying radially from `penc' at the center of the
+          bounding box to `penr' at the edge.
+
+    `RadialShadeDraw(real xmargin=0, real ymargin=xmargin, pen penc,'
+          `pen penr, pen drawpen=nullpen)' Fill with RadialShade and
+          draw the boundary.
+
+
+     For example, to draw a bounding box around a picture with a 0.25 cm
+     margin and output the resulting frame, use the command: shipout(bbox(0.25cm));
+      A `picture' may be fit to a frame with the background color pen
+     `p', using the function `bbox(p,Fill)'.
+
+     The functions pair min(picture pic, user=false);
+     pair max(picture pic, user=false);
+     pair size(picture pic, user=false);
+      calculate the bounds that picture `pic' would have if it were
+     currently fit to a frame using its default size specification.  If
+     `user' is `false' the returned value is in `PostScript'
+     coordinates, otherwise it is in user coordinates.
+
+     The function pair point(picture pic=currentpicture, pair dir, bool user=true);
+      is a convenient way of determining the point on the bounding box
+     of `pic' in the direction `dir' relative to its center, ignoring
+     the contributions from fixed-size objects (such as labels and
+     arrowheads).  If `user' is `true' the returned value is in user
+     coordinates, otherwise it is in `PostScript' coordinates.
+
+     The function pair truepoint(picture pic=currentpicture, pair dir, bool user=true);
+      is identical to `point', except that it also accounts for
+     fixed-size objects, using the scaling transform that picture `pic'
+     would have if currently fit to a frame using its default size
+     specification. If `user' is `true' the returned value is in user
+     coordinates, otherwise it is in `PostScript' coordinates.
+
+     Sometimes it is useful to draw objects on separate pictures and
+     add one picture to another using the `add' function: void add(picture src, bool group=true,
+              filltype filltype=NoFill, bool above=true);
+     void add(picture dest, picture src, bool group=true,
+              filltype filltype=NoFill, bool above=true);
+      The first example adds `src' to `currentpicture'; the second one
+     adds `src' to `dest'.  The `group' option specifies whether or not
+     the graphical user interface `xasy' should treat all of the
+     elements of `src' as a single entity (*note GUI::), `filltype'
+     requests optional background filling or clipping, and `above'
+     specifies whether to add `src' above or below existing objects.
+
+     There are also routines to add a picture or frame `src' specified
+     in postscript coordinates to another picture `dest' (or
+     `currentpicture') about the user coordinate `position': void add(picture src, pair position, bool group=true,
+              filltype filltype=NoFill, bool above=true);
+     void add(picture dest, picture src, pair position,
+              bool group=true, filltype filltype=NoFill, bool above=true);
+     void add(picture dest=currentpicture, frame src, pair position=0,
+              bool group=true, filltype filltype=NoFill, bool above=true);
+     void add(picture dest=currentpicture, frame src, pair position,
+              pair align, bool group=true, filltype filltype=NoFill,
+              bool above=true);
+
+     The optional `align' argument in the last form specifies a
+     direction to use for aligning the frame, in a manner analogous to
+     the `align' argument of `label' (*note label::). However, one key
+     difference is that when `align' is not specified, labels are
+     centered, whereas frames and pictures are aligned so that their
+     origin is at `position'. Illustrations of frame alignment can be
+     found in the examples *note errorbars:: and *note image::. If you
+     want to align three or more subpictures, group them two at a time:
+
+     picture pic1;
+     real size=50;
+     size(pic1,size);
+     fill(pic1,(0,0)--(50,100)--(100,0)--cycle,red);
+
+     picture pic2;
+     size(pic2,size);
+     fill(pic2,unitcircle,green);
+
+     picture pic3;
+     size(pic3,size);
+     fill(pic3,unitsquare,blue);
+
+     picture pic;
+     add(pic,pic1.fit(),(0,0),N);
+     add(pic,pic2.fit(),(0,0),10S);
+
+     add(pic.fit(),(0,0),N);
+     add(pic3.fit(),(0,0),10S);
+
+
+
+     Alternatively, one can use `attach' to automatically increase the
+     size of picture `dest' to accommodate adding a frame `src' about
+     the user coordinate `position': void attach(picture dest=currentpicture, frame src,
+                      pair position=0, bool group=true,
+                      filltype filltype=NoFill, bool above=true);
+     void attach(picture dest=currentpicture, frame src,
+                      pair position, pair align, bool group=true,
+                      filltype filltype=NoFill, bool above=true);
+
+     To erase the contents of a picture (but not the size
+     specification), use the function void erase(picture pic=currentpicture);
+
+     To save a snapshot of `currentpicture', `currentpen', and
+     `currentprojection', use the function `save()'.
+
+     To restore a snapshot of `currentpicture', `currentpen', and
+     `currentprojection', use the function `restore()'.
+
+     Many further examples of picture and frame operations are provided
+     in the base module `plain'.
+
+     It is possible to insert verbatim `PostScript' commands in a
+     picture with one of the routines void postscript(picture pic=currentpicture, string s);
+     void postscript(picture pic=currentpicture, string s, pair min,
+                     pair max)
+      Here `min' and `max' can be used to specify explicit bounds
+     associated with the resulting `PostScript' code.
+
+     Verbatim TeX commands can be inserted in the intermediate `LaTeX'
+     output file with one of the functions void tex(picture pic=currentpicture, string s);
+     void tex(picture pic=currentpicture, string s, pair min, pair max)
+      Here `min' and `max' can be used to specify explicit bounds
+     associated with the resulting TeX code.
+
+     To issue a global TeX command (such as a TeX macro definition) in
+     the TeX preamble (valid for the remainder of the top-level module)
+     use: void texpreamble(string s);
+
+     The TeX environment can be reset to its initial state, clearing all
+     macro definitions, with the function void texreset();
+
+     The routine void usepackage(string s, string options="");
+      provides a convenient abbreviation for texpreamble("\usepackage["+options+"]{"+s+"}");
+      that can be used for importing `LaTeX' packages.
+
+
+
+File: asymptote.info,  Node: Files,  Next: Variable initializers,  Prev: Frames and pictures,  Up: Programming
+
+6.6 Files
+=========
+
+`Asymptote' can read and write text files (including comma-separated
+value) files and portable XDR (External Data Representation) binary
+files.
+
+   An input file must first be opened with
+input(string name="", bool check=true, string comment="#", string mode="");
+ reading is then done by assignment: 
+file fin=input("test.txt");
+real a=fin;
+
+   If the optional boolean argument `check' is `false', no check will
+be made that the file exists. If the file does not exist or is not
+readable, the function `bool error(file)' will return `true'.  The
+first character of the string `comment' specifies a comment character.
+If this character is encountered in a data file, the remainder of the
+line is ignored. When reading strings, a comment character followed
+immediately by another comment character is treated as a single literal
+comment character.
+
+   One can change the current working directory for read operations to
+the contents of the string `s' with the function `string cd(string s)',
+which returns the new working directory. If `string s' is empty, the
+path is reset to the value it had at program startup.
+
+   When reading pairs, the enclosing parenthesis are optional.  Strings
+are also read by assignment, by reading characters up to but not
+including a newline. In addition, `Asymptote' provides the function
+`string getc(file)' to read the next character (treating the comment
+character as an ordinary character) and return it as a string.
+
+   A file named `name' can be open for output with
+file output(string name="", bool update=false, string comment="#", string mode="");
+ If `update=false', any existing data in the file will be erased and
+only write operations can be used on the file.  If `update=true', any
+existing data will be preserved, the position will be set to the
+end-of-file, and both reading and writing operations will be enabled.
+For security reasons, writing to files in directories other than the
+current directory is allowed only if the `-globalwrite' (or `-nosafe')
+command-line option is specified.  The function `string mktemp(string
+s)' may be used to create and return the name of a unique temporary
+file in the current directory based on the string `s'.
+
+   There are two special files: `stdin', which reads from the keyboard,
+and `stdout', which writes to the terminal. The implicit initializer
+for files is `null'.
+
+   Data of a built-in type `T' can be written to an output file by
+calling one of the functions 
+write(string s="", T x, suffix suffix=endl ... T[]);
+write(file file, string s="", T x, suffix suffix=none ... T[]);
+write(file file=stdout, string s="", explicit T[] x ... T[][]);
+write(file file=stdout, T[][]);
+write(file file=stdout, T[][][]);
+write(suffix suffix=endl);
+write(file file, suffix suffix=none);
+ If `file' is not specified, `stdout' is used and terminated by default
+with a newline. If specified, the optional identifying string `s' is
+written before the data `x'.  An arbitrary number of data values may be
+listed when writing scalars or one-dimensional arrays. The `suffix' may
+be one of the following: `none' (do nothing), `flush' (output buffered
+data), `endl' (terminate with a newline and flush), `newl' (terminate
+with a newline), `DOSendl' (terminate with a DOS newline and flush),
+`DOSnewl' (terminate with a DOS newline), `tab' (terminate with a tab),
+or `comma' (terminate with a comma). Here are some simple examples of
+data output:
+file fout=output("test.txt");
+write(fout,1);                  // Writes "1"
+write(fout);                    // Writes a new line
+write(fout,"List: ",1,2,3);     // Writes "List: 1     2     3"
+ A file may be opened with `mode="xdr"', to read or write double
+precision (64-bit) reals and single precision (32-bit) integers in Sun
+Microsystem's XDR (External Data Representation) portable binary format
+(available on all `UNIX' platforms).  Alternatively, a file may also be
+opened with `mode="binary"' to read or write double precision reals and
+single precision integers in the native (nonportable) machine binary
+format.  The virtual member functions `file singlereal(bool b=true)'
+and `file singleint(bool b=true)' be used to change the precision of
+real and integer I/O operations, respectively, for an XDR or binary
+file `f'.  Similarly, the function `file signedint(bool b=true)' can be
+used to modify the signedness of integer reads and writes for an XDR or
+binary file `f'.
+
+   The virtual members `name', `mode', `singlereal', `singleint', and
+`signedint' may be used to query the respective parameters for a given
+file.
+
+   One can test a file for end-of-file with the boolean function
+`eof(file)', end-of-line with `eol(file)', and for I/O errors with
+`error(file)'.  One can flush the output buffers with `flush(file)',
+clear a previous I/O error with `clear(file)', and close the file with
+`close(file)'. The function `int precision(file file=stdout, int
+digits=0)' sets the number of digits of output precision for `file' to
+`digits', provided `digits' is nonzero, and returns the previous
+precision setting. The function `int tell(file)' returns the current
+position in a file relative to the beginning.  The routine `seek(file
+file, int pos)' can be used to change this position, where a negative
+value for the position `pos' is interpreted as relative to the
+end-of-file. For example, one can rewind a file `file' with the command
+`seek(file,0)' and position to the final character in the file with
+`seek(file,-1)'.  The command `seekeof(file)' sets the position to the
+end of the file.
+
+   Assigning `settings.scroll=n' for a positive integer `n' requests a
+pause after every `n' output lines to `stdout'.  One may then press
+`Enter' to continue to the next `n' output lines, `s' followed by
+`Enter' to scroll without further interruption, or `q' followed by
+`Enter' to quit the current output operation. If `n' is negative, the
+output scrolls a page at a time (i.e. by one less than the current
+number of display lines). The default value, `settings.scroll=0',
+specifies continuous scrolling.
+
+   The routines 
+string getstring(string name="", string default="", string prompt="",
+                 bool store=true);
+int getint(string name="", int default=0, string prompt="",
+           bool store=true);
+real getreal(string name="", real default=0, string prompt="",
+             bool store=true);
+pair getpair(string name="", pair default=0, string prompt="",
+             bool store=true);
+triple gettriple(string name="", triple default=(0,0,0), string prompt="",
+                 bool store=true);
+ defined in the module `plain' may be used to prompt for a value from
+`stdin' using the GNU `readline' library.  If `store=true', the history
+of values for `name' is stored in the file `".asy_history_"+name'
+(*note history::). The most recent value in the history will be used to
+provide a default value for subsequent runs.  The default value
+(initially `default') is displayed after `prompt'. These functions are
+based on the internal routines 
+string readline(string prompt="", string name="", bool tabcompletion=false);
+void saveline(string name, string value, bool store=true);
+ Here, `readline' prompts the user with the default value formatted
+according to `prompt', while `saveline' is used to save the string
+`value' in a local history named `name', optionally storing the local
+history in a file `".asy_history_"+name'.
+
+   The routine `history(string name, int n=1)' can be used to look up
+the `n' most recent values (or all values up to `historylines' if
+`n=0') entered for string `name'.  The routine `history(int n=0)'
+returns the interactive history.  For example,
+write(output("transcript.asy"),history());
+ outputs the interactive history to the file `transcript.asy'.
+
+   The function `int delete(string s)' deletes the file named by the
+string `s'. Unless the `-globalwrite' (or `-nosafe') option is enabled,
+the file must reside in the current directory.  The function `int
+rename(string from, string to)' may be used to rename file `from' to
+file `to'.  Unless the `-globalwrite' (or `-nosafe') option is enabled,
+this operation is restricted to the current directory.  The functions
+int convert(string args="", string file="", string format="");
+int animate(string args="", string file="", string format="");
+ call the `ImageMagick' commands `convert' and `animate', respectively,
+with the arguments `args' and the file name constructed from the
+strings `file' and `format'.
+
+
+File: asymptote.info,  Node: Variable initializers,  Next: Structures,  Prev: Files,  Up: Programming
+
+6.7 Variable initializers
+=========================
+
+A variable can be assigned a value when it is declared, as in `int
+x=3;' where the variable `x' is assigned the value `3'.  As well as
+literal constants such as `3', arbitary expressions can be used as
+initializers, as in `real x=2*sin(pi/2);'.
+
+   A variable is not added to the namespace until after the initializer
+is evaluated, so for example, in
+int x=2;
+int x=5*x;
+ the `x' in the initializer on the second line refers to the variable
+`x' declared on the first line.  The second line, then, declares a
+variable `x' shadowing the original `x' and initializes it to the value
+`10'.
+
+   Variables of most types can be declared without an explicit
+initializer and they will be initialized by the default initializer of
+that type:
+
+   * Variables of the numeric types `int', `real', and `pair' are all
+     initialized to zero; variables of type `triple' are initialized to
+     `O=(0,0,0)'.
+
+   * `boolean' variables are initialized to `false'.
+
+   * `string' variables are initialized to the empty string.
+
+   * `transform' variables are initialized to the identity
+     transformation.
+
+   * `path' and `guide' variables are initialized to `nullpath'.
+
+   * `pen' variables are initialized to the default pen.
+
+   * `frame' and `picture' variables are initialized to empty frames
+     and pictures, respectively.
+
+   * `file' variables are initialized to `null'.
+
+   The default initializers for user-defined array, structure, and
+function types are explained in their respective sections.  Some types,
+such as `code', do not have default initializers.  When a variable of
+such a type is introduced, the user must initialize it by explicitly
+giving it a value.
+
+   The default initializer for any type `T' can be redeclared by
+defining the function `T operator init()'.  For instance, `int'
+variables are usually initialized to zero, but in
+int operator init() {
+  return 3;
+}
+int y;
+
+the variable `y' is initialized to `3'.  This example was given for
+illustrative purposes; redeclaring the initializers of built-in types
+is not recommended. Typically, `operator init' is used to define
+sensible defaults for user-defined types.
+
+   The special type `var' may be used to infer the type of a variable
+from its initializer.  If the initializer is an expression of a unique
+type, then the variable will be defined with that type.  For instance,
+var x=5;
+var y=4.3;
+var reddash=red+dashed;
+ is equivalent to
+int x=5;
+real y=4.3;
+pen reddash=red+dashed;
+
+   `var' may also be used with the extended `for' loop syntax.
+
+int[] a = {1,2,3};
+for (var x : a)
+  write(x);
+
+
+File: asymptote.info,  Node: Structures,  Next: Operators,  Prev: Variable initializers,  Up: Programming
+
+6.8 Structures
+==============
+
+Users may also define their own data types as structures, along with
+user-defined operators, much as in C++. By default, structure members
+are `public' (may be read and modified anywhere in the code), but may be
+optionally declared `restricted' (readable anywhere but writeable only
+inside the structure where they are defined) or `private' (readable and
+writable only inside the structure). In a structure definition, the
+keyword `this' can be used as an expression to refer to the enclosing
+structure. Any code at the top-level scope within the structure is
+executed on initialization.
+
+   Variables hold references to structures.  That is, in the example:
+struct T {
+  int x;
+}
+
+T foo;
+T bar=foo;
+bar.x=5;
+
+   The variable `foo' holds a reference to an instance of the structure
+`T'.  When `bar' is assigned the value of `foo', it too now holds a
+reference to the same instance as `foo' does.  The assignment `bar.x=5'
+changes the value of the field `x' in that instance, so that `foo.x'
+will also be equal to `5'.
+
+   The expression `new T' creates a new instance of the structure `T'
+and returns a reference to that instance.  In creating the new
+instance, any code in the body of the record definition is executed.
+For example:
+int Tcount=0;
+struct T {
+  int x;
+  ++Tcount;
+}
+
+T foo;
+
+   Here, the expression `new T' will produce a new instance of the
+class, but will also cause `Tcount' to be incremented, so that it keeps
+track of the number of instances produced.
+
+   The expression `null' can be cast to any structure type to yield a
+null reference, a reference that does not actually refer to any
+instance of the structure.  Trying to use a field of a null reference
+will cause an error.
+
+   The function `bool alias(T,T)' checks to see if two structure
+references refer to the same instance of the structure (or both to
+`null').  For example, in the example code at the start of the section,
+`alias(foo,bar)' would return true, but `alias(foo,new T)' would return
+false, as `new T' creates a new instance of the structure `T'.  The
+boolean operators `==' and `!=' are by default equivalent to `alias' and
+`!alias' respectively, but may be overwritten for a particular type
+(for example, to do a deep comparison).
+
+   After the definition of a structure `T', a variable of type `T' is
+initialized to a new instance (`new T') by default.  During the
+definition of the structure, however, variables of type `T' are
+initialized to `null' by default. This special behaviour is to avoid
+infinite recursion of creating new instances in code such as
+struct tree {
+  int value;
+  tree left;
+  tree right;
+}
+
+   Here is a simple example that illustrates the use of structures:
+struct S {
+  real a=1;
+  real f(real a) {return a+this.a;}
+}
+
+S s;                            // Initializes s with new S;
+
+write(s.f(2));                  // Outputs 3
+
+S operator + (S s1, S s2)
+{
+  S result;
+  result.a=s1.a+s2.a;
+  return result;
+}
+
+write((s+s).f(0));              // Outputs 2
+
+   It is often convenient to have functions that construct new
+instances of a structure.  Say we have a `Person' structure:
+struct Person {
+  string firstname;
+  string lastname;
+}
+
+Person joe;
+joe.firstname="Joe";
+joe.lastname="Jones";
+ Creating a new Person is a chore; it takes three lines to create a new
+instance and to initialize its fields (that's still considerably less
+effort than creating a new person in real life, though).
+
+   We can reduce the work by defining a constructor function
+`Person(string,string)':
+struct Person {
+  string firstname;
+  string lastname;
+
+  static Person Person(string firstname, string lastname) {
+    Person p;
+    p.firstname=firstname;
+    p.lastname=lastname;
+    return p;
+  }
+}
+
+Person joe=Person.Person("Joe", "Jones");
+
+   While it is now easier than before to create a new instance, we still
+have to refer to the constructor by the qualified name `Person.Person'.
+If we add the line
+from Person unravel Person;
+ immediately after the structure definition, then the constructor can
+be used without qualification: `Person joe=Person("Joe", "Jones");'.
+
+   The constructor is now easy to use, but it is quite a hassle to
+define.  If you write a lot of constructors, you will find that you are
+repeating a lot of code in each of them.  Fortunately, your friendly
+neighbourhood Asymptote developers have devised a way to automate much
+of the process.
+
+   If, in the body of a structure, Asymptote encounters the definition
+of a function of the form `void operator init(ARGS)',  it implicitly
+defines a constructor function of the arguments `ARGS' that uses the
+`void operator init' function to initialize a new instance of the
+structure.  That is, it essentially defines the following constructor
+(assuming the structure is called `Foo'):
+
+     static Foo Foo(ARGS) {
+       Foo instance;
+       instance.operator init(ARGS);
+       return instance;
+     }
+
+   This constructor is also implicitly copied to the enclosing scope
+after the end of the structure definition, so that it can used
+subsequently without qualifying it by the structure name.  Our `Person'
+example can thus be implemented as:
+struct Person {
+  string firstname;
+  string lastname;
+
+  void operator init(string firstname, string lastname) {
+    this.firstname=firstname;
+    this.lastname=lastname;
+  }
+}
+
+Person joe=Person("Joe", "Jones");
+
+   The use of `operator init' to implicitly define constructors should
+not be confused with its use to define default values for variables
+(*note Variable initializers::).  Indeed, in the first case, the return
+type of the `operator init' must be `void' while in the second, it must
+be the (non-`void') type of the variable.
+
+   The function `cputime()' returns a structure `cputime' with
+cumulative CPU times broken down into the fields `parent.user',
+`parent.system', `child.user', and `child.system'. For convenience, the
+incremental fields `change.user' and `change.system' indicate the
+change in the corresponding total parent and child CPU times since the
+last call to `cputime()'. The function
+void write(file file=stdout, string s="", cputime c,
+           string format=cputimeformat, suffix suffix=none);
+ displays the incremental user cputime followed by "u", the incremental
+system cputime followed by "s", the total user cputime followed by "U",
+and the total system cputime followed by "S".
+
+   Much like in C++, casting (*note Casts::) provides for an elegant
+implementation of structure inheritance, including virtual functions:
+struct parent {
+  real x;
+  void operator init(int x) {this.x=x;}
+  void virtual(int) {write(0);}
+  void f() {virtual(1);}
+}
+
+void write(parent p) {write(p.x);}
+
+struct child {
+  parent parent;
+  real y=3;
+  void operator init(int x) {parent.operator init(x);}
+  void virtual(int x) {write(x);}
+  parent.virtual=virtual;
+  void f()=parent.f;
+}
+
+parent operator cast(child child) {return child.parent;}
+
+parent p=parent(1);
+child c=child(2);
+
+write(c);                       // Outputs 2;
+
+p.f();                          // Outputs 0;
+c.f();                          // Outputs 1;
+
+write(c.parent.x);              // Outputs 2;
+write(c.y);                     // Outputs 3;
+
+   For further examples of structures, see `Legend' and `picture' in
+the `Asymptote' base module `plain'.
+
+
+File: asymptote.info,  Node: Operators,  Next: Implicit scaling,  Prev: Structures,  Up: Programming
+
+6.9 Operators
+=============
+
+* Menu:
+
+* Arithmetic & logical::        Basic mathematical operators
+* Self & prefix operators::     Increment and decrement
+* User-defined operators::      Overloading operators
+
+
+File: asymptote.info,  Node: Arithmetic & logical,  Next: Self & prefix operators,  Up: Operators
+
+6.9.1 Arithmetic & logical operators
+------------------------------------
+
+`Asymptote' uses the standard binary arithmetic operators.  However,
+when one integer is divided by another, both arguments are converted to
+real values before dividing and a real quotient is returned (since this
+is usually what is intended). The function `int quotient(int x, int y)'
+returns the greatest integer less than or equal to `x/y'. In all other
+cases both operands are promoted to the same type, which will also be
+the type of the result:
+`+'
+     addition 
+
+`-'
+     subtraction 
+
+`*'
+     multiplication 
+
+`/'
+     division 
+
+`%'
+     modulo; the result always has the same sign as the divisor.  In
+     particular, this makes `q*quotient(p,q)+p%q == p' for all integers
+     `p' and nonzero integers `q'.  
+
+`^'
+     power; if the exponent (second argument) is an int, recursive
+     multiplication is used; otherwise, logarithms and exponentials are
+     used (`**' is a synonym for `^').
+
+
+   The usual boolean operators are also defined:
+`=='
+     equals 
+
+`!='
+     not equals 
+
+`<'
+     less than 
+
+`<='
+     less than or equals 
+
+`>='
+     greater than or equals 
+
+`>'
+     greater than 
+
+`&&'
+     and (with conditional evaluation of right-hand argument) 
+
+`&'
+     and 
+
+`||'
+     or (with conditional evaluation of right-hand argument) 
+
+`|'
+     or 
+
+`^'
+     xor 
+
+`!'
+     not
+
+   `Asymptote' also supports the C-like conditional syntax: 
+bool positive=(pi > 0) ? true : false;
+
+   The function `T interp(T a, T b, real t)' returns `(1-t)*a+t*b' for
+nonintegral built-in arithmetic types `T'. If `a' and `b' are pens,
+they are first promoted to the same color space.
+
+   `Asymptote' also defines bitwise functions `int AND(int,int)', `int
+OR(int,int)', `int XOR(int,int)', `int NOT(int)', `int CLZ(int)' (count
+leading zeros), and `int CTZ(int)' (count trailing zeros).
+
+
+File: asymptote.info,  Node: Self & prefix operators,  Next: User-defined operators,  Prev: Arithmetic & logical,  Up: Operators
+
+6.9.2 Self & prefix operators
+-----------------------------
+
+As in C, each of the arithmetic operators `+', `-', `*', `/', `%', and
+`^' can be used as a self operator.  The prefix operators `++'
+(increment by one) and `--' (decrement by one) are also defined.  For
+example,
+int i=1;
+i += 2;
+int j=++i;
+
+is equivalent to the code
+int i=1;
+i=i+2;
+int j=i=i+1;
+
+   However, postfix operators like `i++' and `i--' are not defined
+(because of the inherent ambiguities that would arise with the `--'
+path-joining operator). In the rare instances where `i++' and `i--' are
+really needed, one can substitute the expressions `(++i-1)' and
+`(--i+1)', respectively.
+
+
+File: asymptote.info,  Node: User-defined operators,  Prev: Self & prefix operators,  Up: Operators
+
+6.9.3 User-defined operators
+----------------------------
+
+The following symbols may be used with `operator' to define or redefine
+operators on structures and built-in types:
+- + * / % ^ ! < > == != <= >= & | ^^ .. :: -- --- ++
+<< >> $ $$ @ @@
+ The operators on the second line have precedence one higher than the
+boolean operators `<', `>', `<=', and `>='.
+
+   Guide operators like `..' may be overloaded, say, to write a user
+function that produces a new guide from a given guide:
+guide dots(... guide[] g)=operator ..;
+
+guide operator ..(... guide[] g) {
+  guide G;
+  if(g.length > 0) {
+    write(g[0]);
+    G=g[0];
+  }
+  for(int i=1; i < g.length; ++i) {
+    write(g[i]);
+    write();
+    G=dots(G,g[i]);
+  }
+  return G;
+}
+
+guide g=(0,0){up}..{SW}(100,100){NE}..{curl 3}(50,50)..(10,10);
+write("g=",g);
+
+
+File: asymptote.info,  Node: Implicit scaling,  Next: Functions,  Prev: Operators,  Up: Programming
+
+6.10 Implicit scaling
+=====================
+
+If a numeric literal is in front of certain types of expressions, then
+the two are multiplied:
+int x=2;
+real y=2.0;
+real cm=72/2.540005;
+
+write(3x);
+write(2.5x);
+write(3y);
+write(-1.602e-19 y);
+write(0.5(x,y));
+write(2x^2);
+write(3x+2y);
+write(3(x+2y));
+write(3sin(x));
+write(3(sin(x))^2);
+write(10cm);
+
+   This produces the output
+6
+5
+6
+-3.204e-19
+(1,1)
+8
+10
+18
+2.72789228047704
+2.48046543129542
+283.464008929116
+
+
+File: asymptote.info,  Node: Functions,  Next: Arrays,  Prev: Implicit scaling,  Up: Programming
+
+6.11 Functions
+==============
+
+`Asymptote' functions are treated as variables with a signature
+(non-function variables have null signatures). Variables with the same
+name are allowed, so long as they have distinct signatures.
+
+   Functions arguments are passed by value. To pass an argument by
+reference, simply enclose it in a structure (*note Structures::).
+
+   Here are some significant features of `Asymptote' functions:
+
+  1. Variables with signatures (functions) and without signatures
+     (nonfunction variables) are distinct: int x, x();
+     x=5;
+     x=new int() {return 17;};
+     x=x();              // calls x() and puts the result, 17, in the scalar x
+
+  2. Traditional function definitions are allowed: int sqr(int x)
+     {
+       return x*x;
+     }
+     sqr=null;           // but the function is still just a variable.
+
+  3. Casting can be used to resolve ambiguities: int a, a(), b, b(); // Valid: creates four variables.
+     a=b;                // Invalid: assignment is ambiguous.
+     a=(int) b;          // Valid: resolves ambiguity.
+     (int) (a=b);        // Valid: resolves ambiguity.
+     (int) a=b;          // Invalid: cast expressions cannot be L-values.
+
+     int c();
+     c=a;                // Valid: only one possible assignment.
+
+  4. Anonymous (so-called "high-order") functions are also allowed: typedef int intop(int);
+     intop adder(int m)
+     {
+       return new int(int n) {return m+n;};
+     }
+     intop addby7=adder(7);
+     write(addby7(1));   // Writes 8.
+
+  5. One may redefine a function `f', even for calls to `f' in
+     previously declared functions, by assigning another (anonymous or
+     named) function to it. However, if `f' is overloaded by a new
+     function definition, previous calls will still access the original
+     version of `f', as illustrated in this example: void f() {
+       write("hi");
+     }
+
+     void g() {
+       f();
+     }
+
+     g(); // writes "hi"
+
+     f=new void() {write("bye");};
+
+     g(); // writes "bye"
+
+     void f() {write("overloaded");};
+
+     f(); // writes "overloaded"
+     g(); // writes "bye"
+
+  6. Anonymous functions can be used to redefine a function variable
+     that has been declared (and implicitly initialized to the null
+     function) but not yet explicitly defined: void f(bool b);
+
+     void g(bool b) {
+       if(b) f(b);
+       else write(b);
+     }
+
+     f=new void(bool b) {
+       write(b);
+       g(false);
+     };
+
+     g(true); // Writes true, then writes false.
+
+
+   `Asymptote' is the only language we know of that treats functions as
+variables, but allows overloading by distinguishing variables based on
+their signatures.
+
+   Functions are allowed to call themselves recursively. As in C++,
+infinite nested recursion will generate a stack overflow (reported as a
+segmentation fault, unless a fully working version of the GNU library
+`libsigsegv' (e.g. 2.4 or later) is installed at configuration time).
+
+* Menu:
+
+* Default arguments::           Default values can appear anywhere
+* Named arguments::             Assigning function arguments by keyword
+* Rest arguments::              Functions with a variable number of arguments
+* Mathematical functions::      Standard libm functions
+
+
+File: asymptote.info,  Node: Default arguments,  Next: Named arguments,  Up: Functions
+
+6.11.1 Default arguments
+------------------------
+
+`Asymptote' supports a more flexible mechanism for default function
+arguments than C++: they may appear anywhere in the function prototype.
+Because certain data types are implicitly cast to more sophisticated
+types (*note Casts::) one can often avoid ambiguities by ordering
+function arguments from the simplest to the most complicated.  For
+example, given
+real f(int a=1, real b=0) {return a+b;}
+ then `f(1)' returns 1.0, but `f(1.0)' returns 2.0.
+
+   The value of a default argument is determined by evaluating the
+given `Asymptote' expression in the scope where the called function is
+defined.
+
+
+File: asymptote.info,  Node: Named arguments,  Next: Rest arguments,  Prev: Default arguments,  Up: Functions
+
+6.11.2 Named arguments
+----------------------
+
+It is sometimes difficult to remember the order in which arguments
+appear in a function declaration. Named (keyword) arguments make calling
+functions with multiple arguments easier. Unlike in the C and C++
+languages, an assignment in a function argument is interpreted as an
+assignment to a parameter of the same name in the function signature,
+_not within the local scope_. The command-line option `-d' may be used
+to check `Asymptote' code for cases where a named argument may be
+mistaken for a local assignment.
+
+   When matching arguments to signatures, first all of the keywords are
+matched, then the arguments without names are matched against the
+unmatched formals as usual. For example,
+int f(int x, int y) {
+  return 10x+y;
+}
+write(f(4,x=3));
+ outputs 34, as `x' is already matched when we try to match the unnamed
+argument `4', so it gets matched to the next item, `y'.
+
+   For the rare occasions where it is desirable to assign a value to
+local variable within a function argument (generally _not_ a good
+programming practice), simply enclose the assignment in parentheses.
+For example, given the definition of `f' in the previous example,
+int x;
+write(f(4,(x=3)));
+ is equivalent to the statements
+int x;
+x=3;
+write(f(4,3));
+ and outputs 43.
+
+   Parameters can be specified as "keyword-only" by putting `keyword'
+immediately before the parameter name, as in `int f(int keyword x)' or
+`int f(int keyword x=77)'.  This forces the caller of the function to
+use a named argument to give a value for this parameter.  That is,
+`f(x=42)' is legal, but `f(25)' is not.  Keyword-only parameters must
+be listed after normal parameters in a function definition.
+
+   As a technical detail, we point out that, since variables of the same
+name but different signatures are allowed in the same scope, the code
+int f(int x, int x()) {
+  return x+x();
+}
+int seven() {return 7;}
+ is legal in `Asymptote', with `f(2,seven)' returning 9.  A named
+argument matches the first unmatched formal of the same name, so
+`f(x=2,x=seven)' is an equivalent call, but `f(x=seven,2)' is not, as
+the first argument is matched to the first formal, and `int ()' cannot
+be implicitly cast to `int'.  Default arguments do not affect which
+formal a named argument is matched to, so if `f' were defined as
+int f(int x=3, int x()) {
+  return x+x();
+}
+ then `f(x=seven)' would be illegal, even though `f(seven)' obviously
+would be allowed.
+
+
+File: asymptote.info,  Node: Rest arguments,  Next: Mathematical functions,  Prev: Named arguments,  Up: Functions
+
+6.11.3 Rest arguments
+---------------------
+
+Rest arguments allow one to write functions that take a variable number
+of arguments:
+// This function sums its arguments.
+int sum(... int[] nums) {
+  int total=0;
+  for(int i=0; i < nums.length; ++i)
+    total += nums[i];
+  return total;
+}
+
+sum(1,2,3,4);                       // returns 10
+sum();                              // returns 0
+
+// This function subtracts subsequent arguments from the first.
+int subtract(int start ... int[] subs) {
+  for(int i=0; i < subs.length; ++i)
+    start -= subs[i];
+  return start;
+}
+
+subtract(10,1,2);                   // returns 7
+subtract(10);                       // returns 10
+subtract();                         // illegal
+
+   Putting an argument into a rest array is called _packing_.  One can
+give an explicit list of arguments for the rest argument, so `subtract'
+could alternatively be implemented as
+int subtract(int start ... int[] subs) {
+  return start - sum(... subs);
+}
+
+   One can even combine normal arguments with rest arguments:
+sum(1,2,3 ... new int[] {4,5,6});   // returns 21
+ This builds a new six-element array that is passed to `sum' as `nums'.
+The opposite operation, _unpacking_, is not allowed:
+subtract(... new int[] {10, 1, 2});
+ is illegal, as the start formal is not matched.
+
+   If no arguments are packed, then a zero-length array (as opposed to
+`null') is bound to the rest parameter. Note that default arguments are
+ignored for rest formals and the rest argument is not bound to a
+keyword.
+
+   In some cases, keyword-only parameters are helpful to avoid
+arguments intended for the rest parameter to be assigned to other
+parameters.  For example, here the use of `keyword' is to avoid
+`pnorm(1.0,2.0,0.3)' matching `1.0' to `p'.
+real pnorm(real keyword p=2.0 ... real[] v)
+{
+  return sum(v^p)^(1/p);
+}
+
+   The overloading resolution in `Asymptote' is similar to the function
+matching rules used in C++. Every argument match is given a score.
+Exact matches score better than matches with casting, and matches with
+formals (regardless of casting) score better than packing an argument
+into the rest array.  A candidate is maximal if all of the arguments
+score as well in it as with any other candidate.  If there is one
+unique maximal candidate, it is chosen; otherwise, there is an
+ambiguity error.
+
+int f(path g);
+int f(guide g);
+f((0,0)--(100,100)); // matches the second; the argument is a guide
+
+int g(int x, real y);
+int g(real x, int x);
+
+g(3,4); // ambiguous; the first candidate is better for the first argument,
+        // but the second candidate is better for the second argument
+
+int h(... int[] rest);
+int h(real x ... int[] rest);
+
+h(1,2); // the second definition matches, even though there is a cast,
+        // because casting is preferred over packing
+
+int i(int x ... int[] rest);
+int i(real x, real y ... int[] rest);
+
+i(3,4); // ambiguous; the first candidate is better for the first argument,
+        // but the second candidate is better for the second one
+
+
+File: asymptote.info,  Node: Mathematical functions,  Prev: Rest arguments,  Up: Functions
+
+6.11.4 Mathematical functions
+-----------------------------
+
+`Asymptote' has built-in versions of the standard `libm' mathematical
+real(real) functions `sin', `cos', `tan', `asin', `acos', `atan',
+`exp', `log', `pow10', `log10', `sinh', `cosh', `tanh', `asinh',
+`acosh', `atanh', `sqrt', `cbrt', `fabs', `expm1', `log1p', as well as
+the identity function `identity'.  `Asymptote' also defines the order
+`n' Bessel functions of the first kind `Jn(int n, real)' and second kind
+`Yn(int n, real)', as well as the gamma function `gamma', the error
+function `erf', and the complementary error function `erfc'. The
+standard real(real, real) functions `atan2', `hypot', `fmod',
+`remainder' are also included.
+
+   The functions `degrees(real radians)' and `radians(real degrees)'
+can be used to convert between radians and degrees. The function
+`Degrees(real radians)' returns the angle in degrees in the interval
+[0,360).  For convenience, `Asymptote' defines variants `Sin', `Cos',
+`Tan', `aSin', `aCos', and `aTan' of the standard trigonometric
+functions that use degrees rather than radians.  We also define complex
+versions of the `sqrt', `sin', `cos', `exp', `log', and `gamma'
+functions.
+
+   The functions `floor', `ceil', and `round' differ from their usual
+definitions in that they all return an int value rather than a real
+(since that is normally what one wants).  The functions `Floor',
+`Ceil', and `Round' are respectively similar, except that if the result
+cannot be converted to a valid int, they return `intMax' for positive
+arguments and `intMin' for negative arguments, rather than generating
+an integer overflow.  We also define a function `sgn', which returns
+the sign of its real argument as an integer (-1, 0, or 1).
+
+   There is an `abs(int)' function, as well as an `abs(real)' function
+(equivalent to `fabs(real)'), an `abs(pair)' function (equivalent to
+`length(pair)').
+
+   Random numbers can be seeded with `srand(int)' and generated with
+the `int rand()' function, which returns a random integer between 0 and
+the integer `randMax'. The `unitrand()' function returns a random
+number uniformly distributed in the interval [0,1].  A Gaussian random
+number generator `Gaussrand' and a collection of statistics routines,
+including `histogram', are provided in the base file `stats.asy'.  The
+functions `factorial(int n)', which returns n!, and `choose(int n, int
+k)', which returns n!/(k!(n-k)!), are also defined.
+
+   When configured with the GNU Scientific Library (GSL), available from
+`http://www.gnu.org/software/gsl/', `Asymptote' contains an internal
+module `gsl' that defines the airy functions `Ai(real)', `Bi(real)',
+`Ai_deriv(real)', `Bi_deriv(real)', `zero_Ai(int)', `zero_Bi(int)',
+`zero_Ai_deriv(int)', `zero_Bi_deriv(int)', the Bessel functions
+`I(int, real)', `K(int, real)', `j(int, real)', `y(int, real)',
+`i_scaled(int, real)', `k_scaled(int, real)', `J(real, real)', `Y(real,
+real)', `I(real, real)', `K(real, real)', `zero_J(real, int)', the
+elliptic functions `F(real, real)', `E(real, real)', and `P(real,
+real)', the Jacobi elliptic functions `real[] sncndn(real,real)', the
+exponential/trigonometric integrals `Ei', `Si', and `Ci', the Legendre
+polynomials `Pl(int, real)', and the Riemann zeta function
+`zeta(real)'. For example, to compute the sine integral `Si' of 1.0:
+import gsl;
+write(Si(1.0));
+
+   `Asymptote' also provides a few general purpose numerical routines:
+
+``real newton(int iterations=100, real f(real), real fprime(real), real x, bool verbose=false);''
+     Use Newton-Raphson iteration to solve for a root of a real-valued
+     differentiable function `f', given its derivative `fprime' and an
+     initial guess `x'. Diagnostics for each iteration are printed if
+     `verbose=true'.  If the iteration fails after the maximum allowed
+     number of loops (`iterations'), `realMax' is returned.
+
+``real newton(int iterations=100, real f(real), real fprime(real), real x1, real x2, bool verbose=false);''
+     Use bracketed Newton-Raphson bisection to solve for a root of a
+     real-valued differentiable function `f' within an interval
+     [`x1',`x2'] (on which the endpoint values of `f' have opposite
+     signs), given its derivative `fprime'. Diagnostics for each
+     iteration are printed if `verbose=true'.  If the iteration fails
+     after the maximum allowed number of loops (`iterations'),
+     `realMax' is returned.
+
+``real simpson(real f(real), real a, real b, real acc=realEpsilon, real dxmax=b-a)''
+     returns the integral of `f' from `a' to `b' using adaptive Simpson
+     integration.
+
+
+
+File: asymptote.info,  Node: Arrays,  Next: Casts,  Prev: Functions,  Up: Programming
+
+6.12 Arrays
+===========
+
+* Menu:
+
+* Slices::                      Python-style array slices
+
+   Appending `[]' to a built-in or user-defined type yields an array.
+The array element `i' of an array `A' can be accessed as `A[i]'.  By
+default, attempts to access or assign to an array element using a
+negative index generates an error. Reading an array element with an
+index beyond the length of the array also generates an error; however,
+assignment to an element beyond the length of the array causes the
+array to be resized to accommodate the new element.  One can also index
+an array `A' with an integer array `B': the array `A[B]' is formed by
+indexing array `A' with successive elements of array `B'.  A convenient
+Java-style shorthand exists for iterating over all elements of an
+array; see *note array iteration::.
+
+   The declaration
+real[] A;
+
+initializes `A' to be an empty (zero-length) array. Empty arrays should
+be distinguished from null arrays. If we say
+real[] A=null;
+
+then `A' cannot be dereferenced at all (null arrays have no length and
+cannot be read from or assigned to).
+
+   Arrays can be explicitly initialized like this:
+real[] A={0,1,2};
+
+   Array assignment in `Asymptote' does a shallow copy: only the
+pointer is copied (if one copy if modified, the other will be too).
+The `copy' function listed below provides a deep copy of an array.
+
+   Every array `A' of type `T[]' has the virtual members
+   * `int length',
+
+   * `int cyclic',
+
+   * `int[] keys',
+
+   * `T push(T x)',
+
+   * `void append(T[] a)',
+
+   * `T pop()',
+
+   * `void insert(int i ... T[] x)',
+
+   * `void delete(int i, int j=i)',
+
+   * `void delete()', and
+
+   * `bool initialized(int n)'.
+
+   The member `A.length' evaluates to the length of the array.  Setting
+`A.cyclic=true' signifies that array indices should be reduced modulo
+the current array length. Reading from or writing to a nonempty cyclic
+array never leads to out-of-bounds errors or array resizing.
+
+   The member `A.keys' evaluates to an array of integers containing the
+indices of initialized entries in the array in ascending order.  Hence,
+for an array of length `n' with all entries initialized, `A.keys'
+evaluates to `{0,1,...,n-1}'.  A new keys array is produced each time
+`A.keys' is evaluated.
+
+   The functions `A.push' and `A.append' append their arguments onto
+the end of the array, while `A.insert(int i ... T[] x)' inserts `x'
+into the array at index `i'.  For convenience `A.push' returns the
+pushed item.  The function `A.pop()' pops and returns the last element,
+while `A.delete(int i, int j=i)' deletes elements with indices in the
+range [`i',`j'], shifting the position of all higher-indexed elements
+down. If no arguments are given, `A.delete()' provides a convenient way
+of deleting all elements of `A'. The routine `A.initialized(int n)' can
+be used to examine whether the element at index `n' is initialized.
+Like all `Asymptote' functions, `push', `append', `pop', `insert',
+`delete', and `initialized' can be "pulled off" of the array and used
+on their own. For example,
+int[] A={1};
+A.push(2);         // A now contains {1,2}.
+A.append(A);       // A now contains {1,2,1,2}.
+int f(int)=A.push;
+f(3);              // A now contains {1,2,1,2,3}.
+int g()=A.pop;
+write(g());        // Outputs 3.
+A.delete(0);       // A now contains {2,1,2}.
+A.delete(0,1);       // A now contains {2}.
+A.insert(1,3);     // A now contains {2,3}.
+A.insert(1 ... A); // A now contains {2,2,3,3}
+A.insert(2,4,5);   // A now contains {2,2,4,5,3,3}.
+
+   The `[]' suffix can also appear after the variable name; this is
+sometimes convenient for declaring a list of variables and arrays of
+the same type:
+real a,A[];
+ This declares `a' to be `real' and implicitly declares `A' to be of
+type `real[]'.
+
+   In the following list of built-in array functions, `T' represents a
+generic type. Note that the internal functions `alias', `array',
+`copy', `concat', `sequence', `map', and `transpose', which depend on
+type `T[]', are defined only after the first declaration of a variable
+of type `T[]'.
+
+`new T[]'
+     returns a new empty array of type `T[]';
+
+`new T[] {list}'
+     returns a new array of type `T[]' initialized with `list' (a comma
+     delimited list of elements).
+
+`new T[n]'
+     returns a new array of `n' elements of type `T[]'.  These `n'
+     array elements are not initialized unless they are arrays
+     themselves (in which case they are each initialized to empty
+     arrays).
+
+`T[] array(int n, T value, int depth=intMax)'
+     returns an array consisting of `n' copies of `value'.  If `value'
+     is itself an array, a deep copy of `value' is made for each entry.
+     If `depth' is specified, this deep copying only recurses to the
+     specified number of levels.
+
+`int[] sequence(int n)'
+     if `n >= 1' returns the array `{0,1,...,n-1}' (otherwise returns a
+     null array);
+
+`int[] sequence(int n, int m)'
+     if `m >= n' returns an array `{n,n+1,...,m}' (otherwise returns a
+     null array);
+
+`T[] sequence(T f(int), int n)'
+     if `n >= 1' returns the sequence `{f_i :i=0,1,...n-1}' given a
+     function `T f(int)' and integer `int n' (otherwise returns a null
+     array);
+
+`T[] map(T f(T), T[] a)'
+     returns the array obtained by applying the function `f' to each
+     element of the array `a'. This is equivalent to `sequence(new
+     T(int i) {return f(a[i]);},a.length)'.
+
+`int[] reverse(int n)'
+     if `n >= 1' returns the array `{n-1,n-2,...,0}' (otherwise returns
+     a null array);
+
+`int[] complement(int[] a, int n)'
+     returns the complement of the integer array `a' in
+     `{0,1,2,...,n-1}', so that `b[complement(a,b.length)]' yields the
+     complement of `b[a]'.
+
+`real[] uniform(real a, real b, int n)'
+     if `n >= 1' returns a uniform partition of `[a,b]' into `n'
+     subintervals (otherwise returns a null array);
+
+`int find(bool[], int n=1)'
+     returns the index of the `n'th `true' value or -1 if not found.
+     If `n' is negative, search backwards from the end of the array for
+     the `-n'th value;
+
+`int search(T[] a, T key)'
+     For built-in ordered types `T', searches a sorted array `a' of `n'
+     elements for k, returning the index `i' if `a[i] <= key < a[i+1]',
+     `-1' if `key' is less than all elements of `a', or `n-1' if `key'
+     is greater than or equal to the last element of `a'.
+
+`int search(T[] a, T key, bool less(T i, T j))'
+     searches an array `a' sorted in ascending order such that element
+     `i' precedes element `j' if `less(i,j)' is true;
+
+`T[] copy(T[] a)'
+     returns a deep copy of the array `a';
+
+`T[] concat(... T[][] a)'
+     returns a new array formed by concatenating the given
+     one-dimensional arrays given as arguments;
+
+`bool alias(T[] a, T[] b)'
+     returns `true' if the arrays `a' and `b' are identical;
+
+`T[] sort(T[] a)'
+     For built-in ordered types `T', returns a copy of `a' sorted in
+     ascending order;
+
+`T[][] sort(T[][] a)'
+     For built-in ordered types `T', returns a copy of `a' with the rows
+     sorted by the first column, breaking ties with successively higher
+     columns. For example: string[][] a={{"bob","9"},{"alice","5"},{"pete","7"},
+                   {"alice","4"}};
+     // Row sort (by column 0, using column 1 to break ties):
+     write(sort(a));
+
+     produces alice   4
+     alice   5
+     bob     9
+     pete    7
+
+`T[] sort(T[] a, bool less(T i, T j))'
+     returns a copy of `a' stably sorted in ascending order such that
+     element `i' precedes element `j' if `less(i,j)' is true.
+
+`T[][] transpose(T[][] a)'
+     returns the transpose of `a'.
+
+`T[][][] transpose(T[][][] a, int[] perm)'
+     returns the 3D transpose of `a' obtained by applying the
+     permutation `perm' of `new int[]{0,1,2}' to the indices of each
+     entry.
+
+`T sum(T[] a)'
+     For arithmetic types `T', returns the sum of `a'.  In the case
+     where `T' is `bool', the number of true elements in `a' is
+     returned.
+
+`T min(T[] a)'
+
+`T min(T[][] a)'
+
+`T min(T[][][] a)'
+     For built-in ordered types `T', returns the minimum element of `a'.
+
+`T max(T[] a)'
+
+`T max(T[][] a)'
+
+`T max(T[][][] a)'
+     For built-in ordered types `T', returns the maximum element of `a'.
+
+`T[] min(T[] a, T[] b)'
+     For built-in ordered types `T', and arrays `a' and `b' of the same
+     length, returns an array composed of the minimum of the
+     corresponding elements of `a' and `b'.
+
+`T[] max(T[] a, T[] b)'
+     For built-in ordered types `T', and arrays `a' and `b' of the same
+     length, returns an array composed of the maximum of the
+     corresponding elements of `a' and `b'.
+
+`pair[] pairs(real[] x, real[] y);'
+     For arrays `x' and `y' of the same length, returns the pair array
+     `sequence(new pair(int i) {return (x[i],y[i]);},x.length)'.
+
+`pair[] fft(pair[] a, int sign=1)'
+     returns the Fast Fourier Transform of `a' (if the optional `FFTW'
+     package is installed), using the given `sign'. Here is a simple
+     example: int n=4;
+     pair[] f=sequence(n);
+     write(f);
+     pair[] g=fft(f,-1);
+     write();
+     write(g);
+     f=fft(g,1);
+     write();
+     write(f/n);
+
+`real dot(real[] a, real[] b)'
+     returns the dot product of the vectors `a' and `b'.
+
+`pair dot(pair[] a, pair[] b)'
+     returns the complex dot product `sum(a*conj(b))' of the vectors
+     `a' and `b'.
+
+`real[] tridiagonal(real[] a, real[] b, real[] c, real[] f);'
+     Solve the periodic tridiagonal problem L`x'=`f' and return the
+     solution `x', where `f' is an n vector and L is the n \times n
+     matrix [ b[0] c[0]           a[0]   ]
+     [ a[1] b[1] c[1]             ]
+     [      a[2] b[2] c[2]        ]
+     [                ...         ]
+     [ c[n-1]       a[n-1] b[n-1] ]
+      For Dirichlet boundary conditions (denoted here by `u[-1]' and
+     `u[n]'), replace `f[0]' by `f[0]-a[0]u[-1]' and
+     `f[n-1]-c[n-1]u[n]'; then set `a[0]=c[n-1]=0'.
+
+`real[] solve(real[][] a, real[] b, bool warn=true)'
+     Solve the linear equation `a'x=`b' by LU decomposition and return
+     the solution x, where `a' is an n \times n matrix and `b' is an
+     array of length n.  For example: import math;
+     real[][] a={{1,-2,3,0},{4,-5,6,2},{-7,-8,10,5},{1,50,1,-2}};
+     real[] b={7,19,33,3};
+     real[] x=solve(a,b);
+     write(a); write();
+     write(b); write();
+     write(x); write();
+     write(a*x);
+      If `a' is a singular matrix and `warn' is `false', return an
+     empty array.  If the matrix `a' is tridiagonal, the routine
+     `tridiagonal' provides a more efficient algorithm (*note
+     tridiagonal::).
+
+`real[][] solve(real[][] a, real[][] b, bool warn=true)'
+     Solve the linear equation `a'x=`b' and return the solution x,
+     where `a' is an n \times n matrix and `b' is an n \times m matrix.
+     If `a' is a singular matrix and `warn' is `false', return an empty
+     matrix.
+
+`real[][] identity(int n);'
+     returns the n \times n identity matrix.
+
+`real[][] diagonal(... real[] a)'
+     returns the diagonal matrix with diagonal entries given by a.
+
+`real[][] inverse(real[][] a)'
+     returns the inverse of a square matrix `a'.
+
+``real[] quadraticroots(real a, real b, real c);''
+     This numerically robust solver returns the real roots of the
+     quadratic equation ax^2+bx+c=0, in ascending order. Multiple roots
+     are listed separately.
+
+``pair[] quadraticroots(explicit pair a, explicit pair b, explicit pair c);''
+     This numerically robust solver returns the complex roots of the
+     quadratic equation ax^2+bx+c=0.
+
+``real[] cubicroots(real a, real b, real c, real d);''
+     This numerically robust solver returns the real roots of the cubic
+     equation ax^3+bx^2+cx+d=0. Multiple roots are listed separately.
+
+
+   `Asymptote' includes a full set of vectorized array instructions for
+arithmetic (including self) and logical operations. These
+element-by-element instructions are implemented in C++ code for speed.
+Given
+real[] a={1,2};
+real[] b={3,2};
+ then `a == b' and `a >= 2' both evaluate to the vector `{false, true}'.  To
+test whether all components of `a' and `b' agree, use the boolean
+function `all(a == b)'. One can also use conditionals like `(a >= 2) ?
+a : b', which returns the array `{3,2}', or `write((a >= 2) ? a :
+null', which returns the array `{2}'.
+
+   All of the standard built-in `libm' functions of signature
+`real(real)' also take a real array as an argument, effectively like an
+implicit call to `map'.
+
+   As with other built-in types, arrays of the basic data types can be
+read in by assignment. In this example, the code
+file fin=input("test.txt");
+real[] A=fin;
+
+reads real values into `A' until the end-of-file is reached (or an I/O
+error occurs).
+
+   The virtual members `dimension', `line', `csv', `word', and `read'
+of a file are useful for reading arrays.  For example, if line mode is
+set with `file line(bool b=true)', then reading will stop once the end
+of the line is reached instead:
+file fin=input("test.txt");
+real[] A=fin.line();
+
+   Since string reads by default read up to the end of line anyway,
+line mode normally has no effect on string array reads.  However, there
+is a white-space delimiter mode for reading strings, `file word(bool
+b=true)', which causes string reads to respect white-space delimiters,
+instead of the default end-of-line delimiter:
+file fin=input("test.txt").line().word();
+real[] A=fin;
+
+   Another useful mode is comma-separated-value mode, `file csv(bool
+b=true)', which causes reads to respect comma delimiters:
+file fin=csv(input("test.txt"));
+real[] A=fin;
+
+   To restrict the number of values read, use the `file dimension(int)'
+function:
+file fin=input("test.txt");
+real[] A=dimension(fin,10);
+
+   This reads 10 values into A, unless end-of-file (or end-of-line in
+line mode) occurs first. Attempting to read beyond the end of the file
+will produce a runtime error message. Specifying a value of 0 for the
+integer limit is equivalent to the previous example of reading until
+end-of-file (or end-of-line in line mode) is encountered.
+
+   Two- and three-dimensional arrays of the basic data types can be read
+in like this:
+file fin=input("test.txt");
+real[][] A=fin.dimension(2,3);
+real[][][] B=fin.dimension(2,3,4);
+ Again, an integer limit of zero means no restriction.
+
+   Sometimes the array dimensions are stored with the data as integer
+fields at the beginning of an array. Such 1, 2, or 3 dimensional arrays
+can be read in with the virtual member functions `read(1)', `read(2)',
+or `read(3)', respectively:
+file fin=input("test.txt");
+real[] A=fin.read(1);
+real[][] B=fin.read(2);
+real[][][] C=fin.read(3);
+
+   One, two, and three-dimensional arrays of the basic data types can be
+output with the functions `write(file,T[])', `write(file,T[][])',
+`write(file,T[][][])', respectively.
+
+
+File: asymptote.info,  Node: Slices,  Up: Arrays
+
+6.12.1 Slices
+-------------
+
+Asymptote allows a section of an array to be addressed as a slice using
+a Python-like syntax.  If `A' is an array, the expression `A[m:n]'
+returns a new array consisting of the elements of `A' with indices from
+`m' up to but not including `n'. For example,
+int[] x={0,1,2,3,4,5,6,7,8,9};
+int[] y=x[2:6];  // y={2,3,4,5};
+int[] z=x[5:10]; // z={5,6,7,8,9};
+
+   If the left index is omitted, it is taken be `0'.  If the right
+index is omitted it is taken to be the length of the array.  If both
+are omitted, the slice then goes from the start of the array to the
+end, producing a non-cyclic deep copy of the array.  For example:
+int[] x={0,1,2,3,4,5,6,7,8,9};
+int[] y=x[:4];  // y={0,1,2,3}
+int[] z=x[5:];  // z={5,6,7,8,9}
+int[] w=x[:];   // w={0,1,2,3,4,5,6,7,8,9}, distinct from array x.
+
+   If A is a non-cyclic array, it is illegal to use negative values for
+either of the indices.  If the indices exceed the length of the array,
+however, they are politely truncated to that length.
+
+   For cyclic arrays, the slice `A[m:n]' still consists of the cells
+with indices in the set [`m',`n'), but now negative values and values
+beyond the length of the array are allowed.  The indices simply wrap
+around.  For example:
+
+int[] x={0,1,2,3,4,5,6,7,8,9};
+x.cyclic=true;
+int[] y=x[8:15];  // y={8,9,0,1,2,3,4}.
+int[] z=x[-5:5];  // z={5,6,7,8,9,0,1,2,3,4}
+int[] w=x[-3:17]; // w={7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6}
+
+   Notice that with cyclic arrays, it is possible to include the same
+element of the original array multiple times within a slice.
+Regardless of the original array, arrays produced by slices are always
+non-cyclic.
+
+   If the left and right indices of a slice are the same, the result is
+an empty array.  If the array being sliced is empty, the result is an
+empty array.  Any slice with a left index greater than its right index
+will yield an error.
+
+   Slices can also be assigned to, changing the value of the original
+array.  If the array being assigned to the slice has a different length
+than the slice itself, elements will be inserted or removed from the
+array to accommodate it. For instance:
+string[] toppings={"mayo", "salt", "ham", "lettuce"};
+toppings[0:2]=new string[] {"mustard", "pepper"};
+    // Now toppings={"mustard", "pepper", "ham", "lettuce"}
+toppings[2:3]=new string[] {"turkey", "bacon" };
+    // Now toppings={"mustard", "pepper", "turkey", "bacon", "lettuce"}
+toppings[0:3]=new string[] {"tomato"};
+    // Now toppings={"tomato", "bacon", "lettuce"}
+
+   If an array is assigned to a slice of itself, a copy of the original
+array is assigned to the slice.  That is, code such as `x[m:n]=x' is
+equivalent to `x[m:n]=copy(x)'.  One can use the shorthand `x[m:m]=y'
+to insert the contents of the array `y' into the array `x' starting at
+the location just before `x[m]'.
+
+   For a cyclic array, a slice is bridging if it addresses cells up to
+the end of the array and then continues on to address cells at the
+start of the array.  For instance, if `A' is a cyclic array of length
+10, `A[8:12]', `A[-3:1]', and `A[5:25]' are bridging slices whereas
+`A[3:7]', `A[7:10]', `A[-3:0]' and `A[103:107]' are not.  Bridging
+slices can only be assigned to if the number of elements in the slice
+is exactly equal to the number of elements we are assigning to it.
+Otherwise, there is no clear way to decide which of the new entries
+should be `A[0]' and an error is reported.  Non-bridging slices may be
+assigned an array of any length.
+
+   For a cyclic array `A' an expression of the form
+`A[A.length:A.length]' is equivalent to the expression `A[0:0]' and so
+assigning to this slice will insert values at the start of the array.
+`A.append()' can be used to insert values at the end of the array.
+
+   It is illegal to assign to a slice of a cyclic array that repeats
+any of the cells.
+
+
+File: asymptote.info,  Node: Casts,  Next: Import,  Prev: Arrays,  Up: Programming
+
+6.13 Casts
+==========
+
+`Asymptote' implicitly casts `int' to `real', `int' to `pair', `real'
+to `pair', `pair' to `path', `pair' to `guide', `path' to `guide',
+`guide' to `path', `real' to `pen', `pair[]' to `guide[]', `pair[]' to
+`path[]', `path' to `path[]', and `guide' to `path[]', along with
+various three-dimensional casts defined in `three.asy'.  Implicit casts
+are automatically attempted on assignment and when trying to match
+function calls with possible function signatures. Implicit casting can
+be inhibited by declaring individual arguments `explicit' in the
+function signature, say to avoid an ambiguous function call in the
+following example, which outputs 0:
+int f(pair a) {return 0;}
+int f(explicit real x) {return 1;}
+
+write(f(0));
+
+   Other conversions, say `real' to `int' or `real' to `string',
+require an explicit cast:
+int i=(int) 2.5;
+string s=(string) 2.5;
+
+real[] a={2.5,-3.5};
+int[] b=(int []) a;
+write(stdout,b);     // Outputs 2,-3
+
+   Casting to user-defined types is also possible using `operator cast':
+struct rpair {
+  real radius;
+  real angle;
+}
+
+pair operator cast(rpair x) {
+  return (x.radius*cos(x.angle),x.radius*sin(x.angle));
+}
+
+rpair x;
+x.radius=1;
+x.angle=pi/6;
+
+write(x);            // Outputs (0.866025403784439,0.5)
+
+   One must use care when defining new cast operators. Suppose that in
+some code one wants all integers to represent multiples of 100. To
+convert them to reals, one would first want to multiply them by 100.
+However, the straightforward implementation
+real operator cast(int x) {return x*100;}
+ is equivalent to an infinite recursion, since the result `x*100' needs
+itself to be cast from an integer to a real. Instead, we want to use
+the standard conversion of int to real:
+real convert(int x) {return x*100;}
+real operator cast(int x)=convert;
+
+   Explicit casts are implemented similarly, with `operator ecast'.
+
+
+File: asymptote.info,  Node: Import,  Next: Static,  Prev: Casts,  Up: Programming
+
+6.14 Import
+===========
+
+While `Asymptote' provides many features by default, some applications
+require specialized features contained in external `Asymptote' modules.
+For instance, the lines
+access graph;
+graph.axes();
+ draw x and y axes on a two-dimensional graph.  Here, the command looks
+up the module under the name `graph' in a global dictionary of modules
+and puts it in a new variable named `graph'.  The module is a
+structure, and we can refer to its fields as we usually would with a
+structure.
+
+   Often, one wants to use module functions without having to specify
+the module name.  The code
+from graph access axes;
+ adds the `axes' field of `graph' into the local name space, so that
+subsequently, one can just write `axes()'.  If the given name is
+overloaded, all types and variables of that name are added.  To add
+more than one name, just use a comma-separated list:
+from graph access axes, xaxis, yaxis;
+ Wild card notation can be used to add all non-private fields and types
+of a module to the local name space:
+
+from graph access *;
+
+   Similarly, one can add the non-private fields and types of a
+structure to the local environment with the `unravel' keyword:
+struct matrix {
+  real a,b,c,d;
+}
+
+real det(matrix m) {
+  unravel m;
+  return a*d-b*c;
+}
+ Alternatively, one can unravel selective fields:
+real det(matrix m) {
+  from m unravel a,b,c as C,d;
+  return a*d-b*C;
+}
+
+   The command
+import graph;
+ is a convenient abbreviation for the commands
+access graph;
+unravel graph;
+ That is, `import graph' first loads a module into a structure called
+`graph' and then adds its non-private fields and types to the local
+environment. This way, if a member variable (or function) is
+overwritten with a local variable (or function of the same signature),
+the original one can still be accessed by qualifying it with the module
+name.
+
+   Wild card importing will work fine in most cases, but one does not
+usually know all of the internal types and variables of a module, which
+can also change as the module writer adds or changes features of the
+module.  As such, it is prudent to add `import' commands at the start
+of an `Asymptote' file, so that imported names won't shadow locally
+defined functions.  Still, imported names may shadow other imported
+names, depending on the order in which they were imported, and imported
+functions may cause overloading resolution problems if they have the
+same name as local functions defined later.
+
+   To rename modules or fields when adding them to the local
+environment, use `as':
+access graph as graph2d;
+from graph access xaxis as xline, yaxis as yline;
+
+   The command
+import graph as graph2d;
+ is a convenient abbreviation for the commands
+access graph as graph2d;
+unravel graph2d;
+
+   Except for a few built-in modules, such as `settings', all modules
+are implemented as `Asymptote' files.  When looking up a module that
+has not yet been loaded, `Asymptote' searches the standard search paths
+(*note Search paths::) for the matching file.  The file corresponding
+to that name is read and the code within it is interpreted as the body
+of a structure defining the module.
+
+   If the file name contains nonalphanumeric characters, enclose it
+with quotation marks:
+
+`access "/usr/local/share/asymptote/graph.asy" as graph;'
+
+`from "/usr/local/share/asymptote/graph.asy" access axes;'
+
+`import "/usr/local/share/asymptote/graph.asy" as graph;'
+
+   It is an error if modules import themselves (or each other in a
+cycle).  The module name to be imported must be known at compile time.
+
+   However, you can import an `Asymptote' module determined by the
+string `s' at runtime like this:
+eval("import "+s,true);
+
+   To conditionally execute an array of asy files, use
+void asy(string format, bool overwrite ... string[] s);
+ The file will only be processed, using output format `format', if
+overwrite is `true' or the output file is missing.
+
+   One can evaluate an `Asymptote' expression (without any return
+value, however) contained in the string `s' with: 
+void eval(string s, bool embedded=false);
+ It is not necessary to terminate the string `s' with a semicolon.  If
+`embedded' is `true', the string will be evaluated at the top level of
+the current environment.  If `embedded' is `false' (the default), the
+string will be evaluated in an independent environment, sharing the same
+`settings' module (*note settings::).
+
+   One can evaluate arbitrary `Asymptote' code (which may contain
+unescaped quotation marks) with the command
+void eval(code s, bool embedded=false);
+ Here `code' is a special type used with `quote {}' to enclose
+`Asymptote code' like this:
+real a=1;
+code s=quote {
+  write(a);
+};
+eval(s,true);        // Outputs 1
+
+   To include the contents of an existing file `graph' verbatim (as if
+the contents of the file were inserted at that point), use one of the
+forms:
+include graph;
+
+`include "/usr/local/share/asymptote/graph.asy";'
+
+   To list all global functions and variables defined in a module named
+by the contents of the string `s', use the function
+void list(string s, bool imports=false);
+ Imported global functions and variables are also listed if `imports'
+is `true'.
+
+
+File: asymptote.info,  Node: Static,  Prev: Import,  Up: Programming
+
+6.15 Static
+===========
+
+Static qualifiers allocate the memory address of a variable in a higher
+enclosing level.
+
+   For a function body, the variable is allocated in the block where the
+function is defined; so in the code
+struct s {
+  int count() {
+    static int c=0;
+    ++c;
+    return c;
+  }
+}
+
+there is one instance of the variable `c' for each object `s' (as
+opposed to each call of `count').
+
+   Similarly, in
+int factorial(int n) {
+  int helper(int k) {
+    static int x=1;
+    x *= k;
+    return k == 1 ? x : helper(k-1);
+  }
+  return helper(n);
+}
+
+there is one instance of `x' for every call to `factorial' (and not for
+every call to `helper'), so this is a correct, but ugly, implementation
+of factorial.
+
+   Similarly, a static variable declared within a structure is
+allocated in the block where the structure is defined. Thus,
+struct A {
+  struct B {
+    static pair z;
+  }
+}
+
+creates one object `z' for each object of type `A' created.
+
+   In this example,
+int pow(int n, int k) {
+  struct A {
+    static int x=1;
+    void helper() {
+      x *= n;
+    }
+  }
+  for(int i=0; i < k; ++i) {
+    A a;
+    a.helper();
+  }
+  return A.x;
+}
+
+there is one instance of `x' for each call to `pow', so this is an ugly
+implementation of exponentiation.
+
+   Loop constructs allocate a new frame in every iteration.  This is so
+that higher-order functions can refer to variables of a specific
+iteration of a loop:
+void f();
+for(int i=0; i < 10; ++i) {
+  int x=i;
+  if(x==5) {
+    f=new void () { write(x); }
+  }
+}
+f();
+
+   Here, every iteration of the loop has its own variable `x', so `f()'
+will write `5'.  If a variable in a loop is declared static, it will be
+allocated where the enclosing function or structure was defined (just
+as if it were declared static outside of the loop).  For instance, in:
+void f() {
+  static int x;
+  for(int i=0; i < 10; ++i) {
+    static int y;
+  }
+}
+ both `x' and `y' will be allocated in the same place, which is also
+where `f' is also allocated.
+
+   Statements may also be declared static, in which case they are run
+at the place where the enclosing function or structure is defined.
+Declarations or statements not enclosed in a function or structure
+definition are already at the top level, so static modifiers are
+meaningless.  A warning is given in such a case.
+
+   Since structures can have static fields, it is not always clear for
+a qualified name whether the qualifier is a variable or a type.  For
+instance, in:
+
+struct A {
+  static int x;
+}
+pair A;
+
+int y=A.x;
+ does the `A' in `A.x' refer to the structure or to the pair variable.
+It is the convention in Asymptote that, if there is a non-function
+variable with the same name as the qualifier, the qualifier refers to
+that variable, and not to the type.  This is regardless of what fields
+the variable actually possesses.
+
+
+File: asymptote.info,  Node: LaTeX usage,  Next: Base modules,  Prev: Programming,  Up: Top
+
+7 `LaTeX' usage
+***************
+
+`Asymptote' comes with a convenient `LaTeX' style file `asymptote.sty'
+that makes `LaTeX' `Asymptote'-aware. Entering `Asymptote' code
+directly into the `LaTeX' source file, at the point where it is needed,
+keeps figures organized and avoids the need to invent new file names
+for each figure. Simply add the line `\usepackage{asymptote}' at the
+beginning of your file and enclose your `Asymptote' code within a
+`\begin{asy}...\end{asy}' environment. As with the `LaTeX' `comment'
+environment, the `\end{asy}' command must appear on a line by itself,
+with no trailing commands/comments.  A blank line is not allowed after
+`\begin{asy}'.
+
+   The sample `LaTeX' file below, named `latexusage.tex', can be run as
+follows:
+latex latexusage
+asy latexusage-*.asy
+latex latexusage
+
+or
+pdflatex latexusage
+asy latexusage-*.asy
+pdflatex latexusage
+ To switch between using inline Asymptote code with `latex' and
+`pdflatex' you may first need to remove the files `latexusage-*.tex'.
+
+   An even better method for processing a `LaTeX' file with embedded
+`Asymptote' code is to use the `latexmk' utility from
+
+     `http://www.ctan.org/tex-archive/support/latexmk/'
+   after putting the contents of
+`http://asymptote.svn.sourceforge.net/viewvc/asymptote/trunk/asymptote/doc/latexmkrc'
+in a file `latexmkrc' in the same directory. The command
+latexmk -pdf latexusage
+ will then call `Asymptote' automatically, recompiling only the figures
+that have changed. Since each figure is compiled in a separate system
+process, this method also tends to use less memory.  To store the
+figures in a separate directory named `asy', one can define
+\def\asydir{asy}
+ in `latexusage.tex' and put the contents of
+`http://asymptote.svn.sourceforge.net/viewvc/asymptote/trunk/asymptote/doc/latexmkrc_asydir'
+in a file `latexmkrc' in the same directory.  External `Asymptote' code
+in `filename.asy' should be included with 
+\asyinclude[<options>]{<filename.asy>}
+ so that `latexmk' will recognize when the code is changed. Note that
+`latemk' requires `perl', available from `http://www.perl.org/'.
+
+   One can specify `width', `height', `keepAspect', `viewportwidth',
+`viewportheight', `attach', and `inline'.  `keyval'-style options to
+the `asy' and `asyinclude' environments.  Three-dimensional PRC files
+may either be embedded within the page (the default) or attached as
+annotated (but printable) attachments, using the `attach' option and
+the `attachfile2' (or older `attachfile') `LaTeX' package.  The
+`inline' option generates inline `LaTeX' code instead of EPS or PDF
+files. This makes 2D LaTeX symbols visible to the
+`\begin{asy}...\end{asy}' environment.  In this mode, Asymptote
+correctly aligns 2D LaTeX symbols defined outside of
+`\begin{asy}...\end{asy}', but treats their size as zero; an optional
+second string can be given to `Label' to provide an estimate of the
+unknown label size.
+
+   Note that if the `latex' TeX engine is used with the `inline'
+option, labels might not show up in DVI viewers that cannot handle raw
+`PostScript' code. One can use `dvips'/`dvipdf' to produce
+`PostScript'/PDF output (we recommend using the modified version of
+`dvipdf' in the `Asymptote' patches directory, which accepts the `dvips
+-z' hyperdvi option).
+
+   Here now is `latexusage.tex':
+
+\documentclass[12pt]{article}
+
+% Use this form to include EPS (latex) or PDF (pdflatex) files:
+\usepackage{asymptote}
+
+% Use this form with latex or pdflatex to include inline LaTeX code by default:
+%\usepackage[inline]{asymptote}
+
+% Use this form with latex or pdflatex to create PDF attachments by default:
+%\usepackage[attach]{asymptote}
+
+% Enable this line to support the attach option:
+%\usepackage[dvips]{attachfile2}
+
+\begin{document}
+
+% Optional subdirectory for asy files (no spaces):
+\def\asydir{}
+
+\begin{asydef}
+// Global Asymptote definitions can be put here.
+import three;
+usepackage("bm");
+texpreamble("\def\V#1{\bm{#1}}");
+// One can globally override the default toolbar settings here:
+// settings.toolbar=true;
+\end{asydef}
+
+Here is a venn diagram produced with Asymptote, drawn to width 4cm:
+
+\def\A{A}
+\def\B{\V{B}}
+
+%\begin{figure}
+\begin{center}
+\begin{asy}
+size(4cm,0);
+pen colour1=red;
+pen colour2=green;
+
+pair z0=(0,0);
+pair z1=(-1,0);
+pair z2=(1,0);
+real r=1.5;
+path c1=circle(z1,r);
+path c2=circle(z2,r);
+fill(c1,colour1);
+fill(c2,colour2);
+
+picture intersection=new picture;
+fill(intersection,c1,colour1+colour2);
+clip(intersection,c2);
+
+add(intersection);
+
+draw(c1);
+draw(c2);
+
+//draw("$\A$",box,z1);              // Requires [inline] package option.
+//draw(Label("$\B$","$B$"),box,z2); // Requires [inline] package option.
+draw("$A$",box,z1);
+draw("$\V{B}$",box,z2);
+
+pair z=(0,-2);
+real m=3;
+margin BigMargin=Margin(0,m*dot(unit(z1-z),unit(z0-z)));
+
+draw(Label("$A\cap B$",0),conj(z)--z0,Arrow,BigMargin);
+draw(Label("$A\cup B$",0),z--z0,Arrow,BigMargin);
+draw(z--z1,Arrow,Margin(0,m));
+draw(z--z2,Arrow,Margin(0,m));
+
+shipout(bbox(0.25cm));
+\end{asy}
+%\caption{Venn diagram}\label{venn}
+\end{center}
+%\end{figure}
+
+Each graph is drawn in its own environment. One can specify the width
+and height to \LaTeX\ explicitly. This 3D example can be viewed
+interactively either with Adobe Reader or Asymptote's fast OpenGL-based
+renderer. To support {\tt latexmk}, 3D figures should specify
+\verb+inline=true+. It is sometimes desirable to embed 3D files as annotated
+attachments; this requires the \verb+attach=true+ option as well as the
+\verb+attachfile2+ \LaTeX\ package.
+\begin{center}
+\begin{asy}[height=4cm,inline=true,attach=false,viewportwidth=\linewidth]
+currentprojection=orthographic(5,4,2);
+draw(unitcube,blue);
+label("$V-E+F=2$",(0,1,0.5),3Y,blue+fontsize(17pt));
+\end{asy}
+\end{center}
+
+One can also scale the figure to the full line width:
+\begin{center}
+\begin{asy}[width=\the\linewidth,inline=true]
+pair z0=(0,0);
+pair z1=(2,0);
+pair z2=(5,0);
+pair zf=z1+0.75*(z2-z1);
+
+draw(z1--z2);
+dot(z1,red+0.15cm);
+dot(z2,darkgreen+0.3cm);
+label("$m$",z1,1.2N,red);
+label("$M$",z2,1.5N,darkgreen);
+label("$\hat{\ }$",zf,0.2*S,fontsize(24pt)+blue);
+
+pair s=-0.2*I;
+draw("$x$",z0+s--z1+s,N,red,Arrows,Bars,PenMargins);
+s=-0.5*I;
+draw("$\bar{x}$",z0+s--zf+s,blue,Arrows,Bars,PenMargins);
+s=-0.95*I;
+draw("$X$",z0+s--z2+s,darkgreen,Arrows,Bars,PenMargins);
+\end{asy}
+\end{center}
+\end{document}
+
+
+File: asymptote.info,  Node: Base modules,  Next: Options,  Prev: LaTeX usage,  Up: Top
+
+8 Base modules
+**************
+
+`Asymptote' currently ships with the following base modules:
+
+* Menu:
+
+* plain::                       Default `Asymptote' base file
+* simplex::                     Linear programming: simplex method
+* math::                        Extend `Asymptote''s math capabilities
+* interpolate::                 Interpolation routines
+* geometry::                    Geometry routines
+* trembling::                   Wavy lines
+* stats::                       Statistics routines and histograms
+* patterns::                    Custom fill and draw patterns
+* markers::                     Custom path marker routines
+* tree::                        Dynamic binary search tree
+* binarytree::                  Binary tree drawing module
+* drawtree::                    Tree drawing module
+* syzygy::                      Syzygy and braid drawing module
+* feynman::                     Feynman diagrams
+* roundedpath::                 Round the sharp corners of paths
+* animation::                   Embedded PDF and MPEG movies
+* embed::                       Embedding movies, sounds, and 3D objects
+* slide::                       Making presentations with `Asymptote'
+* MetaPost::                    `MetaPost' compatibility routines
+* unicode::                     Accept `unicode' (UTF-8) characters
+* latin1::                      Accept `ISO 8859-1' characters
+* babel::                       Interface to `LaTeX' `babel' package
+* labelpath::                   Drawing curved labels
+* labelpath3::                  Drawing curved labels in 3D
+* annotate::                    Annotate your PDF files
+* CAD::                         2D CAD pen and measurement functions (DIN 15)
+* graph::                       2D linear & logarithmic graphs
+* palette::                     Color density images and palettes
+* three::                       3D vector graphics
+* obj::                         3D obj files
+* graph3::                      3D linear & logarithmic graphs
+* grid3::                       3D grids
+* solids::                      3D solid geometry
+* tube::                        3D rotation minimizing tubes
+* flowchart::                   Flowchart drawing routines
+* contour::                     Contour lines
+* contour3::                    Contour surfaces
+* slopefield::                  Slope fields
+* ode::                         Ordinary differential equations
+
+
+File: asymptote.info,  Node: plain,  Next: simplex,  Up: Base modules
+
+8.1 `plain'
+===========
+
+This is the default `Asymptote' base file, which defines key parts of
+the drawing language (such as the `picture' structure).
+
+   By default, an implicit `private import plain;' occurs before
+translating a file and before the first command given in interactive
+mode.  This also applies when translating files for module definitions
+(except when translating `plain', of course).  This means that the
+types and functions defined in `plain' are accessible in almost all
+`Asymptote' code. Use the `-noautoplain' command-line option to disable
+this feature.
+
+
+File: asymptote.info,  Node: simplex,  Next: math,  Prev: plain,  Up: Base modules
+
+8.2 `simplex'
+=============
+
+This package solves the two-variable linear programming problem using
+the simplex method. It is used by the module `plain' for automatic
+sizing of pictures.
+
+
+File: asymptote.info,  Node: math,  Next: interpolate,  Prev: simplex,  Up: Base modules
+
+8.3 `math'
+==========
+
+This package extends `Asymptote''s mathematical capabilities with
+useful functions such as
+
+`void drawline(picture pic=currentpicture, pair P, pair Q, pen p=currentpen);'
+     draw the visible portion of the (infinite) line going through `P'
+     and `Q', without altering the size of picture `pic', using pen `p'.
+
+`real intersect(triple P, triple Q, triple n, triple Z);'
+     returns the intersection time of the extension of the line segment
+     `PQ' with the plane perpendicular to `n' and passing through `Z'.
+
+`triple intersectionpoint(triple n0, triple P0, triple n1, triple P1);'
+     Return any point on the intersection of the two planes with normals
+     `n0' and `n1' passing through points `P0' and `P1', respectively.
+     If the planes are parallel, return `(infinity,infinity,infinity)'.
+
+`pair[] quarticroots(real a, real b, real c, real d, real e);'
+     returns the four complex roots of the quartic equation
+     ax^4+bx^3+cx^2+dx+e=0.
+
+`pair[][] fft(pair[][] a, int sign=1)'
+     returns the two-dimensional Fourier transform of a using the given
+     `sign'.
+
+`real time(path g, real x, int n=0)'
+     returns the `n'th intersection time of path `g' with the vertical
+     line through x.
+
+`real time(path g, explicit pair z, int n=0)'
+     returns the `n'th intersection time of path `g' with the horizontal
+     line through `(0,z.y)'.
+
+`real value(path g, real x, int n=0)'
+     returns the `n'th `y' value of `g' at `x'.
+
+`real value(path g, real x, int n=0)'
+     returns the `n'th `x' value of `g' at `y=z.y'.
+
+`real slope(path g, real x, int n=0)'
+     returns the `n'th slope of `g' at `x'.
+
+`real slope(path g, explicit pair z, int n=0)'
+     returns the `n'th slope of `g' at `y=z.y'.
+
+     int[][] segment(bool[] b) returns the indices of consecutive
+     true-element segments of bool[] `b'.
+
+`real[] partialsum(real[] a)'
+     returns the partial sums of a real array `a'.
+
+`real[] partialsum(real[] a, real[] dx)'
+     returns the partial `dx'-weighted sums of a real array `a'.
+
+`bool increasing(real[] a, bool strict=false)'
+     returns, if `strict=false', whether `i > j' implies `a[i] >=
+     a[j]', or if `strict=true', whether `i > j' implies implies `a[i]
+     > a[j]'.
+
+`int unique(real[] a, real x)'
+     if the sorted array `a' does not contain `x', insert it
+     sequentially, returning the index of `x' in the resulting array.
+
+`bool lexorder(pair a, pair b)'
+     returns the strict lexicographical partial order of `a' and `b'.
+
+`bool lexorder(triple a, triple b)'
+     returns the strict lexicographical partial order of `a' and `b'.
+
+
+File: asymptote.info,  Node: interpolate,  Next: geometry,  Prev: math,  Up: Base modules
+
+8.4 `interpolate'
+=================
+
+This module implements Lagrange, Hermite, and standard cubic spline
+interpolation in `Asymptote', as illustrated in the example
+`interpolate1.asy'.
+
+
+File: asymptote.info,  Node: geometry,  Next: trembling,  Prev: interpolate,  Up: Base modules
+
+8.5 `geometry'
+==============
+
+This module, written by Philippe Ivaldi, provides an extensive set of
+geometry routines, including `perpendicular' symbols and a `triangle'
+structure. Link to the documentation for the `geometry' module are
+posted here: `http://asymptote.sourceforge.net/links.html', including
+an extensive set of examples,
+`http://www.piprime.fr/files/asymptote/geometry/', and an index:
+
+     `http://www.piprime.fr/files/asymptote/geometry/modules/geometry.asy.index.type.html'
+
+
+File: asymptote.info,  Node: trembling,  Next: stats,  Prev: geometry,  Up: Base modules
+
+8.6 `trembling'
+===============
+
+This module, written by Philippe Ivaldi and illustrated in the example
+`floatingdisk.asy', allows one to draw wavy lines, as if drawn by hand.
+
+
+File: asymptote.info,  Node: stats,  Next: patterns,  Prev: trembling,  Up: Base modules
+
+8.7 `stats'
+===========
+
+This package implements a Gaussian random number generator and a
+collection of statistics routines, including `histogram' and
+`leastsquares'.
+
+
+File: asymptote.info,  Node: patterns,  Next: markers,  Prev: stats,  Up: Base modules
+
+8.8 `patterns'
+==============
+
+This package implements `Postscript' tiling patterns and includes
+several convenient pattern generation routines.
+
+
+File: asymptote.info,  Node: markers,  Next: tree,  Prev: patterns,  Up: Base modules
+
+8.9 `markers'
+=============
+
+This package implements specialized routines for marking paths and
+angles.  The principal mark routine provided by this package is
+markroutine markinterval(int n=1, frame f, bool rotated=false);
+ which centers `n' copies of frame `f' within uniformly space intervals
+in arclength along the path, optionally rotated by the angle of the
+local tangent.
+
+   The `marker' (*note marker::) routine can be used to construct new
+markers from these predefined frames:
+
+frame stickframe(int n=1, real size=0, pair space=0, real angle=0,
+                 pair offset=0, pen p=currentpen);
+ 
+frame circlebarframe(int n=1, real barsize=0,
+                     real radius=0,real angle=0,
+                     pair offset=0, pen p=currentpen,
+                     filltype filltype=NoFill, bool above=false);
+ 
+frame crossframe(int n=3, real size=0, pair space=0,
+                 real angle=0, pair offset=0, pen p=currentpen);
+ 
+frame tildeframe(int n=1, real size=0, pair space=0,
+                 real angle=0, pair offset=0, pen p=currentpen);
+
+   For convenience, this module also constructs the markers
+`StickIntervalMarker',  `CrossIntervalMarker',
+`CircleBarIntervalMarker', and `TildeIntervalMarker' from the above
+frames. The example `markers1.asy' illustrates the use of these markers:
+
+
+
+
+This package also provides a routine for marking an angle AOB: 
+void markangle(picture pic=currentpicture, Label L="",
+               int n=1, real radius=0, real space=0,
+               pair A, pair O, pair B, arrowbar arrow=None,
+               pen p=currentpen, margin margin=NoMargin,
+               marker marker=nomarker);
+ as illustrated in the example `markers2.asy'.
+
+
+
+
+
+File: asymptote.info,  Node: tree,  Next: binarytree,  Prev: markers,  Up: Base modules
+
+8.10 `tree'
+===========
+
+This package implements an example of a dynamic binary search tree.
+
+
+File: asymptote.info,  Node: binarytree,  Next: drawtree,  Prev: tree,  Up: Base modules
+
+8.11 `binarytree'
+=================
+
+This module can be used to draw an arbitrary binary tree and includes an
+input routine for the special case of a binary search tree, as
+illustrated in the example `binarytreetest.asy':
+
+import binarytree;
+
+picture pic,pic2;
+
+binarytree bt=binarytree(1,2,4,nil,5,nil,nil,0,nil,nil,3,6,nil,nil,7);
+draw(pic,bt,condensed=false);
+
+binarytree st=searchtree(10,5,2,1,3,4,7,6,8,9,15,13,12,11,14,17,16,18,19);
+draw(pic2,st,blue,condensed=true);
+
+add(pic.fit(),(0,0),10N);
+add(pic2.fit(),(0,0),10S);
+
+
+
+
+File: asymptote.info,  Node: drawtree,  Next: syzygy,  Prev: binarytree,  Up: Base modules
+
+8.12 `drawtree'
+===============
+
+This is a simple tree drawing module used by the example `treetest.asy'.
+
+
+File: asymptote.info,  Node: syzygy,  Next: feynman,  Prev: drawtree,  Up: Base modules
+
+8.13 `syzygy'
+=============
+
+This module automates the drawing of braids, relations, and syzygies,
+along with the corresponding equations, as illustrated in the example
+`knots.asy'.
+
+
+File: asymptote.info,  Node: feynman,  Next: roundedpath,  Prev: syzygy,  Up: Base modules
+
+8.14 `feynman'
+==============
+
+This package, contributed by Martin Wiebusch, is useful for drawing
+Feynman diagrams, as illustrated by the examples `eetomumu.asy' and
+`fermi.asy'.
+
+
+File: asymptote.info,  Node: roundedpath,  Next: animation,  Prev: feynman,  Up: Base modules
+
+8.15 `roundedpath'
+==================
+
+This package, contributed by Stefan Knorr, is useful for rounding the
+sharp corners of paths, as illustrated in the example file
+`roundpath.asy'.
+
+
+File: asymptote.info,  Node: animation,  Next: embed,  Prev: roundedpath,  Up: Base modules
+
+8.16 `animation'
+================
+
+This module allows one to generate animations, as illustrated by the
+files `wheel.asy', `wavepacket.asy', and `cube.asy' in the `animations'
+subdirectory of the examples directory. These animations use the
+`ImageMagick' `convert' program to merge multiple images into a GIF or
+MPEG movie.
+
+   The related `animate' module, derived from the `animation' module,
+generates higher-quality portable clickable PDF movies, with optional
+controls. This requires installing the package
+
+     `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/animate.sty'
+   (version 2007/11/30 or later) in a new directory `animate' in the
+local `LaTeX' directory (for example, in
+`/usr/local/share/texmf/tex/latex/animate'). On `UNIX' systems, one
+must then execute the command `texhash'.
+
+   The example `pdfmovie.asy' in the `animations' directory, along with
+the slide presentations `slidemovies.asy' and `intro.asy', illustrate
+the use of embedded PDF movies.  The examples `inlinemovie.tex' and
+`inlinemovie3.tex' show how to generate and embed PDF movies directly
+within a `LaTeX' file (*note LaTeX usage::).  The member function
+string pdf(fit fit=NoBox, real delay=animationdelay, string options="",
+           bool keep=settings.keep, bool multipage=true);
+ of the `animate' structure accepts any of the `animate.sty' options,
+as described here:
+
+     `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/doc/animate.pdf'
+
+
+File: asymptote.info,  Node: embed,  Next: slide,  Prev: animation,  Up: Base modules
+
+8.17 `embed'
+============
+
+This module provides an interface to the `LaTeX' package (included with
+`MikTeX')
+
+     `http://www.ctan.org/tex-archive/macros/latex/contrib/media9'
+   for embedding movies, sounds, and 3D objects into a PDF document.
+
+   A more portable method for embedding movie files, which should work
+on any platform and does not require the `media9' package, is provided
+by using the `external' module instead of `embed'.
+
+   Examples of the above two interfaces is provided in the file
+`embeddedmovie.asy' and `externalmovie.asy' in the `animations'
+subdirectory of the examples directory. For a higher quality embedded
+movie generated directly by `Asymptote', use the `animate' module along
+with the `animate.sty' package to embed a portable PDF animation (*note
+animate::).
+
+   An example of embedding `U3D' code is provided in the file
+`embeddedu3d.asy'.
+
+
+File: asymptote.info,  Node: slide,  Next: MetaPost,  Prev: embed,  Up: Base modules
+
+8.18 `slide'
+============
+
+This package provides a simple yet high-quality facility for making
+presentation slides, including portable embedded PDF animations (see
+the file `slidemovies.asy'). A simple example is provided in the file
+`slidedemo.asy'.
+
+
+File: asymptote.info,  Node: MetaPost,  Next: unicode,  Prev: slide,  Up: Base modules
+
+8.19 `MetaPost'
+===============
+
+This package provides some useful routines to help `MetaPost' users
+migrate old `MetaPost' code to `Asymptote'. Further contributions here
+are welcome.
+
+   Unlike `MetaPost', `Asymptote' does not implicitly solve linear
+equations and therefore does not have the notion of a `whatever'
+unknown. The routine `extension' (*note extension::) provides a useful
+replacement for a common use of `whatever': finding the intersection
+point of the lines through `P', `Q' and `p', `q'. For less common
+occurrences of `whatever', one can use the built-in explicit linear
+equation solver `solve' instead.
+
+
+File: asymptote.info,  Node: unicode,  Next: latin1,  Prev: MetaPost,  Up: Base modules
+
+8.20 `unicode'
+==============
+
+Import this package at the beginning of the file to instruct `LaTeX' to
+accept `unicode' (UTF-8) standardized international characters.  To use
+Cyrillic fonts, you will need to change the font encoding:
+import unicode;
+texpreamble("\usepackage{mathtext}\usepackage[russian]{babel}");
+defaultpen(font("T2A","cmr","m","n"));
+ Support for Chinese, Japanese, and Korean fonts is provided by the CJK
+package:
+
+     `http://www.ctan.org/tex-archive/languages/chinese/CJK/'
+   The following commands enable the CJK song family (within a label,
+you can also temporarily switch to another family, say kai, by
+prepending `"\CJKfamily{kai}"' to the label string):
+texpreamble("\usepackage{CJK}
+\AtBeginDocument{\begin{CJK*}{GBK}{song}}
+\AtEndDocument{\clearpage\end{CJK*}}");
+
+
+File: asymptote.info,  Node: latin1,  Next: babel,  Prev: unicode,  Up: Base modules
+
+8.21 `latin1'
+=============
+
+If you don't have `LaTeX' support for `unicode' installed, you can
+enable support for Western European languages (ISO 8859-1) by importing
+the module `latin1'. This module can be used as a template for
+providing support for other ISO 8859 alphabets.
+
+
+File: asymptote.info,  Node: babel,  Next: labelpath,  Prev: latin1,  Up: Base modules
+
+8.22 `babel'
+============
+
+This module implements the `LaTeX' `babel' package in `Asymptote'. For
+example:
+import babel;
+babel("german");
+
+
+File: asymptote.info,  Node: labelpath,  Next: labelpath3,  Prev: babel,  Up: Base modules
+
+8.23 `labelpath'
+================
+
+This module uses the `PSTricks' `pstextpath' macro to fit labels along
+a path (properly kerned, as illustrated in the example file
+`curvedlabel.asy'), using the command
+void labelpath(picture pic=currentpicture, Label L, path g,
+               string justify=Centered, pen p=currentpen);
+ Here `justify' is one of `LeftJustified', `Centered', or
+`RightJustified'. The x component of a shift transform applied to the
+Label is interpreted as a shift along the curve, whereas the y
+component is interpreted as a shift away from the curve.  All other
+Label transforms are ignored. This package requires the `latex' tex
+engine and inherits the limitations of the `PSTricks' `\pstextpath'
+macro.
+
+
+File: asymptote.info,  Node: labelpath3,  Next: annotate,  Prev: labelpath,  Up: Base modules
+
+8.24 `labelpath3'
+=================
+
+This module, contributed by Jens Schwaiger, implements a 3D version of
+`labelpath' that does not require the `PSTricks' package.  An example
+is provided in `curvedlabel3.asy'.
+
+
+File: asymptote.info,  Node: annotate,  Next: CAD,  Prev: labelpath3,  Up: Base modules
+
+8.25 `annotate'
+===============
+
+This module supports PDF annotations for viewing with `Adobe Reader',
+via the function
+void annotate(picture pic=currentpicture, string title, string text,
+              pair position);
+ Annotations are illustrated in the example file `annotation.asy'.
+Currently, annotations are only implemented for the `latex' (default)
+and `tex' TeX engines.
+
+
+File: asymptote.info,  Node: CAD,  Next: graph,  Prev: annotate,  Up: Base modules
+
+8.26 `CAD'
+==========
+
+This package, contributed by Mark Henning, provides basic pen
+definitions and measurement functions for simple 2D CAD drawings
+according to DIN 15. It is documented separately, in the file `CAD.pdf'.
+
+
+File: asymptote.info,  Node: graph,  Next: palette,  Prev: CAD,  Up: Base modules
+
+8.27 `graph'
+============
+
+This package implements two-dimensional linear and logarithmic graphs,
+including automatic scale and tick selection (with the ability to
+override manually). A graph is a `guide' (that can be drawn with the
+draw command, with an optional legend) constructed with one of the
+following routines:
+
+   * guide graph(picture pic=currentpicture, real f(real), real a, real b,
+                 int n=ngraph, real T(real)=identity,
+                 interpolate join=operator --);
+     guide[] graph(picture pic=currentpicture, real f(real), real a, real b,
+                  int n=ngraph, real T(real)=identity, bool3 cond(real),
+                  interpolate join=operator --);
+
+     Returns a graph using the scaling information for picture `pic'
+     (*note automatic scaling::) of the function `f' on the interval
+     [`T'(`a'),`T'(`b')], sampling at `n' points evenly spaced in
+     [`a',`b'], optionally restricted by the bool3 function `cond' on
+     [`a',`b']. If `cond' is:
+        * `true', the point is added to the existing guide;
+
+        * `default', the point is added to a new guide;
+
+        * `false', the point is omitted and a new guide is begun.
+     The points are connected using the interpolation specified by
+     `join':
+        * `operator --' (linear interpolation; the abbreviation
+          `Straight' is also accepted);
+
+        * `operator ..' (piecewise Bezier cubic spline interpolation;
+          the abbreviation `Spline' is also accepted);
+
+        * `Hermite' (standard cubic spline interpolation using boundary
+          condition `notaknot', `natural',  `periodic', `clamped(real
+          slopea, real slopeb)'), or `monotonic'.  The abbreviation
+          `Hermite' is equivalent to `Hermite(notaknot)' for
+          nonperiodic data and `Hermite(periodic)' for periodic data).
+
+
+   * guide graph(picture pic=currentpicture, real x(real), real y(real),
+                 real a, real b, int n=ngraph, real T(real)=identity,
+                 interpolate join=operator --);
+     guide[] graph(picture pic=currentpicture, real x(real), real y(real),
+                   real a, real b, int n=ngraph, real T(real)=identity,
+                   bool3 cond(real), interpolate join=operator --);
+
+     Returns a graph using the scaling information for picture `pic' of
+     the parametrized function (`x'(t),`y'(t)) for t in the interval
+     [`T'(`a'),`T'(`b')], sampling at `n' points evenly spaced in
+     [`a',`b'], optionally restricted by the bool3 function `cond' on
+     [`a',`b'], using the given interpolation type.
+
+   * guide graph(picture pic=currentpicture, pair z(real), real a, real b,
+                 int n=ngraph, real T(real)=identity,
+                 interpolate join=operator --);
+     guide[] graph(picture pic=currentpicture, pair z(real), real a, real b,
+                   int n=ngraph, real T(real)=identity, bool3 cond(real),
+                   interpolate join=operator --);
+
+     Returns a graph using the scaling information for picture `pic' of
+     the parametrized function `z'(t) for t in the interval
+     [`T'(`a'),`T'(`b')], sampling at `n' points evenly spaced in
+     [`a',`b'], optionally restricted by the bool3 function `cond' on
+     [`a',`b'], using the given interpolation type.
+
+   * guide graph(picture pic=currentpicture, pair[] z,
+                 interpolate join=operator --);
+     guide[] graph(picture pic=currentpicture, pair[] z, bool3[] cond,
+                   interpolate join=operator --);
+
+     Returns a graph using the scaling information for picture `pic' of
+     the elements of the array `z', optionally restricted to those
+     indices for which the elements of the boolean array `cond' are
+     `true', using the given interpolation type.
+
+   * guide graph(picture pic=currentpicture, real[] x, real[] y,
+                 interpolate join=operator --);
+     guide[] graph(picture pic=currentpicture, real[] x, real[] y,
+                   bool3[] cond, interpolate join=operator --);
+
+     Returns a graph using the scaling information for picture `pic' of
+     the elements of the arrays (`x',`y'), optionally restricted to
+     those indices for which the elements of the boolean array `cond'
+     are `true', using the given interpolation type.
+
+   * guide polargraph(picture pic=currentpicture, real f(real), real a,
+                      real b, int n=ngraph, interpolate join=operator --);
+
+     Returns a polar-coordinate graph using the scaling information for
+     picture `pic' of the function `f' on the interval [`a',`b'],
+     sampling at `n' evenly spaced points, with the given interpolation
+     type.
+
+   * guide polargraph(picture pic=currentpicture, real[] r, real[] theta,
+                      interpolate join=operator--);
+      Returns a polar-coordinate graph using the scaling information for
+     picture `pic' of the elements of the arrays (`r',`theta'), using
+     the given interpolation type.
+
+
+
+
+   An axis can be drawn on a picture with one of the following commands:
+
+   * void xaxis(picture pic=currentpicture, Label L="", axis axis=YZero,
+                real xmin=-infinity, real xmax=infinity, pen p=currentpen,
+                ticks ticks=NoTicks, arrowbar arrow=None, bool above=false);
+
+     Draw an x axis on picture `pic' from x=`xmin' to x=`xmax' using
+     pen `p', optionally labelling it with Label `L'. The relative
+     label location along the axis (a real number from [0,1]) defaults
+     to 1 (*note Label::), so that the label is drawn at the end of the
+     axis. An infinite value of `xmin' or `xmax' specifies that the
+     corresponding axis limit will be automatically determined from the
+     picture limits.  The optional `arrow' argument takes the same
+     values as in the `draw' command (*note arrows::). The axis is
+     drawn before any existing objects in `pic' unless `above=true'.
+     The axis placement is determined by one of the following `axis'
+     types:
+
+    `YZero(bool extend=true)'
+          Request an x axis at y=0 (or y=1 on a logarithmic axis)
+          extending to the full dimensions of the picture, unless
+          `extend'=false.
+
+    `YEquals(real Y, bool extend=true)'
+          Request an x axis at y=`Y' extending to the full dimensions
+          of the picture, unless `extend'=false.
+
+    `Bottom(bool extend=false)'
+          Request a bottom axis.
+
+    `Top(bool extend=false)'
+          Request a top axis.
+
+    `BottomTop(bool extend=false)'
+          Request a bottom and top axis.
+
+
+     Custom axis types can be created by following the examples in
+     `graph.asy'.  One can easily override the default values for the
+     standard axis types: import graph;
+
+     YZero=new axis(bool extend=true) {
+       return new void(picture pic, axisT axis) {
+         real y=pic.scale.x.scale.logarithmic ? 1 : 0;
+         axis.value=I*pic.scale.y.T(y);
+         axis.position=1;
+         axis.side=right;
+         axis.align=2.5E;
+         axis.value2=Infinity;
+         axis.extend=extend;
+       };
+     };
+     YZero=YZero();
+
+     The default tick option is `NoTicks'.  The options `LeftTicks',
+     `RightTicks', or `Ticks' can be used to draw ticks on the left,
+     right, or both sides of the path, relative to the direction in
+     which the path is drawn.  These tick routines accept a number of
+     optional arguments: ticks LeftTicks(Label format="", ticklabel ticklabel=null,
+                     bool beginlabel=true, bool endlabel=true,
+                     int N=0, int n=0, real Step=0, real step=0,
+                     bool begin=true, bool end=true, tickmodifier modify=None,
+                     real Size=0, real size=0, bool extend=false,
+                     pen pTick=nullpen, pen ptick=nullpen);
+
+     If any of these parameters are omitted, reasonable defaults will
+     be chosen:
+    `Label format'
+          override the default tick label format (`defaultformat',
+          initially "$%.4g$"), rotation, pen, and alignment (for
+          example, `LeftSide', `Center', or `RightSide') relative to
+          the axis. To enable `LaTeX' math mode fonts, the format
+          string should begin and end with `$' *note format::. If the
+          format string is `trailingzero', trailing zeros will be added
+          to the tick labels; if the format string is `"%"', the tick
+          label will be suppressed;
+
+    `ticklabel'
+          is a function `string(real x)' returning the label (by
+          default, format(format.s,x)) for each major tick value `x';
+
+    `bool beginlabel'
+          include the first label;
+
+    `bool endlabel'
+          include the last label;
+
+    `int N'
+          when automatic scaling is enabled (the default; *note
+          automatic scaling::), divide a linear axis evenly into this
+          many intervals, separated by major ticks; for a logarithmic
+          axis, this is the number of decades between labelled ticks;
+
+    `int n'
+          divide each interval into this many subintervals, separated
+          by minor ticks;
+
+    `real Step'
+          the tick value spacing between major ticks (if `N'=`0');
+
+    `real step'
+          the tick value spacing between minor ticks (if `n'=`0');
+
+    `bool begin'
+          include the first major tick;
+
+    `bool end'
+          include the last major tick;
+
+    `tickmodifier modify;'
+          an optional function that takes and returns a `tickvalue'
+          structure having real[] members `major' and `minor'
+          consisting of the tick values (to allow modification of the
+          automatically generated tick values);
+
+    `real Size'
+          the size of the major ticks (in `PostScript' coordinates);
+
+    `real size'
+          the size of the minor ticks (in `PostScript' coordinates);
+
+    `bool extend;'
+          extend the ticks between two axes (useful for drawing a grid
+          on the graph);
+
+    `pen pTick'
+          an optional pen used to draw the major ticks;
+
+    `pen ptick'
+          an optional pen used to draw the minor ticks.
+
+
+     For convenience, the predefined tickmodifiers `OmitTick(... real[]
+     x)', `OmitTickInterval(real a, real b)', and
+     `OmitTickIntervals(real[] a, real[] b)' can be used to remove
+     specific auto-generated ticks and their labels. The
+     `OmitFormat(string s=defaultformat ... real[] x)' ticklabel can be
+     used to remove specific tick labels but not the corresponding
+     ticks. The tickmodifier `NoZero' is an abbreviation for
+     `OmitTick(0)' and the ticklabel `NoZeroFormat' is an abbrevation
+     for `OmitFormat(0)'.
+
+     It is also possible to specify custom tick locations with
+     `LeftTicks', `RightTicks', and `Ticks' by passing explicit real
+     arrays `Ticks' and (optionally) `ticks' containing the locations
+     of the major and minor ticks, respectively: ticks LeftTicks(Label format="", ticklabel ticklabel=null,
+                     bool beginlabel=true, bool endlabel=true,
+                     real[] Ticks, real[] ticks=new real[],
+                     real Size=0, real size=0, bool extend=false,
+                     pen pTick=nullpen, pen ptick=nullpen)
+
+   * void yaxis(picture pic=currentpicture, Label L="", axis axis=XZero,
+                real ymin=-infinity, real ymax=infinity, pen p=currentpen,
+                ticks ticks=NoTicks, arrowbar arrow=None, bool above=false,
+                bool autorotate=true);
+
+     Draw a y axis on picture `pic' from y=`ymin' to y=`ymax' using pen
+     `p', optionally labelling it with a Label `L' that is autorotated
+     unless `autorotate=false'.  The relative location of the label (a
+     real number from [0,1]) defaults to 1 (*note Label::). An infinite
+     value of `ymin' or `ymax' specifies that the corresponding axis
+     limit will be automatically determined from the picture limits.
+     The optional `arrow' argument takes the same values as in the
+     `draw' command (*note arrows::). The axis is drawn before any
+     existing objects in `pic' unless `above=true'.  The tick type is
+     specified by `ticks' and the axis placement is determined by one
+     of the following `axis' types:
+
+    `XZero(bool extend=true)'
+          Request a y axis at x=0 (or x=1 on a logarithmic axis)
+          extending to the full dimensions of the picture, unless
+          `extend'=false.
+
+    `XEquals(real X, bool extend=true)'
+          Request a y axis at x=`X' extending to the full dimensions of
+          the picture, unless `extend'=false.
+
+    `Left(bool extend=false)'
+          Request a left axis.
+
+    `Right(bool extend=false)'
+          Request a right axis.
+
+    `LeftRight(bool extend=false)'
+          Request a left and right axis.
+
+
+   * For convenience, the functions void xequals(picture pic=currentpicture, Label L="", real x,
+                  bool extend=false, real ymin=-infinity, real ymax=infinity,
+                  pen p=currentpen, ticks ticks=NoTicks, bool above=true,
+                  arrowbar arrow=None);
+      and void yequals(picture pic=currentpicture, Label L="", real y,
+                  bool extend=false, real xmin=-infinity, real xmax=infinity,
+                  pen p=currentpen, ticks ticks=NoTicks, bool above=true,
+                  arrowbar arrow=None);
+      can be respectively used to call `yaxis' and `xaxis' with the
+     appropriate axis types `XEquals(x,extend)' and
+     `YEquals(y,extend)'. This is the recommended way of drawing
+     vertical or horizontal lines and axes at arbitrary locations.
+
+   * void axes(picture pic=currentpicture, Label xlabel="", Label ylabel="",
+               bool extend=true,
+               pair min=(-infinity,-infinity), pair max=(infinity,infinity),
+               pen p=currentpen, arrowbar arrow=None, bool above=false);
+      This convenience routine draws both x and y axes on picture `pic'
+     from `min' to `max', with optional labels `xlabel' and `ylabel'
+     and any arrows specified by `arrow'. The axes are drawn on top of
+     existing objects in `pic' only if `above=true'.
+
+   * void axis(picture pic=currentpicture, Label L="", path g,
+               pen p=currentpen, ticks ticks, ticklocate locate,
+               arrowbar arrow=None, int[] divisor=new int[],
+               bool above=false, bool opposite=false);
+
+     This routine can be used to draw on picture `pic' a general axis
+     based on an arbitrary path `g', using pen `p'.  One can optionally
+     label the axis with Label `L' and add an arrow `arrow'. The tick
+     type is given by `ticks'.  The optional integer array `divisor'
+     specifies what tick divisors to try in the attempt to produce
+     uncrowded tick labels. A `true' value for the flag `opposite'
+     identifies an unlabelled secondary axis (typically drawn opposite
+     a primary axis). The axis is drawn before any existing objects in
+     `pic' unless `above=true'.  The tick locator `ticklocate' is
+     constructed by the routine ticklocate ticklocate(real a, real b, autoscaleT S=defaultS,
+                           real tickmin=-infinity, real tickmax=infinity,
+                           real time(real)=null, pair dir(real)=zero);
+      where `a' and `b' specify the respective tick values at
+     `point(g,0)' and `point(g,length(g))', `S' specifies the
+     autoscaling transformation, the function `real time(real v)'
+     returns the time corresponding to the value `v', and `pair
+     dir(real t)' returns the absolute tick direction as a function of
+     `t' (zero means draw the tick perpendicular to the axis).
+
+   * These routines are useful for manually putting ticks and labels on
+     axes (if the variable `Label' is given as the `Label' argument,
+     the `format' argument will be used to format a string based on the
+     tick location): void xtick(picture pic=currentpicture, Label L="", explicit pair z,
+                pair dir=N, string format="",
+                real size=Ticksize, pen p=currentpen);
+     void xtick(picture pic=currentpicture, Label L="", real x,
+                pair dir=N, string format="",
+                real size=Ticksize, pen p=currentpen);
+     void ytick(picture pic=currentpicture, Label L="", explicit pair z,
+                pair dir=E, string format="",
+                real size=Ticksize, pen p=currentpen);
+     void ytick(picture pic=currentpicture, Label L="", real y,
+                pair dir=E, string format="",
+                real size=Ticksize, pen p=currentpen);
+     void tick(picture pic=currentpicture, pair z,
+               pair dir, real size=Ticksize, pen p=currentpen);
+     void labelx(picture pic=currentpicture, Label L="", explicit pair z,
+                 align align=S, string format="", pen p=currentpen);
+     void labelx(picture pic=currentpicture, Label L="", real x,
+                 align align=S, string format="", pen p=currentpen);
+     void labelx(picture pic=currentpicture, Label L,
+                 string format="", explicit pen p=currentpen);
+     void labely(picture pic=currentpicture, Label L="", explicit pair z,
+                 align align=W, string format="", pen p=currentpen);
+     void labely(picture pic=currentpicture, Label L="", real y,
+                 align align=W, string format="", pen p=currentpen);
+     void labely(picture pic=currentpicture, Label L,
+                 string format="", explicit pen p=currentpen);
+
+   Here are some simple examples of two-dimensional graphs:
+
+  1. This example draws a textbook-style graph of y= exp(x), with the y
+     axis starting at y=0: import graph;
+     size(150,0);
+
+     real f(real x) {return exp(x);}
+     pair F(real x) {return (x,f(x));}
+
+     xaxis("$x$");
+     yaxis("$y$",0);
+
+     draw(graph(f,-4,2,operator ..),red);
+
+     labely(1,E);
+     label("$e^x$",F(1),SE);
+
+
+
+  2. The next example draws a scientific-style graph with a legend.
+     The position of the legend can be adjusted either explicitly or by
+     using the graphical user interface `xasy' (*note GUI::). If an
+     `UnFill(real xmargin=0, real ymargin=xmargin)' or `Fill(pen)'
+     option is specified to `add', the legend will obscure any
+     underlying objects. Here we illustrate how to clip the portion of
+     the picture covered by a label:
+
+     import graph;
+
+     size(400,200,IgnoreAspect);
+
+     real Sin(real t) {return sin(2pi*t);}
+     real Cos(real t) {return cos(2pi*t);}
+
+     draw(graph(Sin,0,1),red,"$\sin(2\pi x)$");
+     draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$");
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,RightTicks(trailingzero));
+
+     label("LABEL",point(0),UnFill(1mm));
+
+     add(legend(),point(E),20E,UnFill);
+
+
+
+     To specify a fixed size for the graph proper, use `attach': import graph;
+
+     size(250,200,IgnoreAspect);
+
+     real Sin(real t) {return sin(2pi*t);}
+     real Cos(real t) {return cos(2pi*t);}
+
+     draw(graph(Sin,0,1),red,"$\sin(2\pi x)$");
+     draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$");
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,RightTicks(trailingzero));
+
+     label("LABEL",point(0),UnFill(1mm));
+
+     attach(legend(),truepoint(E),20E,UnFill);
+      A legend can have multiple entries per line: import graph;
+     size(8cm,6cm,IgnoreAspect);
+
+     typedef real realfcn(real);
+     realfcn F(real p) {
+       return new real(real x) {return sin(p*x);};
+     };
+
+     for(int i=1; i < 5; ++i)
+       draw(graph(F(i*pi),0,1),Pen(i),
+            "$\sin("+(i == 1 ? "" : (string) i)+"\pi x)$");
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,RightTicks(trailingzero));
+
+     attach(legend(2),(point(S).x,truepoint(S).y),10S,UnFill);
+
+
+
+  3. This example draws a graph of one array versus another (both of
+     the same size) using custom tick locations and a smaller font size
+     for the tick labels on the y axis.  import graph;
+
+     size(200,150,IgnoreAspect);
+
+     real[] x={0,1,2,3};
+     real[] y=x^2;
+
+     draw(graph(x,y),red);
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,
+           RightTicks(Label(fontsize(8pt)),new real[]{0,4,9}));
+
+
+
+  4. This example shows how to graph columns of data read from a file.  import graph;
+
+     size(200,150,IgnoreAspect);
+
+     file in=input("filegraph.dat").line();
+     real[][] a=in.dimension(0,0);
+     a=transpose(a);
+
+     real[] x=a[0];
+     real[] y=a[1];
+
+     draw(graph(x,y),red);
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,RightTicks);
+
+
+
+  5. The next example draws two graphs of an array of coordinate pairs,
+     using frame alignment and data markers. In the left-hand graph, the
+     markers, constructed with marker marker(path g, markroutine markroutine=marknodes,
+                   pen p=currentpen, filltype filltype=NoFill,
+                   bool above=true);
+      using the path `unitcircle' (*note filltype::), are drawn below
+     each node. Any frame can be converted to a marker, using marker marker(frame f, markroutine markroutine=marknodes,
+                   bool above=true);
+      In the right-hand graph, the unit n-sided regular polygon
+     `polygon(int n)' and the unit n-point cyclic cross `cross(int n,
+     bool round=true, real r=0)' (where `r' is an optional "inner"
+     radius) are used to build a custom marker frame.  Here
+     `markuniform(bool centered=false, int n, bool rotated=false)' adds
+     this frame at `n' uniformly spaced points along the arclength of
+     the path, optionally rotated by the angle of the local tangent to
+     the path (if centered is true, the frames will be centered within
+     `n' evenly spaced arclength intervals). Alternatively, one can use
+     markroutine `marknodes' to request that the marks be placed at each
+     Bezier node of the path, or markroutine `markuniform(pair z(real
+     t), real a, real b, int n)' to place marks at points `z(t)' for n
+     evenly spaced values of `t' in `[a,b]'.
+
+     These markers are predefined: marker[] Mark={
+       marker(scale(circlescale)*unitcircle),
+       marker(polygon(3)),marker(polygon(4)),
+       marker(polygon(5)),marker(invert*polygon(3)),
+       marker(cross(4)),marker(cross(6))
+     };
+
+     marker[] MarkFill={
+       marker(scale(circlescale)*unitcircle,Fill),marker(polygon(3),Fill),
+       marker(polygon(4),Fill),marker(polygon(5),Fill),
+       marker(invert*polygon(3),Fill)
+     };
+
+     The example also illustrates the `errorbar' routines:
+
+     void errorbars(picture pic=currentpicture, pair[] z, pair[] dp,
+                    pair[] dm={}, bool[] cond={}, pen p=currentpen,
+                    real size=0);
+
+     void errorbars(picture pic=currentpicture, real[] x, real[] y,
+                    real[] dpx, real[] dpy, real[] dmx={}, real[] dmy={},
+                    bool[] cond={}, pen p=currentpen, real size=0);
+
+     Here, the positive and negative extents of the error are given by
+     the absolute values of the elements of the pair array `dp' and the
+     optional pair array `dm'. If `dm' is not specified, the positive
+     and negative extents of the error are assumed to be equal.  import graph;
+
+     picture pic;
+     real xsize=200, ysize=140;
+     size(pic,xsize,ysize,IgnoreAspect);
+
+     pair[] f={(5,5),(50,20),(90,90)};
+     pair[] df={(0,0),(5,7),(0,5)};
+
+     errorbars(pic,f,df,red);
+     draw(pic,graph(pic,f),"legend",
+          marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));
+
+     scale(pic,true);
+
+     xaxis(pic,"$x$",BottomTop,LeftTicks);
+     yaxis(pic,"$y$",LeftRight,RightTicks);
+     add(pic,legend(pic),point(pic,NW),20SE,UnFill);
+
+     picture pic2;
+     size(pic2,xsize,ysize,IgnoreAspect);
+
+     frame mark;
+     filldraw(mark,scale(0.8mm)*polygon(6),green,green);
+     draw(mark,scale(0.8mm)*cross(6),blue);
+
+     draw(pic2,graph(pic2,f),marker(mark,markuniform(5)));
+
+     scale(pic2,true);
+
+     xaxis(pic2,"$x$",BottomTop,LeftTicks);
+     yaxis(pic2,"$y$",LeftRight,RightTicks);
+
+     yequals(pic2,55.0,red+Dotted);
+     xequals(pic2,70.0,red+Dotted);
+
+     // Fit pic to W of origin:
+     add(pic.fit(),(0,0),W);
+
+     // Fit pic2 to E of (5mm,0):
+     add(pic2.fit(),(5mm,0),E);
+
+
+
+  6. A custom mark routine can be also be specified: import graph;
+
+     size(200,100,IgnoreAspect);
+
+     markroutine marks() {
+       return new void(picture pic=currentpicture, frame f, path g) {
+         path p=scale(1mm)*unitcircle;
+         for(int i=0; i <= length(g); ++i) {
+           pair z=point(g,i);
+           frame f;
+           if(i % 4 == 0) {
+             fill(f,p);
+             add(pic,f,z);
+           } else {
+             if(z.y > 50) {
+               pic.add(new void(frame F, transform t) {
+                   path q=shift(t*z)*p;
+                   unfill(F,q);
+                   draw(F,q);
+                 });
+             } else {
+               draw(f,p);
+               add(pic,f,z);
+             }
+           }
+         }
+       };
+     }
+
+     pair[] f={(5,5),(40,20),(55,51),(90,30)};
+
+     draw(graph(f),marker(marks()));
+
+     scale(true);
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,RightTicks);
+
+
+
+  7. This example shows how to label an axis with arbitrary strings.  import graph;
+
+     size(400,150,IgnoreAspect);
+
+     real[] x=sequence(12);
+     real[] y=sin(2pi*x/12);
+
+     scale(false);
+
+     string[] month={"Jan","Feb","Mar","Apr","May","Jun",
+                     "Jul","Aug","Sep","Oct","Nov","Dec"};
+
+     draw(graph(x,y),red,MarkFill[0]);
+
+     xaxis(BottomTop,LeftTicks(new string(real x) {
+           return month[round(x % 12)];}));
+     yaxis("$y$",LeftRight,RightTicks(4));
+
+
+
+  8. The next example draws a graph of a parametrized curve.  The calls
+     to xlimits(picture pic=currentpicture, real min=-infinity,
+             real max=infinity, bool crop=NoCrop);
+      and the analogous function `ylimits' can be uncommented to set
+     the respective axes limits for picture `pic' to the specified
+     `min' and `max' values. Alternatively, the function void limits(picture pic=currentpicture, pair min, pair max, bool crop=NoCrop);
+      can be used to limit the axes to the box having opposite vertices
+     at the given pairs). Existing objects in picture `pic' will be
+     cropped to lie within the given limits if `crop'=`Crop'. The
+     function `crop(picture pic)' can be used to crop a graph to the
+     current graph limits.  import graph;
+
+     size(0,200);
+
+     real x(real t) {return cos(2pi*t);}
+     real y(real t) {return sin(2pi*t);}
+
+     draw(graph(x,y,0,1));
+
+     //limits((0,-1),(1,0),Crop);
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,RightTicks(trailingzero));
+
+
+
+     The next example illustrates how one can extract a common axis
+     scaling factor.  import graph;
+
+     axiscoverage=0.9;
+     size(200,IgnoreAspect);
+
+     real[] x={-1e-11,1e-11};
+     real[] y={0,1e6};
+
+     real xscale=round(log10(max(x)));
+     real yscale=round(log10(max(y)))-1;
+
+     draw(graph(x*10^(-xscale),y*10^(-yscale)),red);
+
+     xaxis("$x/10^{"+(string) xscale+"}$",BottomTop,LeftTicks);
+     yaxis("$y/10^{"+(string) yscale+"}$",LeftRight,RightTicks(trailingzero));
+
+
+
+     Axis scaling can be requested and/or automatic selection of the
+     axis limits can be inhibited with one of these `scale' routines: void scale(picture pic=currentpicture, scaleT x, scaleT y);
+
+     void scale(picture pic=currentpicture, bool xautoscale=true,
+                bool yautoscale=xautoscale, bool zautoscale=yautoscale);
+
+     This sets the scalings for picture `pic'. The `graph' routines
+     accept an optional `picture' argument for determining the
+     appropriate scalings to use; if none is given, it uses those set
+     for `currentpicture'.
+
+     Two frequently used scaling routines `Linear' and `Log' are
+     predefined in `graph'.
+
+     All picture coordinates (including those in paths and those given
+     to the `label' and `limits' functions) are always treated as linear
+     (post-scaled) coordinates. Use pair Scale(picture pic=currentpicture, pair z);
+      to convert a graph coordinate into a scaled picture coordinate.
+
+     The x and y components can be individually scaled using the
+     analogous routines real ScaleX(picture pic=currentpicture, real x);
+     real ScaleY(picture pic=currentpicture, real y);
+
+     The predefined scaling routines can be given two optional boolean
+     arguments: `automin=false' and `automax=automin'. These default to
+     `false' but can be respectively set to `true' to enable automatic
+     selection of "nice" axis minimum and maximum values. The `Linear'
+     scaling can also take as optional final arguments a multiplicative
+     scaling factor and intercept (e.g. for a depth axis, `Linear(-1)'
+     requests axis reversal).
+
+     For example, to draw a log/log graph of a function, use
+     `scale(Log,Log)': import graph;
+
+     size(200,200,IgnoreAspect);
+
+     real f(real t) {return 1/t;}
+
+     scale(Log,Log);
+
+     draw(graph(f,0.1,10));
+
+     //limits((1,0.1),(10,0.5),Crop);
+
+     dot(Label("(3,5)",align=S),Scale((3,5)));
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$y$",LeftRight,RightTicks);
+
+
+
+     By extending the ticks, one can easily produce a logarithmic grid: import graph;
+     size(200,200,IgnoreAspect);
+
+     real f(real t) {return 1/t;}
+
+     scale(Log,Log);
+     draw(graph(f,0.1,10),red);
+     pen thin=linewidth(0.5*linewidth());
+     xaxis("$x$",BottomTop,LeftTicks(begin=false,end=false,extend=true,
+                                     ptick=thin));
+     yaxis("$y$",LeftRight,RightTicks(begin=false,end=false,extend=true,
+                                      ptick=thin));
+
+
+
+     One can also specify custom tick locations and formats for
+     logarithmic axes: import graph;
+
+     size(300,175,IgnoreAspect);
+     scale(Log,Log);
+     draw(graph(identity,5,20));
+     xlimits(5,20);
+     ylimits(1,100);
+     xaxis("$M/M_\odot$",BottomTop,LeftTicks(DefaultFormat,
+                                             new real[] {6,10,12,14,16,18}));
+     yaxis("$\nu_{\rm upp}$ [Hz]",LeftRight,RightTicks(DefaultFormat));
+
+
+
+     It is easy to draw logarithmic graphs with respect to other bases: import graph;
+     size(200,IgnoreAspect);
+
+     // Base-2 logarithmic scale on y-axis:
+
+     real log2(real x) {static real log2=log(2); return log(x)/log2;}
+     real pow2(real x) {return 2^x;}
+
+     scaleT yscale=scaleT(log2,pow2,logarithmic=true);
+     scale(Linear,yscale);
+
+     real f(real x) {return 1+x^2;}
+
+     draw(graph(f,-4,4));
+
+     yaxis("$y$",ymin=1,ymax=f(5),RightTicks(Label(Fill(white))),EndArrow);
+     xaxis("$x$",xmin=-5,xmax=5,LeftTicks,EndArrow);
+
+
+
+     Here is an example of "broken" linear x and logarithmic y axes
+     that omit the segments [3,8] and [100,1000], respectively.  In the
+     case of a logarithmic axis, the break endpoints are automatically
+     rounded to the nearest integral power of the base.  import graph;
+
+     size(200,150,IgnoreAspect);
+
+     // Break the x axis at 3; restart at 8:
+     real a=3, b=8;
+
+     // Break the y axis at 100; restart at 1000:
+     real c=100, d=1000;
+
+     scale(Broken(a,b),BrokenLog(c,d));
+
+     real[] x={1,2,4,6,10};
+     real[] y=x^4;
+
+     draw(graph(x,y),red,MarkFill[0]);
+
+     xaxis("$x$",BottomTop,LeftTicks(Break(a,b)));
+     yaxis("$y$",LeftRight,RightTicks(Break(c,d)));
+
+     label(rotate(90)*Break,(a,point(S).y));
+     label(rotate(90)*Break,(a,point(N).y));
+     label(Break,(point(W).x,ScaleY(c)));
+     label(Break,(point(E).x,ScaleY(c)));
+
+
+
+  9. `Asymptote' can draw secondary axes with the routines picture secondaryX(picture primary=currentpicture, void f(picture));
+     picture secondaryY(picture primary=currentpicture, void f(picture));
+
+     In this example, `secondaryY' is used to draw a secondary linear y
+     axis against a primary logarithmic y axis: import graph;
+     texpreamble("\def\Arg{\mathop {\rm Arg}\nolimits}");
+
+     size(10cm,5cm,IgnoreAspect);
+
+     real ampl(real x) {return 2.5/(1+x^2);}
+     real phas(real x) {return -atan(x)/pi;}
+
+     scale(Log,Log);
+     draw(graph(ampl,0.01,10));
+     ylimits(0.001,100);
+
+     xaxis("$\omega\tau_0$",BottomTop,LeftTicks);
+     yaxis("$|G(\omega\tau_0)|$",Left,RightTicks);
+
+     picture q=secondaryY(new void(picture pic) {
+         scale(pic,Log,Linear);
+         draw(pic,graph(pic,phas,0.01,10),red);
+         ylimits(pic,-1.0,1.5);
+         yaxis(pic,"$\Arg G/\pi$",Right,red,
+               LeftTicks("$% #.1f$",
+                         begin=false,end=false));
+         yequals(pic,1,Dotted);
+       });
+     label(q,"(1,0)",Scale(q,(1,0)),red);
+     add(q);
+
+
+
+     A secondary logarithmic y axis can be drawn like this: import graph;
+
+     size(9cm,6cm,IgnoreAspect);
+     string data="secondaryaxis.csv";
+
+     file in=input(data).line().csv();
+
+     string[] titlelabel=in;
+     string[] columnlabel=in;
+
+     real[][] a=in.dimension(0,0);
+     a=transpose(a);
+     real[] t=a[0], susceptible=a[1], infectious=a[2], dead=a[3], larvae=a[4];
+     real[] susceptibleM=a[5], exposed=a[6],infectiousM=a[7];
+
+     scale(true);
+
+     draw(graph(t,susceptible,t >= 10 & t <= 15));
+     draw(graph(t,dead,t >= 10 & t <= 15),dashed);
+
+     xaxis("Time ($\tau$)",BottomTop,LeftTicks);
+     yaxis(Left,RightTicks);
+
+     picture secondary=secondaryY(new void(picture pic) {
+         scale(pic,Linear(true),Log(true));
+         draw(pic,graph(pic,t,infectious,t >= 10 & t <= 15),red);
+         yaxis(pic,Right,red,LeftTicks(begin=false,end=false));
+       });
+
+     add(secondary);
+     label(shift(5mm*N)*"Proportion of crows",point(NW),E);
+
+
+
+ 10. Here is a histogram example, which uses the `stats' module.  import graph;
+     import stats;
+
+     size(400,200,IgnoreAspect);
+
+     int n=10000;
+     real[] a=new real[n];
+     for(int i=0; i < n; ++i) a[i]=Gaussrand();
+
+     draw(graph(Gaussian,min(a),max(a)),blue);
+
+     // Optionally calculate "optimal" number of bins a la Shimazaki and Shinomoto.
+     int N=bins(a);
+
+     histogram(a,min(a),max(a),N,normalize=true,low=0,lightred,black,bars=false);
+
+     xaxis("$x$",BottomTop,LeftTicks);
+     yaxis("$dP/dx$",LeftRight,RightTicks(trailingzero));
+
+
+
+ 11. Here is an example of reading column data in from a file and a
+     least-squares fit, using the `stats' module.  size(400,200,IgnoreAspect);
+
+     import graph;
+     import stats;
+
+     file fin=input("leastsquares.dat").line();
+
+     real[][] a=fin.dimension(0,0);
+     a=transpose(a);
+
+     real[] t=a[0], rho=a[1];
+
+     // Read in parameters from the keyboard:
+     //real first=getreal("first");
+     //real step=getreal("step");
+     //real last=getreal("last");
+
+     real first=100;
+     real step=50;
+     real last=700;
+
+     // Remove negative or zero values of rho:
+     t=rho > 0 ? t : null;
+     rho=rho > 0 ? rho : null;
+
+     scale(Log(true),Linear(true));
+
+     int n=step > 0 ? ceil((last-first)/step) : 0;
+
+     real[] T,xi,dxi;
+
+     for(int i=0; i <= n; ++i) {
+       real first=first+i*step;
+       real[] logrho=(t >= first & t <= last) ? log(rho) : null;
+       real[] logt=(t >= first & t <= last) ? -log(t) : null;
+
+       if(logt.length < 2) break;
+
+       // Fit to the line logt=L.m*logrho+L.b:
+       linefit L=leastsquares(logt,logrho);
+
+       T.push(first);
+       xi.push(L.m);
+       dxi.push(L.dm);
+     }
+
+     draw(graph(T,xi),blue);
+     errorbars(T,xi,dxi,red);
+
+     crop();
+
+     ylimits(0);
+
+     xaxis("$T$",BottomTop,LeftTicks);
+     yaxis("$\xi$",LeftRight,RightTicks);
+
+
+
+ 12. Here is an example that illustrates the general `axis' routine.  import graph;
+     size(0,100);
+
+     path g=ellipse((0,0),1,2);
+
+     scale(true);
+
+     axis(Label("C",align=10W),g,LeftTicks(endlabel=false,8,end=false),
+          ticklocate(0,360,new real(real v) {
+              path h=(0,0)--max(abs(max(g)),abs(min(g)))*dir(v);
+              return intersect(g,h)[0];}));
+
+
+
+ 13. To draw a vector field of `n' arrows evenly spaced along the
+     arclength of a path, use the routine picture vectorfield(path vector(real), path g, int n, bool truesize=false,
+                         pen p=currentpen, arrowbar arrow=Arrow);
+      as illustrated in this simple example of a flow field: import graph;
+     defaultpen(1.0);
+
+     size(0,150,IgnoreAspect);
+
+     real arrowsize=4mm;
+     real arrowlength=2arrowsize;
+
+     typedef path vector(real);
+
+     // Return a vector interpolated linearly between a and b.
+     vector vector(pair a, pair b) {
+       return new path(real x) {
+         return (0,0)--arrowlength*interp(a,b,x);
+       };
+     }
+
+     real f(real x) {return 1/x;}
+
+     real epsilon=0.5;
+     path g=graph(f,epsilon,1/epsilon);
+
+     int n=3;
+     draw(g);
+     xaxis("$x$");
+     yaxis("$y$");
+
+     add(vectorfield(vector(W,W),g,n,true));
+     add(vectorfield(vector(NE,NW),(0,0)--(point(E).x,0),n,true));
+     add(vectorfield(vector(NE,NE),(0,0)--(0,point(N).y),n,true));
+
+
+
+ 14. To draw a vector field of `nx'\times`ny' arrows in `box(a,b)', use
+     the routine picture vectorfield(path vector(pair), pair a, pair b,
+                         int nx=nmesh, int ny=nx, bool truesize=false,
+                         real maxlength=truesize ? 0 : maxlength(a,b,nx,ny),
+                         bool cond(pair z)=null, pen p=currentpen,
+                         arrowbar arrow=Arrow, margin margin=PenMargin)
+      as illustrated in this example: import graph;
+     size(100);
+
+     pair a=(0,0);
+     pair b=(2pi,2pi);
+
+     path vector(pair z) {return (0,0)--(sin(z.x),cos(z.y));}
+
+     add(vectorfield(vector,a,b));
+
+
+
+ 15. The following scientific graphs, which illustrate many features of
+     `Asymptote''s graphics routines, were generated from the examples
+     `diatom.asy' and `westnile.asy', using the comma-separated data in
+     `diatom.csv' and `westnile.csv'.
+
+
+
+File: asymptote.info,  Node: palette,  Next: three,  Prev: graph,  Up: Base modules
+
+8.28 `palette'
+==============
+
+`Asymptote' can also generate color density images and palettes. The
+following palettes are predefined in `palette.asy':
+
+`pen[] Grayscale(int NColors=256)'
+     a grayscale palette;
+
+`pen[] Rainbow(int NColors=32766)'
+     a rainbow spectrum;
+
+`pen[] BWRainbow(int NColors=32761)'
+     a rainbow spectrum tapering off to black/white at the ends;
+
+`pen[] BWRainbow2(int NColors=32761)'
+     a double rainbow palette tapering off to black/white at the ends,
+     with a linearly scaled intensity.
+
+`pen[] Wheel(int NColors=32766)'
+     a full color wheel palette;
+
+`pen[] Gradient(int NColors=256 ... pen[] p)'
+     a palette varying linearly over the specified array of pens, using
+     NColors in each interpolation interval;
+
+
+   The function `cmyk(pen[] Palette)' may be used to convert any of
+these palettes to the CMYK colorspace.
+
+   A color density plot using palette `palette' can be generated from a
+function `f'(x,y) and added to a picture `pic': 
+bounds image(picture pic=currentpicture, real f(real, real),
+             range range=Full, pair initial, pair final,
+             int nx=ngraph, int ny=nx, pen[] palette, bool antialias=false)
+ The function `f' will be sampled at `nx' and `ny' evenly spaced points
+over a rectangle defined by the points `initial' and `final',
+respecting the current graphical scaling of `pic'. The color space is
+scaled according to the z axis scaling (*note automatic scaling::). A
+bounds structure for the function values is returned:
+struct bounds {
+  real min;
+  real max;
+  // Possible tick intervals:
+  int[] divisor;
+}
+ This information can be used for generating an optional palette bar.
+The palette color space corresponds to a range of values specified by
+the argument `range', which can be `Full', `Automatic', or an explicit
+range `Range(real min, real max)'.  Here `Full' specifies a range
+varying from the minimum to maximum values of the function over the
+sampling interval, while `Automatic' selects "nice" limits.  The
+example `imagecontour.asy' illustrates how level sets (contour lines)
+can be drawn on a color density plot (*note contour::).
+
+   A color density plot can also be generated from an explicit real[][]
+array `data': 
+bounds image(picture pic=currentpicture, real[][] f, range range=Full,
+             pair initial, pair final, pen[] palette,
+             bool transpose=(initial.x < final.x && initial.y < final.y),
+             bool copy=true, bool antialias=false);
+ If the initial point is to the left and below the final point, by
+default the array indices are interpreted according to the Cartesian
+convention (first index: x, second index: y) rather than the usual
+matrix convention (first index: -y, second index: x).
+
+   To construct an image from an array of irregularly spaced points and
+an array of values `f' at these points, use one of the routines
+bounds image(picture pic=currentpicture, pair[] z, real[] f,
+             range range=Full, pen[] palette)
+bounds image(picture pic=currentpicture, real[] x, real[] y, real[] f,
+             range range=Full, pen[] palette)
+
+   An optionally labelled palette bar may be generated with the routine
+void palette(picture pic=currentpicture, Label L="", bounds bounds,
+             pair initial, pair final, axis axis=Right, pen[] palette,
+             pen p=currentpen, paletteticks ticks=PaletteTicks,
+             bool copy=true, bool antialias=false);
+ The color space of `palette' is taken to be over bounds `bounds' with
+scaling given by the z scaling of `pic'.  The palette orientation is
+specified by `axis', which may be one of `Right', `Left', `Top', or
+`Bottom'.  The bar is drawn over the rectangle from `initial' to
+`final'.  The argument `paletteticks' is a special tick type (*note
+ticks::) that takes the following arguments:
+paletteticks PaletteTicks(Label format="", ticklabel ticklabel=null,
+                          bool beginlabel=true, bool endlabel=true,
+                          int N=0, int n=0, real Step=0, real step=0,
+                          pen pTick=nullpen, pen ptick=nullpen);
+
+   The image and palette bar can be fit to a frame and added and
+optionally aligned to a picture at the desired location:
+
+size(12cm,12cm);
+
+import graph;
+import palette;
+
+int n=256;
+real ninv=2pi/n;
+real[][] v=new real[n][n];
+
+for(int i=0; i < n; ++i)
+  for(int j=0; j < n; ++j)
+    v[i][j]=sin(i*ninv)*cos(j*ninv);
+
+pen[] Palette=BWRainbow();
+
+picture bar;
+
+bounds range=image(v,(0,0),(1,1),Palette);
+palette(bar,"$A$",range,(0,0),(0.5cm,8cm),Right,Palette,
+        PaletteTicks("$%+#.1f$"));
+add(bar.fit(),point(E),30E);
+
+
+
+Here is an example that uses logarithmic scaling of the function values:
+
+import graph;
+import palette;
+
+size(10cm,10cm,IgnoreAspect);
+
+real f(real x, real y) {
+  return 0.9*pow10(2*sin(x/5+2*y^0.25)) + 0.1*(1+cos(10*log(y)));
+}
+
+scale(Linear,Log,Log);
+
+pen[] Palette=BWRainbow();
+
+bounds range=image(f,Automatic,(0,1),(100,100),nx=200,Palette);
+
+xaxis("$x$",BottomTop,LeftTicks,above=true);
+yaxis("$y$",LeftRight,RightTicks,above=true);
+
+palette("$f(x,y)$",range,(0,200),(100,250),Top,Palette,
+        PaletteTicks(ptick=linewidth(0.5*linewidth())));
+
+
+
+One can also draw an image directly from a two-dimensional pen array or
+a function `pen f(int, int)':
+void image(picture pic=currentpicture, pen[][] data,
+           pair initial, pair final,
+           bool transpose=(initial.x < final.x && initial.y < final.y),
+           bool copy=true, bool antialias=false);
+void image(picture pic=currentpicture, pen f(int, int), int width, int height,
+           pair initial, pair final,
+           bool transpose=(initial.x < final.x && initial.y < final.y),
+           bool antialias=false);
+ as illustrated in the following examples:
+
+size(200);
+
+import palette;
+
+int n=256;
+real ninv=2pi/n;
+pen[][] v=new pen[n][n];
+
+for(int i=0; i < n; ++i)
+  for(int j=0; j < n; ++j)
+    v[i][j]=rgb(0.5*(1+sin(i*ninv)),0.5*(1+cos(j*ninv)),0);
+
+image(v,(0,0),(1,1));
+
+
+
+import palette;
+
+size(200);
+
+real fracpart(real x) {return (x-floor(x));}
+
+pair pws(pair z) {
+  pair w=(z+exp(pi*I/5)/0.9)/(1+z/0.9*exp(-pi*I/5));
+  return exp(w)*(w^3-0.5*I);
+}
+
+int N=512;
+
+pair a=(-1,-1);
+pair b=(0.5,0.5);
+real dx=(b-a).x/N;
+real dy=(b-a).y/N;
+
+pen f(int u, int v) {
+  pair z=a+(u*dx,v*dy);
+  pair w=pws(z);
+  real phase=degrees(w,warn=false);
+  real modulus=w == 0 ? 0: fracpart(log(abs(w)));
+  return hsv(phase,1,sqrt(modulus));
+}
+
+image(f,N,N,(0,0),(300,300),antialias=true);
+
+
+
+For convenience, the module `palette' also defines functions that may
+be used to construct a pen array from a given function and palette:
+pen[] palette(real[] f, pen[] palette);
+pen[][] palette(real[][] f, pen[] palette);
+
+
+File: asymptote.info,  Node: three,  Next: obj,  Prev: palette,  Up: Base modules
+
+8.29 `three'
+============
+
+This module fully extends the notion of guides and paths in `Asymptote'
+to three dimensions. It introduces the new types guide3, path3, and
+surface.  Guides in three dimensions are specified with the same syntax
+as in two dimensions except that triples `(x,y,z)' are used in place of
+pairs `(x,y)' for the nodes and direction specifiers.  This
+generalization of John Hobby's spline algorithm is shape-invariant under
+three-dimensional rotation, scaling, and shifting, and reduces in the
+planar case to the two-dimensional algorithm used in `Asymptote',
+`MetaPost', and `MetaFont' [cf. J. C. Bowman, Proceedings in Applied
+Mathematics and Mechanics, 7:1, 2010021-2010022 (2007)].
+
+   For example, a unit circle in the XY plane may be filled and drawn
+like this:
+
+import three;
+
+size(100);
+
+path3 g=(1,0,0)..(0,1,0)..(-1,0,0)..(0,-1,0)..cycle;
+draw(g);
+draw(O--Z,red+dashed,Arrow3);
+draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle));
+dot(g,red);
+
+
+and then distorted into a saddle:
+
+import three;
+
+size(100,0);
+path3 g=(1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle;
+draw(g);
+draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle));
+dot(g,red);
+
+
+Module `three' provides constructors for converting two-dimensional
+paths to three-dimensional ones, and vice-versa: 
+path3 path3(path p, triple plane(pair)=XYplane);
+path path(path3 p, pair P(triple)=xypart);
+
+   A Bezier surface, the natural two-dimensional generalization of
+Bezier curves, is defined in `three_surface.asy' as a structure
+containing an array of Bezier patches. Surfaces may drawn with one of
+the routines
+void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1,
+          material surfacepen=currentpen, pen meshpen=nullpen,
+          light light=currentlight, light meshlight=light, string name="",
+          render render=defaultrender);
+void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1,
+          material[] surfacepen, pen meshpen,
+          light light=currentlight, light meshlight=light, string name="",
+          render render=defaultrender);
+void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1,
+          material[] surfacepen, pen[] meshpen=nullpens,
+          light light=currentlight, light meshlight=light, string name="",
+          render render=defaultrender);
+
+ The parameters `nu' and `nv' specify the number of subdivisions for
+drawing optional mesh lines for each Bezier patch. The optional `name'
+parameter is used as a prefix for naming the surface patches in the PRC
+model tree.  Here material is a structure defined in `three_light.asy':
+struct material {
+  pen[] p; // diffusepen,ambientpen,emissivepen,specularpen
+  real opacity;
+  real shininess;
+...
+}
+ These material properties are used to implement `OpenGL'-style
+lighting, based on the Phong-Blinn specular model. Sample Bezier
+surfaces are contained in the example files `BezierSurface.asy',
+`teapot.asy', and `parametricsurface.asy'. The structure `render'
+contains specialized rendering options documented at the beginning of
+module `three.asy'.
+
+   The examples `elevation.asy' and `sphericalharmonic.asy' illustrate
+how to draw a surface with patch-dependent colors.  The examples
+`vertexshading' and `smoothelevation' illustrate vertex-dependent
+colors, which is supported for both `Asymptote''s native `OpenGL'
+renderer and two-dimensional projections. Since the PRC output format
+does not currently support vertex shading of Bezier surfaces, PRC
+patches are shaded with the mean of the four vertex colors.
+
+   A surface can be constructed from a cyclic `path3' with the
+constructor
+surface surface(path3 external, triple[] internal=new triple[],
+                triple[] normals=new triple[], pen[] colors=new pen[],
+                bool3 planar=default);
+ and then filled:
+draw(surface(path3(polygon(5))),red,nolight);
+draw(surface(unitcircle3),red,nolight);
+draw(surface(unitcircle3,new pen[] {red,green,blue,black}),nolight);
+ The last example constructs a patch with vertex-specific colors.  A
+three-dimensional planar surface in the plane `plane' can be
+constructed from a two-dimensional cyclic path `g' with the constructor 
+surface surface(path p, triple plane(pair)=XYplane);
+ and then filled:
+draw(surface((0,0)--E+2N--2E--E+N..0.2E..cycle),red);
+ Planar Bezier surfaces patches are constructed using Orest Shardt's
+`bezulate' routine, which decomposes (possibly nonsimply connected)
+regions bounded (according to the `zerowinding' fill rule) by simple
+cyclic paths (intersecting only at the endpoints) into subregions
+bounded by cyclic paths of length `4' or less.
+
+   A more efficient routine also exists for drawing tessellations
+composed of many 3D triangles, with specified vertices, and optional
+normals or vertex colors: 
+void draw(picture pic=currentpicture, triple[] v, int[][] vi,
+          triple[] n={}, int[][] ni={}, material m=currentpen, pen[] p={},
+          int[][] pi={}, light light=currentlight);
+ Here, the triple array `v' lists the distinct vertices, while the
+array `vi' lists integer arrays of length 3 containing the indices of
+`v' corresponding to the vertices of each triangle. Similarly, the
+arguments `n' and `ni' contain optional normal data and `p' and `pi'
+contain optional pen vertex data.  An example of this tessellation
+facility is given in `triangles.asy'.
+
+   Arbitrary thick three-dimensional curves and line caps (which the
+`OpenGL' standard does not require implementations to provide) are
+constructed with
+tube tube(path3 p, real width, render render=defaultrender);
+ this returns a tube structure representing a tube of diameter `width'
+centered approximately on `g'. The tube structure consists of a surface
+`s' and the actual tube center, path3 `center'.  Drawing thick lines as
+tubes can be slow to render, especially with the `Adobe Reader'
+renderer. The setting `thick=false' can be used to disable this feature
+and force all lines to be drawn with `linewidth(0)' (one pixel wide,
+regardless of the resolution). By default, mesh and contour lines in
+three-dimensions are always drawn thin, unless an explicit line width
+is given in the pen parameter or the setting `thin' is set to `false'.
+The pens `thin()' and `thick()' defined in plain_pens.asy can also be
+used to override these defaults for specific draw commands.
+
+There are four choices for viewing 3D `Asymptote' output:
+  1. Use the native `Asymptote' adaptive `OpenGL'-based renderer (with
+     the command-line option `-V' and the default settings
+     `outformat=""' and `render=-1'). If you encounter warnings from
+     your graphics card driver, try specifying `-glOptions=-indirect'
+     on the command line. On `UNIX' systems with graphics support for
+     multisampling, the sample width can be controlled with the setting
+     `multisample'. An initial screen position can be specified with
+     the pair setting `position', where negative values are interpreted
+     as relative to the corresponding maximum screen dimension. The
+     default settings import settings;
+     leftbutton=new string[] {"rotate","zoom","shift","pan"};
+     middlebutton=new string[] {"menu"};
+     rightbutton=new string[] {"zoom/menu","rotateX","rotateY","rotateZ"};
+     wheelup=new string[] {"zoomin"};
+     wheeldown=new string[] {"zoomout"};
+      bind the mouse buttons as follows:
+        * Left: rotate
+
+        * Shift Left: zoom
+
+        * Ctrl Left: shift viewport
+
+        * Alt Left: pan
+
+        * Middle: menu (must be unmodified; ignores Shift, Ctrl, and
+          Alt)
+
+        * Wheel Up: zoom in
+
+        * Wheel Down: zoom out
+
+        * Right: zoom/menu (must be unmodified)
+
+        * Right double click: menu
+
+        * Shift Right: rotate about the X axis
+
+        * Ctrl Right: rotate about the Y axis
+
+        * Alt Right: rotate about the Z axis
+
+     The keyboard shortcuts are: 
+        * h: home
+
+        * f: toggle fitscreen
+
+        * x: spin about the X axis
+
+        * y: spin about the Y axis
+
+        * z: spin about the Z axis
+
+        * s: stop spinning
+
+        * m: rendering mode (solid/mesh/patch)
+
+        * e: export
+
+        * c: show camera parameters
+
+        * p: play animation
+
+        * r: reverse animation
+
+        * : step animation
+
+        * +: expand
+
+        * =: expand
+
+        * >: expand
+
+        * -: shrink
+
+        * _: shrink
+
+        * <: shrink
+
+        * q: exit
+
+        * Ctrl-q: exit
+
+  2. Render the scene to a specified rasterized format `outformat' at
+     the resolution of `n' pixels per `bp', as specified by the setting
+     `render=n'. A negative value of `n' is interpreted as `|2n|' for
+     EPS and PDF formats and `|n|' for other formats. The default value
+     of `render' is -1.  By default, the scene is internally rendered
+     at twice the specified resolution; this can be disabled by setting
+     `antialias=1'.  High resolution rendering is done by tiling the
+     image. If your graphics card allows it, the rendering can be made
+     more efficient by increasing the maximum tile size `maxtile' to
+     your screen dimensions (indicated by `maxtile=(0,0)'. If your
+     video card generates unwanted black stripes in the output, try
+     setting the horizontal and vertical components of `maxtiles' to
+     something less than your screen dimensions. The tile size is also
+     limited by the setting `maxviewport', which restricts the maximum
+     width and height of the viewport. On `UNIX' systems some graphics
+     drivers support batch mode (`-noV') rendering in an iconified
+     window; this can be enabled with the setting `iconify=true'.  Some
+     (broken) `UNIX' graphics drivers may require the command line
+     setting `-glOptions=-indirect', which requests (slower) indirect
+     rendering.
+
+  3. Embed the 3D PRC format in a PDF file and view the resulting PDF
+     file with version `9.0' or later of `Adobe Reader'.  In addition
+     to the default `settings.prc=true', this requires
+     `settings.outformat="pdf"', which can be specified by the command
+     line option `-f pdf', put in the `Asymptote' configuration file
+     (*note configuration file::), or specified in the script before
+     `three.asy' (or `graph3.asy') is imported.  The `media9' LaTeX
+     package is also required (*note embed::).  The example `pdb.asy'
+     illustrates how one can generate a list of predefined views (see
+     `100d.views').  A stationary preview image with a resolution of
+     `n' pixels per `bp' can be embedded with the setting `render=n';
+     this allows the file to be viewed with other `PDF' viewers.
+     Alternatively, the file `externalprc.tex' illustrates how the
+     resulting PRC and rendered image files can be extracted and
+     processed in a separate `LaTeX' file. However, see *note LaTeX
+     usage:: for an easier way to embed three-dimensional `Asymptote'
+     pictures within `LaTeX'.  For specialized applications where only
+     the raw PRC file is required, specify `settings.outformat="prc"'.
+     The open-source PRC specification is available from
+     `http://livedocs.adobe.com/acrobat_sdk/9/Acrobat9_HTMLHelp/API_References/PRCReference/PRC_Format_Specification/'.
+
+  4. Project the scene to a two-dimensional vector (EPS or PDF) format
+     with `render=0'. Only limited hidden surface removal facilities
+     are currently available with this approach (*note PostScript3D::).
+
+
+   Automatic picture sizing in three dimensions is accomplished with
+double deferred drawing. The maximal desired dimensions of the scene in
+each of the three dimensions can optionally be specified with the
+routine 
+void size3(picture pic=currentpicture, real x, real y=x, real z=y,
+          bool keepAspect=pic.keepAspect);
+ The resulting simplex linear programming problem is then solved to
+produce a 3D version of a frame (actually implemented as a 3D picture).
+The result is then fit with another application of deferred drawing to
+the viewport dimensions corresponding to the usual two-dimensional
+picture `size' parameters. The global pair `viewportmargin' may be used
+to add horizontal and vertical margins to the viewport dimensions.
+Alternatively, a minimum `viewportsize' may be specified.  A 3D picture
+`pic' can be explicitly fit to a 3D frame by calling 
+frame pic.fit3(projection P=currentprojection);
+ and then added to picture `dest' about `position' with 
+void add(picture dest=currentpicture, frame src, triple position=(0,0,0));
+
+   For convenience, the `three' module defines `O=(0,0,0)',
+`X=(1,0,0)', `Y=(0,1,0)', and `Z=(0,0,1)', along with a unitcircle in
+the XY plane:
+path3 unitcircle3=X..Y..-X..-Y..cycle;
+
+   A general (approximate) circle can be drawn perpendicular to the
+direction `normal' with the routine
+path3 circle(triple c, real r, triple normal=Z);
+
+   A circular arc centered at `c' with radius `r' from
+`c+r*dir(theta1,phi1)' to `c+r*dir(theta2,phi2)', drawing
+counterclockwise relative to the normal vector
+`cross(dir(theta1,phi1),dir(theta2,phi2))' if `theta2 > theta1' or if
+`theta2 == theta1' and `phi2 >= phi1', can be constructed with
+path3 arc(triple c, real r, real theta1, real phi1, real theta2, real phi2,
+          triple normal=O);
+ The normal must be explicitly specified if `c' and the endpoints are
+colinear. If `r' < 0, the complementary arc of radius `|r|' is
+constructed.  For convenience, an arc centered at `c' from triple `v1'
+to `v2' (assuming `|v2-c|=|v1-c|') in the direction CCW
+(counter-clockwise) or CW (clockwise) may also be constructed with
+path3 arc(triple c, triple v1, triple v2, triple normal=O,
+          bool direction=CCW);
+ When high accuracy is needed, the routines `Circle' and `Arc' defined
+in `graph3' may be used instead.  See *note GaussianSurface:: for an
+example of a three-dimensional circular arc.
+
+   The representation `O--O+u--O+u+v--O+v--cycle' of the plane passing
+through point `O' with normal `cross(u,v)' is returned by
+path3 plane(triple u, triple v, triple O=O);
+ A three-dimensional box with opposite vertices at triples `v1' and
+`v2' may be drawn with the function 
+path3[] box(triple v1, triple v2);
+ For example, a unit box is predefined as 
+path3[] unitbox=box(O,(1,1,1));
+ `Asymptote' also provides optimized definitions for the
+three-dimensional paths `unitsquare3' and `unitcircle3', along with the
+surfaces `unitdisk', `unitplane', `unitcube', `unitcylinder',
+`unitcone', `unitsolidcone', `unitfrustum(real t1, real t2)',
+`unitsphere', and `unithemisphere'.
+
+These projections to two dimensions are predefined:
+`oblique'
+
+`oblique(real angle)'
+     The point `(x,y,z)' is projected to `(x-0.5z,y-0.5z)'.  If an
+     optional real argument is given, the negative z axis is drawn at
+     this angle in degrees.  The projection `obliqueZ' is a synonym for
+     `oblique'.
+
+`obliqueX'
+
+`obliqueX(real angle)'
+     The point `(x,y,z)' is projected to `(y-0.5x,z-0.5x)'.  If an
+     optional real argument is given, the negative x axis is drawn at
+     this angle in degrees.
+
+`obliqueY'
+
+`obliqueY(real angle)'
+     The point `(x,y,z)' is projected to `(x+0.5y,z+0.5y)'.  If an
+     optional real argument is given, the positive y axis is drawn at
+     this angle in degrees.
+
+`orthographic(triple camera, triple up=Z, triple target=O,
+     real zoom=1, pair viewportshift=0, bool showtarget=true,
+     bool center=false)'
+     This projects from three to two dimensions using the view as seen
+     at a point infinitely far away in the direction `unit(camera)',
+     orienting the camera so that, if possible, the vector `up' points
+     upwards. Parallel lines are projected to parallel lines. The
+     bounding volume is expanded to include `target' if
+     `showtarget=true'.  If `center=true', the target will be adjusted
+     to the center of the bounding volume.
+
+`orthographic(real x, real y, real z, triple up=Z, triple target=O,
+     real zoom=1, pair viewportshift=0, bool showtarget=true,
+     bool center=false)'
+     This is equivalent to orthographic((x,y,z),up,target,zoom,viewportshift,showtarget,center)
+
+     The routine triple camera(real alpha, real beta);
+      can be used to compute the camera position with the x axis below
+     the horizontal at angle `alpha', the y axis below the horizontal
+     at angle `beta', and the z axis up.
+
+`perspective(triple camera, triple up=Z, triple target=O,
+     real zoom=1, real angle=0, pair viewportshift=0,
+     bool showtarget=true, bool autoadjust=true,
+     bool center=autoadjust)'
+     This projects from three to two dimensions, taking account of
+     perspective, as seen from the location `camera' looking at
+     `target', orienting the camera so that, if possible, the vector
+     `up' points upwards.  If `render=0', projection of
+     three-dimensional cubic Bezier splines is implemented by
+     approximating a two-dimensional nonuniform rational B-spline
+     (NURBS) with a two-dimensional Bezier curve containing additional
+     nodes and control points. If `autoadjust=true', the camera will
+     automatically be adjusted to lie outside the bounding volume for
+     all possible interactive rotations about `target'.  If
+     `center=true', the target will be adjusted to the center of the
+     bounding volume.
+
+`perspective(real x, real y, real z, triple up=Z, triple target=O,
+     real zoom=1, real angle=0, pair viewportshift=0,
+     bool showtarget=true, bool autoadjust=true,
+     bool center=autoadjust)'
+     This is equivalent to perspective((x,y,z),up,target,zoom,angle,viewportshift,showtarget,
+                 autoadjust,center)
+
+The default projection, `currentprojection', is initially set to
+`perspective(5,4,2)'.
+
+   We also define standard orthographic views used in technical drawing:
+projection LeftView=orthographic(-X,showtarget=true);
+projection RightView=orthographic(X,showtarget=true);
+projection FrontView=orthographic(-Y,showtarget=true);
+projection BackView=orthographic(Y,showtarget=true);
+projection BottomView=orthographic(-Z,showtarget=true);
+projection TopView=orthographic(Z,showtarget=true);
+ The function 
+void addViews(picture dest=currentpicture, picture src,
+              projection[][] views=SixViewsUS,
+              bool group=true, filltype filltype=NoFill);
+ adds to picture `dest' an array of views of picture `src' using the
+layout projection[][] `views'. The default layout `SixViewsUS' aligns
+the projection `FrontView' below `TopView' and above `BottomView', to
+the right of `LeftView' and left of `RightView' and `BackView'.  The
+predefined layouts are: 
+projection[][] ThreeViewsUS={{TopView},
+                             {FrontView,RightView}};
+
+projection[][] SixViewsUS={{null,TopView},
+                           {LeftView,FrontView,RightView,BackView},
+                           {null,BottomView}};
+
+projection[][] ThreeViewsFR={{RightView,FrontView},
+                             {null,TopView}};
+
+projection[][] SixViewsFR={{null,BottomView},
+                           {RightView,FrontView,LeftView,BackView},
+                           {null,TopView}};
+
+projection[][] ThreeViews={{FrontView,TopView,RightView}};
+
+projection[][] SixViews={{FrontView,TopView,RightView},
+                         {BackView,BottomView,LeftView}};
+
+   A triple or path3 can be projected to a pair or path, with
+`project(triple, projection P=currentprojection)' or `project(path3,
+projection P=currentprojection)'.
+
+   It is occasionally useful to be able to invert a projection, sending
+a pair `z' onto the plane perpendicular to `normal' and passing through
+`point': 
+triple invert(pair z, triple normal, triple point,
+              projection P=currentprojection);
+ A pair `z' on the projection plane can be inverted to a triple with
+the routine
+triple invert(pair z, projection P=currentprojection);
+ A pair direction `dir' on the projection plane can be inverted to a
+triple direction relative to a point `v' with the routine
+triple invert(pair dir, triple v, projection P=currentprojection).
+
+   Three-dimensional objects may be transformed with one of the
+following built-in transform3 types (the identity transformation is
+`identity4'):
+
+`shift(triple v)'
+     translates by the triple `v';
+
+`xscale3(real x)'
+     scales by `x' in the x direction;
+
+`yscale3(real y)'
+     scales by `y' in the y direction;
+
+`zscale3(real z)'
+     scales by `z' in the z direction;
+
+`scale3(real s)'
+     scales by `s' in the x, y, and z directions;
+
+`scale(real x, real y, real z)'
+     scales by `x' in the x direction, by `y' in the y direction, and
+     by `z' in the z direction; 
+
+`rotate(real angle, triple v)'
+     rotates by `angle' in degrees about an axis `v' through the origin;
+
+`rotate(real angle, triple u, triple v)'
+     rotates by `angle' in degrees about the axis `u--v';
+
+`reflect(triple u, triple v, triple w)'
+     reflects about the plane through `u', `v', and `w'.  
+
+   When not multiplied on the left by a transform3, three-dimensional
+TeX Labels are drawn as Bezier surfaces directly on the projection
+plane: 
+void label(picture pic=currentpicture, Label L, triple position,
+           align align=NoAlign, pen p=currentpen,
+           light light=nolight, string name="",
+           render render=defaultrender, interaction interaction=
+           settings.autobillboard ? Billboard : Embedded)
+ The optional `name' parameter is used as a prefix for naming the label
+patches in the PRC model tree.  The default interaction is `Billboard',
+which means that labels are rotated interactively so that they always
+face the camera.  The interaction `Embedded' means that the label
+interacts as a normal `3D' surface, as illustrated in the example
+`billboard.asy'.  Alternatively, a label can be transformed from the
+`XY' plane by an explicit transform3 or mapped to a specified
+two-dimensional plane with the predefined transform3 types `XY', `YZ',
+`ZX', `YX', `ZY', `ZX'. There are also modified versions of these
+transforms that take an optional argument `projection
+P=currentprojection' that rotate and/or flip the label so that it is
+more readable from the initial viewpoint.
+
+   A transform3 that projects in the direction `dir' onto the plane
+with normal `n' through point `O' is returned by
+transform3 planeproject(triple n, triple O=O, triple dir=n);
+ One can use 
+triple normal(path3 p);
+ to find the unit normal vector to a planar three-dimensional path `p'.
+As illustrated in the example `planeproject.asy', a transform3 that
+projects in the direction `dir' onto the plane defined by a planar path
+`p' is returned by
+transform3 planeproject(path3 p, triple dir=normal(p));
+
+   The functions 
+surface extrude(path p, triple axis=Z);
+surface extrude(Label L, triple axis=Z);
+ return the surface obtained by extruding path `p' or Label `L' along
+`axis'.
+
+   Three-dimensional versions of the path functions `length', `size',
+`point', `dir', `accel', `radius', `precontrol', `postcontrol',
+`arclength', `arctime', `reverse', `subpath', `intersect',
+`intersections', `intersectionpoint', `intersectionpoints', `min',
+`max', `cyclic', and `straight' are also defined.
+
+   The routine 
+real[][] intersections(path3 p, surface s, real fuzz=-1);
+ returns the intersection times of a path `p' with a surface `s' as a
+sorted array of real arrays of length 3, and 
+triple[] intersectionpoints(path3 p, surface s, real fuzz=-1);
+ returns the corresponding intersection points.  Here, the computations
+are performed to the absolute error specified by `fuzz', or if `fuzz <
+0', to machine precision.
+
+   Here is an example showing all five guide3 connectors:
+
+import graph3;
+
+size(200);
+
+currentprojection=orthographic(500,-500,500);
+
+triple[] z=new triple[10];
+
+z[0]=(0,100,0); z[1]=(50,0,0); z[2]=(180,0,0);
+
+for(int n=3; n <= 9; ++n)
+  z[n]=z[n-3]+(200,0,0);
+
+path3 p=z[0]..z[1]---z[2]::{Y}z[3]
+&z[3]..z[4]--z[5]::{Y}z[6]
+&z[6]::z[7]---z[8]..{Y}z[9];
+
+draw(p,grey+linewidth(4mm),currentlight);
+
+xaxis3(Label(XY()*"$x$",align=-3Y),red,above=true);
+yaxis3(Label(XY()*"$y$",align=-3X),red,above=true);
+
+
+
+Three-dimensional versions of bars or arrows can be drawn with one of
+the specifiers `None', `Blank', `BeginBar3', `EndBar3' (or equivalently
+`Bar3'), `Bars3', `BeginArrow3', `MidArrow3', `EndArrow3' (or
+equivalently `Arrow3'), `Arrows3', `BeginArcArrow3', `EndArcArrow3' (or
+equivalently `ArcArrow3'), `MidArcArrow3', and `ArcArrows3'.
+Three-dimensional bars accept the optional arguments `(real size=0,
+triple dir=O)'. If `size=O', the default bar length is used; if
+`dir=O', the bar is drawn perpendicular to the path and the initial
+viewing direction. The predefined three-dimensional arrowhead styles
+are `DefaultHead3', `HookHead3', `TeXHead3'.  Versions of the
+two-dimensional arrowheads lifted to three-dimensional space and
+aligned according to the initial viewpoint (or an optionally specified
+`normal' vector) are also defined: `DefaultHead2(triple normal=O)',
+`HookHead2(triple normal=O)', `TeXHead2(triple normal=O)'. These are
+illustrated in the example `arrows3.asy'.
+
+   Module `three' also defines the three-dimensional margins
+`NoMargin3', `BeginMargin3', `EndMargin3', `Margin3', `Margins3',
+`BeginPenMargin2', `EndPenMargin2', `PenMargin2', `PenMargins2',
+`BeginPenMargin3', `EndPenMargin3', `PenMargin3', `PenMargins3',
+`BeginDotMargin3', `EndDotMargin3', `DotMargin3', `DotMargins3',
+`Margin3', and `TrueMargin3'.
+
+   The routine
+void pixel(picture pic=currentpicture, triple v, pen p=currentpen,
+           real width=1);
+ can be used to draw on picture `pic' a pixel of width `width' at
+position `v' using pen `p'.
+
+   Further three-dimensional examples are provided in the files
+`near_earth.asy', `conicurv.asy', and (in the `animations'
+subdirectory) `cube.asy'.
+
+   Limited support for projected vector graphics (effectively
+three-dimensional nonrendered `PostScript') is available with the
+setting `render=0'. This currently only works for piecewise planar
+surfaces, such as those produced by the parametric `surface' routines
+in the `graph3' module. Surfaces produced by the `solids' package will
+also be properly rendered if the parameter `nslices' is sufficiently
+large.
+
+   In the module `bsp', hidden surface removal of planar pictures is
+implemented using a binary space partition and picture clipping.  A
+planar path is first converted to a structure `face' derived from
+`picture'. A `face' may be given to a two-dimensional drawing routine
+in place of any `picture' argument.  An array of such faces may then be
+drawn, removing hidden surfaces:
+void add(picture pic=currentpicture, face[] faces,
+         projection P=currentprojection);
+ Labels may be projected to two dimensions, using projection `P', onto
+the plane passing through point `O' with normal `cross(u,v)' by
+multiplying it on the left by the transform
+transform transform(triple u, triple v, triple O=O,
+                    projection P=currentprojection);
+
+   Here is an example that shows how a binary space partition may be
+used to draw a two-dimensional vector graphics projection of three
+orthogonal intersecting planes:
+
+size(6cm,0);
+import bsp;
+
+real u=2.5;
+real v=1;
+
+currentprojection=oblique;
+
+path3 y=plane((2u,0,0),(0,2v,0),(-u,-v,0));
+path3 l=rotate(90,Z)*rotate(90,Y)*y;
+path3 g=rotate(90,X)*rotate(90,Y)*y;
+
+face[] faces;
+filldraw(faces.push(y),project(y),yellow);
+filldraw(faces.push(l),project(l),lightgrey);
+filldraw(faces.push(g),project(g),green);
+
+add(faces);
+
+
+
+
+File: asymptote.info,  Node: obj,  Next: graph3,  Prev: three,  Up: Base modules
+
+8.30 `obj'
+==========
+
+This module allows one to construct surfaces from simple obj files, as
+illustrated in the example files `galleon.asy' and `triceratops.asy'.
+
+
+File: asymptote.info,  Node: graph3,  Next: grid3,  Prev: obj,  Up: Base modules
+
+8.31 `graph3'
+=============
+
+This module implements three-dimensional versions of the functions in
+`graph.asy'.  To draw an x axis in three dimensions, use the routine
+void xaxis3(picture pic=currentpicture, Label L="", axis axis=YZZero,
+            real xmin=-infinity, real xmax=infinity, pen p=currentpen,
+            ticks3 ticks=NoTicks3, arrowbar3 arrow=None, bool above=false);
+ Analogous routines `yaxis' and `zaxis' can be used to draw y and z
+axes in three dimensions.  There is also a routine for drawing all
+three axis:
+void axes3(picture pic=currentpicture,
+           Label xlabel="", Label ylabel="", Label zlabel="",
+           bool extend=false,
+           triple min=(-infinity,-infinity,-infinity),
+           triple max=(infinity,infinity,infinity),
+           pen p=currentpen, arrowbar3 arrow=None);
+
+The predefined three-dimensional axis types are
+axis YZEquals(real y, real z, triple align=O, bool extend=false);
+axis XZEquals(real x, real z, triple align=O, bool extend=false);
+axis XYEquals(real x, real y, triple align=O, bool extend=false);
+axis YZZero(triple align=O, bool extend=false);
+axis XZZero(triple align=O, bool extend=false);
+axis XYZero(triple align=O, bool extend=false);
+axis Bounds(int type=Both, int type2=Both, triple align=O, bool extend=false);
+ The optional `align' parameter to these routines can be used to
+specify the default axis and tick label alignments. The `Bounds' axis
+accepts two type parameters, each of which must be one of `Min', `Max',
+or `Both'. These parameters specify which of the four possible
+three-dimensional bounding box edges should be drawn.
+
+   The three-dimensional tick options are `NoTicks3', `InTicks',
+`OutTicks', and `InOutTicks'. These specify the tick directions for the
+`Bounds' axis type; other axis types inherit the direction that would
+be used for the `Bounds(Min,Min)' axis.
+
+   Here is an example of a helix and bounding box axes with ticks and
+axis labels, using orthographic projection:
+
+import graph3;
+
+size(0,200);
+size3(200,IgnoreAspect);
+
+currentprojection=orthographic(4,6,3);
+
+real x(real t) {return cos(2pi*t);}
+real y(real t) {return sin(2pi*t);}
+real z(real t) {return t;}
+
+path3 p=graph(x,y,z,0,2.7,operator ..);
+
+draw(p,Arrow3);
+
+scale(true);
+
+xaxis3(XZ()*"$x$",Bounds,red,InTicks(Label,2,2));
+yaxis3(YZ()*"$y$",Bounds,red,InTicks(beginlabel=false,Label,2,2));
+zaxis3(XZ()*"$z$",Bounds,red,InTicks);
+
+
+
+The next example illustrates three-dimensional x, y, and z axes,
+without autoscaling of the axis limits: 
+
+import graph3;
+
+size(0,200);
+size3(200,IgnoreAspect);
+
+currentprojection=perspective(5,2,2);
+
+scale(Linear,Linear,Log);
+
+xaxis3("$x$",0,1,red,OutTicks(2,2));
+yaxis3("$y$",0,1,red,OutTicks(2,2));
+zaxis3("$z$",1,30,red,OutTicks(beginlabel=false));
+
+
+
+One can also place ticks along a general three-dimensional axis: 
+
+import graph3;
+
+size(0,100);
+
+path3 g=yscale3(2)*unitcircle3;
+currentprojection=perspective(10,10,10);
+
+axis(Label("C",position=0,align=15X),g,InTicks(endlabel=false,8,end=false),
+     ticklocate(0,360,new real(real v) {
+         path3 h=O--max(abs(max(g)),abs(min(g)))*dir(90,v);
+         return intersect(g,h)[0];},
+       new triple(real t) {return cross(dir(g,t),Z);}));
+
+
+
+Surface plots of matrices and functions over the region `box(a,b)' in
+the XY plane are also implemented:
+surface surface(real[][] f, pair a, pair b, bool[][] cond={});
+surface surface(real[][] f, pair a, pair b, splinetype xsplinetype,
+                splinetype ysplinetype=xsplinetype, bool[][] cond={});
+surface surface(real[][] f, real[] x, real[] y,
+                splinetype xsplinetype=null, splinetype ysplinetype=xsplinetype,
+                bool[][] cond={})
+surface surface(triple[][] f, bool[][] cond={});
+surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx,
+                bool cond(pair z)=null);
+surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx,
+                splinetype xsplinetype, splinetype ysplinetype=xsplinetype,
+                bool cond(pair z)=null);
+surface surface(triple f(pair z), real[] u, real[] v,
+                splinetype[] usplinetype, splinetype[] vsplinetype=Spline,
+                bool cond(pair z)=null);
+surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu,
+                bool cond(pair z)=null);
+surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu,
+                splinetype[] usplinetype, splinetype[] vsplinetype=Spline,
+                bool cond(pair z)=null);
+ The final two versions draw parametric surfaces for a function f(u,v)
+over the parameter space `box(a,b)', as illustrated in the example
+`parametricsurface.asy'.  An optional splinetype `Spline' may be
+specified.  The boolean array or function `cond' can be used to control
+which surface mesh cells are actually drawn (by default all mesh cells
+over `box(a,b)' are drawn).  Surface lighting is illustrated in the
+example files `parametricsurface.asy' and `sinc.asy'.  Lighting can be
+disabled by setting `light=nolight', as in this example of a Gaussian
+surface:
+
+import graph3;
+
+size(200,0);
+
+currentprojection=perspective(10,8,4);
+
+real f(pair z) {return 0.5+exp(-abs(z)^2);}
+
+draw((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle);
+
+draw(arc(0.12Z,0.2,90,60,90,25),ArcArrow3);
+
+surface s=surface(f,(-1,-1),(1,1),nx=5,Spline);
+
+xaxis3(Label("$x$"),red,Arrow3);
+yaxis3(Label("$y$"),red,Arrow3);
+zaxis3(XYZero(extend=true),red,Arrow3);
+
+draw(s,lightgray,meshpen=black+thick(),nolight,render(merge=true));
+
+label("$O$",O,-Z+Y,red);
+
+
+A mesh can be drawn without surface filling by specifying `nullpen' for
+the surfacepen.
+
+   A vector field of `nu'\times`nv' arrows on a parametric surface `f'
+over `box(a,b)' can be drawn with the routine 
+picture vectorfield(path3 vector(pair v), triple f(pair z), pair a, pair b,
+                    int nu=nmesh, int nv=nu, bool truesize=false,
+                    real maxlength=truesize ? 0 : maxlength(f,a,b,nu,nv),
+                    bool cond(pair z)=null, pen p=currentpen,
+                    arrowbar3 arrow=Arrow3, margin3 margin=PenMargin3)
+ as illustrated in the examples `vectorfield3.asy' and
+`vectorfieldsphere.asy'.
+
+
+File: asymptote.info,  Node: grid3,  Next: solids,  Prev: graph3,  Up: Base modules
+
+8.32 `grid3'
+============
+
+This module, contributed by Philippe Ivaldi, can be used for drawing 3D
+grids. Here is an example (further examples can be found in `grid3.asy'
+and at `http://www.piprime.fr/files/asymptote/grid3/'):
+
+import grid3;
+
+size(8cm,0,IgnoreAspect);
+currentprojection=orthographic(0.5,1,0.5);
+
+scale(Linear, Linear, Log);
+
+limits((-2,-2,1),(0,2,100));
+
+grid3(XYZgrid);
+
+xaxis3(Label("$x$",position=EndPoint,align=S),Bounds(Min,Min),
+       OutTicks());
+yaxis3(Label("$y$",position=EndPoint,align=S),Bounds(Min,Min),OutTicks());
+zaxis3(Label("$z$",position=EndPoint,align=(-1,0.5)),Bounds(Min,Min),
+       OutTicks(beginlabel=false));
+
+
+
+
+File: asymptote.info,  Node: solids,  Next: tube,  Prev: grid3,  Up: Base modules
+
+8.33 `solids'
+=============
+
+This solid geometry package defines a structure `revolution' that can
+be used to fill and draw surfaces of revolution. The following example
+uses it to display the outline of a circular cylinder of radius 1 with
+axis `O--1.5unit(Y+Z)' with perspective projection:
+
+import solids;
+
+size(0,100);
+
+revolution r=cylinder(O,1,1.5,Y+Z);
+draw(r,heavygreen);
+
+
+
+Further illustrations are provided in the example files `cylinder.asy',
+`cones.asy', `hyperboloid.asy', and `torus.asy'.
+
+   The structure `skeleton' contains the three-dimensional wireframe
+used to visualize a volume of revolution:
+struct skeleton {
+  struct curve {
+    path3[] front;
+    path3[] back;
+  }
+  // transverse skeleton (perpendicular to axis of revolution)
+  curve transverse;
+  // longitudinal skeleton (parallel to axis of revolution)
+  curve longitudinal;
+}
+
+
+File: asymptote.info,  Node: tube,  Next: flowchart,  Prev: solids,  Up: Base modules
+
+8.34 `tube'
+===========
+
+This package extends the `tube' surfaces constructed in
+`three_arrows.asy' to arbitrary cross sections, colors, and spine
+transformations. The routine
+surface tube(path3 g, coloredpath section,
+             transform T(real)=new transform(real t) {return identity();},
+             real corner=1, real relstep=0);
+ draws a tube along `g' with cross section `section', after applying
+the transformation `T(t)' at `relpoint(g,t)'.  The parameter `corner'
+controls the number of elementary tubes at the angular points of `g'. A
+nonzero value of `relstep' specifies a fixed relative time step (in the
+sense of `relpoint(g,t)') to use in constructing elementary tubes along
+`g'.  The type `coloredpath' is a generalization of `path' to which a
+`path' can be cast: 
+struct coloredpath
+{
+  path p;
+  pen[] pens(real);
+  int colortype=coloredSegments;
+}
+ Here `p' defines the cross section and the method `pens(real t)'
+returns an array of pens (interpreted as a cyclic array) used for
+shading the tube patches at `relpoint(g,t)'. If
+`colortype=coloredSegments', the tube patches are filled as if each
+segment of the section was colored with the pen returned by `pens(t)',
+whereas if `colortype=coloredNodes', the tube components are vertex
+shaded as if the nodes of the section were colored.
+
+   A `coloredpath' can be constructed with one of the routines:
+coloredpath coloredpath(path p, pen[] pens(real),
+                        int colortype=coloredSegments);
+coloredpath coloredpath(path p, pen[] pens=new pen[] {currentpen},
+                        int colortype=coloredSegments);
+coloredpath coloredpath(path p, pen pen(real));
+ In the second case, the pens are independent of the relative time.  In
+the third case, the array of pens contains only one pen, which depends
+of the relative time.
+
+   The casting of `path' to `coloredpath' allows the use of a `path'
+instead of a `coloredpath'; in this case the shading behaviour is the
+default shading behavior for a surface.
+
+   An example of `tube' is provided in the file `trefoilknot.asy'.
+Further examples can be found at
+`http://www.piprime.fr/files/asymptote/tube/'.
+
+
+File: asymptote.info,  Node: flowchart,  Next: contour,  Prev: tube,  Up: Base modules
+
+8.35 `flowchart'
+================
+
+This package provides routines for drawing flowcharts. The primary
+structure is a `block', which represents a single block on the
+flowchart. The following eight functions return a position on the
+appropriate edge of the block, given picture transform `t':
+
+pair block.top(transform t=identity());
+pair block.left(transform t=identity());
+pair block.right(transform t=identity());
+pair block.bottom(transform t=identity());
+pair block.topleft(transform t=identity());
+pair block.topright(transform t=identity());
+pair block.bottomleft(transform t=identity());
+pair block.bottomright(transform t=identity());
+ 
+
+To obtain an arbitrary position along the boundary of the block in user
+coordinates, use:
+pair block.position(real x, transform t=identity());
+ 
+
+The center of the block in user coordinates is stored in `block.center'
+and the block size in `PostScript' coordinates is given by `block.size'.
+
+A frame containing the block is returned by
+frame block.draw(pen p=currentpen);
+ 
+
+   The following block generation routines accept a Label, string, or
+frame for their object argument:
+
+"rectangular block with an optional header (and padding `dx' around header and body):"
+     block rectangle(object header, object body, pair center=(0,0),
+                     pen headerpen=mediumgray, pen bodypen=invisible,
+                     pen drawpen=currentpen,
+                     real dx=3, real minheaderwidth=minblockwidth,
+                     real minheaderheight=minblockwidth,
+                     real minbodywidth=minblockheight,
+                     real minbodyheight=minblockheight);
+     block rectangle(object body, pair center=(0,0),
+                     pen fillpen=invisible, pen drawpen=currentpen,
+                     real dx=3, real minwidth=minblockwidth,
+                     real minheight=minblockheight);
+
+"parallelogram block:"
+     block parallelogram(object body, pair center=(0,0),
+                         pen fillpen=invisible, pen drawpen=currentpen,
+                         real dx=3, real slope=2,
+                         real minwidth=minblockwidth,
+                         real minheight=minblockheight);
+
+"diamond-shaped block:"
+     block diamond(object body, pair center=(0,0),
+                   pen fillpen=invisible, pen drawpen=currentpen,
+                   real ds=5, real dw=1,
+                   real height=20, real minwidth=minblockwidth,
+                   real minheight=minblockheight);
+
+"circular block:"
+     block circle(object body, pair center=(0,0), pen fillpen=invisible,
+                  pen drawpen=currentpen, real dr=3,
+                  real mindiameter=mincirclediameter);
+
+"rectangular block with rounded corners:"
+     block roundrectangle(object body, pair center=(0,0),
+                          pen fillpen=invisible, pen drawpen=currentpen,
+                          real ds=5, real dw=0, real minwidth=minblockwidth,
+                          real minheight=minblockheight);
+
+"rectangular block with beveled edges:"
+     block bevel(object body, pair center=(0,0), pen fillpen=invisible,
+                 pen drawpen=currentpen, real dh=5, real dw=5,
+                 real minwidth=minblockwidth, real minheight=minblockheight);
+
+
+   To draw paths joining the pairs in `point' with right-angled lines,
+use the routine: 
+path path(pair point[] ... flowdir dir[]);
+ The entries in `dir' identify whether successive segments between the
+pairs specified by `point' should be drawn in the `Horizontal' or
+`Vertical' direction.
+
+   Here is a simple flowchart example (see also the example
+`controlsystem.asy'):
+
+size(0,300);
+
+import flowchart;
+
+block block1=rectangle(Label("Example",magenta),
+		       pack(Label("Start:",heavygreen),"",Label("$A:=0$",blue),
+			    "$B:=1$"),(-0.5,3),palegreen,paleblue,red);
+block block2=diamond(Label("Choice?",blue),(0,2),palegreen,red);
+block block3=roundrectangle("Do something",(-1,1));
+block block4=bevel("Don't do something",(1,1));
+block block5=circle("End",(0,0));
+
+draw(block1);
+draw(block2);
+draw(block3);
+draw(block4);
+draw(block5);
+
+add(new void(picture pic, transform t) {
+    blockconnector operator --=blockconnector(pic,t);
+    //    draw(pic,block1.right(t)--block2.top(t));
+    block1--Right--Down--Arrow--block2;
+    block2--Label("Yes",0.5,NW)--Left--Down--Arrow--block3;
+    block2--Right--Label("No",0.5,NE)--Down--Arrow--block4;
+    block4--Down--Left--Arrow--block5;
+    block3--Down--Right--Arrow--block5;
+  });
+
+
+
+
+File: asymptote.info,  Node: contour,  Next: contour3,  Prev: flowchart,  Up: Base modules
+
+8.36 `contour'
+==============
+
+This package draws contour lines.  To construct contours corresponding
+to the values in a real array `c' for a function `f' on `box(a,b)', use
+the routine
+guide[][] contour(real f(real, real), pair a, pair b,
+                  real[] c, int nx=ngraph, int ny=nx,
+                  interpolate join=operator --, int subsample=1);
+ The integers `nx' and `ny' define the resolution.  The default
+resolution, `ngraph x ngraph' (here `ngraph' defaults to `100') can be
+increased for greater accuracy.  The default interpolation operator is
+`operator --' (linear). Spline interpolation (`operator ..') may
+produce smoother contours but it can also lead to overshooting.  The
+`subsample' parameter indicates the number of interior points that
+should be used to sample contours within each `1 x 1' box; the default
+value of `1' is usually sufficient.
+
+   To construct contours for an array of data values on a uniform
+two-dimensional lattice on `box(a,b)', use
+guide[][] contour(real[][] f, pair a, pair b, real[] c,
+                  interpolate join=operator --, int subsample=1);
+
+   To construct contours for an array of data values on a nonoverlapping
+regular mesh specified by the two-dimensional array `z',
+guide[][] contour(pair[][] z, real[][] f, real[] c,
+                  interpolate join=operator --, int subsample=1);
+
+ To construct contours for an array of values `f' specified at
+irregularly positioned points `z', use the routine
+guide[][] contour(pair[] z, real[] f, real[] c, interpolate join=operator --);
+ The contours themselves can be drawn with one of the routines
+void draw(picture pic=currentpicture, Label[] L=new Label[],
+          guide[][] g, pen p=currentpen);
+
+void draw(picture pic=currentpicture, Label[] L=new Label[],
+          guide[][] g, pen[] p);
+
+   The following simple example draws the contour at value `1' for the
+function z=x^2+y^2, which is a unit circle:
+
+import contour;
+size(75);
+
+real f(real a, real b) {return a^2+b^2;}
+draw(contour(f,(-1,-1),(1,1),new real[] {1}));
+
+
+
+The next example draws and labels multiple contours for the function
+z=x^2-y^2 with the resolution `100 x 100', using a dashed pen for
+negative contours and a solid pen for positive (and zero) contours:
+
+import contour;
+
+size(200);
+
+real f(real x, real y) {return x^2-y^2;}
+int n=10;
+real[] c=new real[n];
+for(int i=0; i < n; ++i) c[i]=(i-n/2)/n;
+
+pen[] p=sequence(new pen(int i) {
+    return (c[i] >= 0 ? solid : dashed)+fontsize(6pt);
+  },c.length);
+
+Label[] Labels=sequence(new Label(int i) {
+    return Label(c[i] != 0 ? (string) c[i] : "",Relative(unitrand()),(0,0),
+                 UnFill(1bp));
+  },c.length);
+
+draw(Labels,contour(f,(-1,-1),(1,1),c),p);
+
+
+
+The next example illustrates how contour lines can be drawn on color
+density images:
+
+import graph;
+import palette;
+import contour;
+
+size(10cm,10cm,IgnoreAspect);
+
+pair a=(0,0);
+pair b=(2pi,2pi);
+
+real f(real x, real y) {return cos(x)*sin(y);}
+
+int N=200;
+int Divs=10;
+int divs=2;
+
+defaultpen(1bp);
+pen Tickpen=black;
+pen tickpen=gray+0.5*linewidth(currentpen);
+pen[] Palette=BWRainbow();
+
+bounds range=image(f,Automatic,a,b,N,Palette);
+
+// Major contours
+
+real[] Cvals=uniform(range.min,range.max,Divs);
+draw(contour(f,a,b,Cvals,N,operator --),Tickpen);
+
+// Minor contours
+real[] cvals;
+for(int i=0; i < Cvals.length-1; ++i)
+  cvals.append(uniform(Cvals[i],Cvals[i+1],divs)[1:divs]);
+draw(contour(f,a,b,cvals,N,operator --),tickpen);
+
+xaxis("$x$",BottomTop,LeftTicks,above=true);
+yaxis("$y$",LeftRight,RightTicks,above=true);
+
+palette("$f(x,y)$",range,point(NW)+(0,0.5),point(NE)+(0,1),Top,Palette,
+        PaletteTicks(N=Divs,n=divs,Tickpen,tickpen));
+
+
+
+Finally, here is an example that illustrates the construction of
+contours from irregularly spaced data:
+
+import contour;
+
+size(200);
+
+int n=100;
+
+real f(real a, real b) {return a^2+b^2;}
+
+srand(1);
+
+real r() {return 1.1*(rand()/randMax*2-1);}
+
+pair[] points=new pair[n];
+real[] values=new real[n];
+
+for(int i=0; i < n; ++i) {
+  points[i]=(r(),r());
+  values[i]=f(points[i].x,points[i].y);
+}
+
+draw(contour(points,values,new real[]{0.25,0.5,1},operator ..),blue);
+
+
+
+In the above example, the contours of irregularly spaced data are
+constructed by first creating a triangular mesh from an array `z' of
+pairs:
+
+int[][] triangulate(pair[] z);
+
+size(200);
+int np=100;
+pair[] points;
+
+real r() {return 1.2*(rand()/randMax*2-1);}
+
+for(int i=0; i < np; ++i)
+  points.push((r(),r()));
+
+int[][] trn=triangulate(points);
+
+for(int i=0; i < trn.length; ++i) {
+  draw(points[trn[i][0]]--points[trn[i][1]]);
+  draw(points[trn[i][1]]--points[trn[i][2]]);
+  draw(points[trn[i][2]]--points[trn[i][0]]);
+}
+
+for(int i=0; i < np; ++i)
+  dot(points[i],red);
+
+
+
+The example `Gouraudcontour' illustrates how to produce color density
+images over such irregular triangular meshes.  `Asymptote' uses a
+robust version of Paul Bourke's Delaunay triangulation algorithm based
+on the public-domain exact arithmetic predicates written by Jonathan
+Shewchuk.
+
+
+File: asymptote.info,  Node: contour3,  Next: slopefield,  Prev: contour,  Up: Base modules
+
+8.37 `contour3'
+===============
+
+This package draws surfaces described as the null space of real-valued
+functions of (x,y,z) or real[][][] matrices.  Its usage is illustrated
+in the example file `magnetic.asy'.
+
+
+File: asymptote.info,  Node: slopefield,  Next: ode,  Prev: contour3,  Up: Base modules
+
+8.38 `slopefield'
+=================
+
+To draw a slope field for the differential equation dy/dx=f(x,y) (or
+dy/dx=f(x)), use:
+picture slopefield(real f(real,real), pair a, pair b,
+                   int nx=nmesh, int ny=nx,
+                   real tickfactor=0.5, pen p=currentpen,
+                   arrowbar arrow=None);
+ Here, the points `a' and `b' are the lower left and upper right
+corners of the rectangle in which the slope field is to be drawn, `nx'
+and `ny' are the respective number of ticks in the x and y directions,
+`tickfactor' is the fraction of the minimum cell dimension to use for
+drawing ticks, and `p' is the pen to use for drawing the slope fields.
+The return value is a picture that can be added to `currentpicture' via
+the `add(picture)' command.
+
+   The function 
+path curve(pair c, real f(real,real), pair a, pair b);
+ takes a point (`c') and a slope field-defining function `f' and
+returns, as a path, the curve passing through that point. The points
+`a' and `b' represent the rectangular boundaries over which the curve
+is interpolated.
+
+   Both `slopefield' and `curve' alternatively accept a function `real
+f(real)' that depends on x only, as seen in this example:
+
+import slopefield;
+
+size(200);
+
+real func(real x) {return 2x;}
+add(slopefield(func,(-3,-3),(3,3),20,Arrow));
+draw(curve((0,0),func,(-3,-3),(3,3)),red);
+
+
+
+
+File: asymptote.info,  Node: ode,  Prev: slopefield,  Up: Base modules
+
+8.39 `ode'
+==========
+
+The `ode' module, illustrated in the example `odetest.asy', implements
+a number of explicit numerical integration schemes for ordinary
+differential equations.
+
+
+File: asymptote.info,  Node: Options,  Next: Interactive mode,  Prev: Base modules,  Up: Top
+
+9 Command-line options
+**********************
+
+Type `asy -h' to see the full list of command-line options supported by
+`Asymptote':
+
+Usage: ../asy [options] [file ...]
+
+Options (negate by replacing - with -no):
+
+-V,-View               View output; command-line only
+-a,-align C|B|T|Z      Center, Bottom, Top, or Zero page alignment [C]
+-antialias n           Antialiasing width for rasterized output [2]
+-arcballradius pixels  Arcball radius [750]
+-auto3D                Automatically activate 3D scene [true]
+-autobillboard         3D labels always face viewer by default [true]
+-autoimport string     Module to automatically import
+-autoplain             Enable automatic importing of plain [true]
+-autoplay              Autoplay 3D animations [false]
+-autorotate            Enable automatic PDF page rotation [false]
+-axes3                 Show 3D axes in PDF output [true]
+-batchMask             Mask fpu exceptions in batch mode [false]
+-batchView             View output in batch mode [false]
+-bw                    Convert all colors to black and white [false]
+-cd directory          Set current directory; command-line only
+-cmyk                  Convert rgb colors to cmyk [false]
+-c,-command string     Command to autoexecute
+-compact               Conserve memory at the expense of speed [false]
+-d,-debug              Enable debugging messages [false]
+-divisor n             Garbage collect using purge(divisor=n) [2]
+-doubleclick ms        Emulated double-click timeout [200]
+-embed                 Embed rendered preview image [true]
+-exitonEOF             Exit interactive mode on EOF [true]
+-fitscreen             Fit rendered image to screen [true]
+-framedelay ms         Additional frame delay [0]
+-framerate frames/s    Animation speed [30]
+-globalwrite           Allow write to other directory [false]
+-gray                  Convert all colors to grayscale [false]
+-h,-help               Show summary of options; command-line only
+-historylines n        Retain n lines of history [1000]
+-iconify               Iconify rendering window [false]
+-inlineimage           Generate inline embedded image [false]
+-inlinetex             Generate inline TeX code [false]
+-interactiveMask       Mask fpu exceptions in interactive mode [true]
+-interactiveView       View output in interactive mode [true]
+-interactiveWrite      Write expressions entered at the prompt to stdout [true]
+-k,-keep               Keep intermediate files [false]
+-keepaux               Keep intermediate LaTeX .aux files [false]
+-level n               Postscript level [3]
+-l,-listvariables      List available global functions and variables [false]
+-localhistory          Use a local interactive history file [false]
+-loop                  Loop 3D animations [false]
+-m,-mask               Mask fpu exceptions; command-line only
+-maxtile pair          Maximum rendering tile size [(1024,768)]
+-maxviewport pair      Maximum viewport size [(2048,2048)]
+-multiline             Input code over multiple lines at the prompt [false]
+-multipleView          View output from multiple batch-mode files [false]
+-multisample n         Multisampling width for screen images [4]
+-offscreen             Use offscreen rendering [false]
+-O,-offset pair        PostScript offset [(0,0)]
+-f,-outformat format   Convert each output file to specified format
+-o,-outname name       Alternative output directory/filename
+-p,-parseonly          Parse file [false]
+-pdfreload             Automatically reload document in pdfviewer [false]
+-pdfreloaddelay usec   Delay before attempting initial pdf reload [750000]
+-position pair         Initial 3D rendering screen position [(0,0)]
+-prc                   Embed 3D PRC graphics in PDF output [true]
+-prompt string         Prompt [> ]
+-prompt2 string        Continuation prompt for multiline input  [..]
+-q,-quiet              Suppress welcome message [false]
+-render n              Render 3D graphics using n pixels per bp (-1=auto) [-1]
+-resizestep step       Resize step [1.2]
+-reverse               reverse 3D animations [false]
+-rgb                   Convert cmyk colors to rgb [false]
+-safe                  Disable system call [true]
+-scroll n              Scroll standard output n lines at a time [0]
+-spinstep deg/s        Spin speed [60]
+-svgemulation          Emulate unimplemented SVG shading [false]
+-tabcompletion         Interactive prompt auto-completion [true]
+-tex engine            latex|pdflatex|xelatex|tex|pdftex|context|none [latex]
+-thick                 Render thick 3D lines [true]
+-thin                  Render thin 3D lines [true]
+-threads               Use POSIX threads for 3D rendering [true]
+-toolbar               Show 3D toolbar in PDF output [true]
+-s,-translate          Show translated virtual machine code [false]
+-twice                 Run LaTeX twice (to resolve references) [false]
+-twosided              Use two-sided 3D lighting model for rendering [true]
+-u,-user string        General purpose user string
+-v,-verbose            Increase verbosity level (can specify multiple times) [0]
+-version               Show version; command-line only
+-wait                  Wait for child processes to finish before exiting [false]
+-warn string           Enable warning; command-line only
+-where                 Show where listed variables are declared [false]
+-zoomfactor factor     Zoom step factor [1.05]
+-zoomstep step         Mouse motion zoom step [0.1]
+
+ All boolean options can be negated by prepending `no' to the option
+name.
+
+   If no arguments are given, `Asymptote' runs in interactive mode
+(*note Interactive mode::). In this case, the default output file is
+`out.eps'.
+
+   If `-' is given as the file argument, `Asymptote' reads from
+standard input.
+
+   If multiple files are specified, they are treated as separate
+`Asymptote' runs.
+
+   If the string `autoimport' is nonempty, a module with this name is
+automatically imported for each run as the final step in loading module
+`plain'.
+
+   Default option values may be entered as `Asymptote' code in a
+configuration file named `config.asy' (or the file specified by the
+environment variable `ASYMPTOTE_CONFIG' or `-config' option).
+`Asymptote' will look for this file in its usual search path (*note
+Search paths::). Typically the configuration file is placed in the
+`.asy' directory in the user's home directory (`%USERPROFILE%\.asy'
+under `MSDOS').  Configuration variables are accessed using the long
+form of the option names:
+import settings;
+outformat="pdf";
+batchView=false;
+interactiveView=true;
+batchMask=false;
+interactiveMask=true;
+ Command-line options override these defaults. Most configuration
+variables may also be changed at runtime.  The advanced configuration
+variables `dvipsOptions', `hyperrefOptions', `convertOptions',
+`gsOptions', `psviewerOptions', `pdfviewerOptions', `pdfreloadOptions',
+`glOptions', and `dvisvgmOptions' allow specialized options to be
+passed as a string to the respective applications or libraries. The
+default value of `hyperrefOptions' is
+`setpagesize=false,unicode,pdfborder=0 0 0'.
+
+   If you insert
+import plain;
+settings.autoplain=true;
+ at the beginning of the configuration file, it can contain arbitrary
+`Asymptote' code.
+
+   The default output format is EPS for the (default) `latex' and `tex'
+tex engine and PDF for the `pdflatex', `xelatex', and `context' tex
+engines.  Alternative output formats may be produced using the `-f'
+option (or `outformat' setting).
+
+   To produce SVG output, you will need `dvisvgm' (version 0.8.7 or
+later) from `http://dvisvgm.sourceforge.net' and must use the `latex'
+or `tex' tex engine. You might need to adjust the configuration
+variable `libgs' to point to the location of your ghostscript library
+`libgs.so' (or to an empty string, depending on how `dvisvgm' was
+configured).
+
+   `Asymptote' can also produce any output format supported by the
+`ImageMagick' `convert' program (version 6.3.5 or later recommended; an
+`Invalid Parameter' error message indicates that the `MSDOS' utility
+`convert' is being used instead of the one that comes with
+`ImageMagick').  The optional setting `-render n' requests an output
+resolution of `n' pixels per `bp'. Antialiasing is controlled by the
+parameter `antialias', which by default specifies a sampling width of 2
+pixels.  To give other options to `convert', use the `convertOptions'
+setting or call convert manually. This example emulates how `Asymptote'
+produces antialiased `tiff' output at one pixel per `bp':
+asy -o - venn | convert -alpha Off -density 144x144 -geometry 50%x eps:- venn.tiff
+
+   If the option `-nosafe' is given, `Asymptote' runs in unsafe mode.
+This enables the `int system(string s)' and `int system(string[] s)'
+calls, allowing one to execute arbitrary shell commands. The default
+mode, `-safe', disables this call.
+
+   A `PostScript' offset may be specified as a pair (in `bp' units)
+with the `-O' option:
+asy -O 0,0 file
+ The default offset is zero. The default value of the page alignment
+setting `align' is `Center'.
+
+   The `-c' (`command') option may be used to execute arbitrary
+`Asymptote' code on the command line as a string. It is not necessary
+to terminate the string with a semicolon. Multiple `-c' options are
+executed in the order they are given. For example
+asy -c 2+2 -c "sin(1)" -c "size(100); draw(unitsquare)"
+ produces the output
+4
+0.841470984807897
+ and draws a unitsquare of size `100'.
+
+   The `-u' (`user') option may be used to specify arbitrary
+`Asymptote' settings on the command line as a string. It is not
+necessary to terminate the string with a semicolon. Multiple `-u'
+options are executed in the order they are given. Command-line code like
+`-u x=sqrt(2)' can be executed within a module like this:
+real x;
+usersetting();
+write(x);
+
+   When the `-l' (`listvariables') option is used with file arguments,
+only global functions and variables defined in the specified file(s)
+are listed.
+
+   Additional debugging output is produced with each additional `-v'
+option:
+`-v'
+     Display top-level module and final output file names.
+
+`-vv'
+     Also display imported and included module names and final `LaTeX'
+     and `dvips' processing information.
+
+`-vvv'
+     Also output `LaTeX' bidirectional pipe diagnostics.
+
+`-vvvv'
+     Also output knot guide solver diagnostics.
+
+`-vvvvv'
+     Also output `Asymptote' traceback diagnostics.
+
+
+File: asymptote.info,  Node: Interactive mode,  Next: GUI,  Prev: Options,  Up: Top
+
+10 Interactive mode
+*******************
+
+Interactive mode is entered by executing the command `asy' with no file
+arguments. When the `-multiline' option is disabled (the default), each
+line must be a complete `Asymptote' statement (unless explicitly
+continued by a final backslash character `\'); it is not necessary to
+terminate input lines with a semicolon.  If one assigns
+`settings.multiline=true', interactive code can be entered over
+multiple lines; in this mode, the automatic termination of interactive
+input lines by a semicolon is inhibited. Multiline mode is useful for
+cutting and pasting `Asymptote' code directly into the interactive
+input buffer.
+
+   Interactive mode can be conveniently used as a calculator:
+expressions entered at the interactive prompt (for which a
+corresponding `write' function exists) are automatically evaluated and
+written to `stdout'.  If the expression is non-writable, its type
+signature will be printed out instead. In either case, the expression
+can be referred to using the symbol `%' in the next line input at the
+prompt.  For example:
+> 2+3
+5
+> %*4
+20
+> 1/%
+0.05
+> sin(%)
+0.0499791692706783
+> currentpicture
+<picture currentpicture>
+> %.size(200,0)
+>
+
+   The `%' symbol, when used as a variable, is shorthand for the
+identifier `operator answer', which is set by the prompt after each
+written expression evaluation.
+
+   The following special commands are supported only in interactive mode
+and must be entered immediately after the prompt:
+
+`help'
+     view the manual;
+
+`erase'
+     erase `currentpicture'; 
+
+`reset'
+     reset the `Asymptote' environment to its initial state, except for
+     changes to the settings module (*note settings::), the current
+     directory (*note cd::), and breakpoints (*note Debugger::); 
+
+`input FILE'
+     does an interactive reset, followed by the command `include FILE'.
+     If the file name `FILE' contains nonalphanumeric characters,
+     enclose it with quotation marks.  A trailing semi-colon followed
+     by optional `Asymptote' commands may be entered on the same line.  
+
+`quit'
+     exit interactive mode (`exit' is a synonym; the abbreviation `q'
+     is also accepted unless there exists a top-level variable named
+     `q').  A history of the most recent 1000 (this number can be
+     changed with the `historylines' configuration variable) previous
+     commands will be retained in the file `.asy/history' in the user's
+     home directory (unless the command-line option `-localhistory' was
+     specified, in which case the history will be stored in the file
+     `.asy_history' in the current directory).
+
+
+   Typing `ctrl-C' interrupts the execution of `Asymptote' code and
+returns control to the interactive prompt.
+
+   Interactive mode is implemented with the GNU `readline' library,
+with command history and auto-completion. To customize the key
+bindings, see:
+`http://cnswww.cns.cwru.edu/php/chet/readline/readline.html'
+
+   The file `asymptote.py' in the `Asymptote' system directory provides
+an alternative way of entering `Asymptote' commands interactively,
+coupled with the full power of `Python'. Copy this file to your `Python
+path' and then execute from within `Python' the commands
+from asymptote import *
+g=asy()
+g.size(200)
+g.draw("unitcircle")
+g.send("draw(unitsquare)")
+g.fill("unitsquare, blue")
+g.clip("unitcircle")
+g.label("\"$O$\", (0,0), SW")
+
+
+File: asymptote.info,  Node: GUI,  Next: PostScript to Asymptote,  Prev: Interactive mode,  Up: Top
+
+11 Graphical User Interface
+***************************
+
+In the event that adjustments to the final figure are required, the
+preliminary Graphical User Interface (GUI) `xasy' included with
+`Asymptote' allows you to move graphical objects and draw new ones.
+The modified figure can then be saved as a normal `Asymptote' file.
+
+* Menu:
+
+* GUI installation::            Installing `xasy'
+* GUI usage::
+
+
+File: asymptote.info,  Node: GUI installation,  Next: GUI usage,  Up: GUI
+
+11.1 GUI installation
+=====================
+
+As `xasy' is written in the interactive scripting language `Python/TK',
+it requires `Python' (`http://www.python.org'), the `Python Imaging
+Library' (`http://www.pythonware.com/products/pil/'), and the `tkinter'
+package (included with `Python' under `Microsoft Windows') be
+installed. `Fedora Linux' users can either install `tkinter' with the
+commands
+yum install tkinter
+yum install tk-devel
+ or manually install the `tkinter', `tix', `tk', and `tk-devel'
+packages.
+
+   Pictures are deconstructed into the PNG image format, which supports
+full alpha channel transparency. Under `Microsoft Windows', this
+requires `Python 2.7.4' and the `Python Imaging Library':
+
+     `http://www.python.org/ftp/python/2.7.4/python-2.7.4.msi'
+
+     `http://effbot.org/downloads/PIL-1.1.7.win32-py2.7.exe'.
+   On `UNIX' systems, place
+`http://effbot.org/downloads/Imaging-1.1.7.tar.gz' in the `Asymptote'
+source directory, and type (as the root user):
+tar -zxf Imaging-1.1.7.tar.gz
+cd Imaging-1.1.7
+python setup.py install
+
+
+File: asymptote.info,  Node: GUI usage,  Prev: GUI installation,  Up: GUI
+
+11.2 GUI usage
+==============
+
+A wheel mouse is convenient for raising and lowering objects within
+`xasy', to expose the object to be moved. If a wheel mouse is not
+available, mouse `Button-2' can be used to repeatedly lower an object
+instead. When run from the command line, `xasy' accepts a command line
+option `-x n', which sets the initial magnification to `n'.
+
+   Deconstruction of compound objects (such as arrows) can be prevented
+by enclosing them within the commands
+void begingroup(picture pic=currentpicture);
+void endgroup(picture pic=currentpicture);
+ By default, the elements of a picture or frame will be grouped
+together on adding them to a picture. However, the elements of a frame
+added to another frame are not grouped together by default: their
+elements will be individually deconstructed (*note add::).
+
+
+File: asymptote.info,  Node: PostScript to Asymptote,  Next: Help,  Prev: GUI,  Up: Top
+
+12 `PostScript' to `Asymptote'
+******************************
+
+The excellent `PostScript' editor `pstoedit' (version 3.50 or later;
+available from `http://sourceforge.net/projects/pstoedit/') includes an
+`Asymptote' backend. Unlike virtually all other `pstoedit' backends,
+this driver includes native clipping, even-odd fill rule, `PostScript'
+subpath, and full image support. Here is an example: `asy -V
+/usr/local/share/doc/asymptote/examples/venn.asy'
+pstoedit -f asy venn.eps test.asy
+asy -V test
+
+If the line widths aren't quite correct, try giving `pstoedit' the
+`-dis' option.  If the fonts aren't typeset correctly, try giving
+`pstoedit' the `-dt' option.
+
+
+File: asymptote.info,  Node: Help,  Next: Debugger,  Prev: PostScript to Asymptote,  Up: Top
+
+13 Help
+*******
+
+A list of frequently asked questions (FAQ) is maintained at
+
+     `http://asymptote.sourceforge.net/FAQ'
+   Questions on installing and using `Asymptote' that are not addressed
+in the FAQ should be sent to the `Asymptote' forum:
+
+     `http://sourceforge.net/p/asymptote/discussion/409349'
+   Including an example that illustrates what you are trying to do will
+help you get useful feedback.  `LaTeX' problems can often be diagnosed
+with the `-vv' or `-vvv' command-line options.  Contributions in the
+form of patches or `Asymptote' modules can be posted here:
+
+     `http://sourceforge.net/tracker/?atid=685685&group_id=120000'
+   To receive announcements of upcoming releases, please subscribe to
+`Asymptote' at
+
+     `http://freshmeat.net/projects/asy'
+   If you find a bug in `Asymptote', please check (if possible) whether
+the bug is still present in the latest `Subversion' developmental code
+(*note Subversion::) before submitting a bug report. New bugs can be
+submitted using the Bug Tracking System at
+
+     `http://sourceforge.net/projects/asymptote'
+   To see if the bug has already been fixed, check bugs with Status
+`Closed' and recent lines in
+
+     `http://asymptote.sourceforge.net/ChangeLog'
+   `Asymptote' can be configured with the optional GNU library
+`libsigsegv', available from `http://libsigsegv.sourceforge.net', which
+allows one to distinguish user-generated `Asymptote' stack overflows
+(*note stack overflow::) from true segmentation faults (due to internal
+C++ programming errors; please submit the `Asymptote' code that
+generates such segmentation faults along with your bug report).
+
+
+File: asymptote.info,  Node: Debugger,  Next: Credits,  Prev: Help,  Up: Top
+
+14 Debugger
+***********
+
+Asymptote now includes a line-based (as opposed to code-based) debugger
+that can assist the user in following flow control. To set a break
+point in file `file' at line `line', use the command
+
+void stop(string file, int line, code s=quote{});
+ The optional argument `s' may be used to conditionally set the variable
+`ignore' in `plain_debugger.asy' to `true'. For example, the first 10
+instances of this breakpoint will be ignored (the variable `int
+count=0' is defined in `plain_debugger.asy'):
+stop("test",2,quote{ignore=(++count <= 10);});
+
+   To set a break point in file `file' at the first line containing the
+string `text', use
+
+void stop(string file, string text, code s=quote{});
+ To list all breakpoints, use: 
+void breakpoints();
+ To clear a breakpoint, use: 
+void clear(string file, int line);
+ To clear all breakpoints, use:
+void clear();
+
+   The following commands may be entered at the debugging prompt:
+
+``h''
+     help; 
+
+``c''
+     continue execution;
+
+``i''
+     step to the next instruction;
+
+``s''
+     step to the next executable line;
+
+``n''
+     step to the next executable line in the current file;
+
+``f''
+     step to the next file;
+
+``r''
+     return to the file associated with the most recent breakpoint;
+
+``t''
+     toggle tracing (`-vvvvv') mode;
+
+``q''
+     quit debugging and end execution;
+
+``x''
+     exit the debugger and run to completion.
+
+   Arbitrary `Asymptote' code may also be entered at the debugging
+prompt; however, since the debugger is implemented with `eval',
+currently only top-level (global) variables can be displayed or
+modified.
+
+   The debugging prompt may be entered manually with the call
+void breakpoint(code s=quote{});
+
+
+File: asymptote.info,  Node: Credits,  Next: Index,  Prev: Debugger,  Up: Top
+
+15 Acknowledgments
+******************
+
+Financial support for the development of `Asymptote' was generously
+provided by the Natural Sciences and Engineering Research Council of
+Canada, the Pacific Institute for Mathematical Sciences, and the
+University of Alberta Faculty of Science.
+
+   We also would like to acknowledge the previous work of John D. Hobby,
+author of the program `MetaPost' that inspired the development of
+`Asymptote', and Donald E. Knuth, author of TeX and `MetaFont' (on
+which `MetaPost' is based).
+
+   The authors of `Asymptote' are Andy Hammerlindl, John Bowman, and
+Tom Prince. Sean Healy designed the `Asymptote' logo. Other
+contributors include Michail Vidiassov, Radoslav Marinov, Orest Shardt,
+Chris Savage, Philippe Ivaldi, Olivier Guibe', Jacques Pienaar, Mark
+Henning, Steve Melenchuk, Martin Wiebusch, and Stefan Knorr.
+
+
+File: asymptote.info,  Node: Index,  Prev: Credits,  Up: Top
+
+Index
+*****
+
+
+* Menu:
+
+* !:                                     Arithmetic & logical.
+                                                              (line  68)
+* != <1>:                                Arithmetic & logical.
+                                                              (line  38)
+* !=:                                    Structures.          (line  52)
+* % <1>:                                 Interactive mode.    (line  17)
+* %:                                     Arithmetic & logical.
+                                                              (line  23)
+* %=:                                    Self & prefix operators.
+                                                              (line   6)
+* & <1>:                                 Arithmetic & logical.
+                                                              (line  56)
+* &:                                     Bezier curves.       (line  86)
+* &&:                                    Arithmetic & logical.
+                                                              (line  53)
+* * <1>:                                 Arithmetic & logical.
+                                                              (line  17)
+* *:                                     Pens.                (line  15)
+* **:                                    Arithmetic & logical.
+                                                              (line  31)
+* *=:                                    Self & prefix operators.
+                                                              (line   6)
+* + <1>:                                 Arithmetic & logical.
+                                                              (line  13)
+* +:                                     Pens.                (line  15)
+* ++:                                    Self & prefix operators.
+                                                              (line   6)
+* +=:                                    Self & prefix operators.
+                                                              (line   6)
+* -:                                     Arithmetic & logical.
+                                                              (line  14)
+* -- <1>:                                Self & prefix operators.
+                                                              (line   6)
+* --:                                    Tutorial.            (line 127)
+* ---:                                   Bezier curves.       (line  86)
+* -=:                                    Self & prefix operators.
+                                                              (line   6)
+* -c:                                    Options.             (line 180)
+* -l:                                    Options.             (line 199)
+* -u:                                    Options.             (line 190)
+* -V <1>:                                Tutorial.            (line  19)
+* -V:                                    Configuring.         (line   6)
+* ..:                                    Tutorial.            (line 127)
+* .asy:                                  Search paths.        (line  14)
+* /:                                     Arithmetic & logical.
+                                                              (line  20)
+* /=:                                    Self & prefix operators.
+                                                              (line   6)
+* 2D graphs:                             graph.               (line   6)
+* 3D graphs:                             graph3.              (line   6)
+* 3D grids:                              grid3.               (line   6)
+* 3D PostScript:                         three.               (line 594)
+* ::                                     Arithmetic & logical.
+                                                              (line  73)
+* :::                                    Bezier curves.       (line  70)
+* <:                                     Arithmetic & logical.
+                                                              (line  41)
+* <=:                                    Arithmetic & logical.
+                                                              (line  44)
+* == <1>:                                Arithmetic & logical.
+                                                              (line  37)
+* ==:                                    Structures.          (line  52)
+* >:                                     Arithmetic & logical.
+                                                              (line  50)
+* >=:                                    Arithmetic & logical.
+                                                              (line  47)
+* ?:                                     Arithmetic & logical.
+                                                              (line  73)
+* ^:                                     Arithmetic & logical.
+                                                              (line  28)
+* ^=:                                    Self & prefix operators.
+                                                              (line   6)
+* ^^:                                    Tutorial.            (line 134)
+* a4:                                    Configuring.         (line  61)
+* abort:                                 Data types.          (line 339)
+* abs <1>:                               Mathematical functions.
+                                                              (line  35)
+* abs:                                   Data types.          (line  62)
+* accel <1>:                             three.               (line 520)
+* accel:                                 Paths and guides.    (line 117)
+* access:                                Import.              (line   6)
+* acknowledgments:                       Credits.             (line   6)
+* aCos:                                  Mathematical functions.
+                                                              (line  20)
+* acos:                                  Mathematical functions.
+                                                              (line   6)
+* acosh:                                 Mathematical functions.
+                                                              (line   6)
+* add <1>:                               three.               (line 284)
+* add:                                   Frames and pictures. (line 196)
+* addViews:                              three.               (line 406)
+* adjust:                                Pens.                (line 115)
+* Ai:                                    Mathematical functions.
+                                                              (line  48)
+* Ai_deriv:                              Mathematical functions.
+                                                              (line  48)
+* Airy:                                  Mathematical functions.
+                                                              (line  48)
+* alias <1>:                             Arrays.              (line 181)
+* alias:                                 Structures.          (line  52)
+* align:                                 Options.             (line 174)
+* Align:                                 label.               (line  12)
+* all:                                   Arrays.              (line 329)
+* Allow:                                 Pens.                (line 327)
+* AND:                                   Arithmetic & logical.
+                                                              (line  80)
+* and:                                   Bezier curves.       (line  56)
+* angle:                                 Data types.          (line  70)
+* animate <1>:                           animation.           (line  12)
+* animate <2>:                           Files.               (line 154)
+* animate:                               Configuring.         (line  67)
+* animation:                             animation.           (line   6)
+* annotate:                              annotate.            (line   6)
+* antialias <1>:                         Options.             (line 145)
+* antialias:                             three.               (line 222)
+* append <1>:                            Arrays.              (line  39)
+* append:                                Files.               (line  36)
+* arc:                                   three.               (line 296)
+* Arc:                                   Paths and guides.    (line  32)
+* arc:                                   Paths and guides.    (line  22)
+* ArcArrow:                              draw.                (line  26)
+* ArcArrow3:                             three.               (line 561)
+* ArcArrows:                             draw.                (line  26)
+* ArcArrows3:                            three.               (line 561)
+* arclength <1>:                         three.               (line 520)
+* arclength:                             Paths and guides.    (line 144)
+* arcpoint:                              Paths and guides.    (line 154)
+* arctime <1>:                           three.               (line 520)
+* arctime:                               Paths and guides.    (line 148)
+* arguments:                             Default arguments.   (line   6)
+* arithmetic operators:                  Arithmetic & logical.
+                                                              (line   6)
+* array:                                 Arrays.              (line 122)
+* array iteration:                       Programming.         (line  33)
+* arrays:                                Arrays.              (line   6)
+* arrow:                                 label.               (line  71)
+* Arrow:                                 draw.                (line  26)
+* arrow:                                 Drawing commands.    (line  31)
+* arrow keys:                            Tutorial.            (line  37)
+* Arrow3:                                three.               (line 561)
+* Arrows:                                draw.                (line  26)
+* arrows:                                draw.                (line  26)
+* Arrows3:                               three.               (line 561)
+* as:                                    Import.              (line  68)
+* ascii:                                 Data types.          (line 286)
+* aSin:                                  Mathematical functions.
+                                                              (line  20)
+* asin:                                  Mathematical functions.
+                                                              (line   6)
+* asinh:                                 Mathematical functions.
+                                                              (line   6)
+* Aspect:                                Frames and pictures. (line  54)
+* assert:                                Data types.          (line 344)
+* assignment:                            Programming.         (line   8)
+* asy <1>:                               Import.              (line 102)
+* asy:                                   Data types.          (line 334)
+* asy-mode:                              Editing modes.       (line   6)
+* asy.vim:                               Editing modes.       (line  33)
+* asyinclude:                            LaTeX usage.         (line  46)
+* asymptote.sty:                         LaTeX usage.         (line   6)
+* asymptote.xml:                         Editing modes.       (line  49)
+* ASYMPTOTE_CONFIG:                      Options.             (line 116)
+* aTan:                                  Mathematical functions.
+                                                              (line  20)
+* atan:                                  Mathematical functions.
+                                                              (line   6)
+* atan2:                                 Mathematical functions.
+                                                              (line   6)
+* atanh:                                 Mathematical functions.
+                                                              (line   6)
+* atleast:                               Bezier curves.       (line  56)
+* attach <1>:                            graph.               (line 416)
+* attach <2>:                            LaTeX usage.         (line  51)
+* attach:                                Frames and pictures. (line 252)
+* autoadjust:                            three.               (line 372)
+* autoimport:                            Options.             (line 112)
+* automatic scaling:                     graph.               (line 682)
+* axialshade:                            fill.                (line  43)
+* axis <1>:                              graph3.              (line  67)
+* axis:                                  graph.               (line 879)
+* azimuth:                               Data types.          (line 126)
+* babel:                                 babel.               (line   6)
+* background color:                      Frames and pictures. (line 168)
+* BackView:                              three.               (line 399)
+* Bar:                                   draw.                (line  19)
+* Bar3:                                  three.               (line 561)
+* Bars:                                  draw.                (line  19)
+* Bars3:                                 three.               (line 561)
+* barsize:                               draw.                (line  19)
+* base modules:                          Base modules.        (line   6)
+* basealign:                             Pens.                (line 168)
+* baseline:                              label.               (line  91)
+* batch mode:                            Tutorial.            (line   6)
+* beep:                                  Data types.          (line 357)
+* BeginArcArrow:                         draw.                (line  26)
+* BeginArcArrow3:                        three.               (line 561)
+* BeginArrow:                            draw.                (line  26)
+* BeginArrow3:                           three.               (line 561)
+* BeginBar:                              draw.                (line  19)
+* BeginBar3:                             three.               (line 561)
+* BeginDotMargin:                        draw.                (line  42)
+* BeginDotMargin3:                       three.               (line 577)
+* BeginMargin:                           draw.                (line  42)
+* BeginMargin3:                          three.               (line 577)
+* BeginPenMargin:                        draw.                (line  42)
+* BeginPenMargin2:                       three.               (line 577)
+* BeginPenMargin3:                       three.               (line 577)
+* BeginPoint:                            label.               (line  56)
+* Bessel:                                Mathematical functions.
+                                                              (line  48)
+* bevel:                                 flowchart.           (line  75)
+* beveljoin:                             Pens.                (line 138)
+* Bezier curves:                         Bezier curves.       (line   6)
+* bezulate:                              three.               (line 104)
+* Bi:                                    Mathematical functions.
+                                                              (line  48)
+* Bi_deriv:                              Mathematical functions.
+                                                              (line  48)
+* Billboard:                             three.               (line 490)
+* binary:                                Files.               (line  75)
+* binary format:                         Files.               (line  75)
+* binary operators:                      Arithmetic & logical.
+                                                              (line   6)
+* binarytree:                            binarytree.          (line   6)
+* black stripes:                         three.               (line 222)
+* Blank:                                 draw.                (line  26)
+* block.bottom:                          flowchart.           (line  19)
+* block.bottomleft:                      flowchart.           (line  19)
+* block.bottomright:                     flowchart.           (line  19)
+* block.center:                          flowchart.           (line  26)
+* block.draw:                            flowchart.           (line  31)
+* block.left:                            flowchart.           (line  19)
+* block.position:                        flowchart.           (line  24)
+* block.right:                           flowchart.           (line  19)
+* block.top:                             flowchart.           (line  19)
+* block.topleft:                         flowchart.           (line  19)
+* block.topright:                        flowchart.           (line  19)
+* bool:                                  Data types.          (line  14)
+* bool3:                                 Data types.          (line  23)
+* boolean operators:                     Arithmetic & logical.
+                                                              (line   6)
+* Bottom:                                graph.               (line 134)
+* BottomTop:                             graph.               (line 140)
+* BottomView:                            three.               (line 399)
+* bounding box:                          Frames and pictures. (line 168)
+* Bounds:                                graph3.              (line  21)
+* box <1>:                               three.               (line 318)
+* box:                                   Frames and pictures. (line  22)
+* bp:                                    Tutorial.            (line  26)
+* brace:                                 Paths and guides.    (line  44)
+* break:                                 Programming.         (line  29)
+* breakpoints:                           Debugger.            (line  21)
+* brick:                                 Pens.                (line 251)
+* broken axis:                           graph.               (line 782)
+* bug reports:                           Help.                (line  23)
+* buildcycle:                            Paths and guides.    (line 260)
+* Button-1:                              GUI.                 (line   6)
+* Button-2:                              GUI.                 (line   6)
+* BWRainbow:                             palette.             (line  15)
+* BWRainbow2:                            palette.             (line  18)
+* C string:                              Data types.          (line 191)
+* CAD:                                   CAD.                 (line   6)
+* calculateTransform:                    Frames and pictures. (line 107)
+* camera:                                three.               (line 367)
+* casts:                                 Casts.               (line   6)
+* cbrt:                                  Mathematical functions.
+                                                              (line   6)
+* cd:                                    Files.               (line  25)
+* ceil:                                  Mathematical functions.
+                                                              (line  26)
+* center:                                three.               (line 351)
+* Center:                                label.               (line  61)
+* checker:                               Pens.                (line 251)
+* Chinese:                               unicode.             (line  12)
+* choose:                                Mathematical functions.
+                                                              (line  39)
+* Ci:                                    Mathematical functions.
+                                                              (line  48)
+* circle <1>:                            flowchart.           (line  64)
+* circle:                                three.               (line 292)
+* Circle:                                Paths and guides.    (line  17)
+* circle:                                Paths and guides.    (line  10)
+* circlebarframe:                        markers.             (line  18)
+* CJK:                                   unicode.             (line  12)
+* clamped:                               graph.               (line  37)
+* clear <1>:                             Debugger.            (line  23)
+* clear:                                 Files.               (line  92)
+* clip:                                  fill.                (line 115)
+* CLZ:                                   Arithmetic & logical.
+                                                              (line  80)
+* cm:                                    Tutorial.            (line  63)
+* cmd:                                   Configuring.         (line  34)
+* cmyk:                                  Pens.                (line  34)
+* colatitude:                            Data types.          (line 131)
+* color:                                 Pens.                (line  23)
+* coloredNodes:                          tube.                (line  25)
+* coloredpath:                           tube.                (line  18)
+* coloredSegments:                       tube.                (line  25)
+* colorless:                             Pens.                (line  54)
+* colors:                                Pens.                (line  51)
+* comma:                                 Files.               (line  61)
+* comma-separated-value mode:            Arrays.              (line 362)
+* command-line options <1>:              Options.             (line   6)
+* command-line options:                  Configuring.         (line  84)
+* comment character:                     Files.               (line  16)
+* compass directions:                    Tutorial.            (line 106)
+* Compiling from UNIX source:            Compiling from UNIX source.
+                                                              (line   6)
+* complement:                            Arrays.              (line 150)
+* concat:                                Arrays.              (line 177)
+* conditional <1>:                       Arithmetic & logical.
+                                                              (line  73)
+* conditional:                           Programming.         (line   8)
+* config:                                Options.             (line 116)
+* configuration file <1>:                Options.             (line 116)
+* configuration file:                    Configuring.         (line  23)
+* configuring:                           Configuring.         (line   6)
+* conj:                                  Data types.          (line  59)
+* constructors:                          Structures.          (line  91)
+* context:                               Options.             (line 145)
+* continue <1>:                          Debugger.            (line  31)
+* continue:                              Programming.         (line  29)
+* contour:                               contour.             (line   9)
+* contour3:                              contour3.            (line   6)
+* controls <1>:                          three.               (line   6)
+* controls:                              Bezier curves.       (line  45)
+* controlSpecifier:                      Paths and guides.    (line 393)
+* convert <1>:                           Options.             (line 145)
+* convert <2>:                           animation.           (line   6)
+* convert <3>:                           Files.               (line 154)
+* convert:                               Configuring.         (line  67)
+* convertOptions:                        Options.             (line 131)
+* Coons shading:                         fill.                (line  78)
+* copy:                                  Arrays.              (line 174)
+* Cos:                                   Mathematical functions.
+                                                              (line  20)
+* cos:                                   Mathematical functions.
+                                                              (line   6)
+* cosh:                                  Mathematical functions.
+                                                              (line   6)
+* cputime:                               Structures.          (line 169)
+* crop:                                  graph.               (line 637)
+* cropping graphs:                       graph.               (line 637)
+* cross <1>:                             graph.               (line 485)
+* cross:                                 Data types.          (line 169)
+* crossframe:                            markers.             (line  23)
+* crosshatch:                            Pens.                (line 267)
+* csv:                                   Arrays.              (line 362)
+* CTZ:                                   Arithmetic & logical.
+                                                              (line  80)
+* cubicroots:                            Arrays.              (line 318)
+* curl <1>:                              three.               (line   6)
+* curl:                                  Bezier curves.       (line  66)
+* curlSpecifier:                         Paths and guides.    (line 405)
+* currentpen:                            Pens.                (line   6)
+* currentprojection:                     three.               (line 396)
+* curve:                                 slopefield.          (line  20)
+* custom axis types:                     graph.               (line 144)
+* custom mark routine:                   graph.               (line 577)
+* custom tick locations:                 graph.               (line 249)
+* cut:                                   Paths and guides.    (line 242)
+* cycle <1>:                             three.               (line   6)
+* cycle:                                 Tutorial.            (line  75)
+* cyclic <1>:                            three.               (line 520)
+* cyclic <2>:                            Arrays.              (line  39)
+* cyclic:                                Paths and guides.    (line  76)
+* Cyrillic:                              unicode.             (line   7)
+* dashdotted:                            Pens.                (line  95)
+* dashed:                                Pens.                (line  95)
+* data types:                            Data types.          (line   6)
+* date:                                  Data types.          (line 298)
+* Debian:                                UNIX binary distributions.
+                                                              (line  19)
+* debugger:                              Debugger.            (line   6)
+* declaration:                           Programming.         (line   8)
+* deconstruct:                           GUI usage.           (line   6)
+* default arguments:                     Default arguments.   (line   6)
+* defaultformat:                         graph.               (line 175)
+* DefaultHead:                           draw.                (line  26)
+* DefaultHead3:                          three.               (line 561)
+* defaultpen:                            Pens.                (line  46)
+* defaultrender:                         three.               (line  47)
+* deferred drawing:                      simplex.             (line   6)
+* Degrees:                               Mathematical functions.
+                                                              (line  17)
+* degrees <1>:                           Mathematical functions.
+                                                              (line  17)
+* degrees:                               Data types.          (line  75)
+* delete <1>:                            Arrays.              (line  39)
+* delete:                                Files.               (line 149)
+* description:                           Description.         (line   6)
+* diagonal:                              Arrays.              (line 303)
+* diamond:                               flowchart.           (line  57)
+* dimension:                             Arrays.              (line 367)
+* dir <1>:                               three.               (line 520)
+* dir <2>:                               Paths and guides.    (line 100)
+* dir <3>:                               Data types.          (line  87)
+* dir:                                   Search paths.        (line  10)
+* direction specifier:                   Bezier curves.       (line   6)
+* directory:                             Files.               (line  25)
+* dirSpecifier:                          Paths and guides.    (line 387)
+* dirtime:                               Paths and guides.    (line 157)
+* display:                               Configuring.         (line  67)
+* do:                                    Programming.         (line  29)
+* DOSendl:                               Files.               (line  61)
+* DOSnewl:                               Files.               (line  61)
+* dot <1>:                               Arrays.              (line 259)
+* dot <2>:                               Data types.          (line 100)
+* dot:                                   draw.                (line  83)
+* DotMargin:                             draw.                (line  42)
+* DotMargin3:                            three.               (line 577)
+* DotMargins:                            draw.                (line  42)
+* DotMargins3:                           three.               (line 577)
+* dotted:                                Pens.                (line  95)
+* double deferred drawing:               three.               (line 269)
+* double precision:                      Files.               (line  75)
+* draw:                                  three.               (line 112)
+* Draw:                                  Frames and pictures. (line 147)
+* draw:                                  draw.                (line 110)
+* Draw:                                  draw.                (line  26)
+* draw:                                  Drawing commands.    (line  31)
+* drawing commands:                      Drawing commands.    (line   6)
+* drawline:                              math.                (line   9)
+* drawtree:                              drawtree.            (line   9)
+* dvips:                                 Configuring.         (line  67)
+* dvipsOptions:                          Options.             (line 131)
+* dvisvgm <1>:                           Options.             (line 150)
+* dvisvgm:                               Configuring.         (line  67)
+* dvisvgmOptions:                        Options.             (line 131)
+* E <1>:                                 Mathematical functions.
+                                                              (line  48)
+* E:                                     Tutorial.            (line 106)
+* Editing modes:                         Editing modes.       (line   6)
+* Ei:                                    Mathematical functions.
+                                                              (line  48)
+* ellipse <1>:                           Frames and pictures. (line  22)
+* ellipse:                               Paths and guides.    (line  39)
+* elliptic functions:                    Mathematical functions.
+                                                              (line  48)
+* else:                                  Programming.         (line   8)
+* emacs:                                 Editing modes.       (line   6)
+* embed:                                 embed.               (line   6)
+* Embedded:                              three.               (line 490)
+* empty:                                 Frames and pictures. (line   7)
+* EndArcArrow:                           draw.                (line  26)
+* EndArcArrow3:                          three.               (line 561)
+* EndArrow:                              draw.                (line  26)
+* EndArrow3:                             three.               (line 561)
+* EndBar:                                draw.                (line  19)
+* EndBar3:                               three.               (line 561)
+* EndDotMargin:                          draw.                (line  42)
+* EndDotMargin3:                         three.               (line 577)
+* endl:                                  Files.               (line  61)
+* EndMargin:                             draw.                (line  42)
+* EndMargin3:                            three.               (line 577)
+* EndPenMargin:                          draw.                (line  42)
+* EndPenMargin2:                         three.               (line 577)
+* EndPenMargin3:                         three.               (line 577)
+* EndPoint:                              label.               (line  56)
+* envelope:                              Frames and pictures. (line  22)
+* environment variables:                 Configuring.         (line  88)
+* eof <1>:                               Arrays.              (line 344)
+* eof:                                   Files.               (line  92)
+* eol <1>:                               Arrays.              (line 344)
+* eol:                                   Files.               (line  92)
+* EPS <1>:                               Options.             (line 145)
+* EPS:                                   label.               (line  79)
+* erase <1>:                             Frames and pictures. (line   7)
+* erase <2>:                             Data types.          (line 241)
+* erase:                                 Tutorial.            (line  37)
+* erf:                                   Mathematical functions.
+                                                              (line   6)
+* erfc:                                  Mathematical functions.
+                                                              (line   6)
+* error:                                 Files.               (line  16)
+* error bars:                            graph.               (line 533)
+* errorbars:                             graph.               (line 485)
+* eval:                                  Import.              (line  98)
+* evenodd <1>:                           Pens.                (line 152)
+* evenodd:                               Tutorial.            (line 148)
+* exit <1>:                              Debugger.            (line  57)
+* exit <2>:                              Interactive mode.    (line  59)
+* exit:                                  Data types.          (line 348)
+* exp:                                   Mathematical functions.
+                                                              (line   6)
+* expi:                                  Data types.          (line  83)
+* explicit:                              Casts.               (line   6)
+* explicit casts:                        Casts.               (line  21)
+* expm1:                                 Mathematical functions.
+                                                              (line   6)
+* exponential integral:                  Mathematical functions.
+                                                              (line  48)
+* extendcap:                             Pens.                (line 129)
+* extension <1>:                         MetaPost.            (line  10)
+* extension:                             Paths and guides.    (line 237)
+* external:                              embed.               (line  12)
+* extrude:                               three.               (line 514)
+* F:                                     Mathematical functions.
+                                                              (line  48)
+* fabs:                                  Mathematical functions.
+                                                              (line   6)
+* face:                                  three.               (line 602)
+* factorial:                             Mathematical functions.
+                                                              (line  39)
+* Fedora:                                UNIX binary distributions.
+                                                              (line  15)
+* feynman:                               feynman.             (line   6)
+* fft <1>:                               math.                (line  26)
+* fft:                                   Arrays.              (line 246)
+* FFTW:                                  Compiling from UNIX source.
+                                                              (line  58)
+* file <1>:                              Debugger.            (line  45)
+* file:                                  Files.               (line   6)
+* Fill:                                  Frames and pictures. (line 133)
+* fill <1>:                              fill.                (line  17)
+* fill:                                  draw.                (line 116)
+* Fill:                                  draw.                (line  26)
+* FillDraw:                              Frames and pictures. (line 123)
+* filldraw:                              fill.                (line  11)
+* FillDraw:                              draw.                (line  26)
+* filloutside:                           fill.                (line  27)
+* fillrule:                              Pens.                (line 152)
+* find <1>:                              Arrays.              (line 159)
+* find:                                  Data types.          (line 226)
+* firstcut:                              Paths and guides.    (line 252)
+* fit:                                   Frames and pictures. (line 103)
+* fit3:                                  three.               (line 282)
+* fixedscaling:                          Frames and pictures. (line  74)
+* floor:                                 Mathematical functions.
+                                                              (line  26)
+* flowchart:                             flowchart.           (line   6)
+* flush:                                 Files.               (line  61)
+* fmod:                                  Mathematical functions.
+                                                              (line   6)
+* font:                                  Pens.                (line 192)
+* font command:                          Pens.                (line 192)
+* fontcommand:                           Pens.                (line 207)
+* fontsize:                              Pens.                (line 178)
+* for:                                   Programming.         (line   8)
+* format <1>:                            Options.             (line 145)
+* format:                                Data types.          (line 269)
+* forum:                                 Help.                (line   6)
+* frame:                                 Frames and pictures. (line   7)
+* from:                                  Import.              (line  17)
+* FrontView:                             three.               (line 399)
+* function declarations:                 Functions.           (line  67)
+* function shading:                      fill.                (line 100)
+* Function shading:                      fill.                (line 100)
+* functions <1>:                         Mathematical functions.
+                                                              (line   6)
+* functions:                             Functions.           (line   6)
+* functionshade:                         fill.                (line 100)
+* gamma:                                 Mathematical functions.
+                                                              (line   6)
+* Gaussrand:                             Mathematical functions.
+                                                              (line  39)
+* geometry:                              geometry.            (line   6)
+* getc:                                  Files.               (line  30)
+* getpair:                               Files.               (line 117)
+* getreal:                               Files.               (line 117)
+* getstring:                             Files.               (line 117)
+* gettriple:                             Files.               (line 117)
+* glOptions <1>:                         Options.             (line 131)
+* glOptions:                             three.               (line 222)
+* GNU Scientific Library:                Mathematical functions.
+                                                              (line  48)
+* gouraudshade:                          fill.                (line  62)
+* Gradient:                              palette.             (line  25)
+* gradient shading:                      fill.                (line  32)
+* graph:                                 graph.               (line   6)
+* graph3:                                graph3.              (line   6)
+* graphic:                               label.               (line  79)
+* graphical user interface:              GUI.                 (line   6)
+* gray:                                  Pens.                (line  25)
+* Grayscale:                             palette.             (line   9)
+* grayscale:                             Pens.                (line  25)
+* grid <1>:                              graph.               (line 733)
+* grid:                                  Pens.                (line 251)
+* grid3:                                 grid3.               (line   6)
+* gs:                                    Configuring.         (line   6)
+* gsl:                                   Mathematical functions.
+                                                              (line  48)
+* GSL:                                   Compiling from UNIX source.
+                                                              (line  58)
+* gsOptions:                             Options.             (line 131)
+* GUI:                                   GUI.                 (line   6)
+* GUI installation:                      GUI installation.    (line   6)
+* GUI usage:                             GUI usage.           (line   6)
+* guide:                                 Paths and guides.    (line 314)
+* guide3:                                three.               (line   6)
+* hatch:                                 Pens.                (line 267)
+* height:                                LaTeX usage.         (line  51)
+* help <1>:                              Debugger.            (line  30)
+* help <2>:                              Help.                (line   6)
+* help:                                  Interactive mode.    (line  44)
+* Hermite:                               graph.               (line  37)
+* Hermite(splinetype splinetype:         graph.               (line  37)
+* hex <1>:                               Pens.                (line  60)
+* hex:                                   Data types.          (line 283)
+* hexidecimal <1>:                       Pens.                (line  59)
+* hexidecimal:                           Data types.          (line 283)
+* hidden surface removal:                three.               (line 602)
+* histogram:                             Mathematical functions.
+                                                              (line  39)
+* history <1>:                           Interactive mode.    (line  59)
+* history:                               Files.               (line 142)
+* historylines:                          Interactive mode.    (line  64)
+* HookHead:                              draw.                (line  26)
+* HookHead3:                             three.               (line 561)
+* Horizontal:                            flowchart.           (line  81)
+* hyperrefOptions:                       Options.             (line 131)
+* hypot:                                 Mathematical functions.
+                                                              (line   6)
+* I:                                     Mathematical functions.
+                                                              (line  48)
+* i_scaled:                              Mathematical functions.
+                                                              (line  48)
+* iconic:                                three.               (line 222)
+* identity <1>:                          Arrays.              (line 300)
+* identity <2>:                          Mathematical functions.
+                                                              (line   6)
+* identity:                              Transforms.          (line  24)
+* identity4:                             three.               (line 450)
+* if:                                    Programming.         (line   8)
+* IgnoreAspect:                          Frames and pictures. (line  58)
+* image:                                 palette.             (line  34)
+* ImageMagick <1>:                       Options.             (line 145)
+* ImageMagick <2>:                       animation.           (line   6)
+* ImageMagick:                           Configuring.         (line  67)
+* images:                                palette.             (line   6)
+* implicit casts:                        Casts.               (line   6)
+* implicit linear solver:                MetaPost.            (line  10)
+* implicit scaling:                      Implicit scaling.    (line   6)
+* import:                                Import.              (line  46)
+* inches:                                Tutorial.            (line  63)
+* incircle:                              Paths and guides.    (line 303)
+* include:                               Import.              (line 127)
+* including images:                      label.               (line  79)
+* increasing:                            math.                (line  59)
+* inf:                                   Data types.          (line  33)
+* inheritance:                           Structures.          (line 181)
+* initialized:                           Arrays.              (line  39)
+* initializers:                          Variable initializers.
+                                                              (line   6)
+* inline:                                LaTeX usage.         (line  51)
+* InOutTicks:                            graph3.              (line  35)
+* input <1>:                             Interactive mode.    (line  48)
+* input:                                 Files.               (line  10)
+* insert <1>:                            Arrays.              (line  39)
+* insert:                                Data types.          (line 237)
+* inside:                                Paths and guides.    (line 284)
+* inst:                                  Debugger.            (line  36)
+* installation:                          Installation.        (line   6)
+* int:                                   Data types.          (line  28)
+* integer division:                      Arithmetic & logical.
+                                                              (line   6)
+* interactive mode:                      Interactive mode.    (line   6)
+* interior:                              Paths and guides.    (line 280)
+* international characters:              unicode.             (line   6)
+* interp:                                Arithmetic & logical.
+                                                              (line  76)
+* interpolate:                           interpolate.         (line   6)
+* intersect <1>:                         three.               (line 520)
+* intersect <2>:                         math.                (line  13)
+* intersect:                             Paths and guides.    (line 186)
+* intersectionpoint <1>:                 three.               (line 520)
+* intersectionpoint <2>:                 math.                (line  17)
+* intersectionpoint:                     Paths and guides.    (line 229)
+* intersectionpoints <1>:                three.               (line 520)
+* intersectionpoints:                    Paths and guides.    (line 233)
+* intersections <1>:                     three.               (line 520)
+* intersections:                         Paths and guides.    (line 197)
+* InTicks:                               graph3.              (line  35)
+* intMax:                                Data types.          (line  28)
+* intMin:                                Data types.          (line  28)
+* inverse <1>:                           Arrays.              (line 306)
+* inverse:                               Transforms.          (line  16)
+* invert:                                three.               (line 440)
+* invisible:                             Pens.                (line  39)
+* isnan:                                 Data types.          (line  33)
+* J:                                     Mathematical functions.
+                                                              (line   6)
+* Japanese:                              unicode.             (line  12)
+* K:                                     Mathematical functions.
+                                                              (line  48)
+* k_scaled:                              Mathematical functions.
+                                                              (line  48)
+* Kate:                                  Editing modes.       (line  49)
+* KDE editor:                            Editing modes.       (line  49)
+* keepAspect <1>:                        LaTeX usage.         (line  51)
+* keepAspect:                            Frames and pictures. (line  54)
+* keyboard bindings::                    three.               (line 181)
+* keys:                                  Arrays.              (line  39)
+* keyword:                               Named arguments.     (line  37)
+* keyword-only:                          Named arguments.     (line  37)
+* keywords:                              Named arguments.     (line   6)
+* Korean:                                unicode.             (line  12)
+* label:                                 three.               (line 484)
+* Label <1>:                             graph.               (line 343)
+* Label:                                 label.               (line  14)
+* label:                                 clip.                (line  16)
+* Label:                                 draw.                (line  98)
+* labelpath:                             labelpath.           (line   6)
+* labelpath3:                            labelpath3.          (line   6)
+* labelx:                                graph.               (line 343)
+* labely:                                graph.               (line 343)
+* Landscape:                             Frames and pictures. (line  95)
+* lastcut:                               Paths and guides.    (line 256)
+* lasy-mode:                             Editing modes.       (line   6)
+* latex:                                 Options.             (line 145)
+* LaTeX fonts:                           Pens.                (line 192)
+* LaTeX usage:                           LaTeX usage.         (line   6)
+* latexmk:                               LaTeX usage.         (line  30)
+* latin1:                                latin1.              (line   6)
+* latitude:                              Data types.          (line 136)
+* latticeshade:                          fill.                (line  32)
+* layer:                                 Drawing commands.    (line  16)
+* leastsquares <1>:                      graph.               (line 901)
+* leastsquares:                          stats.               (line   6)
+* Left:                                  graph.               (line 284)
+* LeftRight:                             graph.               (line 290)
+* LeftSide:                              label.               (line  61)
+* LeftTicks:                             graph.               (line 161)
+* LeftView:                              three.               (line 399)
+* legend <1>:                            graph.               (line 432)
+* legend <2>:                            draw.                (line  64)
+* legend:                                Drawing commands.    (line  31)
+* Legendre:                              Mathematical functions.
+                                                              (line  48)
+* length <1>:                            three.               (line 520)
+* length <2>:                            Arrays.              (line  39)
+* length <3>:                            Paths and guides.    (line  67)
+* length:                                Data types.          (line  62)
+* letter:                                Configuring.         (line  61)
+* lexorder:                              math.                (line  68)
+* libgs <1>:                             Options.             (line 150)
+* libgs:                                 Configuring.         (line  67)
+* libm routines:                         Mathematical functions.
+                                                              (line   6)
+* libsigsegv <1>:                        Help.                (line  33)
+* libsigsegv:                            Functions.           (line  88)
+* limits:                                graph.               (line 637)
+* line:                                  Arrays.              (line 344)
+* line mode:                             Arrays.              (line 344)
+* Linear:                                graph.               (line 682)
+* linecap:                               Pens.                (line 129)
+* linejoin:                              Pens.                (line 138)
+* lineskip:                              Pens.                (line 178)
+* linetype:                              Pens.                (line 115)
+* linewidth:                             Pens.                (line 119)
+* locale:                                Data types.          (line 293)
+* Log:                                   graph.               (line 682)
+* log:                                   Mathematical functions.
+                                                              (line   6)
+* log-log graph:                         graph.               (line 713)
+* log10:                                 Mathematical functions.
+                                                              (line   6)
+* log1p:                                 Mathematical functions.
+                                                              (line   6)
+* log2 graph:                            graph.               (line 762)
+* logarithmic graph:                     graph.               (line 713)
+* logical operators:                     Arithmetic & logical.
+                                                              (line   6)
+* longdashdotted:                        Pens.                (line  95)
+* longdashed:                            Pens.                (line  95)
+* longitude:                             Data types.          (line 141)
+* loop:                                  Programming.         (line   8)
+* MacOS X binary distributions:          MacOS X binary distributions.
+                                                              (line   6)
+* makepen:                               Pens.                (line 300)
+* map:                                   Arrays.              (line 141)
+* Margin:                                draw.                (line  42)
+* Margin3:                               three.               (line 577)
+* margins:                               three.               (line 275)
+* Margins:                               draw.                (line  42)
+* Margins3:                              three.               (line 577)
+* mark:                                  graph.               (line 485)
+* markangle:                             markers.             (line  38)
+* marker:                                graph.               (line 485)
+* markers:                               markers.             (line   6)
+* marknodes:                             graph.               (line 485)
+* markuniform:                           graph.               (line 485)
+* mask:                                  Data types.          (line  33)
+* math:                                  math.                (line   6)
+* mathematical functions:                Mathematical functions.
+                                                              (line   6)
+* max <1>:                               three.               (line 520)
+* max <2>:                               Arrays.              (line 225)
+* max <3>:                               Frames and pictures. (line   7)
+* max:                                   Paths and guides.    (line 269)
+* maxbound:                              Data types.          (line 106)
+* maxtile:                               three.               (line 222)
+* maxtimes:                              Paths and guides.    (line 224)
+* maxviewport:                           three.               (line 222)
+* MetaPost:                              MetaPost.            (line   6)
+* MetaPost ... :                         Bezier curves.       (line  70)
+* MetaPost cutafter:                     Paths and guides.    (line 257)
+* MetaPost cutbefore:                    Paths and guides.    (line 253)
+* MetaPost pickup:                       Pens.                (line   6)
+* MetaPost whatever:                     MetaPost.            (line  10)
+* Microsoft Windows:                     Microsoft Windows.   (line   6)
+* MidArcArrow:                           draw.                (line  26)
+* MidArcArrow3:                          three.               (line 561)
+* MidArrow:                              draw.                (line  26)
+* MidArrow3:                             three.               (line 561)
+* midpoint:                              Paths and guides.    (line 171)
+* MidPoint:                              label.               (line  56)
+* min <1>:                               three.               (line 520)
+* min <2>:                               Arrays.              (line 218)
+* min <3>:                               Frames and pictures. (line   7)
+* min:                                   Paths and guides.    (line 265)
+* minbound:                              Data types.          (line 103)
+* minipage:                              label.               (line 118)
+* mintimes:                              Paths and guides.    (line 219)
+* miterjoin:                             Pens.                (line 138)
+* miterlimit:                            Pens.                (line 147)
+* mktemp:                                Files.               (line  44)
+* mm:                                    Tutorial.            (line  63)
+* mode:                                  Files.               (line  75)
+* monotonic:                             graph.               (line  37)
+* mouse:                                 GUI.                 (line   6)
+* mouse bindings:                        three.               (line 149)
+* Move:                                  Pens.                (line 339)
+* MoveQuiet:                             Pens.                (line 345)
+* multisample:                           three.               (line 140)
+* N:                                     Tutorial.            (line 106)
+* name:                                  Files.               (line  88)
+* named arguments:                       Named arguments.     (line   6)
+* natural:                               graph.               (line  37)
+* new <1>:                               Arrays.              (line 109)
+* new:                                   Structures.          (line   6)
+* newframe:                              Frames and pictures. (line   7)
+* newl:                                  Files.               (line  61)
+* newton:                                Mathematical functions.
+                                                              (line  66)
+* next:                                  Debugger.            (line  42)
+* NFSS:                                  Pens.                (line 192)
+* nobasealign:                           Pens.                (line 168)
+* NoFill <1>:                            Frames and pictures. (line 141)
+* NoFill:                                draw.                (line  26)
+* NoMargin:                              draw.                (line  42)
+* NoMargin3:                             three.               (line 577)
+* none:                                  Files.               (line  61)
+* None:                                  draw.                (line  19)
+* normal:                                three.               (line 506)
+* nosafe:                                Options.             (line 169)
+* NOT:                                   Arithmetic & logical.
+                                                              (line  80)
+* notaknot:                              graph.               (line  37)
+* NoTicks:                               graph.               (line 161)
+* NoTicks3:                              graph3.              (line  35)
+* null:                                  Structures.          (line   6)
+* nullpen <1>:                           Frames and pictures. (line 127)
+* nullpen:                               label.               (line  14)
+* NURBS:                                 three.               (line 376)
+* O:                                     three.               (line 287)
+* obj:                                   obj.                 (line   9)
+* oblique:                               three.               (line 332)
+* obliqueX:                              three.               (line 340)
+* obliqueY:                              three.               (line 347)
+* obliqueZ:                              three.               (line 332)
+* ode:                                   ode.                 (line   9)
+* offset <1>:                            Options.             (line 174)
+* offset:                                Pens.                (line 115)
+* OmitTick:                              graph.               (line 239)
+* OmitTickInterval:                      graph.               (line 239)
+* OmitTickIntervals:                     graph.               (line 239)
+* opacity:                               Pens.                (line 222)
+* open:                                  Files.               (line  12)
+* OpenGL:                                three.               (line 140)
+* operator:                              User-defined operators.
+                                                              (line   6)
+* operator --:                           graph.               (line  31)
+* operator ..:                           graph.               (line  34)
+* operator answer:                       Interactive mode.    (line  37)
+* operator cast:                         Casts.               (line  30)
+* operator ecast:                        Casts.               (line  57)
+* operator init <1>:                     Structures.          (line 134)
+* operator init:                         Variable initializers.
+                                                              (line   6)
+* operators:                             Operators.           (line   6)
+* options:                               Options.             (line   6)
+* OR:                                    Arithmetic & logical.
+                                                              (line  80)
+* orientation:                           Frames and pictures. (line  95)
+* orthographic:                          three.               (line 351)
+* outformat:                             three.               (line 140)
+* outprefix:                             Frames and pictures. (line  83)
+* output <1>:                            Options.             (line 145)
+* output:                                Files.               (line  36)
+* OutTicks:                              graph3.              (line  35)
+* overloading functions:                 Functions.           (line  44)
+* overwrite:                             Pens.                (line 324)
+* P:                                     Mathematical functions.
+                                                              (line  48)
+* pack:                                  label.               (line 101)
+* packing:                               Rest arguments.      (line  30)
+* pair <1>:                              Data types.          (line  43)
+* pair:                                  Tutorial.            (line  51)
+* pairs:                                 Arrays.              (line 242)
+* paperheight:                           Configuring.         (line  61)
+* papertype:                             Configuring.         (line  61)
+* paperwidth:                            Configuring.         (line  61)
+* parallelogram:                         flowchart.           (line  50)
+* parametric surface:                    graph3.              (line 101)
+* parametrized curve:                    graph.               (line 637)
+* partialsum:                            math.                (line  53)
+* patch-dependent colors:                three.               (line  81)
+* path <1>:                              flowchart.           (line  81)
+* path <2>:                              three.               (line  43)
+* path:                                  Paths and guides.    (line   7)
+* path markers:                          graph.               (line 485)
+* path3:                                 three.               (line   6)
+* path[]:                                Tutorial.            (line 134)
+* patterns <1>:                          patterns.            (line   6)
+* patterns:                              Pens.                (line 238)
+* PDF:                                   Options.             (line 145)
+* pdflatex:                              Options.             (line 145)
+* pdfreloadOptions:                      Options.             (line 131)
+* pdfviewer:                             Configuring.         (line   6)
+* pdfviewerOptions:                      Options.             (line 131)
+* pen:                                   Pens.                (line   6)
+* PenMargin:                             draw.                (line  42)
+* PenMargin2:                            three.               (line 577)
+* PenMargin3:                            three.               (line 577)
+* PenMargins:                            draw.                (line  42)
+* PenMargins2:                           three.               (line 577)
+* PenMargins3:                           three.               (line 577)
+* periodic:                              graph.               (line  37)
+* perl:                                  LaTeX usage.         (line  30)
+* perpendicular:                         geometry.            (line   6)
+* perspective:                           three.               (line 376)
+* picture:                               Frames and pictures. (line  35)
+* picture alignment:                     Frames and pictures. (line 209)
+* piecewisestraight:                     Paths and guides.    (line  83)
+* pixel:                                 three.               (line 584)
+* Pl:                                    Mathematical functions.
+                                                              (line  48)
+* plain:                                 plain.               (line   6)
+* planar:                                three.               (line  89)
+* plane:                                 three.               (line 314)
+* planeproject:                          three.               (line 503)
+* point <1>:                             three.               (line 520)
+* point:                                 Paths and guides.    (line  86)
+* polar:                                 Data types.          (line 121)
+* polargraph:                            graph.               (line  90)
+* polygon:                               graph.               (line 485)
+* pop:                                   Arrays.              (line  39)
+* Portrait:                              Frames and pictures. (line  95)
+* postcontrol <1>:                       three.               (line 520)
+* postcontrol:                           Paths and guides.    (line 137)
+* postfix operators:                     Self & prefix operators.
+                                                              (line  19)
+* postscript:                            Frames and pictures. (line 271)
+* PostScript fonts:                      Pens.                (line 210)
+* PostScript subpath:                    Tutorial.            (line 134)
+* pow10:                                 Mathematical functions.
+                                                              (line   6)
+* prc:                                   three.               (line 243)
+* precision:                             Files.               (line  92)
+* precontrol <1>:                        three.               (line 520)
+* precontrol:                            Paths and guides.    (line 130)
+* prefix operators:                      Self & prefix operators.
+                                                              (line   6)
+* private:                               Structures.          (line   6)
+* programming:                           Programming.         (line   6)
+* pstoedit:                              PostScript to Asymptote.
+                                                              (line   6)
+* psview:                                Microsoft Windows.   (line  16)
+* psviewer:                              Configuring.         (line   6)
+* psviewerOptions:                       Options.             (line 131)
+* pt:                                    Tutorial.            (line  63)
+* public:                                Structures.          (line   6)
+* push:                                  Arrays.              (line  39)
+* Python usage:                          Interactive mode.    (line  80)
+* quadraticroots:                        Arrays.              (line 309)
+* quarticroots:                          math.                (line  22)
+* quick reference:                       Description.         (line  80)
+* quit <1>:                              Debugger.            (line  54)
+* quit <2>:                              Interactive mode.    (line  59)
+* quit:                                  Tutorial.            (line  37)
+* quote:                                 Import.              (line 116)
+* quotient:                              Arithmetic & logical.
+                                                              (line   6)
+* RadialShade:                           Frames and pictures. (line 159)
+* radialshade:                           fill.                (line  51)
+* RadialShadeDraw:                       Frames and pictures. (line 163)
+* radians:                               Mathematical functions.
+                                                              (line  17)
+* radius <1>:                            three.               (line 520)
+* radius:                                Paths and guides.    (line 126)
+* Rainbow:                               palette.             (line  12)
+* rand:                                  Mathematical functions.
+                                                              (line  39)
+* randMax:                               Mathematical functions.
+                                                              (line  39)
+* read:                                  Arrays.              (line 385)
+* reading:                               Files.               (line  12)
+* reading string arrays:                 Arrays.              (line 354)
+* readline:                              Files.               (line 134)
+* real:                                  Data types.          (line  33)
+* realDigits:                            Data types.          (line  33)
+* realEpsilon:                           Data types.          (line  33)
+* realMax:                               Data types.          (line  33)
+* realMin:                               Data types.          (line  33)
+* realmult:                              Data types.          (line  97)
+* rectangle:                             flowchart.           (line  37)
+* recursion:                             Functions.           (line  88)
+* reference:                             Description.         (line  80)
+* reflect:                               Transforms.          (line  51)
+* Relative:                              label.               (line  51)
+* relpoint:                              Paths and guides.    (line 167)
+* reltime:                               Paths and guides.    (line 163)
+* remainder:                             Mathematical functions.
+                                                              (line   6)
+* rename:                                Files.               (line 151)
+* render <1>:                            Options.             (line 145)
+* render:                                three.               (line  47)
+* replace:                               Data types.          (line 254)
+* resetdefaultpen:                       Pens.                (line 353)
+* rest arguments:                        Rest arguments.      (line   6)
+* restore:                               Frames and pictures. (line 265)
+* restricted:                            Structures.          (line   6)
+* return:                                Debugger.            (line  48)
+* reverse <1>:                           three.               (line 520)
+* reverse <2>:                           Arrays.              (line 146)
+* reverse <3>:                           Paths and guides.    (line 174)
+* reverse:                               Data types.          (line 250)
+* rewind:                                Files.               (line  92)
+* rfind:                                 Data types.          (line 231)
+* rgb:                                   Pens.                (line  30)
+* Riemann zeta function:                 Mathematical functions.
+                                                              (line  48)
+* Right:                                 graph.               (line 287)
+* RightSide:                             label.               (line  61)
+* RightTicks:                            graph.               (line 161)
+* RightView:                             three.               (line 399)
+* rotate:                                three.               (line 471)
+* Rotate:                                label.               (line  36)
+* Rotate(pair z):                        label.               (line  39)
+* round:                                 Mathematical functions.
+                                                              (line  26)
+* roundcap:                              Pens.                (line 129)
+* roundedpath:                           roundedpath.         (line   6)
+* roundjoin:                             Pens.                (line 138)
+* roundrectangle:                        flowchart.           (line  69)
+* RPM:                                   UNIX binary distributions.
+                                                              (line   6)
+* runtime imports:                       Import.              (line  98)
+* Russian:                               unicode.             (line   7)
+* S:                                     Tutorial.            (line 106)
+* safe:                                  Options.             (line 169)
+* save:                                  Frames and pictures. (line 262)
+* saveline:                              Files.               (line 134)
+* scale:                                 three.               (line 470)
+* Scale:                                 graph.               (line 698)
+* scale <1>:                             graph.               (line 682)
+* scale <2>:                             Transforms.          (line  39)
+* scale:                                 Pens.                (line 115)
+* Scale:                                 label.               (line  45)
+* scale3:                                three.               (line 467)
+* scaled graph:                          graph.               (line 663)
+* scientific graph:                      graph.               (line 397)
+* scroll:                                Files.               (line 108)
+* search:                                Arrays.              (line 164)
+* search paths:                          Search paths.        (line   6)
+* Seascape:                              Frames and pictures. (line 100)
+* secondary axis:                        graph.               (line 812)
+* secondaryX:                            graph.               (line 812)
+* secondaryY:                            graph.               (line 812)
+* seconds:                               Data types.          (line 306)
+* seek:                                  Files.               (line  92)
+* seekeof:                               Files.               (line  92)
+* segment:                               math.                (line  50)
+* segmentation fault:                    Help.                (line  33)
+* self operators:                        Self & prefix operators.
+                                                              (line   6)
+* sequence:                              Arrays.              (line 128)
+* settings <1>:                          Options.             (line 116)
+* settings:                              Configuring.         (line  23)
+* sgn:                                   Mathematical functions.
+                                                              (line  26)
+* shading:                               fill.                (line  32)
+* shift <1>:                             three.               (line 455)
+* shift:                                 Transforms.          (line  27)
+* Shift:                                 label.               (line  33)
+* shiftless:                             Transforms.          (line  53)
+* shipout:                               Frames and pictures. (line  83)
+* showtarget:                            three.               (line 351)
+* Si:                                    Mathematical functions.
+                                                              (line  48)
+* side:                                  Paths and guides.    (line 299)
+* signedint:                             Files.               (line  75)
+* SimpleHead:                            draw.                (line  26)
+* simplex:                               simplex.             (line   6)
+* simpson:                               Mathematical functions.
+                                                              (line  82)
+* Sin:                                   Mathematical functions.
+                                                              (line  20)
+* sin:                                   Mathematical functions.
+                                                              (line   6)
+* single precision:                      Files.               (line  75)
+* singleint:                             Files.               (line  75)
+* singlereal:                            Files.               (line  75)
+* sinh:                                  Mathematical functions.
+                                                              (line   6)
+* SixViews:                              three.               (line 414)
+* SixViewsFR:                            three.               (line 414)
+* SixViewsUS:                            three.               (line 414)
+* size <1>:                              Options.             (line 145)
+* size <2>:                              three.               (line 520)
+* size <3>:                              Frames and pictures. (line  43)
+* size:                                  Paths and guides.    (line  72)
+* size3:                                 three.               (line 272)
+* slant:                                 Transforms.          (line  45)
+* Slant:                                 label.               (line  42)
+* sleep:                                 Data types.          (line 351)
+* slice:                                 Paths and guides.    (line 242)
+* slices:                                Slices.              (line   6)
+* slide:                                 slide.               (line   6)
+* slope:                                 math.                (line  44)
+* slopefield:                            slopefield.          (line   6)
+* sncndn:                                Mathematical functions.
+                                                              (line  48)
+* solid:                                 Pens.                (line  95)
+* solids:                                solids.              (line   9)
+* solve:                                 Arrays.              (line 278)
+* sort:                                  Arrays.              (line 184)
+* Spline <1>:                            graph3.              (line 101)
+* Spline:                                graph.               (line  34)
+* split:                                 Data types.          (line 263)
+* sqrt:                                  Mathematical functions.
+                                                              (line   6)
+* squarecap:                             Pens.                (line 129)
+* srand:                                 Mathematical functions.
+                                                              (line  39)
+* stack overflow <1>:                    Help.                (line  33)
+* stack overflow:                        Functions.           (line  88)
+* static:                                Static.              (line   6)
+* stats:                                 stats.               (line   6)
+* stdin:                                 Files.               (line  48)
+* stdout:                                Files.               (line  48)
+* step:                                  Debugger.            (line  39)
+* stickframe:                            markers.             (line  16)
+* stop:                                  Debugger.            (line  10)
+* straight:                              three.               (line 520)
+* Straight:                              graph.               (line  31)
+* straight:                              Paths and guides.    (line  79)
+* strftime:                              Data types.          (line 298)
+* string:                                Data types.          (line 181)
+* stroke:                                fill.                (line  36)
+* strokepath:                            Paths and guides.    (line 308)
+* strptime:                              Data types.          (line 306)
+* struct:                                Structures.          (line   6)
+* structures:                            Structures.          (line   6)
+* subpath <1>:                           three.               (line 520)
+* subpath:                               Paths and guides.    (line 177)
+* subpictures:                           Frames and pictures. (line 103)
+* substr:                                Data types.          (line 246)
+* Subversion:                            Subversion.          (line   6)
+* sum:                                   Arrays.              (line 213)
+* superpath:                             Tutorial.            (line 134)
+* Suppress:                              Pens.                (line 331)
+* SuppressQuiet:                         Pens.                (line 335)
+* surface <1>:                           graph3.              (line 101)
+* surface:                               three.               (line  47)
+* SVG:                                   Options.             (line 150)
+* SVN:                                   Subversion.          (line   6)
+* system <1>:                            Options.             (line 169)
+* system:                                Data types.          (line 328)
+* syzygy:                                syzygy.              (line   6)
+* tab:                                   Files.               (line  61)
+* tab completion:                        Tutorial.            (line  37)
+* Tan:                                   Mathematical functions.
+                                                              (line  20)
+* tan:                                   Mathematical functions.
+                                                              (line   6)
+* tanh:                                  Mathematical functions.
+                                                              (line   6)
+* target:                                three.               (line 351)
+* tell:                                  Files.               (line  92)
+* tension <1>:                           three.               (line   6)
+* tension:                               Bezier curves.       (line  56)
+* tensionSpecifier:                      Paths and guides.    (line 399)
+* tensor product shading:                fill.                (line  78)
+* tensorshade:                           fill.                (line  78)
+* tessellation:                          three.               (line 112)
+* tex <1>:                               Options.             (line 145)
+* tex:                                   Frames and pictures. (line 278)
+* TeX fonts:                             Pens.                (line 201)
+* TeX string:                            Data types.          (line 181)
+* texcommand:                            Configuring.         (line  67)
+* TeXHead:                               draw.                (line  26)
+* TeXHead3:                              three.               (line 561)
+* texpath <1>:                           label.               (line 115)
+* texpath:                               Configuring.         (line  67)
+* texpreamble:                           Frames and pictures. (line 286)
+* texreset:                              Frames and pictures. (line 289)
+* textbook graph:                        graph.               (line 372)
+* tgz:                                   UNIX binary distributions.
+                                                              (line   6)
+* thick:                                 three.               (line 123)
+* thin:                                  three.               (line 123)
+* this:                                  Structures.          (line   6)
+* three:                                 three.               (line   6)
+* ThreeViews:                            three.               (line 414)
+* ThreeViewsFR:                          three.               (line 414)
+* ThreeViewsUS:                          three.               (line 414)
+* tick:                                  graph.               (line 343)
+* Ticks:                                 graph.               (line 161)
+* ticks:                                 graph.               (line 161)
+* tildeframe:                            markers.             (line  26)
+* tile:                                  Pens.                (line 251)
+* tilings:                               Pens.                (line 238)
+* time <1>:                              math.                (line  30)
+* time:                                  Data types.          (line 298)
+* times:                                 Paths and guides.    (line 211)
+* Top:                                   graph.               (line 137)
+* TopView:                               three.               (line 399)
+* trace:                                 Debugger.            (line  51)
+* trailingzero:                          graph.               (line 175)
+* transform <1>:                         three.               (line 495)
+* transform:                             Transforms.          (line   6)
+* transform3:                            three.               (line 450)
+* transparency:                          Pens.                (line 222)
+* transpose:                             Arrays.              (line 205)
+* tree:                                  tree.                (line   9)
+* trembling:                             trembling.           (line   6)
+* triangle:                              geometry.            (line   6)
+* triangles:                             three.               (line 112)
+* triangulate:                           contour.             (line 156)
+* tridiagonal:                           Arrays.              (line 266)
+* trigonometric integrals:               Mathematical functions.
+                                                              (line  48)
+* triple:                                Data types.          (line 110)
+* TrueMargin:                            draw.                (line  42)
+* TrueMargin3:                           three.               (line 577)
+* tube <1>:                              tube.                (line   6)
+* tube:                                  three.               (line 123)
+* tutorial:                              Tutorial.            (line   6)
+* type1cm:                               Pens.                (line 178)
+* typedef <1>:                           Functions.           (line  36)
+* typedef:                               Data types.          (line 361)
+* U3D:                                   embed.               (line  23)
+* undefined:                             Paths and guides.    (line 273)
+* UnFill:                                Frames and pictures. (line 152)
+* unfill:                                fill.                (line 110)
+* UnFill:                                draw.                (line  26)
+* unicode:                               unicode.             (line   6)
+* uniform:                               Arrays.              (line 155)
+* Uninstall:                             Uninstall.           (line   6)
+* unique:                                math.                (line  64)
+* unit:                                  Data types.          (line  80)
+* unitbox <1>:                           three.               (line 320)
+* unitbox:                               Tutorial.            (line 155)
+* unitcircle <1>:                        three.               (line 287)
+* unitcircle:                            Tutorial.            (line 128)
+* unitrand:                              Mathematical functions.
+                                                              (line  39)
+* unitsize <1>:                          Frames and pictures. (line  64)
+* unitsize:                              Tutorial.            (line  86)
+* UNIX binary distributions:             UNIX binary distributions.
+                                                              (line   6)
+* unpacking:                             Rest arguments.      (line  39)
+* unravel:                               Import.              (line  30)
+* up:                                    three.               (line 351)
+* update:                                Files.               (line  36)
+* UpsideDown:                            Frames and pictures. (line  95)
+* usepackage:                            Frames and pictures. (line 291)
+* user coordinates:                      Tutorial.            (line  86)
+* user-defined operators:                User-defined operators.
+                                                              (line   6)
+* usleep:                                Data types.          (line 354)
+* value:                                 math.                (line  38)
+* var:                                   Variable initializers.
+                                                              (line  63)
+* variable initializers:                 Variable initializers.
+                                                              (line   6)
+* vectorfield:                           graph.               (line 974)
+* vectorfield3:                          graph3.              (line 160)
+* vectorization:                         Arrays.              (line 323)
+* verbatim:                              Frames and pictures. (line 271)
+* vertex-dependent colors:               three.               (line  81)
+* Vertical:                              flowchart.           (line  81)
+* viewportheight:                        LaTeX usage.         (line  51)
+* viewportmargin:                        three.               (line 275)
+* viewportsize:                          three.               (line 275)
+* viewportwidth:                         LaTeX usage.         (line  51)
+* views:                                 three.               (line 243)
+* vim:                                   Editing modes.       (line  33)
+* virtual functions:                     Structures.          (line 181)
+* void:                                  Data types.          (line  10)
+* W:                                     Tutorial.            (line 106)
+* whatever:                              Paths and guides.    (line 237)
+* Wheel:                                 palette.             (line  22)
+* wheel mouse:                           GUI.                 (line   6)
+* while:                                 Programming.         (line  29)
+* white-space string delimiter mode:     Arrays.              (line 354)
+* width:                                 LaTeX usage.         (line  51)
+* windingnumber:                         Paths and guides.    (line 273)
+* word:                                  Arrays.              (line 354)
+* write <1>:                             Arrays.              (line 394)
+* write:                                 Files.               (line  53)
+* X:                                     three.               (line 287)
+* xasy:                                  GUI.                 (line   6)
+* xaxis3:                                graph3.              (line   7)
+* xdr:                                   Files.               (line  75)
+* xelatex:                               Options.             (line 145)
+* xequals:                               graph.               (line 294)
+* XEquals:                               graph.               (line 280)
+* xlimits:                               graph.               (line 637)
+* XOR:                                   Arithmetic & logical.
+                                                              (line  80)
+* xpart:                                 Data types.          (line  91)
+* xscale:                                Transforms.          (line  33)
+* xscale3:                               three.               (line 458)
+* xtick:                                 graph.               (line 343)
+* XY:                                    three.               (line 480)
+* XYEquals:                              graph3.              (line  21)
+* XYZero:                                graph3.              (line  21)
+* XZEquals:                              graph3.              (line  21)
+* XZero:                                 graph.               (line 275)
+* XZZero:                                graph3.              (line  21)
+* Y <1>:                                 three.               (line 287)
+* Y:                                     Mathematical functions.
+                                                              (line   6)
+* yaxis3:                                graph3.              (line   7)
+* yequals:                               graph.               (line 294)
+* YEquals:                               graph.               (line 130)
+* ylimits:                               graph.               (line 637)
+* ypart:                                 Data types.          (line  94)
+* yscale:                                Transforms.          (line  36)
+* yscale3:                               three.               (line 461)
+* ytick:                                 graph.               (line 343)
+* YX:                                    three.               (line 495)
+* YZ:                                    three.               (line 495)
+* YZEquals:                              graph3.              (line  21)
+* YZero:                                 graph.               (line 125)
+* YZZero:                                graph3.              (line  21)
+* Z:                                     three.               (line 287)
+* zaxis3:                                graph3.              (line   7)
+* zero_Ai:                               Mathematical functions.
+                                                              (line  48)
+* zero_Ai_deriv:                         Mathematical functions.
+                                                              (line  48)
+* zero_Bi:                               Mathematical functions.
+                                                              (line  48)
+* zero_Bi_deriv:                         Mathematical functions.
+                                                              (line  48)
+* zero_J:                                Mathematical functions.
+                                                              (line  48)
+* zerowinding:                           Pens.                (line 152)
+* zeta:                                  Mathematical functions.
+                                                              (line  48)
+* zpart:                                 Data types.          (line 163)
+* zscale3:                               three.               (line 464)
+* ZX:                                    three.               (line 495)
+* ZY:                                    three.               (line 495)
+* |:                                     Arithmetic & logical.
+                                                              (line  62)
+* ||:                                    Arithmetic & logical.
+                                                              (line  59)
+
+
+
+Tag Table:
+Node: Top575
+Node: Description6859
+Node: Installation10475
+Node: UNIX binary distributions11519
+Node: MacOS X binary distributions12625
+Node: Microsoft Windows13509
+Ref: psview14219
+Node: Configuring15153
+Node: Search paths19373
+Node: Compiling from UNIX source20215
+Node: Editing modes23112
+Node: Subversion25544
+Node: Uninstall25992
+Node: Tutorial26342
+Ref: unitcircle30640
+Node: Drawing commands32696
+Node: draw34407
+Ref: arrows35555
+Node: fill40798
+Ref: gradient shading41842
+Node: clip46399
+Node: label46991
+Ref: Label47589
+Node: Bezier curves53392
+Node: Programming57094
+Ref: array iteration57908
+Node: Data types59014
+Ref: format68211
+Node: Paths and guides72464
+Ref: circle72718
+Ref: extension82276
+Node: Pens89331
+Ref: fillrule96699
+Ref: basealign97596
+Ref: transparency100422
+Ref: makepen103865
+Ref: overwrite104703
+Node: Transforms105913
+Node: Frames and pictures107704
+Ref: envelope108845
+Ref: size109928
+Ref: unitsize110915
+Ref: shipout111975
+Ref: filltype114308
+Ref: add117445
+Ref: add about118391
+Ref: tex121329
+Node: Files122203
+Ref: cd123186
+Ref: scroll127860
+Node: Variable initializers130775
+Node: Structures133500
+Node: Operators140902
+Node: Arithmetic & logical141216
+Node: Self & prefix operators143189
+Node: User-defined operators143977
+Node: Implicit scaling144888
+Node: Functions145451
+Ref: stack overflow148204
+Node: Default arguments148768
+Node: Named arguments149507
+Node: Rest arguments152078
+Node: Mathematical functions155199
+Node: Arrays159864
+Ref: sort166853
+Ref: tridiagonal169257
+Ref: solve170485
+Node: Slices174679
+Node: Casts178569
+Node: Import180534
+Node: Static185771
+Node: LaTeX usage188665
+Node: Base modules195077
+Node: plain197577
+Node: simplex198229
+Node: math198502
+Node: interpolate201207
+Node: geometry201486
+Node: trembling202080
+Node: stats202349
+Node: patterns202609
+Node: markers202845
+Node: tree204628
+Node: binarytree204816
+Node: drawtree205436
+Node: syzygy205640
+Node: feynman205914
+Node: roundedpath206189
+Node: animation206472
+Ref: animate206892
+Node: embed208031
+Node: slide208998
+Node: MetaPost209338
+Node: unicode210054
+Node: latin1210942
+Node: babel211310
+Node: labelpath211539
+Node: labelpath3212359
+Node: annotate212670
+Node: CAD213141
+Node: graph213451
+Ref: ticks220580
+Ref: pathmarkers233907
+Ref: marker234372
+Ref: markuniform234723
+Ref: errorbars236514
+Ref: automatic scaling240551
+Node: palette251180
+Ref: images251298
+Ref: image255470
+Ref: logimage255948
+Ref: penimage257009
+Ref: penfunctionimage257230
+Node: three257954
+Ref: PostScript3D283633
+Node: obj285325
+Node: graph3285577
+Ref: GaussianSurface290732
+Node: grid3291836
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+End Tag Table