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-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
-                            03 Apr 2018
-                          
-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://www.github.com/vectorgraphics/asymptote/base/graph.asy for the
-definition of NoZero):
-
-import graph;
-
-size(10cm);
-
-real f(real x) {return x^2;}
- 
-draw(graph(f,-2,2));
-
-xaxis(Ticks(NoZero));
-yaxis(Ticks(NoZero));
-
-label("$0$",(0,0),SW);
-(iii) explicitly remove specific tick labels and draw them manually (see
-http://www.github.com/vectorgraphics/asymptote/base/graph.asy for the
-definition of NoZeroFormat):
-
-import graph;
-
-size(10cm);
-
-real f(real x) {return x^2;}
- 
-draw(graph(f,-2,2));
-
-xaxis(Ticks(NoZeroFormat));
-yaxis(Ticks(NoZeroFormat));
-
-label("$0$",(0,0),SW);
-(iv) use the xasy GUI to move overlapping labels;
-
-(v) change the Label argument of LeftTicks, RightTicks, or Ticks to:
-
-Label(currentpen+overwrite(Move))
-Solution (v) will move labels that might otherwise overwrite a previous
-label. Other possible overwrite arguments are Allow (allows overlapping
-labels; the default), Suppress (an overlapping label will not be written
-at all), SuppressQuiet, and MoveQuiet. The last two achieve the same
-result as the non-quiet types, but will not notify you which labels are
-overlapping. See:  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).
-