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author | Norbert Preining <preining@logic.at> | 2018-04-06 05:21:01 +0000 |
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committer | Norbert Preining <preining@logic.at> | 2018-04-06 05:21:01 +0000 |
commit | a11ba95f5b305c7d01cf2b6aec5640a6b1831117 (patch) | |
tree | 028e9aa29fb00177617b77a8d804a7bce694d5b0 /Build/source/utils/asymptote/doc | |
parent | 0de24c07adcc80181a7aee919e1316a6149dda56 (diff) |
asymptote 2.43
git-svn-id: svn://tug.org/texlive/trunk@47319 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build/source/utils/asymptote/doc')
-rw-r--r-- | Build/source/utils/asymptote/doc/CAD.pdf | bin | 66745 -> 0 bytes | |||
-rw-r--r-- | Build/source/utils/asymptote/doc/FAQ/asy-faq.info | 1671 | ||||
-rw-r--r-- | Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf | bin | 32004 -> 0 bytes | |||
-rw-r--r-- | Build/source/utils/asymptote/doc/asy-latex.pdf | bin | 194542 -> 0 bytes | |||
-rw-r--r-- | Build/source/utils/asymptote/doc/asy.1 | 300 | ||||
-rw-r--r-- | Build/source/utils/asymptote/doc/asyRefCard.pdf | bin | 54839 -> 0 bytes | |||
-rw-r--r-- | Build/source/utils/asymptote/doc/asymptote.pdf | bin | 1279444 -> 0 bytes | |||
-rw-r--r-- | Build/source/utils/asymptote/doc/asymptote.texi | 12 | ||||
-rw-r--r-- | Build/source/utils/asymptote/doc/png/asymptote.info | 10245 |
9 files changed, 6 insertions, 12222 deletions
diff --git a/Build/source/utils/asymptote/doc/CAD.pdf b/Build/source/utils/asymptote/doc/CAD.pdf Binary files differdeleted file mode 100644 index eaeb2b6bcd9..00000000000 --- a/Build/source/utils/asymptote/doc/CAD.pdf +++ /dev/null diff --git a/Build/source/utils/asymptote/doc/FAQ/asy-faq.info b/Build/source/utils/asymptote/doc/FAQ/asy-faq.info deleted file mode 100644 index 155fb75c2eb..00000000000 --- a/Build/source/utils/asymptote/doc/FAQ/asy-faq.info +++ /dev/null @@ -1,1671 +0,0 @@ -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). - diff --git a/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf b/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf Binary files differdeleted file mode 100644 index 73c874c90a7..00000000000 --- a/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf +++ /dev/null diff --git a/Build/source/utils/asymptote/doc/asy-latex.pdf b/Build/source/utils/asymptote/doc/asy-latex.pdf Binary files differdeleted file mode 100644 index 458739be2aa..00000000000 --- a/Build/source/utils/asymptote/doc/asy-latex.pdf +++ /dev/null diff --git a/Build/source/utils/asymptote/doc/asy.1 b/Build/source/utils/asymptote/doc/asy.1 deleted file mode 100644 index e8fbc42290d..00000000000 --- a/Build/source/utils/asymptote/doc/asy.1 +++ /dev/null @@ -1,300 +0,0 @@ -.\" 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 \-aligndir pair -Directional page alignment (overrides align) [(0,0)]. -.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 text and noninteractive stdout [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|lualatex|tex|pdftex|luatex|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 Binary files differdeleted file mode 100644 index 0d9489a98a9..00000000000 --- a/Build/source/utils/asymptote/doc/asyRefCard.pdf +++ /dev/null diff --git a/Build/source/utils/asymptote/doc/asymptote.pdf b/Build/source/utils/asymptote/doc/asymptote.pdf Binary files differdeleted file mode 100644 index df69e68a5d1..00000000000 --- a/Build/source/utils/asymptote/doc/asymptote.pdf +++ /dev/null diff --git a/Build/source/utils/asymptote/doc/asymptote.texi b/Build/source/utils/asymptote/doc/asymptote.texi index 278a57541c6..0857cc6fce8 100644 --- a/Build/source/utils/asymptote/doc/asymptote.texi +++ b/Build/source/utils/asymptote/doc/asymptote.texi @@ -11,7 +11,7 @@ This file documents @code{Asymptote}, version @value{VERSION}. @url{http://asymptote.sourceforge.net} -Copyright @copyright{} 2004-16 Andy Hammerlindl, John Bowman, and Tom Prince. +Copyright @copyright{} 2004-18 Andy Hammerlindl, John Bowman, and Tom Prince. @quotation Permission is granted to copy, distribute and/or modify this document @@ -316,10 +316,10 @@ Users may also wish to monitor the @code{Asymptote} forum: @cindex @acronym{RPM} @cindex @code{tgz} We release both @code{tgz} and @acronym{RPM} binary distributions of -@code{Asymptote}. The root user can install the @code{Linux i386} @code{tgz} +@code{Asymptote}. The root user can install the @code{Linux x86_64} @code{tgz} distribution of version @code{x.xx} of @code{Asymptote} with the commands: @verbatim -tar -C / -zxf asymptote-x.xx.i386.tgz +tar -C / -zxf asymptote-x.xx.x86_64.tgz texhash @end verbatim @noindent @@ -758,9 +758,9 @@ To compile without optimization, use the command @code{make CFLAGS=-g}. @section Uninstall @cindex uninstall -To uninstall a @code{Linux i386} binary distribution, use the commands +To uninstall a @code{Linux x86_64} binary distribution, use the commands @verbatim -tar -zxvf asymptote-x.xx.i386.tgz | xargs --replace=% rm /% +tar -zxvf asymptote-x.xx.x86_64.tgz | xargs --replace=% rm /% texhash @end verbatim @@ -9893,7 +9893,7 @@ Martin Wiebusch, and Stefan Knorr. @c LocalWords: differentiable vectorization vectorized asydir normals quartic @c LocalWords: wavepacket kerned parametrized specular hyperboloid Bourke's @c LocalWords: Michail 0pt 1filll 's 3D latin1 labelpath3 2D graph3 -@c LocalWords: grid3 contour3 i386 psv a4 gsview32 freeglut 'load ' +@c LocalWords: grid3 contour3 x86_64 psv a4 gsview32 freeglut 'load ' @c LocalWords: 'asy 'lasy 'auto 5bp 1cm sqrtx01 4g extenda extendb @c LocalWords: bb llx 2S 100pt 3t bezier2 bool3 x0 angle1 angle2 z1 @c LocalWords: z2 before' struct X11 x11colors type1cm 12pt OT1 5mm diff --git a/Build/source/utils/asymptote/doc/png/asymptote.info b/Build/source/utils/asymptote/doc/png/asymptote.info deleted file mode 100644 index bae9887b4db..00000000000 --- a/Build/source/utils/asymptote/doc/png/asymptote.info +++ /dev/null @@ -1,10245 +0,0 @@ -This is asymptote.info, produced by makeinfo version 6.4 from -asymptote.texi. - -This file documents 'Asymptote', version 2.42. - - <http://asymptote.sourceforge.net> - - Copyright (C) 2004-16 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, Prev: (dir), Up: (dir) - -Asymptote -********* - -This file documents 'Asymptote', version 2.42. - - <http://asymptote.sourceforge.net> - - Copyright (C) 2004-16 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 -* Git:: Getting the latest development source -* Uninstall:: Goodbye, 'Asymptote'! - -Tutorial - -* Drawing in batch mode:: Run 'Asymptote' on a text file -* Drawing in interactive mode:: Running 'Asymptote' interactively -* Figure size:: Specifying the figure size -* Labels:: Adding 'LaTeX' labels -* Paths:: Drawing lines and curves - -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 -* smoothcontour3:: Smooth implicit surfaces -* slopefield:: Slope fields -* ode:: Ordinary differential equations - -Graphical User Interface - -* GUI installation:: Installing 'xasy' -* GUI usage:: Using 'xasy' to edit objects - - - -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 -drawing. 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 drawing, - 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/> -Clicking on an example file name in this manual, like 'Pythagoras', will -display the PDF output, whereas clicking on its '.asy' extension will -show the corresponding 'Asymptote' code in a separate window. - - 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 -* Git:: 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://sourceforge.net/projects/asymptote> -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, Prev: Installation, 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 -dnf --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 'Asymptote' binary -available at - - <http://www.macports.org/> - -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 (we recommend -<https://www.tug.org/texlive> or <http://www.miktex.org>) will be -required to typeset labels. You will also need to install 'GPL -Ghostscript' version 9.14 or later from -<http://downloads.ghostscript.com/public>. - - To view 'PostScript' output, you can install the program 'gsview' -available from <http://www.cs.wisc.edu/~ghost/gsview/>. - - The 'ImageMagick' package from -<http://www.imagemagick.org/script/binary-releases.php> - -is required to support output formats other than EPS, 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). - - 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://downloads.ghostscript.com/public>. - - 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: -config -texpath -texcommand -dvips -dvisvgm -libgs -convert -display -animate - - Warnings (such as "unbounded" and "offaxis") 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 the source release -'asymptote-x.xx.src.tgz' in the subdirectory 'x.xx' under - - <http://sourceforge.net/projects/asymptote/files/> - - 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-7.4.2.tar.gz> -<http://www.ivmaisoft.com/_bin/atomic_ops/libatomic_ops-7.4.2.tar.gz> in -the 'Asymptote' source directory. - - On 'UNIX' platforms (other than 'MacOS X'), we recommend using -version '3.0.0' of the 'freeglut' library. To compile 'freeglut', -download - <http://prdownloads.sourceforge.net/freeglut/freeglut-3.0.0.tar.gz> -and type (as the root user): -gunzip freeglut-3.0.0.tar.gz -tar -xf freeglut-3.0.0.tar -cd freeglut-3.0.0 -./configure --prefix=/usr -cmake . -make -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 CXXFLAGS=-I/opt/local/include LDFLAGS=-L/opt/local/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: Git, 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: Git, Next: Uninstall, Prev: Editing modes, Up: Installation - -2.8 Git -======= - -The following commands are needed to install the latest development -version of 'Asymptote' using 'git': -git clone http://github.com/vectorgraphics/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: Git, Up: Installation - -2.9 Uninstall -============= - -To uninstall a '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 -********** - -* Menu: - -* Drawing in batch mode:: Run 'Asymptote' on a text file -* Drawing in interactive mode:: Running 'Asymptote' interactively -* Figure size:: Specifying the figure size -* Labels:: Adding 'LaTeX' labels -* Paths:: Drawing lines and curves - -A concise introduction to 'Asymptote' is given here. For a more -thorough introduction, see the excellent 'Asymptote' tutorial written by -Charles Staats: - - <http://math.uchicago.edu/~cstaats/Charles_Staats_III/Notes_and_papers_files/asymptote_tutorial.pdf> - - Another 'Asymptote' tutorial is available as a wiki, with images -rendered by an online Asymptote engine: - - <http://www.artofproblemsolving.com/wiki/?title=Asymptote_(Vector_Graphics_Language)> - - -File: asymptote.info, Node: Drawing in batch mode, Next: Drawing in interactive mode, Prev: Tutorial, Up: 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: - - [diagonal] -Here, the '--' connector joins the two points '(0,0)' and '(100,100)' -with a line segment. - - -File: asymptote.info, Node: Drawing in interactive mode, Next: Figure size, Prev: Drawing in batch mode, Up: Tutorial - -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::. - - -File: asymptote.info, Node: Figure size, Next: Labels, Prev: Drawing in interactive mode, Up: Tutorial - -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)); - - [diagonal] - - 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); - - [bigdiagonal] - - 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); - - [square] -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); - - -File: asymptote.info, Node: Labels, Next: Paths, Prev: Figure size, Up: Tutorial - -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); - - [labelsquare] - - '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'). - - -File: asymptote.info, Node: Paths, Prev: Labels, Up: Tutorial - -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); - - [quartercircle] -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); - - - [superpath] - -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); - - [cube] - - 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>. - - -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, Prev: Drawing commands, 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'. 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 using TeX engines -that produce PDF output (*note texengines::): 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' and '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: - - [CDlabel] -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 - - [(1-t)^3*z_0+3t(1-t)^2*c_0+3t^2(1-t)*c_1+t^3*z_1 for 0 <=t <= 1.] - - 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: - - [bezier2] - - 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}); - - [dots] -with -draw((0,0){up}::(100,25){right}::(200,0){down}); - - [colons] - - 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 -************* - -* 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? - -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. - - -File: asymptote.info, Node: Data types, Next: Paths and guides, Prev: Programming, 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 variables 'inf' and 'nan', along with the 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'; - - 'real cross(explicit pair z, explicit pair w)' - returns the 2D scalar product 'z.x*w.y-z.y*w.x'; - - 'real orient(pair a, pair b, pair c);' - returns a positive (negative) value if 'a--b--c--cycle' is - oriented counterclockwise (clockwise) or zero if all three - points are colinear. Equivalently, a positive (negative) - value is returned if 'c' lies to the left (right) of the line - through 'a' and 'b' or zero if 'c' lies on this line. The - value returned can be expressed in terms of the 2D scalar - cross product as 'cross(a-c,b-c)', which is the determinant - |a.x a.y 1| - |b.x b.y 1| - |c.x c.y 1| - - 'real incircle(pair a, pair b, pair c, pair d);' - returns a positive (negative) value if 'd' lies inside - (outside) the circle passing through the - counterclockwise-oriented points 'a,b,c' or zero if 'd' lies - on the this circle. The value returned is the determinant - |a.x a.y a.x^2+a.y^2 1| - |b.x b.y b.x^2+b.y^2 1| - |c.x c.y c.x^2+c.y^2 1| - |d.x d.y d.x^2+d.y^2 1| - - '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[] array(string s)' - returns an array of strings obtained by splitting 's' into - individual characters. The inverse operation is provided by - 'operator +(...string[] a)'. - - '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), following the - behaviour of the C function 'fprintf'), except that only one - data field is allowed. - - 'string format(string s=defaultformat, bool forcemath=false, 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 's' specifies math mode or - 'forcemath=true', 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); - - [join] - - 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::). - - '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); - - - [mexicanhat] - - 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': - - [colors] - - 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(); - - [linetype] - - 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://mirror.ctan.org/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")); - - [tile] - - 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")); - - [hatch] - - 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); - - [makepen] - - 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 - '<http://asymptote.sourceforge.net/gallery/.pdf>.asy' 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); - - - [subpictures] - - 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=new T; -T foo; -Here, 'new T' produces a new instance of the class, which causes -'Tcount' to be incremented, tracking the number of instances produced. -The declarations 'T foo=new T' and 'T foo' are equivalent: the second -form implicitly creates a new instance of 'T'. That is, 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; -} - - 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'). In example at the beginning of this 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). - - 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=new Person; - p.firstname=firstname; - p.lastname=lastname; - return p; - } -} - -Person joe=Person.Person("Joe", "Jones"); - - While it is now easier than before to create a new instance, we still -have to refer to the constructor by the qualified name 'Person.Person'. -If we add the line -from Person unravel Person; -immediately after the structure definition, then the constructor can be -used without qualification: 'Person joe=Person("Joe", "Jones");'. - - The constructor is now easy to use, but it is quite a hassle to -define. If you write a lot of constructors, you will find that you are -repeating a lot of code in each of them. Fortunately, your friendly -neighbourhood Asymptote developers have devised a way to automate much -of the process. - - If, in the body of a structure, Asymptote encounters the definition -of a function of the form 'void operator init(ARGS)', it implicitly -defines a constructor function of the arguments 'ARGS' that uses the -'void operator init' function to initialize a new instance of the -structure. That is, it essentially defines the following constructor -(assuming the structure is called 'Foo'): - - static Foo Foo(ARGS) { - Foo instance=new Foo; - instance.operator init(ARGS); - return instance; - } - - This constructor is also implicitly copied to the enclosing scope -after the end of the structure definition, so that it can used -subsequently without qualifying it by the structure name. Our 'Person' -example can thus be implemented as: -struct Person { - string firstname; - string lastname; - - void operator init(string firstname, string lastname) { - this.firstname=firstname; - this.lastname=lastname; - } -} - -Person joe=Person("Joe", "Jones"); - - The use of 'operator init' to implicitly define constructors should -not be confused with its use to define default values for variables -(*note Variable initializers::). Indeed, in the first case, the return -type of the 'operator init' must be 'void' while in the second, it must -be the (non-'void') type of the variable. - - The function 'cputime()' returns a structure 'cputime' with -cumulative CPU times broken down into the fields 'parent.user', -'parent.system', 'child.user', and 'child.system'. For convenience, the -incremental fields 'change.user' and 'change.system' indicate the change -in the corresponding total parent and child CPU times since the last -call to 'cputime()'. The function -void write(file file=stdout, string s="", cputime c, - string format=cputimeformat, suffix suffix=none); -displays the incremental user cputime followed by "u", the incremental -system cputime followed by "s", the total user cputime followed by "U", -and the total system cputime followed by "S". - - Much like in C++, casting (*note Casts::) provides for an elegant -implementation of structure inheritance, including virtual functions: -struct parent { - real x; - void operator init(int x) {this.x=x;} - void virtual(int) {write(0);} - void f() {virtual(1);} -} - -void write(parent p) {write(p.x);} - -struct child { - parent parent; - real y=3; - void operator init(int x) {parent.operator init(x);} - void virtual(int x) {write(x);} - parent.virtual=virtual; - void f()=parent.f; -} - -parent operator cast(child child) {return child.parent;} - -parent p=parent(1); -child c=child(2); - -write(c); // Outputs 2; - -p.f(); // Outputs 0; -c.f(); // Outputs 1; - -write(c.parent.x); // Outputs 2; -write(c.y); // Outputs 3; - - For further examples of structures, see 'Legend' and 'picture' in the -'Asymptote' base module 'plain'. - - -File: asymptote.info, Node: Operators, Next: Implicit scaling, Prev: Structures, Up: Programming - -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, Prev: 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 typically what is intended; otherwise one can use the function 'int -quotient(int x, int y)', which returns 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 -'-' - subtractiona -'*' - multiplication -'/' - division -'#' - integer division; equivalent to 'quotient(x,y)'. Noting that the - 'Python3' community adopted our comment symbol ('//') for integer - division, we decided to reciprocate and use their comment symbol - for integer division in 'Asymptote'! -'%' - modulo; the result always has the same sign as the divisor. In - particular, this makes 'q*(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), 'int CTZ(int)' (count trailing zeros), 'int -popcount(int)' (count bits populated by ones), and 'int bitreverse(int -a, int bits)' (reverse bits within a word of length bits). - - -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 -============== - -* 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 - -'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). - - -File: asymptote.info, Node: Default arguments, Next: Named arguments, Prev: Functions, 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[] a, int n=1)' - returns the index of the 'n'th 'true' value in the boolean array - 'a' or -1 if not found. If 'n' is negative, search backwards from - the end of the array for the '-n'th value; - -'int[] findall(bool[] a)' - returns the indices of all 'true' values in the boolean array 'a'. - -'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 unnormalized 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); - - 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, Prev: Arrays, 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 - In situations where casting from a string to a type 'T' fails, an -uninitialized variable is returned; this condition can be detected with -the function 'bool initialized(T);' -int i=(int) "2.5"; -assert(initialized(i),"Invalid cast."); - -real x=(real) "2.5a"; -assert(initialized(x),"Invalid cast."); - - 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' -(v1.33 or later required) 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://mirror.ctan.org/support/latexmk/> -after putting the contents of -<http://sourceforge.net/p/asymptote/code/HEAD/tree/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://sourceforge.net/p/asymptote/code/HEAD/tree/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 latex files (no spaces): -\def\asylatexdir{} -% 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} -[latexusage] - -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 -* smoothcontour3:: Smooth implicit surfaces -* slopefield:: Slope fields -* ode:: Ordinary differential equations - - -File: asymptote.info, Node: plain, Next: simplex, Prev: Base modules, 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, explicit pair z, 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: - - - [markers1] - - 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'. - - - [markers2] - - -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); - - - [binarytreetest] - - -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://mirror.ctan.org/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://mirror.ctan.org/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://mirror.ctan.org/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://mirror.ctan.org/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 the - module '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$",F(1),SE); - - - [exp] - - 2. The next example draws a scientific-style graph with a legend. The - position of the legend can be adjusted either explicitly or by - using the graphical user interface - '<http://asymptote.sourceforge.net/gallery/.pdf>.asy' (*note - GUI::). If an 'UnFill(real xmargin=0, real ymargin=xmargin)' or - 'Fill(pen)' option is specified to 'add', the legend will obscure - any underlying objects. Here we illustrate how to clip the portion - of the picture covered by a label: - - import graph; - - size(400,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\sin(2\pi x)$"); - draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$"); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - label("LABEL",point(0),UnFill(1mm)); - - add(legend(),point(E),20E,UnFill); - - [lineargraph0] - - To specify a fixed size for the graph proper, use 'attach': - import graph; - - size(250,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\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$",LeftRight,RightTicks(trailingzero)); - - attach(legend(2),(point(S).x,truepoint(S).y),10S,UnFill); - - [legend] - - 3. This example draws a graph of one array versus another (both of the - same size) using custom tick locations and a smaller font size for - the tick labels on the y axis. - import graph; - - size(200,150,IgnoreAspect); - - real[] x={0,1,2,3}; - real[] y=x^2; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight, - RightTicks(Label(fontsize(8pt)),new real[]{0,4,9})); - - [datagraph] - - 4. This example shows how to graph columns of data read from a file. - import graph; - - size(200,150,IgnoreAspect); - - file in=input("filegraph.dat").line(); - real[][] a=in; - a=transpose(a); - - real[] x=a[0]; - real[] y=a[1]; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - [filegraph] - - 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$",LeftRight,RightTicks); - - yequals(pic2,55.0,red+Dotted); - xequals(pic2,70.0,red+Dotted); - - // Fit pic to W of origin: - add(pic.fit(),(0,0),W); - - // Fit pic2 to E of (5mm,0): - add(pic2.fit(),(5mm,0),E); - - - [errorbars] - - 6. A custom mark routine can be also be specified: - import graph; - - size(200,100,IgnoreAspect); - - markroutine marks() { - return new void(picture pic=currentpicture, frame f, path g) { - path p=scale(1mm)*unitcircle; - for(int i=0; i <= length(g); ++i) { - pair z=point(g,i); - frame f; - if(i % 4 == 0) { - fill(f,p); - add(pic,f,z); - } else { - if(z.y > 50) { - pic.add(new void(frame F, transform t) { - path q=shift(t*z)*p; - unfill(F,q); - draw(F,q); - }); - } else { - draw(f,p); - add(pic,f,z); - } - } - } - }; - } - - pair[] f={(5,5),(40,20),(55,51),(90,30)}; - - draw(graph(f),marker(marks())); - - scale(true); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - [graphmarkers] - - 7. This example shows how to label an axis with arbitrary strings. - import graph; - - size(400,150,IgnoreAspect); - - real[] x=sequence(12); - real[] y=sin(2pi*x/12); - - scale(false); - - string[] month={"Jan","Feb","Mar","Apr","May","Jun", - "Jul","Aug","Sep","Oct","Nov","Dec"}; - - draw(graph(x,y),red,MarkFill[0]); - - xaxis(BottomTop,LeftTicks(new string(real x) { - return month[round(x % 12)];})); - yaxis("$y$",LeftRight,RightTicks(4)); - - [monthaxis] - - 8. The next example draws a graph of a parametrized curve. The calls - to - xlimits(picture pic=currentpicture, real min=-infinity, - real max=infinity, bool crop=NoCrop); - and the analogous function 'ylimits' can be uncommented to set the - respective axes limits for picture 'pic' to the specified 'min' and - 'max' values. Alternatively, the function - void limits(picture pic=currentpicture, pair min, pair max, bool crop=NoCrop); - can be used to limit the axes to the box having opposite vertices - at the given pairs). Existing objects in picture 'pic' will be - cropped to lie within the given limits if 'crop'='Crop'. The - function 'crop(picture pic)' can be used to crop a graph to the - current graph limits. - import graph; - - size(0,200); - - real x(real t) {return cos(2pi*t);} - real y(real t) {return sin(2pi*t);} - - draw(graph(x,y,0,1)); - - //limits((0,-1),(1,0),Crop); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - - - [parametricgraph] - - The next example illustrates how one can extract a common axis - scaling factor. - import graph; - - axiscoverage=0.9; - size(200,IgnoreAspect); - - real[] x={-1e-11,1e-11}; - real[] y={0,1e6}; - - real xscale=round(log10(max(x))); - real yscale=round(log10(max(y)))-1; - - draw(graph(x*10^(-xscale),y*10^(-yscale)),red); - - xaxis("$x/10^{"+(string) xscale+"}$",BottomTop,LeftTicks); - yaxis("$y/10^{"+(string) yscale+"}$",LeftRight,RightTicks(trailingzero)); - - [scaledgraph] - - Axis scaling can be requested and/or automatic selection of the - axis limits can be inhibited with one of these 'scale' routines: - void scale(picture pic=currentpicture, scaleT x, scaleT y); - - void scale(picture pic=currentpicture, bool xautoscale=true, - bool yautoscale=xautoscale, bool zautoscale=yautoscale); - - This sets the scalings for picture 'pic'. The 'graph' routines - accept an optional 'picture' argument for determining the - appropriate scalings to use; if none is given, it uses those set - for 'currentpicture'. - - Two frequently used scaling routines 'Linear' and 'Log' are - predefined in 'graph'. - - All picture coordinates (including those in paths and those given - to the 'label' and 'limits' functions) are always treated as linear - (post-scaled) coordinates. Use - pair Scale(picture pic=currentpicture, pair z); - to convert a graph coordinate into a scaled picture coordinate. - - The x and y components can be individually scaled using the - analogous routines - real ScaleX(picture pic=currentpicture, real x); - real ScaleY(picture pic=currentpicture, real y); - - The predefined scaling routines can be given two optional boolean - arguments: 'automin=false' and 'automax=automin'. These default to - 'false' but can be respectively set to 'true' to enable automatic - selection of "nice" axis minimum and maximum values. The 'Linear' - scaling can also take as optional final arguments a multiplicative - scaling factor and intercept (e.g. for a depth axis, 'Linear(-1)' - requests axis reversal). - - For example, to draw a log/log graph of a function, use - 'scale(Log,Log)': - import graph; - - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - - draw(graph(f,0.1,10)); - - //limits((1,0.1),(10,0.5),Crop); - - dot(Label("(3,5)",align=S),Scale((3,5))); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - [loggraph] - - By extending the ticks, one can easily produce a logarithmic grid: - import graph; - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - draw(graph(f,0.1,10),red); - pen thin=linewidth(0.5*linewidth()); - xaxis("$x$",BottomTop,LeftTicks(begin=false,end=false,extend=true, - ptick=thin)); - yaxis("$y$",LeftRight,RightTicks(begin=false,end=false,extend=true, - ptick=thin)); - - - - [loggrid] - - One can also specify custom tick locations and formats for - logarithmic axes: - import graph; - - size(300,175,IgnoreAspect); - scale(Log,Log); - draw(graph(identity,5,20)); - xlimits(5,20); - ylimits(1,100); - xaxis("$M/M_\odot$",BottomTop,LeftTicks(DefaultFormat, - new real[] {6,10,12,14,16,18})); - yaxis("$\nu_{\rm upp}$ [Hz]",LeftRight,RightTicks(DefaultFormat)); - - - [logticks] - - 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); - - [log2graph] - - 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))); - - - [brokenaxis] - - 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/sqrt(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); - - - [Bode] - - 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; - 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); - - - [secondaryaxis] - - 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)); - - - [histogram] - - 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; - 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); - - [leastsquares] - - 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];})); - - [generalaxis] - - 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)); - - - [flow] - - 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)); - - [vectorfield] - - 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'. - - - [diatom] - - [westnile] - - -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); - - [image] - - 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()))); - - - - [logimage] - - 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)); - - - [penimage] - -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); - - [penfunctionimage] - - 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); - - [unitcircle3] -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); - - [saddle] - - 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=nolight, 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=nolight, 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=nolight, 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.asy' and 'smoothelevation.asy' 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[], - pen[] colors=new pen[], bool3 planar=default); -and then filled: -draw(surface(unitsquare3,new triple[] {X,Y,Z,O}),red); -draw(surface(O--X{Y}..Y{-X}--cycle,new triple[] {Z}),red); -draw(surface(path3(polygon(5))),red,nolight); -draw(surface(unitcircle3),red,nolight); -draw(surface(unitcircle3,new pen[] {red,green,blue,black}),nolight); -The first example draws a Bezier patch and the second example draws a -Bezier triangle. The third and fourth examples are planar surfaces. -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[] intersect(path3 p, surface s, real fuzz=-1); -returns a real array of length 3 containing the intersection times, if -any, of a path 'p' with a surface 's'. The routine -real[][] intersections(path3 p, surface s, real fuzz=-1); -returns all (unless there are infinitely many) 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. The routine -real orient(triple a, triple b, triple c, triple d); -is a numerically robust computation of 'dot(cross(a-d,b-d),c-d)', which -is the determinant -|a.x a.y a.z 1| -|b.x b.y b.z 1| -|c.x c.y c.z 1| -|d.x d.y d.z 1| - - The routine -real insphere(triple a, triple b, triple c, triple d, triple e); -returns a positive (negative) value if 'e' lies inside (outside) the -sphere passing through points 'a,b,c,d' oriented so that -'dot(cross(a-d,b-d),c-d)' is positive, or zero if all five points are -cospherical. The value returned is the determinant -|a.x a.y a.z a.x^2+a.y^2+a.z^2 1| -|b.x b.y b.z b.x^2+b.y^2+b.z^2 1| -|c.x c.y c.z c.x^2+c.y^2+c.z^2 1| -|d.x d.y d.z d.x^2+d.y^2+d.z^2 1| -|e.x e.y e.z e.x^2+e.y^2+e.z^2 1| - - 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); - - [join3] - - 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); - - - [planes] - - -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); - - [helix] - - 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)); - - [axis3] - - 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);})); - - - [generalaxis3] - - 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); - - [GaussianSurface] -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)); - - - [grid3xyz] - - -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); - - [cylinderskeleton] - - 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; - }); - - [flowchartdemo] - - -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})); - - [onecontour] - - 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); - - [multicontour] - - 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)); - - [imagecontour] - - 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); - - [irregularcontour] - - 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); - - [triangulate] - - The example 'Gouraudcontour.asy' 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: smoothcontour3, 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: smoothcontour3, Next: slopefield, Prev: contour3, Up: Base modules - -8.38 'smoothcontour3' -===================== - -This module, written by Charles Staats, draws implicitly defined -surfaces with smooth appearance. The purpose of this module is similar -to that of 'contour3': given a real-valued function f(x,y,z), construct -the surface described by the equation f(x,y,z) = 0. The -'smoothcontour3' module generally produces nicer results than -'contour3', but takes longer to compile. Additionally, the algorithm -assumes that the function and the surface are both smooth; if they are -not, then 'contour3' may be a better choice. - - To construct the null surface of a function 'f(triple)' or -'ff(real,real,real)' over 'box(a,b)', use the routine -surface implicitsurface(real f(triple)=null, - real ff(real,real,real)=null, - triple a, - triple b, - int n=nmesh, - bool keyword overlapedges=false, - int keyword nx=n, - int keyword ny=n, - int keyword nz=n, - int keyword maxdepth=8, - bool usetriangles=true); -The optional parameter 'overlapedges' attempts to compensate for an -artifact that can cause the renderer to "see through" the boundary -between patches. Although it defaults to 'false', it should usually be -set to 'true'. The example 'genustwo.asy' illustrates the use of this -function. Additional examples, together with a more in-depth -explanation of the module's usage and pitfalls, are available at -<https://github.com/charlesstaats/smoothcontour3>. - - -File: asymptote.info, Node: slopefield, Next: ode, Prev: smoothcontour3, Up: Base modules - -8.39 '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); - - - - [slopefield1] - - -File: asymptote.info, Node: ode, Prev: slopefield, Up: Base modules - -8.40 '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] --aligndir pair Directional page alignment (overrides align) [(0,0)] --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 text and noninteractive stdout [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|lualatex|tex|pdftex|luatex|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', 'context', 'luatex', -and 'lualatex' tex engines. Alternative output formats may be produced -using the '-f' option (or 'outformat' setting). - - To produce SVG output, you will need 'dvisvgm' (version 1.5.3 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 pair 'aligndir' specifies an optional -direction on the boundary of the page (mapped to the rectangle -[-1,1]\times[-1,1]) to which the picture should be aligned; the default -value '(0,0)' species center alignment. - - 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 -*************************** - -* Menu: - -* GUI installation:: Installing 'xasy' -* GUI usage:: Using 'xasy' to edit objects - -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. - - -File: asymptote.info, Node: GUI installation, Next: GUI usage, Prev: GUI, 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 'Pillow' fork of the -'Python Imaging Library',and the 'tkinter' package (included with -'Python' under 'Microsoft Windows'). 'Fedora Linux' users can either -install 'tkinter' and 'Pillow' with the commands -dnf install tkinter -dnf install tk-devel -dnf install python-pillow-tk -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' or later and version '3.1.0' of the 'Pillow' -fork of the 'Python Imaging Library', available from - <http://pypi.python.org/pypi/Pillow> - - -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/p/asymptote/patches> -To receive announcements of upcoming releases, please subscribe to -'Asymptote' at - <http://freecode.com/projects/asy> -If you find a bug in 'Asymptote', please check (if possible) whether the -bug is still present in the latest 'git' developmental code (*note -Git::) before submitting a bug report. New bugs can be reported at - <https://github.com/vectorgraphics/asymptote/issues> -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 Orest Shardt, Jesse Frohlich, Michail Vidiassov, Charles Staats, -Philippe Ivaldi, Olivier Guibe', Radoslav Marinov, Jeff Samuelson, Chris -Savage, 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 57) -* !=: Structures. (line 62) -* != <1>: Arithmetic & logical. - (line 37) -* #: Arithmetic & logical. - (line 20) -* %: Arithmetic & logical. - (line 25) -* % <1>: Interactive mode. (line 16) -* %=: Self & prefix operators. - (line 6) -* &: Bezier curves. (line 84) -* & <1>: Arithmetic & logical. - (line 49) -* &&: Arithmetic & logical. - (line 47) -* *: Pens. (line 15) -* * <1>: Arithmetic & logical. - (line 16) -* **: Arithmetic & logical. - (line 31) -* *=: Self & prefix operators. - (line 6) -* +: Pens. (line 15) -* + <1>: Arithmetic & logical. - (line 13) -* ++: Self & prefix operators. - (line 6) -* +=: Self & prefix operators. - (line 6) -* -: Arithmetic & logical. - (line 14) -* --: Paths. (line 16) -* -- <1>: Self & prefix operators. - (line 6) -* ---: Bezier curves. (line 84) -* -=: Self & prefix operators. - (line 6) -* -c: Options. (line 183) -* -l: Options. (line 202) -* -u: Options. (line 193) -* -V: Configuring. (line 6) -* -V <1>: Drawing in batch mode. - (line 16) -* ..: Paths. (line 16) -* .asy: Search paths. (line 12) -* /: Arithmetic & logical. - (line 18) -* /=: Self & prefix operators. - (line 6) -* 2D graphs: graph. (line 6) -* 3D graphs: graph3. (line 6) -* 3D grids: grid3. (line 6) -* 3D PostScript: three. (line 580) -* :: Arithmetic & logical. - (line 61) -* ::: Bezier curves. (line 70) -* <: Arithmetic & logical. - (line 39) -* <=: Arithmetic & logical. - (line 41) -* ==: Structures. (line 62) -* == <1>: Arithmetic & logical. - (line 36) -* >: Arithmetic & logical. - (line 45) -* >=: Arithmetic & logical. - (line 43) -* ?: Arithmetic & logical. - (line 61) -* ^: Arithmetic & logical. - (line 29) -* ^ <1>: Arithmetic & logical. - (line 55) -* ^=: Self & prefix operators. - (line 6) -* ^^: Paths. (line 23) -* |: Arithmetic & logical. - (line 53) -* ||: Arithmetic & logical. - (line 51) -* a4: Configuring. (line 58) -* abort: Data types. (line 363) -* abs: Data types. (line 65) -* abs <1>: Mathematical functions. - (line 35) -* accel: Paths and guides. (line 126) -* accel <1>: Paths and guides. (line 132) -* accel <2>: three. (line 484) -* access: Import. (line 6) -* acknowledgments: Credits. (line 6) -* acos: Mathematical functions. - (line 6) -* aCos: Mathematical functions. - (line 20) -* acosh: Mathematical functions. - (line 6) -* add: Frames and pictures. - (line 212) -* add <1>: Frames and pictures. - (line 228) -* add <2>: three. (line 256) -* addViews: three. (line 377) -* adjust: Pens. (line 119) -* Ai: Mathematical functions. - (line 48) -* Airy: Mathematical functions. - (line 48) -* Ai_deriv: Mathematical functions. - (line 48) -* alias: Structures. (line 62) -* alias <1>: Arrays. (line 174) -* Align: label. (line 12) -* aligndir: Options. (line 175) -* all: Arrays. (line 322) -* Allow: Pens. (line 343) -* and: Bezier curves. (line 56) -* AND: Arithmetic & logical. - (line 68) -* angle: Data types. (line 73) -* animate: Configuring. (line 64) -* animate <1>: Files. (line 155) -* animate <2>: animation. (line 12) -* animation: animation. (line 6) -* animation <1>: animation. (line 6) -* annotate: annotate. (line 6) -* antialias: three. (line 195) -* antialias <1>: Options. (line 146) -* append: Files. (line 36) -* append <1>: Arrays. (line 39) -* arc: Paths and guides. (line 24) -* Arc: Paths and guides. (line 37) -* arc <1>: three. (line 267) -* ArcArrow: draw. (line 26) -* ArcArrow3: three. (line 547) -* ArcArrows: draw. (line 26) -* ArcArrows3: three. (line 547) -* arclength: Paths and guides. (line 153) -* arclength <1>: three. (line 484) -* arcpoint: Paths and guides. (line 163) -* arctime: Paths and guides. (line 157) -* arctime <1>: three. (line 484) -* arguments: Default arguments. (line 6) -* arithmetic operators: Arithmetic & logical. - (line 6) -* array: Data types. (line 283) -* array <1>: Arrays. (line 112) -* array iteration: Programming. (line 52) -* arrays: Arrays. (line 6) -* arrow: Drawing commands. (line 31) -* Arrow: draw. (line 26) -* arrow <1>: label. (line 70) -* arrow keys: Drawing in interactive mode. - (line 11) -* Arrow3: three. (line 547) -* arrows: draw. (line 26) -* Arrows: draw. (line 26) -* Arrows3: three. (line 547) -* as: Import. (line 67) -* ascii: Data types. (line 308) -* ascii <1>: Data types. (line 308) -* asin: Mathematical functions. - (line 6) -* aSin: Mathematical functions. - (line 20) -* asinh: Mathematical functions. - (line 6) -* Aspect: Frames and pictures. - (line 59) -* assert: Data types. (line 368) -* assignment: Programming. (line 26) -* asy: Data types. (line 358) -* asy <1>: Import. (line 101) -* asy-mode: Editing modes. (line 6) -* asy.vim: Editing modes. (line 32) -* asyinclude: LaTeX usage. (line 45) -* asymptote.sty: LaTeX usage. (line 6) -* asymptote.xml: Editing modes. (line 48) -* ASYMPTOTE_CONFIG: Options. (line 117) -* atan: Mathematical functions. - (line 6) -* aTan: Mathematical functions. - (line 20) -* atan2: Mathematical functions. - (line 6) -* atanh: Mathematical functions. - (line 6) -* atleast: Bezier curves. (line 56) -* attach: Frames and pictures. - (line 273) -* attach <1>: LaTeX usage. (line 50) -* attach <2>: graph. (line 407) -* autoadjust: three. (line 342) -* autoimport: Options. (line 113) -* automatic scaling: graph. (line 691) -* automatic scaling <1>: graph. (line 691) -* axialshade: fill. (line 43) -* axis: graph. (line 906) -* axis <1>: graph. (line 989) -* axis <2>: graph3. (line 66) -* axis <3>: graph3. (line 82) -* azimuth: Data types. (line 153) -* babel: babel. (line 6) -* background color: Frames and pictures. - (line 180) -* BackView: three. (line 370) -* Bar: draw. (line 19) -* Bar3: three. (line 547) -* Bars: draw. (line 19) -* Bars3: three. (line 547) -* barsize: draw. (line 19) -* base modules: Base modules. (line 6) -* basealign: Pens. (line 177) -* baseline: label. (line 90) -* batch mode: Drawing in batch mode. - (line 6) -* beep: Data types. (line 381) -* BeginArcArrow: draw. (line 26) -* BeginArcArrow3: three. (line 547) -* BeginArrow: draw. (line 26) -* BeginArrow3: three. (line 547) -* BeginBar: draw. (line 19) -* BeginBar3: three. (line 547) -* BeginDotMargin: draw. (line 42) -* BeginDotMargin3: three. (line 563) -* BeginMargin: draw. (line 42) -* BeginMargin3: three. (line 563) -* BeginPenMargin: draw. (line 42) -* BeginPenMargin2: three. (line 563) -* BeginPenMargin3: three. (line 563) -* BeginPoint: label. (line 55) -* Bessel: Mathematical functions. - (line 48) -* bevel: flowchart. (line 72) -* beveljoin: Pens. (line 145) -* Bezier curves: Bezier curves. (line 6) -* Bezier patch: three. (line 88) -* Bezier triangle: three. (line 88) -* bezulate: three. (line 106) -* Bi: Mathematical functions. - (line 48) -* Billboard: three. (line 454) -* binary: Files. (line 76) -* binary format: Files. (line 76) -* binary operators: Arithmetic & logical. - (line 6) -* binarytree: binarytree. (line 6) -* Bi_deriv: Mathematical functions. - (line 48) -* black stripes: three. (line 195) -* Blank: draw. (line 26) -* block.bottom: flowchart. (line 19) -* block.bottomleft: flowchart. (line 19) -* block.bottomright: flowchart. (line 19) -* block.center: flowchart. (line 24) -* block.draw: flowchart. (line 29) -* block.left: flowchart. (line 19) -* block.position: flowchart. (line 23) -* 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 25) -* boolean operators: Arithmetic & logical. - (line 6) -* Bottom: graph. (line 132) -* BottomTop: graph. (line 138) -* BottomView: three. (line 370) -* bounding box: Frames and pictures. - (line 180) -* Bounds: graph3. (line 21) -* box: Frames and pictures. - (line 25) -* box <1>: Frames and pictures. - (line 130) -* box <2>: three. (line 289) -* box <3>: three. (line 291) -* bp: Drawing in batch mode. - (line 23) -* brace: Paths and guides. (line 51) -* break: Programming. (line 48) -* breakpoints: Debugger. (line 21) -* brick: Pens. (line 265) -* broken axis: graph. (line 802) -* bug reports: Help. (line 19) -* buildcycle: Paths and guides. (line 270) -* Button-1: GUI. (line 6) -* Button-2: GUI. (line 6) -* BWRainbow: palette. (line 15) -* BWRainbow2: palette. (line 18) -* C string: Data types. (line 216) -* CAD: CAD. (line 6) -* calculateTransform: Frames and pictures. - (line 118) -* camera: three. (line 336) -* casts: Casts. (line 6) -* cbrt: Mathematical functions. - (line 6) -* cd: Files. (line 25) -* ceil: Mathematical functions. - (line 26) -* Center: label. (line 60) -* center: three. (line 319) -* checker: Pens. (line 265) -* Chinese: unicode. (line 12) -* choose: Mathematical functions. - (line 39) -* Ci: Mathematical functions. - (line 48) -* circle: Paths and guides. (line 10) -* Circle: Paths and guides. (line 18) -* circle <1>: three. (line 263) -* circle <2>: flowchart. (line 61) -* circlebarframe: markers. (line 18) -* CJK: unicode. (line 12) -* clamped: graph. (line 36) -* clear: Files. (line 93) -* clear <1>: Debugger. (line 23) -* clip: clip. (line 6) -* CLZ: Arithmetic & logical. - (line 68) -* cm: Figure size. (line 18) -* cmd: Configuring. (line 31) -* cmyk: Pens. (line 34) -* colatitude: Data types. (line 158) -* color: Pens. (line 23) -* coloredNodes: tube. (line 25) -* coloredpath: tube. (line 18) -* coloredSegments: tube. (line 25) -* colorless: Pens. (line 53) -* colors: Pens. (line 50) -* comma: Files. (line 61) -* comma-separated-value mode: Arrays. (line 354) -* command-line options: Configuring. (line 83) -* command-line options <1>: Options. (line 6) -* comment character: Files. (line 16) -* compass directions: Labels. (line 18) -* Compiling from UNIX source: Compiling from UNIX source. - (line 6) -* complement: Arrays. (line 140) -* concat: Arrays. (line 170) -* conditional: Programming. (line 26) -* conditional <1>: Arithmetic & logical. - (line 61) -* config: Configuring. (line 64) -* config <1>: Options. (line 117) -* configuration file: Configuring. (line 21) -* configuration file <1>: Options. (line 117) -* configuring: Configuring. (line 6) -* conj: Data types. (line 62) -* constructors: Structures. (line 91) -* context: Options. (line 146) -* continue: Programming. (line 48) -* continue <1>: Debugger. (line 31) -* contour: contour. (line 6) -* contour3: contour3. (line 6) -* controls: Bezier curves. (line 45) -* controls <1>: three. (line 6) -* controlSpecifier: Paths and guides. (line 396) -* convert: Configuring. (line 64) -* convert <1>: Files. (line 155) -* convert <2>: animation. (line 6) -* convert <3>: Options. (line 146) -* convertOptions: Options. (line 132) -* Coons shading: fill. (line 77) -* copy: Arrays. (line 167) -* cos: Mathematical functions. - (line 6) -* Cos: Mathematical functions. - (line 20) -* cosh: Mathematical functions. - (line 6) -* cputime: Structures. (line 169) -* crop: graph. (line 640) -* cropping graphs: graph. (line 640) -* cross: Data types. (line 106) -* cross <1>: Data types. (line 196) -* cross <2>: graph. (line 481) -* crossframe: markers. (line 22) -* crosshatch: Pens. (line 282) -* csv: Arrays. (line 354) -* CTZ: Arithmetic & logical. - (line 68) -* cubicroots: Arrays. (line 311) -* curl: Bezier curves. (line 66) -* curl <1>: three. (line 6) -* curlSpecifier: Paths and guides. (line 408) -* currentpen: Pens. (line 6) -* currentprojection: three. (line 367) -* curve: slopefield. (line 20) -* custom axis types: graph. (line 141) -* custom mark routine: graph. (line 578) -* custom tick locations: graph. (line 233) -* cut: Paths and guides. (line 251) -* cycle: Figure size. (line 29) -* cycle <1>: Paths. (line 16) -* cycle <2>: three. (line 6) -* cyclic: Paths and guides. (line 85) -* cyclic <1>: Paths and guides. (line 376) -* cyclic <2>: Arrays. (line 39) -* cyclic <3>: three. (line 484) -* Cyrillic: unicode. (line 7) -* dashdotted: Pens. (line 98) -* dashed: Pens. (line 98) -* data types: Data types. (line 6) -* date: Data types. (line 320) -* Debian: UNIX binary distributions. - (line 19) -* debugger: Debugger. (line 6) -* declaration: Programming. (line 26) -* deconstruct: GUI usage. (line 6) -* default arguments: Default arguments. (line 6) -* defaultformat: graph. (line 175) -* DefaultHead: draw. (line 26) -* DefaultHead3: three. (line 547) -* defaultpen: Pens. (line 45) -* defaultpen <1>: Pens. (line 118) -* defaultpen <2>: Pens. (line 123) -* defaultpen <3>: Pens. (line 135) -* defaultpen <4>: Pens. (line 188) -* defaultpen <5>: Pens. (line 343) -* defaultpen <6>: Pens. (line 367) -* defaultrender: three. (line 46) -* deferred drawing: simplex. (line 6) -* degrees: Data types. (line 78) -* degrees <1>: Mathematical functions. - (line 17) -* Degrees: Mathematical functions. - (line 17) -* delete: Files. (line 150) -* delete <1>: Arrays. (line 39) -* description: Description. (line 6) -* diagonal: Arrays. (line 296) -* diamond: flowchart. (line 54) -* dimension: Arrays. (line 359) -* dir: Search paths. (line 9) -* dir <1>: Data types. (line 90) -* dir <2>: Data types. (line 180) -* dir <3>: Paths and guides. (line 109) -* dir <4>: three. (line 484) -* direction specifier: Bezier curves. (line 6) -* directory: Files. (line 25) -* dirSpecifier: Paths and guides. (line 390) -* dirtime: Paths and guides. (line 166) -* display: Configuring. (line 64) -* do: Programming. (line 48) -* DOSendl: Files. (line 61) -* DOSnewl: Files. (line 61) -* dot: draw. (line 82) -* dot <1>: Data types. (line 103) -* dot <2>: Data types. (line 193) -* dot <3>: Arrays. (line 251) -* dot <4>: Arrays. (line 254) -* DotMargin: draw. (line 42) -* DotMargin3: three. (line 563) -* DotMargins: draw. (line 42) -* DotMargins3: three. (line 563) -* dotted: Pens. (line 98) -* double deferred drawing: three. (line 241) -* double precision: Files. (line 76) -* draw: Drawing commands. (line 31) -* draw <1>: draw. (line 6) -* Draw: draw. (line 26) -* draw <2>: draw. (line 109) -* Draw <1>: Frames and pictures. - (line 160) -* draw <3>: three. (line 114) -* drawing commands: Drawing commands. (line 6) -* drawline: math. (line 9) -* drawtree: drawtree. (line 6) -* dvips: Configuring. (line 64) -* dvipsOptions: Options. (line 132) -* dvisvgm: Configuring. (line 64) -* dvisvgm <1>: Options. (line 151) -* dvisvgmOptions: Options. (line 132) -* E: Labels. (line 18) -* E <1>: Mathematical functions. - (line 48) -* Editing modes: Editing modes. (line 6) -* Ei: Mathematical functions. - (line 48) -* ellipse: Paths and guides. (line 45) -* ellipse <1>: Frames and pictures. - (line 25) -* elliptic functions: Mathematical functions. - (line 48) -* else: Programming. (line 26) -* emacs: Editing modes. (line 6) -* embed: embed. (line 6) -* Embedded: three. (line 454) -* empty: Frames and pictures. - (line 7) -* EndArcArrow: draw. (line 26) -* EndArcArrow3: three. (line 547) -* EndArrow: draw. (line 26) -* EndArrow3: three. (line 547) -* EndBar: draw. (line 19) -* EndBar3: three. (line 547) -* EndDotMargin: draw. (line 42) -* EndDotMargin3: three. (line 563) -* endl: Files. (line 61) -* EndMargin: draw. (line 42) -* EndMargin3: three. (line 563) -* EndPenMargin: draw. (line 42) -* EndPenMargin2: three. (line 563) -* EndPenMargin3: three. (line 563) -* EndPoint: label. (line 55) -* envelope: Frames and pictures. - (line 25) -* environment variables: Configuring. (line 87) -* eof: Files. (line 93) -* eof <1>: Arrays. (line 336) -* eol: Files. (line 93) -* eol <1>: Arrays. (line 336) -* EPS: label. (line 78) -* EPS <1>: Options. (line 146) -* erase: Drawing in interactive mode. - (line 11) -* erase <1>: Data types. (line 256) -* erase <2>: Frames and pictures. - (line 7) -* erase <3>: Frames and pictures. - (line 281) -* erf: Mathematical functions. - (line 6) -* erfc: Mathematical functions. - (line 6) -* error: Files. (line 16) -* error <1>: Files. (line 93) -* error bars: graph. (line 532) -* errorbars: graph. (line 481) -* eval: Import. (line 97) -* eval <1>: Import. (line 107) -* evenodd: Paths. (line 37) -* evenodd <1>: Pens. (line 160) -* exit: Data types. (line 372) -* exit <1>: Interactive mode. (line 54) -* exit <2>: Debugger. (line 56) -* exp: Mathematical functions. - (line 6) -* expi: Data types. (line 86) -* expi <1>: Data types. (line 176) -* explicit: Casts. (line 6) -* explicit casts: Casts. (line 21) -* expm1: Mathematical functions. - (line 6) -* exponential integral: Mathematical functions. - (line 48) -* extendcap: Pens. (line 135) -* extension: Paths and guides. (line 246) -* extension <1>: MetaPost. (line 10) -* external: embed. (line 11) -* extrude: three. (line 478) -* F: Mathematical functions. - (line 48) -* fabs: Mathematical functions. - (line 6) -* face: three. (line 588) -* factorial: Mathematical functions. - (line 39) -* Fedora: UNIX binary distributions. - (line 15) -* feynman: feynman. (line 6) -* fft: Arrays. (line 237) -* fft <1>: math. (line 26) -* FFTW: Compiling from UNIX source. - (line 63) -* file: Files. (line 6) -* file <1>: Debugger. (line 44) -* Fill: draw. (line 26) -* fill: draw. (line 114) -* fill <1>: fill. (line 6) -* fill <2>: fill. (line 17) -* Fill <1>: Frames and pictures. - (line 146) -* FillDraw: draw. (line 26) -* filldraw: fill. (line 11) -* FillDraw <1>: Frames and pictures. - (line 136) -* filloutside: fill. (line 27) -* fillrule: Pens. (line 160) -* find: Data types. (line 241) -* find <1>: Arrays. (line 149) -* findall: Arrays. (line 154) -* firstcut: Paths and guides. (line 262) -* fit: Frames and pictures. - (line 113) -* fit3: three. (line 254) -* fixedscaling: Frames and pictures. - (line 81) -* floor: Mathematical functions. - (line 26) -* flowchart: flowchart. (line 6) -* flush: Files. (line 61) -* flush <1>: Files. (line 93) -* fmod: Mathematical functions. - (line 6) -* font: Pens. (line 202) -* font command: Pens. (line 202) -* fontcommand: Pens. (line 217) -* fontsize: Pens. (line 188) -* for: Programming. (line 26) -* format: Data types. (line 289) -* format <1>: Options. (line 146) -* forum: Help. (line 6) -* frame: Frames and pictures. - (line 7) -* from: Import. (line 16) -* FrontView: three. (line 370) -* function declarations: Functions. (line 79) -* Function shading: fill. (line 99) -* function shading: fill. (line 99) -* functions: Functions. (line 6) -* functions <1>: Mathematical functions. - (line 6) -* functionshade: fill. (line 99) -* gamma: Mathematical functions. - (line 6) -* Gaussrand: Mathematical functions. - (line 39) -* geometry: geometry. (line 6) -* getc: Files. (line 30) -* getpair: Files. (line 118) -* getreal: Files. (line 118) -* getstring: Files. (line 118) -* gettriple: Files. (line 118) -* git: Git. (line 6) -* glOptions: three. (line 195) -* glOptions <1>: Options. (line 132) -* 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 78) -* graphical user interface: GUI. (line 6) -* gray: Pens. (line 25) -* grayscale: Pens. (line 25) -* Grayscale: palette. (line 9) -* grid: Pens. (line 265) -* grid <1>: graph. (line 747) -* grid3: grid3. (line 6) -* gs: Configuring. (line 6) -* GSL: Compiling from UNIX source. - (line 63) -* gsl: Mathematical functions. - (line 48) -* gsOptions: Options. (line 132) -* 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 282) -* height: LaTeX usage. (line 50) -* help: Interactive mode. (line 42) -* help <1>: Help. (line 6) -* help <2>: Debugger. (line 30) -* Hermite: graph. (line 36) -* Hermite(splinetype splinetype: graph. (line 36) -* hex: Data types. (line 305) -* hex <1>: Pens. (line 60) -* hexidecimal: Data types. (line 305) -* hexidecimal <1>: Pens. (line 58) -* hidden surface removal: three. (line 588) -* histogram: Mathematical functions. - (line 39) -* history: Files. (line 143) -* history <1>: Interactive mode. (line 54) -* historylines: Interactive mode. (line 57) -* HookHead: draw. (line 26) -* HookHead3: three. (line 547) -* Horizontal: flowchart. (line 77) -* hyperrefOptions: Options. (line 132) -* hypot: Mathematical functions. - (line 6) -* I: Mathematical functions. - (line 48) -* iconic: three. (line 195) -* identity: Transforms. (line 24) -* identity <1>: Mathematical functions. - (line 6) -* identity <2>: Arrays. (line 293) -* identity4: three. (line 422) -* if: Programming. (line 26) -* IgnoreAspect: Frames and pictures. - (line 63) -* image: palette. (line 33) -* image <1>: palette. (line 58) -* ImageMagick: Configuring. (line 64) -* ImageMagick <1>: animation. (line 6) -* ImageMagick <2>: Options. (line 146) -* images: palette. (line 6) -* implicit casts: Casts. (line 6) -* implicit linear solver: MetaPost. (line 10) -* implicit scaling: Implicit scaling. (line 6) -* implicitsurface: smoothcontour3. (line 16) -* import: Import. (line 45) -* inches: Figure size. (line 18) -* incircle: Data types. (line 120) -* include: Import. (line 126) -* including images: label. (line 78) -* increasing: math. (line 59) -* inf: Data types. (line 35) -* inheritance: Structures. (line 181) -* initialized: Arrays. (line 39) -* initializers: Variable initializers. - (line 6) -* inline: LaTeX usage. (line 50) -* InOutTicks: graph3. (line 35) -* input: Files. (line 10) -* input <1>: Files. (line 12) -* input <2>: Interactive mode. (line 45) -* input <3>: Interactive mode. (line 49) -* insert: Data types. (line 252) -* insert <1>: Arrays. (line 39) -* inside: Paths and guides. (line 294) -* inside <1>: Paths and guides. (line 299) -* inside <2>: Paths and guides. (line 305) -* insphere: three. (line 510) -* inst: Debugger. (line 35) -* installation: Installation. (line 6) -* int: Data types. (line 30) -* integer division: Arithmetic & logical. - (line 20) -* interactive mode: Drawing in interactive mode. - (line 6) -* interactive mode <1>: Interactive mode. (line 6) -* interior: Paths and guides. (line 290) -* international characters: unicode. (line 6) -* interp: Arithmetic & logical. - (line 64) -* interpolate: interpolate. (line 6) -* intersect: Paths and guides. (line 195) -* intersect <1>: math. (line 13) -* intersect <2>: three. (line 484) -* intersectionpoint: Paths and guides. (line 238) -* intersectionpoint <1>: math. (line 17) -* intersectionpoint <2>: three. (line 484) -* intersectionpoints: Paths and guides. (line 242) -* intersectionpoints <1>: three. (line 484) -* intersectionpoints <2>: three. (line 497) -* intersections: Paths and guides. (line 206) -* intersections <1>: Paths and guides. (line 213) -* intersections <2>: three. (line 484) -* intersections <3>: three. (line 490) -* InTicks: graph3. (line 35) -* intMax: Data types. (line 30) -* intMin: Data types. (line 30) -* inverse: Transforms. (line 16) -* inverse <1>: Arrays. (line 299) -* invert: three. (line 412) -* invisible: Pens. (line 39) -* isnan: Data types. (line 35) -* i_scaled: Mathematical functions. - (line 48) -* J: Mathematical functions. - (line 6) -* J <1>: Mathematical functions. - (line 48) -* Japanese: unicode. (line 12) -* K: Mathematical functions. - (line 48) -* Kate: Editing modes. (line 48) -* KDE editor: Editing modes. (line 48) -* keepAspect: Frames and pictures. - (line 59) -* keepAspect <1>: Frames and pictures. - (line 63) -* keepAspect <2>: LaTeX usage. (line 50) -* keyboard bindings:: three. (line 173) -* keys: Arrays. (line 39) -* keyword: Named arguments. (line 37) -* keyword-only: Named arguments. (line 37) -* keywords: Named arguments. (line 6) -* Korean: unicode. (line 12) -* k_scaled: Mathematical functions. - (line 48) -* label: Labels. (line 6) -* Label: draw. (line 97) -* label <1>: label. (line 6) -* Label <1>: label. (line 14) -* Label <2>: graph. (line 330) -* label <2>: three. (line 448) -* labelpath: labelpath. (line 6) -* labelpath3: labelpath3. (line 6) -* labelx: graph. (line 330) -* labely: graph. (line 330) -* Landscape: Frames and pictures. - (line 104) -* lastcut: Paths and guides. (line 266) -* lasy-mode: Editing modes. (line 6) -* latex: Options. (line 146) -* LaTeX fonts: Pens. (line 202) -* LaTeX usage: LaTeX usage. (line 6) -* latexmk: LaTeX usage. (line 30) -* latin1: latin1. (line 6) -* latitude: Data types. (line 163) -* latticeshade: fill. (line 32) -* layer: Drawing commands. (line 16) -* leastsquares: stats. (line 6) -* leastsquares <1>: graph. (line 930) -* Left: graph. (line 269) -* LeftRight: graph. (line 275) -* LeftSide: label. (line 60) -* LeftTicks: graph. (line 160) -* LeftTicks <1>: graph. (line 233) -* LeftView: three. (line 370) -* legend: Drawing commands. (line 31) -* legend <1>: draw. (line 64) -* legend <2>: graph. (line 425) -* Legendre: Mathematical functions. - (line 48) -* length: Data types. (line 65) -* length <1>: Data types. (line 144) -* length <2>: Data types. (line 238) -* length <3>: Paths and guides. (line 76) -* length <4>: Paths and guides. (line 373) -* length <5>: Arrays. (line 39) -* length <6>: three. (line 484) -* letter: Configuring. (line 58) -* lexorder: math. (line 67) -* lexorder <1>: math. (line 70) -* libgs: Configuring. (line 64) -* libgs <1>: Options. (line 151) -* libm routines: Mathematical functions. - (line 6) -* libsigsegv: Functions. (line 100) -* libsigsegv <1>: Help. (line 27) -* limits: graph. (line 640) -* line: Arrays. (line 336) -* line <1>: Arrays. (line 340) -* line mode: Arrays. (line 336) -* Linear: graph. (line 691) -* linecap: Pens. (line 135) -* linejoin: Pens. (line 145) -* lineskip: Pens. (line 188) -* linetype: Pens. (line 119) -* linewidth: Pens. (line 123) -* locale: Data types. (line 315) -* log: Mathematical functions. - (line 6) -* Log: graph. (line 691) -* log-log graph: graph. (line 725) -* log10: Mathematical functions. - (line 6) -* log1p: Mathematical functions. - (line 6) -* log2 graph: graph. (line 781) -* logarithmic graph: graph. (line 725) -* logical operators: Arithmetic & logical. - (line 6) -* longdashdotted: Pens. (line 98) -* longdashed: Pens. (line 98) -* longitude: Data types. (line 168) -* loop: Programming. (line 26) -* lualatex: Options. (line 146) -* luatex: Options. (line 146) -* MacOS X binary distributions: MacOS X binary distributions. - (line 6) -* makepen: Pens. (line 318) -* map: Arrays. (line 131) -* Margin: draw. (line 42) -* Margin <1>: draw. (line 42) -* Margin3: three. (line 563) -* Margin3 <1>: three. (line 563) -* Margins: draw. (line 42) -* margins: three. (line 247) -* Margins3: three. (line 563) -* mark: graph. (line 481) -* markangle: markers. (line 35) -* marker: graph. (line 481) -* markers: markers. (line 6) -* marknodes: graph. (line 481) -* markuniform: graph. (line 481) -* mask: Data types. (line 35) -* math: math. (line 6) -* mathematical functions: Mathematical functions. - (line 6) -* max: Paths and guides. (line 279) -* max <1>: Frames and pictures. - (line 7) -* max <2>: Arrays. (line 218) -* max <3>: Arrays. (line 228) -* max <4>: three. (line 484) -* maxbound: Data types. (line 134) -* maxbound <1>: Data types. (line 204) -* maxtile: three. (line 195) -* maxtimes: Paths and guides. (line 233) -* maxviewport: three. (line 195) -* MetaPost: MetaPost. (line 6) -* MetaPost ... : Bezier curves. (line 70) -* MetaPost cutafter: Paths and guides. (line 267) -* MetaPost cutbefore: Paths and guides. (line 263) -* MetaPost pickup: Pens. (line 6) -* MetaPost whatever: MetaPost. (line 10) -* Microsoft Windows: Microsoft Windows. (line 6) -* MidArcArrow: draw. (line 26) -* MidArcArrow3: three. (line 547) -* MidArrow: draw. (line 26) -* MidArrow3: three. (line 547) -* MidPoint: label. (line 55) -* midpoint: Paths and guides. (line 180) -* min: Paths and guides. (line 275) -* min <1>: Frames and pictures. - (line 7) -* min <2>: Arrays. (line 213) -* min <3>: Arrays. (line 223) -* min <4>: three. (line 484) -* minbound: Data types. (line 131) -* minbound <1>: Data types. (line 201) -* minipage: label. (line 116) -* mintimes: Paths and guides. (line 228) -* miterjoin: Pens. (line 145) -* miterlimit: Pens. (line 155) -* mktemp: Files. (line 44) -* mm: Figure size. (line 18) -* mode: Files. (line 76) -* mode <1>: Files. (line 89) -* monotonic: graph. (line 36) -* mouse: GUI. (line 6) -* mouse bindings: three. (line 151) -* Move: Pens. (line 355) -* MoveQuiet: Pens. (line 361) -* multisample: three. (line 142) -* N: Labels. (line 18) -* name: Files. (line 89) -* named arguments: Named arguments. (line 6) -* nan: Data types. (line 35) -* natural: graph. (line 36) -* new: Structures. (line 6) -* new <1>: Arrays. (line 100) -* new <2>: Arrays. (line 103) -* newframe: Frames and pictures. - (line 7) -* newl: Files. (line 61) -* newton: Mathematical functions. - (line 66) -* newton <1>: Mathematical functions. - (line 73) -* next: Debugger. (line 41) -* NFSS: Pens. (line 202) -* nobasealign: Pens. (line 177) -* NoFill: draw. (line 26) -* NoFill <1>: Frames and pictures. - (line 154) -* NoMargin: draw. (line 42) -* NoMargin3: three. (line 563) -* None: draw. (line 19) -* None <1>: draw. (line 26) -* none: Files. (line 61) -* normal: three. (line 470) -* nosafe: Options. (line 170) -* NOT: Arithmetic & logical. - (line 68) -* notaknot: graph. (line 36) -* NoTicks: graph. (line 160) -* NoTicks3: graph3. (line 35) -* null: Structures. (line 6) -* nullpen: label. (line 14) -* nullpen <1>: Frames and pictures. - (line 140) -* nullpen <2>: Frames and pictures. - (line 149) -* NURBS: three. (line 346) -* O: three. (line 259) -* obj: obj. (line 6) -* oblique: three. (line 302) -* obliqueX: three. (line 309) -* obliqueY: three. (line 315) -* obliqueZ: three. (line 302) -* ode: ode. (line 6) -* offset: Pens. (line 119) -* offset <1>: Options. (line 175) -* OmitTick: graph. (line 223) -* OmitTickInterval: graph. (line 223) -* OmitTickIntervals: graph. (line 223) -* opacity: Pens. (line 233) -* open: Files. (line 12) -* OpenGL: three. (line 142) -* operator: User-defined operators. - (line 6) -* operator +(...string[] a).: Data types. (line 283) -* operator --: graph. (line 30) -* operator ..: graph. (line 33) -* operator answer: Interactive mode. (line 35) -* operator cast: Casts. (line 38) -* operator ecast: Casts. (line 65) -* operator init: Variable initializers. - (line 6) -* operator init <1>: Structures. (line 134) -* operators: Operators. (line 6) -* options: Options. (line 6) -* OR: Arithmetic & logical. - (line 68) -* orient: Data types. (line 108) -* orient <1>: three. (line 501) -* orientation: Frames and pictures. - (line 104) -* orthographic: three. (line 319) -* outformat: three. (line 142) -* outprefix: Frames and pictures. - (line 91) -* output: Files. (line 36) -* output <1>: Options. (line 146) -* OutTicks: graph3. (line 35) -* overloading functions: Functions. (line 55) -* overwrite: Pens. (line 340) -* P: Mathematical functions. - (line 48) -* pack: label. (line 100) -* packing: Rest arguments. (line 30) -* pair: Figure size. (line 6) -* pair <1>: Data types. (line 46) -* pairs: Arrays. (line 233) -* paperheight: Configuring. (line 58) -* papertype: Configuring. (line 58) -* paperwidth: Configuring. (line 58) -* parallelogram: flowchart. (line 47) -* parametric surface: graph3. (line 99) -* parametrized curve: graph. (line 640) -* partialsum: math. (line 53) -* partialsum <1>: math. (line 56) -* patch-dependent colors: three. (line 79) -* path: Paths. (line 6) -* path <1>: Paths and guides. (line 7) -* path <2>: three. (line 42) -* path <3>: flowchart. (line 77) -* path markers: graph. (line 481) -* path3: three. (line 6) -* path3 <1>: three. (line 42) -* path[]: Paths. (line 23) -* patterns: Pens. (line 251) -* patterns <1>: patterns. (line 6) -* PDF: Options. (line 146) -* pdflatex: Options. (line 146) -* pdfreloadOptions: Options. (line 132) -* pdfviewer: Configuring. (line 6) -* pdfviewerOptions: Options. (line 132) -* pen: Pens. (line 6) -* PenMargin: draw. (line 42) -* PenMargin2: three. (line 563) -* PenMargin3: three. (line 563) -* PenMargins: draw. (line 42) -* PenMargins2: three. (line 563) -* PenMargins3: three. (line 563) -* periodic: graph. (line 36) -* perl: LaTeX usage. (line 30) -* perpendicular: geometry. (line 6) -* perspective: three. (line 346) -* picture: Frames and pictures. - (line 39) -* picture alignment: Frames and pictures. - (line 228) -* piecewisestraight: Paths and guides. (line 92) -* pixel: three. (line 570) -* Pl: Mathematical functions. - (line 48) -* plain: plain. (line 6) -* planar: three. (line 88) -* plane: three. (line 285) -* planeproject: three. (line 467) -* point: Paths and guides. (line 95) -* point <1>: Paths and guides. (line 379) -* point <2>: three. (line 484) -* polar: Data types. (line 148) -* polargraph: graph. (line 88) -* polygon: graph. (line 481) -* pop: Arrays. (line 39) -* Portrait: Frames and pictures. - (line 104) -* postcontrol: Paths and guides. (line 146) -* postcontrol <1>: three. (line 484) -* postfix operators: Self & prefix operators. - (line 19) -* postscript: Frames and pictures. - (line 294) -* PostScript fonts: Pens. (line 220) -* PostScript subpath: Paths. (line 23) -* pow10: Mathematical functions. - (line 6) -* prc: three. (line 216) -* precision: Files. (line 93) -* precontrol: Paths and guides. (line 139) -* precontrol <1>: three. (line 484) -* prefix operators: Self & prefix operators. - (line 6) -* private: Structures. (line 6) -* programming: Programming. (line 6) -* pstoedit: PostScript to Asymptote. - (line 6) -* psviewer: Configuring. (line 6) -* psviewerOptions: Options. (line 132) -* pt: Figure size. (line 18) -* public: Structures. (line 6) -* push: Arrays. (line 39) -* Python usage: Interactive mode. (line 72) -* quadraticroots: Arrays. (line 302) -* quadraticroots <1>: Arrays. (line 307) -* quarticroots: math. (line 22) -* quick reference: Description. (line 81) -* quit: Drawing in interactive mode. - (line 11) -* quit <1>: Interactive mode. (line 54) -* quit <2>: Debugger. (line 53) -* quote: Import. (line 115) -* quotient: Arithmetic & logical. - (line 6) -* radialshade: fill. (line 51) -* RadialShade: Frames and pictures. - (line 172) -* RadialShadeDraw: Frames and pictures. - (line 176) -* radians: Mathematical functions. - (line 17) -* radius: Paths and guides. (line 135) -* radius <1>: three. (line 484) -* Rainbow: palette. (line 12) -* rand: Mathematical functions. - (line 39) -* randMax: Mathematical functions. - (line 39) -* read: Arrays. (line 376) -* reading: Files. (line 12) -* reading string arrays: Arrays. (line 346) -* readline: Files. (line 135) -* real: Data types. (line 35) -* realDigits: Data types. (line 35) -* realEpsilon: Data types. (line 35) -* realMax: Data types. (line 35) -* realMin: Data types. (line 35) -* realmult: Data types. (line 100) -* rectangle: flowchart. (line 34) -* recursion: Functions. (line 100) -* reference: Description. (line 81) -* reflect: Transforms. (line 42) -* Relative: label. (line 50) -* Relative <1>: label. (line 60) -* relpoint: Paths and guides. (line 176) -* reltime: Paths and guides. (line 172) -* remainder: Mathematical functions. - (line 6) -* rename: Files. (line 152) -* render: three. (line 46) -* render <1>: three. (line 142) -* render <2>: Options. (line 146) -* replace: Data types. (line 269) -* resetdefaultpen: Pens. (line 367) -* rest arguments: Rest arguments. (line 6) -* restore: Frames and pictures. - (line 288) -* restricted: Structures. (line 6) -* return: Debugger. (line 47) -* reverse: Data types. (line 265) -* reverse <1>: Paths and guides. (line 183) -* reverse <2>: Paths and guides. (line 382) -* reverse <3>: Arrays. (line 136) -* reverse <4>: three. (line 484) -* rewind: Files. (line 93) -* rfind: Data types. (line 246) -* rgb: Pens. (line 30) -* rgb <1>: Pens. (line 58) -* Riemann zeta function: Mathematical functions. - (line 48) -* Right: graph. (line 272) -* RightSide: label. (line 60) -* RightTicks: graph. (line 160) -* RightTicks <1>: graph. (line 233) -* RightView: three. (line 370) -* Rotate: label. (line 36) -* rotate: three. (line 438) -* Rotate(pair z): label. (line 39) -* round: Mathematical functions. - (line 26) -* roundcap: Pens. (line 135) -* roundedpath: roundedpath. (line 6) -* roundjoin: Pens. (line 145) -* roundrectangle: flowchart. (line 66) -* RPM: UNIX binary distributions. - (line 6) -* runtime imports: Import. (line 97) -* Russian: unicode. (line 7) -* S: Labels. (line 18) -* safe: Options. (line 170) -* save: Frames and pictures. - (line 285) -* saveline: Files. (line 135) -* Scale: label. (line 45) -* scale: Pens. (line 119) -* scale <1>: Transforms. (line 34) -* scale <2>: Transforms. (line 36) -* scale <3>: graph. (line 691) -* Scale <1>: graph. (line 708) -* scale <4>: three. (line 437) -* scale3: three. (line 435) -* scaled graph: graph. (line 671) -* scientific graph: graph. (line 388) -* scroll: Files. (line 109) -* search: Arrays. (line 157) -* search <1>: Arrays. (line 163) -* search paths: Search paths. (line 6) -* Seascape: Frames and pictures. - (line 110) -* secondary axis: graph. (line 834) -* secondaryX: graph. (line 834) -* secondaryY: graph. (line 834) -* seconds: Data types. (line 329) -* seek: Files. (line 93) -* seekeof: Files. (line 93) -* segment: math. (line 50) -* segmentation fault: Help. (line 27) -* self operators: Self & prefix operators. - (line 6) -* sequence: Arrays. (line 118) -* settings: Configuring. (line 21) -* settings <1>: Options. (line 117) -* sgn: Mathematical functions. - (line 26) -* shading: fill. (line 32) -* Shift: label. (line 33) -* shift: Transforms. (line 26) -* shift <1>: Transforms. (line 28) -* shift <2>: Transforms. (line 44) -* shift <3>: three. (line 427) -* shiftless: Transforms. (line 44) -* shipout: Frames and pictures. - (line 91) -* showtarget: three. (line 319) -* Si: Mathematical functions. - (line 48) -* signedint: Files. (line 76) -* signedint <1>: Files. (line 89) -* SimpleHead: draw. (line 26) -* simplex: simplex. (line 6) -* simpson: Mathematical functions. - (line 82) -* sin: Mathematical functions. - (line 6) -* Sin: Mathematical functions. - (line 20) -* single precision: Files. (line 76) -* singleint: Files. (line 76) -* singleint <1>: Files. (line 89) -* singlereal: Files. (line 76) -* singlereal <1>: Files. (line 89) -* sinh: Mathematical functions. - (line 6) -* SixViews: three. (line 385) -* SixViewsFR: three. (line 385) -* SixViewsUS: three. (line 385) -* size: Figure size. (line 6) -* size <1>: Paths and guides. (line 81) -* size <2>: Paths and guides. (line 370) -* size <3>: Frames and pictures. - (line 48) -* size <4>: Frames and pictures. - (line 74) -* size <5>: three. (line 484) -* size <6>: Options. (line 146) -* size3: three. (line 244) -* Slant: label. (line 42) -* slant: Transforms. (line 38) -* sleep: Data types. (line 375) -* slice: Paths and guides. (line 251) -* slice <1>: Paths and guides. (line 262) -* slices: Slices. (line 6) -* slide: slide. (line 6) -* slope: math. (line 44) -* slope <1>: math. (line 47) -* slopefield: slopefield. (line 6) -* smoothcontour3: smoothcontour3. (line 6) -* sncndn: Mathematical functions. - (line 48) -* solid: Pens. (line 98) -* solids: solids. (line 6) -* solve: Arrays. (line 271) -* solve <1>: Arrays. (line 287) -* sort: Arrays. (line 177) -* sort <1>: Arrays. (line 181) -* sort <2>: Arrays. (line 196) -* Spline: graph. (line 33) -* Spline <1>: graph3. (line 99) -* split: Data types. (line 278) -* sqrt: Mathematical functions. - (line 6) -* squarecap: Pens. (line 135) -* srand: Mathematical functions. - (line 39) -* stack overflow: Functions. (line 100) -* stack overflow <1>: Functions. (line 100) -* stack overflow <2>: Help. (line 27) -* static: Static. (line 6) -* stats: stats. (line 6) -* stdin: Files. (line 48) -* stdout: Files. (line 48) -* step: Debugger. (line 38) -* stickframe: markers. (line 16) -* stop: Debugger. (line 10) -* straight: Paths and guides. (line 88) -* Straight: graph. (line 30) -* straight <1>: three. (line 484) -* strftime: Data types. (line 320) -* strftime <1>: Data types. (line 345) -* string: Data types. (line 207) -* string <1>: Data types. (line 311) -* stroke: fill. (line 36) -* stroke <1>: clip. (line 6) -* strokepath: Paths and guides. (line 309) -* strptime: Data types. (line 329) -* struct: Structures. (line 6) -* structures: Structures. (line 6) -* subpath: Paths and guides. (line 186) -* subpath <1>: three. (line 484) -* subpictures: Frames and pictures. - (line 113) -* substr: Data types. (line 261) -* sum: Arrays. (line 208) -* superpath: Paths. (line 23) -* Suppress: Pens. (line 347) -* SuppressQuiet: Pens. (line 351) -* surface: three. (line 46) -* surface <1>: three. (line 88) -* surface <2>: three. (line 102) -* surface <3>: graph3. (line 99) -* SVG: Options. (line 151) -* system: Data types. (line 353) -* system <1>: Options. (line 170) -* syzygy: syzygy. (line 6) -* tab: Files. (line 61) -* tab completion: Drawing in interactive mode. - (line 11) -* tan: Mathematical functions. - (line 6) -* Tan: Mathematical functions. - (line 20) -* tanh: Mathematical functions. - (line 6) -* target: three. (line 319) -* tell: Files. (line 93) -* tension: Bezier curves. (line 56) -* tension <1>: three. (line 6) -* tensionSpecifier: Paths and guides. (line 402) -* tensor product shading: fill. (line 77) -* tensorshade: fill. (line 77) -* tessellation: three. (line 114) -* tex: Frames and pictures. - (line 302) -* tex <1>: Options. (line 146) -* TeX fonts: Pens. (line 211) -* TeX string: Data types. (line 207) -* texcommand: Configuring. (line 64) -* TeXHead: draw. (line 26) -* TeXHead3: three. (line 547) -* texpath: Configuring. (line 64) -* texpath <1>: label. (line 113) -* texpreamble: Frames and pictures. - (line 311) -* texreset: Frames and pictures. - (line 315) -* textbook graph: graph. (line 360) -* tgz: UNIX binary distributions. - (line 6) -* thick: three. (line 125) -* thin: three. (line 125) -* this: Structures. (line 6) -* three: three. (line 6) -* ThreeViews: three. (line 385) -* ThreeViewsFR: three. (line 385) -* ThreeViewsUS: three. (line 385) -* tick: graph. (line 330) -* ticks: graph. (line 160) -* Ticks: graph. (line 160) -* Ticks <1>: graph. (line 233) -* tildeframe: markers. (line 24) -* tile: Pens. (line 265) -* tilings: Pens. (line 251) -* time: Data types. (line 320) -* time <1>: Data types. (line 345) -* time <2>: math. (line 30) -* time <3>: math. (line 34) -* times: Paths and guides. (line 220) -* times <1>: Paths and guides. (line 224) -* Top: graph. (line 135) -* TopView: three. (line 370) -* trace: Debugger. (line 50) -* trailingzero: graph. (line 175) -* transform: Transforms. (line 6) -* transform <1>: three. (line 459) -* transform3: three. (line 422) -* transparency: Pens. (line 233) -* transpose: Arrays. (line 200) -* transpose <1>: Arrays. (line 203) -* tree: tree. (line 6) -* trembling: trembling. (line 6) -* triangle: geometry. (line 6) -* triangles: three. (line 114) -* triangulate: contour. (line 149) -* tridiagonal: Arrays. (line 258) -* trigonometric integrals: Mathematical functions. - (line 48) -* triple: Data types. (line 137) -* TrueMargin: draw. (line 42) -* TrueMargin3: three. (line 563) -* tube: three. (line 125) -* tube <1>: tube. (line 6) -* tutorial: Tutorial. (line 6) -* type1cm: Pens. (line 188) -* typedef: Data types. (line 384) -* typedef <1>: Functions. (line 46) -* U3D: embed. (line 22) -* undefined: Paths and guides. (line 283) -* UnFill: draw. (line 26) -* unfill: fill. (line 109) -* UnFill <1>: Frames and pictures. - (line 165) -* UnFill <2>: Frames and pictures. - (line 168) -* unicode: unicode. (line 6) -* uniform: Arrays. (line 145) -* uninstall: Uninstall. (line 6) -* unique: math. (line 63) -* unit: Data types. (line 83) -* unit <1>: Data types. (line 173) -* unitbox: Paths. (line 44) -* unitbox <1>: three. (line 291) -* unitcircle: Paths. (line 17) -* unitcircle <1>: Paths. (line 17) -* unitcircle <2>: three. (line 259) -* unitrand: Mathematical functions. - (line 39) -* unitsize: Figure size. (line 39) -* unitsize <1>: Frames and pictures. - (line 69) -* UNIX binary distributions: UNIX binary distributions. - (line 6) -* unpacking: Rest arguments. (line 39) -* unravel: Import. (line 29) -* up: three. (line 319) -* update: Files. (line 36) -* UpsideDown: Frames and pictures. - (line 104) -* UpsideDown <1>: Frames and pictures. - (line 110) -* usepackage: Frames and pictures. - (line 318) -* user coordinates: Figure size. (line 39) -* user-defined operators: User-defined operators. - (line 6) -* usleep: Data types. (line 378) -* value: math. (line 38) -* value <1>: math. (line 41) -* var: Variable initializers. - (line 55) -* variable initializers: Variable initializers. - (line 6) -* vectorfield: graph. (line 1005) -* vectorfield <1>: graph. (line 1044) -* vectorfield3: graph3. (line 157) -* vectorization: Arrays. (line 315) -* verbatim: Frames and pictures. - (line 294) -* vertex-dependent colors: three. (line 79) -* Vertical: flowchart. (line 77) -* viewportheight: LaTeX usage. (line 50) -* viewportmargin: three. (line 247) -* viewportsize: three. (line 247) -* viewportwidth: LaTeX usage. (line 50) -* views: three. (line 216) -* vim: Editing modes. (line 32) -* virtual functions: Structures. (line 181) -* void: Data types. (line 10) -* W: Labels. (line 18) -* whatever: Paths and guides. (line 246) -* Wheel: palette. (line 22) -* wheel mouse: GUI. (line 6) -* while: Programming. (line 48) -* white-space string delimiter mode: Arrays. (line 346) -* width: LaTeX usage. (line 50) -* windingnumber: Paths and guides. (line 283) -* word: Arrays. (line 346) -* write: Files. (line 53) -* write <1>: Arrays. (line 385) -* X: three. (line 259) -* xasy: GUI. (line 6) -* xaxis3: graph3. (line 7) -* xdr: Files. (line 76) -* xelatex: Options. (line 146) -* XEquals: graph. (line 265) -* xequals: graph. (line 278) -* xlimits: graph. (line 640) -* XOR: Arithmetic & logical. - (line 68) -* xpart: Data types. (line 94) -* xpart <1>: Data types. (line 184) -* xscale: Transforms. (line 30) -* xscale3: three. (line 429) -* xtick: graph. (line 330) -* XY: three. (line 444) -* XY <1>: three. (line 459) -* XYEquals: graph3. (line 21) -* XYZero: graph3. (line 21) -* XZEquals: graph3. (line 21) -* XZero: graph. (line 260) -* XZZero: graph3. (line 21) -* Y: Mathematical functions. - (line 6) -* Y <1>: Mathematical functions. - (line 48) -* Y <2>: three. (line 259) -* yaxis3: graph3. (line 7) -* YEquals: graph. (line 128) -* yequals: graph. (line 278) -* ylimits: graph. (line 640) -* ypart: Data types. (line 97) -* ypart <1>: Data types. (line 187) -* yscale: Transforms. (line 32) -* yscale3: three. (line 431) -* ytick: graph. (line 330) -* YX: three. (line 459) -* YZ: three. (line 459) -* YZEquals: graph3. (line 21) -* YZero: graph. (line 123) -* YZZero: graph3. (line 21) -* Z: three. (line 259) -* zaxis3: graph3. (line 7) -* zerowinding: Pens. (line 160) -* 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) -* zeta: Mathematical functions. - (line 48) -* zpart: Data types. (line 190) -* zscale3: three. (line 433) -* ZX: three. (line 459) -* ZX <1>: three. (line 459) -* ZY: three. 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