diff options
| author | Karl Berry <karl@freefriends.org> | 2009-06-29 00:33:00 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2009-06-29 00:33:00 +0000 |
| commit | 566483b69737178fcdbc660393211871ac4c4e85 (patch) | |
| tree | 5562051f07569114ef9b7803cb8be0d43abe0eb0 | |
| parent | 50d15141640d062a1528132d10af8ae1e4d0279a (diff) | |
remove stale files
git-svn-id: svn://tug.org/texlive/trunk@13996 c570f23f-e606-0410-a88d-b1316a301751
| -rw-r--r-- | Build/source/utils/asymptote/.cvsignore | 17 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/base/asy-keywords.el | 17 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/png/asymptote.info | 9929 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/png/asymptote.info-1 | 7593 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/png/asymptote.info-2 | 1795 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6.patch | 156 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6msdos.patch | 52 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/patches/movie15_20090323.patch | 11 |
8 files changed, 0 insertions, 19570 deletions
diff --git a/Build/source/utils/asymptote/.cvsignore b/Build/source/utils/asymptote/.cvsignore deleted file mode 100644 index df332c67bb9..00000000000 --- a/Build/source/utils/asymptote/.cvsignore +++ /dev/null @@ -1,17 +0,0 @@ -*.d -*.eps -*.gif -camp.tab.cc -camp.tab.h -camp.output -lex.yy.cc -asy -configure -config.status -config.log -Makefile -autom4te.cache -config.h -config.h.in -.asy_history -genrun.cc diff --git a/Build/source/utils/asymptote/base/asy-keywords.el b/Build/source/utils/asymptote/base/asy-keywords.el deleted file mode 100644 index f699de8de8a..00000000000 --- a/Build/source/utils/asymptote/base/asy-keywords.el +++ /dev/null @@ -1,17 +0,0 @@ -;; -;; This file is automatically generated by asy-list.pl. -;; Changes will be overwritten. -;; -(defvar asy-keywords-version "1.73") - -(defvar asy-keyword-name '( -and controls tension atleast curl if else while for do return break continue struct typedef new access import unravel from include quote static public private restricted this explicit true false null cycle newframe operator )) - -(defvar asy-type-name '( -Braid Label Legend Rmf TreeNode abscissa arc arrowhead binarytree binarytreeNode block bool bool3 bounds bqe circle conic coord coordsys cputime ellipse file filltype frame grid3 guide horner hsv hyperbola indexedTransform int inversion key line linefit marginT marker mass object pair parabola path path3 pen picture point position projection real revolution scaleT scientific segment side slice splitface string surface tensionSpecifier ticklocate ticksgridT tickvalues transform transformation tree triangle trilinear triple vector vertex void )) - -(defvar asy-function-name '( -AND Arc ArcArrow ArcArrows Arrow Arrows Automatic AvantGarde BBox BWRainbow BWRainbow2 Bar Bars BeginArcArrow BeginArrow BeginBar BeginDotMargin BeginMargin BeginPenMargin Blank Bookman Bottom BottomTop Bounds Break Broken BrokenLog Ceil Circle CircleBarIntervalMarker Cos Courier CrossIntervalMarker DefaultFormat DefaultLogFormat Degrees Dir DotMargin DotMargins Dotted Draw Drawline Embed EndArcArrow EndArrow EndBar EndDotMargin EndMargin EndPenMargin Fill FillDraw Floor Format Full Gaussian Gaussrand Gaussrandpair Gradient Grayscale Helvetica Hermite HookHead InOutTicks InTicks J Label Landscape Left LeftRight LeftTicks Legend Linear Link Log LogFormat Margin Margins Mark MidArcArrow MidArrow NOT NewCenturySchoolBook NoBox NoMargin NoModifier NoTicks NoTicks3 NoZero NoZeroFormat None OR OmitFormat OmitTick OutTicks Ox Oy Palatino PaletteTicks Pen PenMargin PenMargins Pentype Portrait RadialShade Rainbow Range Relative Right RightTicks Rotate Round Scale ScaleX ScaleY ScaleZ Seascape Shift Sin Slant Spline StickIntervalMarker Straight Symbol Tan TeXify Ticks Ticks3 TildeIntervalMarker TimesRoman Top TrueMargin UnFill UpsideDown Wheel X XEquals XOR XY XYEquals XYZero XYgrid XZEquals XZZero XZero XZgrid Y YEquals YXgrid YZ YZEquals YZZero YZero YZgrid Z ZX ZXgrid ZYgrid ZapfChancery ZapfDingbats _cputime _draw _eval _image _labelpath _strokepath _texpath aCos aSin aTan abort abs accel acos acosh acot acsc add addArrow addMargins addSaveFunction addnode addnodes addpenarc addpenline addseg adjust alias align all altitude angabscissa angle angpoint animate annotate anticomplementary antipedal apply approximate arc arcarrowsize arccircle arcdir arcfromcenter arcfromfocus arclength arcnodesnumber arcpoint arcsubtended arcsubtendedcenter arctime arctopath array arrow arrow2 arrowbase arrowbasepoints arrowsize asec asin asinh ask assert asy asycode asydir asyfigure asyfilecode asyinclude asywrite atan atan2 atanh atbreakpoint atexit atime attach attract atupdate autoformat autoscale autoscale3 axes axes3 axialshade axis axiscoverage azimuth babel background bangles bar barmarksize barsize basealign baseline bbox beep beginclip begingroup beginpoint between bevel bezier bezierP bezierPP bezierPPP bezulate bibliography bibliographystyle binarytree binarytreeNode binomial binput bins bisector bisectorpoint bispline blend boutput box bqe breakpoint breakpoints brick buildRestoreDefaults buildRestoreThunk buildcycle bulletcolor canonical canonicalcartesiansystem cartesiansystem case1 case2 case3 cbrt cd ceil center centerToFocus centroid cevian change2 changecoordsys checkSegment checkconditionlength checker checklengths checkposition checktriangle choose circle circlebarframe circlemarkradius circlenodesnumber circumcenter circumcircle clamped clear clip clipdraw close cmyk code colatitude collect collinear color colorless colors colorspace comma compassmark complement complementary concat concurrent cone conic conicnodesnumber conictype conj connect containmentTree contains contour contour3 controlSpecifier convert coordinates coordsys copy cos cosh cot countIntersections cputime crop cropcode cross crossframe crosshatch crossmarksize csc csv cubicroots curabscissa curlSpecifier curpoint currentarrow currentexitfunction currentmomarrow currentpolarconicroutine curve cut cutafter cutbefore cyclic cylinder debugger deconstruct defaultdir defaultformat defaultpen defaultspline defined degenerate degrees delete deletepreamble determinant diagonal diamond diffdiv dimension dir dirSpecifier dirtime display distance divisors do_overpaint dot dotframe dotsize downcase draw drawAll drawDoubleLine drawFermion drawGhost drawGluon drawMomArrow drawPhoton drawScalar drawVertex drawVertexBox drawVertexBoxO drawVertexBoxX drawVertexO drawVertexOX drawVertexTriangle drawVertexTriangleO drawVertexX drawarrow drawarrow2 drawline drawtick duplicate elle ellipse ellipsenodesnumber embed embed3 empty enclose endScript endclip endgroup endl endpoint endpoints eof eol equation equations erase erf erfc error errorbar errorbars euler eval excenter excircle exit exitXasyMode exitfunction exp expi expm1 exradius extend extension extouch fabs factorial fermat fft fhorner figure file filecode fill filldraw filloutside fillrule filltype find finite firstcut firstframe fit fixedscaling floor flush fmdefaults fmod focusToCenter font fontcommand fontsize foot format frac frequency fromCenter fromFocus fspline functionshade gamma generate_random_backtrace generateticks gergonne getc getint getpair getreal getstring gettriple gluon gouraudshade graph graphic gray grestore grid grid3 gsave halfbox hatch hdiffdiv hermite hex histogram history hline hprojection hsv hyperbola hyperbolanodesnumber hyperlink hypot identity image incenter incentral incircle increasing incrementposition indexedTransform initXasyMode initdefaults input inradius insert inside interactive interior interp interpolate intersect intersection intersectionpoint intersectionpoints intersections intouch inverse inversion invisible is3D isDuplicate isogonal isogonalconjugate isotomic isotomicconjugate isparabola italic item key kurtosis kurtosisexcess label labelaxis labelmargin labelpath labels labeltick labelx labelx3 labely labely3 labelz labelz3 lastcut latex latitude latticeshade layer layout ldexp leastsquares legend legenditem length lift limits line linear linecap linejoin linemargin lineskip linetype linewidth link list locale locate locatefile location log log10 log1p logaxiscoverage longitude lookup magnetize makeNode makedraw makepen map margin markangle markangleradius markanglespace markarc marker markinterval marknodes markrightangle markuniform mass masscenter massformat math max max3 maxbound maxcoords maxlength maxratio maxtimes mean medial median midpoint min min3 minbound minipage minratio mintimes miterlimit momArrowPath momarrowsize monotonic nativeformat natural needshipout newl newpage newslide newton newtree nextframe nextnormal nextpage nib nodabscissa none normalvideo notaknot numberpage nurb object offset onpath opacity opposite orientation orig_circlenodesnumber orig_circlenodesnumber1 orig_draw orig_ellipsenodesnumber orig_ellipsenodesnumber1 orig_hyperbolanodesnumber orig_parabolanodesnumber origin orthic orthocentercenter outformat outline outprefix output overwrite pack pairs palette parabola parabolanodesnumber parallel partialsum path path3 pattern pause pdf pedal periodic perp perpendicular perpendicularmark phantom photon piecewisestraight point polar polarconicroutine polargraph polygon postcontrol postscript pow10 ppoint prc prc0 precision precontrol prepend print_random_addresses project projection purge pwhermite quadrant quadraticroots quantize quarticroots quotient radialshade radians radicalcenter radicalline radius rand randompath rd read1 read2 read3 readline realmult realquarticroots rectangle rectangular rectify reflect relabscissa relative relativedistance reldir relpoint reltime remainder remark removeDuplicates rename replace report rescale rescale2 resetdefaultpen restore restoredefaults reverse reversevideo rf rfind rgb rgba rgbint rmf rms rotate rotateO rotation round roundbox roundedpath roundrectangle samecoordsys sameside sample save savedefaults saveline scale scale3 scaleO scaleT scaleless scientific search searchtree sec secondaryX secondaryY seconds section sector seek seekeof segment sequence setpens sgn sgnd sharpangle sharpdegrees shift shiftless shipout shipout3 show side simeq simpson sin single sinh size size3 skewness skip slant sleep slope slopefield solve sort sourceline sphere split sqrt square srand standardizecoordsys startScript startTrembling stdev step stickframe stickmarksize stickmarkspace stop straight straightness string stripdirectory stripextension stripfile strokepath subdivide subitem subpath substr sum surface symmedial symmedian system tab tableau tan tangent tangential tangents tanh tell tensionSpecifier tensorshade tex texcolor texify texpath texpreamble texreset texshipout textpath thick thin tick tickMax tickMax3 tickMin tickMin3 ticklabelshift ticklocate tildeframe tildemarksize tile tiling time times title titlepage topbox transform transformation transpose tremble trembleFuzz tremble_circlenodesnumber tremble_circlenodesnumber1 tremble_draw tremble_ellipsenodesnumber tremble_ellipsenodesnumber1 tremble_hyperbolanodesnumber tremble_marknodes tremble_markuniform tremble_parabolanodesnumber triangle triangleAbc triangleabc triangulate tricoef tridiagonal trilinear trim trueMagnetize truepoint tube uncycle unfill uniform unit unitrand unitsize unityroot unstraighten upcase updatefunction upscale uptodate usepackage usersetting usleep value variance variancebiased vbox vector vectorfield verbatim view vline vprojection windingnumber word write xaxis xaxis3 xaxis3At xaxisAt xequals xinput xlimits xoutput xpart xscale xscaleO xtick xtick3 xtrans yaxis yaxis3 yaxis3At yaxisAt yequals ylimits ypart yscale yscaleO ytick ytick3 ytrans zaxis3 zaxis3At zero zero3 zlimits zpart ztick ztick3 ztrans )) - -(defvar asy-variable-name '( -AliceBlue Align Allow AntiqueWhite Apricot Aqua Aquamarine Aspect Azure BeginPoint Beige Bisque Bittersweet Black BlanchedAlmond Blue BlueGreen BlueViolet Both Break BrickRed Brown BurlyWood BurntOrange CCW CW CadetBlue CarnationPink Center Centered Cerulean Chartreuse Chocolate Coral CornflowerBlue Cornsilk Crimson Crop Cyan Dandelion DarkBlue DarkCyan DarkGoldenrod DarkGray DarkGreen DarkKhaki DarkMagenta DarkOliveGreen DarkOrange DarkOrchid DarkRed DarkSalmon DarkSeaGreen DarkSlateBlue DarkSlateGray DarkTurquoise DarkViolet DeepPink DeepSkyBlue DefaultHead DimGray DodgerBlue Dotted Draw E ENE EPS ESE Emerald EndPoint Fill FillDraw FireBrick FloralWhite ForestGreen Fuchsia Gainsboro GhostWhite Gold Goldenrod Gray Green GreenYellow Honeydew HookHead Horizontal HotPink I IgnoreAspect IndianRed Indigo Ivory JOIN_IN JOIN_OUT JungleGreen Khaki Label Lavender LavenderBlush LawnGreen LeftJustified LeftSide LemonChiffon LightBlue LightCoral LightCyan LightGoldenrodYellow LightGreen LightGrey LightPink LightSalmon LightSeaGreen LightSkyBlue LightSlateGray LightSteelBlue LightYellow Lime LimeGreen Linear Linen Log Logarithmic Magenta Mahogany Mark MarkFill Maroon Max MediumAquamarine MediumBlue MediumOrchid MediumPurple MediumSeaGreen MediumSlateBlue MediumSpringGreen MediumTurquoise MediumVioletRed Melon MidPoint MidnightBlue Min MintCream MistyRose Moccasin Move MoveQuiet Mulberry N NE NNE NNW NW NavajoWhite Navy NavyBlue NoAlign NoCrop NoFill NoSide OldLace Olive OliveDrab OliveGreen Orange OrangeRed Orchid Ox Oy PaleGoldenrod PaleGreen PaleTurquoise PaleVioletRed PapayaWhip Peach PeachPuff Periwinkle Peru PineGreen Pink Plum PowderBlue ProcessBlue Purple RawSienna Red RedOrange RedViolet Rhodamine RightJustified RightSide RosyBrown RoyalBlue RoyalPurple RubineRed S SE SSE SSW SW SaddleBrown Salmon SandyBrown SeaGreen Seashell Sepia Sienna Silver SimpleHead SkyBlue SlateBlue SlateGray Snow SpringGreen SteelBlue Suppress SuppressQuiet Tan TeXHead Teal TealBlue Thistle Ticksize Tomato Turquoise UnFill VERSION Value Vertical Violet VioletRed W WNW WSW Wheat White WhiteSmoke WildStrawberry XYAlign YAlign Yellow YellowGreen YellowOrange addpenarc addpenline align allowstepping angularsystem animationdelay appendsuffix arcarrowangle arcarrowfactor arrow2sizelimit arrowangle arrowbarb arrowdir arrowfactor arrowhookfactor arrowlength arrowsizelimit arrowtexfactor authorpen axis axiscoverage axislabelfactor background backgroundcolor backgroundpen barfactor barmarksizefactor basealign baselinetemplate beveljoin bigvertexpen bigvertexsize black blue bm bottom bp brown bullet byfoci byvertices camerafactor chartreuse circlemarkradiusfactor circlenodesnumberfactor circleprecision circlescale cm codefile codepen codeskip colorPen coloredNodes coloredSegments conditionlength conicnodesfactor count cputimeformat crossmarksizefactor currentcoordsys currentpatterns currentpen currentpicture currentposition currentprojection curvilinearsystem cuttings cyan darkblue darkbrown darkcyan darkgray darkgreen darkgrey darkmagenta darkolive darkred dashdotted dashed datepen dateskip debuggerlines debugging deepblue deepcyan deepgray deepgreen deepgrey deepmagenta deepred default defaultS defaultbackpen defaultcoordsys defaultfilename defaultformat defaultmassformat defaultpen diagnostics differentlengths dot dotfactor dotframe dotted doublelinepen doublelinespacing down ellipsenodesnumberfactor eps epsgeo epsilon evenodd extendcap fermionpen figureborder figuremattpen firstnode firststep foregroundcolor fuchsia fuzz gapfactor ghostpen gluonamplitude gluonpen gluonratio gray green grey hatchepsilon havepagenumber heavyblue heavycyan heavygray heavygreen heavygrey heavymagenta heavyred hline hwratio hyperbolanodesnumberfactor identity4 ignore inXasyMode inch inches includegraphicscommand incommensurate inf infinity institutionpen intMax intMin invert invisible itempen itemskip itemstep labelmargin landscape lastnode left legendhskip legendlinelength legendmargin legendmarkersize legendmaxrelativewidth legendvskip lightblue lightcyan lightgray lightgreen lightgrey lightmagenta lightolive lightred lightyellow linemargin longdashdotted longdashed magenta magneticPoints magneticRadius mantissaBits markangleradius markangleradiusfactor markanglespace markanglespacefactor mediumblue mediumcyan mediumgray mediumgreen mediumgrey mediummagenta mediumred mediumyellow middle minDistDefault minblockheight minblockwidth mincirclediameter minipagemargin minipagewidth minvertexangle miterjoin mm momarrowfactor momarrowlength momarrowmargin momarrowoffset momarrowpen monoPen morepoints nCircle newbulletcolor ngraph nil nmesh nobasealign nodeMarginDefault nodesystem nomarker nopoint noprimary nullpath nullpen numarray oldbulletcolor olive orange origin overpaint page pageheight pagemargin pagenumberalign pagenumberpen pagenumberposition pagewidth paleblue palecyan palegray palegreen palegrey palemagenta palered paleyellow parabolanodesnumberfactor perpfactor phi photonamplitude photonpen photonratio pi pink plain plus preamblenodes pt purple r3 r4a r4b randMax realDigits realEpsilon realMax realMin red relativesystem reverse right roundcap roundjoin royalblue salmon saveFunctions scalarpen sequencereal settings shipped signedtrailingzero solid springgreen sqrtEpsilon squarecap squarepen startposition stdin stdout stepfraction steppagenumberpen stepping stickframe stickmarksizefactor stickmarkspacefactor textpen ticksize tildeframe tildemarksizefactor tinv titlealign titlepagepen titlepageposition titlepen titleskip top trailingzero treeLevelStep treeMinNodeWidth treeNodeStep trembleAngle trembleFrequency trembleRandom tremblingMode undefined unitcircle unitsquare up urlpen urlskip version vertexpen vertexsize viewportsize vline white wye xformStack yellow ylabelwidth zerotickfuzz zerowinding )) 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 79354b1366e..00000000000 --- a/Build/source/utils/asymptote/doc/png/asymptote.info +++ /dev/null @@ -1,9929 +0,0 @@ -This is asymptote.info, produced by makeinfo version 4.7 from -../asymptote.texi. - - This file documents `Asymptote', version 1.78. - - `http://asymptote.sourceforge.net' - - Copyright (C) 2004-9 Andy Hammerlindl, John Bowman, and Tom Prince. - - Permission is granted to copy, distribute and/or modify this - document under the terms of the GNU Lesser General Public License - (see the file LICENSE in the top-level source directory). - - -INFO-DIR-SECTION Languages -START-INFO-DIR-ENTRY -* asymptote: (asymptote/asymptote). Vector graphics language. -END-INFO-DIR-ENTRY - - -File: asymptote.info, Node: Top, Next: Description, Up: (dir) - -Asymptote -********* - -This file documents `Asymptote', version 1.78. - - `http://asymptote.sourceforge.net' - - Copyright (C) 2004-9 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 -* Programming:: The `Asymptote' vector graphics language -* LaTeX usage:: Embedding `Asymptote' commands within `LaTeX' -* Base modules:: Base modules shipped with `Asymptote' -* Options:: Command-line options -* Interactive mode:: Typing `Asymptote' commands interactively -* GUI:: Graphical user interface -* PostScript to Asymptote:: `Asymptote' backend to `pstoedit' -* Help:: Where to get help and submit bug reports -* Debugger:: Squish those bugs! -* Credits:: Contributions and acknowledgments -* Index:: General index - - --- The Detailed Node Listing --- - -Installation - -* UNIX binary distributions:: Prebuilt `UNIX' binaries -* MacOS X binary distributions:: Prebuilt `MacOS X' binaries -* Microsoft Windows:: Prebuilt `Microsoft Windows' binary -* Configuring:: Configuring `Asymptote' for your system -* Search paths:: Where `Asymptote' looks for your files -* Compiling from UNIX source:: Building `Asymptote' from scratch -* Editing modes:: Convenient `emacs' and `vim' modes -* Subversion:: Getting the latest development source -* Uninstall:: Goodbye, `Asymptote'! - -Drawing commands - -* draw:: Draw a path on a picture or frame -* fill:: Fill a cyclic path on a picture or frame -* clip:: Clip a picture or frame to a cyclic path -* label:: Label a point on a picture - -Programming - -* Data types:: void, bool, int, real, pair, triple, string -* Paths and guides:: -* 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' packages -* Static:: Where to allocate your variable? - -Operators - -* Arithmetic & logical:: Basic mathematical operators -* Self & prefix operators:: Increment and decrement -* User-defined operators:: Overloading operators - -Functions - -* Default arguments:: Default values can appear anywhere -* Named arguments:: Assigning function arguments by keyword -* Rest arguments:: Functions with a variable number of arguments -* Mathematical functions:: Standard libm functions - - -Arrays - -* Slices:: Python-style array slices - -Base modules - -* plain:: Default `Asymptote' base file -* simplex:: Linear programming: simplex method -* math:: Extend `Asymptote''s math capabilities -* interpolate:: Interpolation routines -* geometry:: Geometry routines -* trembling:: Wavy lines -* stats:: Statistics routines and histograms -* patterns:: Custom fill and draw patterns -* markers:: Custom path marker routines -* tree:: Dynamic binary search tree -* binarytree:: Binary tree drawing module -* drawtree:: Tree drawing module -* syzygy:: Syzygy and braid drawing module -* feynman:: Feynman diagrams -* roundedpath:: Round the sharp corners of paths -* animation:: Embedded PDF and MPEG movies -* embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with `Asymptote' -* MetaPost:: `MetaPost' compatibility routines -* unicode:: Accept `unicode' (UTF-8) characters -* latin1:: Accept `ISO 8859-1' characters -* babel:: Interface to `LaTeX' `babel' package -* labelpath:: Drawing curved labels -* labelpath3:: Drawing curved labels in 3D -* annotate:: Annotate your PDF files -* CAD:: 2D CAD pen and measurement functions (DIN 15) -* graph:: 2D linear & logarithmic graphs -* palette:: Color density images and palettes -* three:: 3D vector graphics -* obj:: 3D obj files -* graph3:: 3D linear & logarithmic graphs -* grid3:: 3D grids -* solids:: 3D solid geometry -* tube:: 3D rotation minimizing tubes -* flowchart:: Flowchart drawing routines -* contour:: Contour lines -* contour3:: Contour surfaces -* slopefield:: Slope fields -* ode:: Ordinary differential equations - -Graphical User Interface - -* GUI Installation:: Installing `xasy' -* GUI Usage:: - - -File: asymptote.info, Node: Description, Next: Installation, Prev: Top, Up: Top - -1 Description -************* - -`Asymptote' is a powerful descriptive vector graphics language that -provides a mathematical coordinate-based framework for technical -drawings. Labels and equations are typeset with `LaTeX', for overall -document consistency, yielding the same high-quality level of -typesetting that `LaTeX' provides for scientific text. By default it -produces `PostScript' output, but it can also generate any format that -the `ImageMagick' package can produce. - - A major advantage of `Asymptote' over other graphics packages is -that it is a high-level programming language, as opposed to just a -graphics program: it can therefore exploit the best features of the -script (command-driven) and graphical-user-interface (GUI) methods for -producing figures. The rudimentary GUI `xasy' included with the package -allows one to move script-generated objects around. To make `Asymptote' -accessible to the average user, this GUI is currently being developed -into a full-fledged interface that can generate objects directly. -However, the script portion of the language is now ready for general -use by users who are willing to learn a few simple `Asymptote' graphics -commands (*note Drawing commands::). - - `Asymptote' is mathematically oriented (e.g. one can use complex -multiplication to rotate a vector) and uses `LaTeX' to do the -typesetting of labels. This is an important feature for scientific -applications. It was inspired by an earlier drawing program (with a -weaker syntax and capabilities) called `MetaPost'. - - The `Asymptote' vector graphics language provides: - - * a standard for typesetting mathematical figures, just as - TeX/`LaTeX' is the de-facto standard for typesetting equations. - - * `LaTeX' typesetting of labels, for overall document consistency; - - * the ability to generate and embed 3D vector PRC graphics into PDF - files; - - * a natural coordinate-based framework for technical drawings, - inspired by `MetaPost', with a much cleaner, powerful C++-like - programming syntax; - - * compilation of figures into virtual machine code for speed, without - sacrificing portability; - - * the power of a script-based language coupled to the convenience of - a GUI; - - * customization using its own C++-like graphics programming language; - - * sensible defaults for graphical features, with the ability to - override; - - * a high-level mathematically oriented interface to the `PostScript' - language for vector graphics, including affine transforms and - complex variables; - - * functions that can create new (anonymous) functions; - - * deferred drawing that uses the simplex method to solve overall size - constraint issues between fixed-sized objects (labels and - arrowheads) and objects that should scale with figure size; - - - Many of the features of `Asymptote' are written in the `Asymptote' -language itself. While the stock version of `Asymptote' is designed for -mathematics typesetting needs, one can write `Asymptote' modules that -tailor it to specific applications. A scientific graphing module has -already been written (*note graph::). Examples of `Asymptote' code and -output, including animations, are available at - - `http://asymptote.sourceforge.net/gallery/'. - Links to many external resources, including an excellent user-written -`Asymptote' tutorial can be found at - - `http://asymptote.sourceforge.net/links.html'. - - -File: asymptote.info, Node: Installation, Next: Tutorial, Prev: Description, Up: Top - -2 Installation -************** - -* Menu: - -* UNIX binary distributions:: Prebuilt `UNIX' binaries -* MacOS X binary distributions:: Prebuilt `MacOS X' binaries -* Microsoft Windows:: Prebuilt `Microsoft Windows' binary -* Configuring:: Configuring `Asymptote' for your system -* Search paths:: Where `Asymptote' looks for your files -* Compiling from UNIX source:: Building `Asymptote' from scratch -* Editing modes:: Convenient `emacs' and `vim' modes -* Subversion:: Getting the latest development source -* Uninstall:: Goodbye, `Asymptote'! - - After following the instructions for your specific distribution, -please see also *Note Configuring::. - -We recommend subscribing to new release announcements at - - `http://freshmeat.net/projects/asy' - Users may also wish to monitor the `Asymptote' forum: - - `http://sourceforge.net/forum/monitor.php?forum_id=409349' - - -File: asymptote.info, Node: UNIX binary distributions, Next: MacOS X binary distributions, Up: Installation - -2.1 UNIX binary distributions -============================= - -We release both `tgz' and RPM binary distributions of `Asymptote'. The -root user can install the `Linux i386' `tgz' distribution of version -`x.xx' of `Asymptote' with the commands: - -tar -C / -zxf asymptote-x.xx.i386.tgz -texhash - The `texhash' command, which installs LaTeX style files, is optional. -The executable file will be `/usr/local/bin/asy') and example code will -be installed by default in `/tmp/ainst/share/doc/asymptote/examples'. - -Fedora users can easily install the most recent version of `Asymptote' -with the command - -yum --enablerepo=rawhide install asymptote - -To install the latest version of `Asymptote' on a Debian-based -distribution (e.g. Ubuntu, Mepis, Linspire) follow the instructions for -compiling from `UNIX' source (*note Compiling from UNIX source::). -Alternatively, Debian users can install one of Hubert Chan's prebuilt -`Asymptote' binaries from - - `http://ftp.debian.org/debian/pool/main/a/asymptote' - - -File: asymptote.info, Node: MacOS X binary distributions, Next: Microsoft Windows, Prev: UNIX binary distributions, Up: Installation - -2.2 MacOS X binary distributions -================================ - -`MacOS X' users can either compile the `UNIX' source code (*note -Compiling from UNIX source::) or install the contributed `Asymptote' -binary available at - -`http://www.hmug.org/pub/MacOS_X/X/Applications/Publishing/asymptote/' - -Because these preconfigured binary distributions have strict -architecture and library dependencies that many installations do not -satisfy, we recommend installing `Asymptote' directly from the official -source: - - `http://sourceforge.net/project/showfiles.php?group_id=120000' - -Note that many `MacOS X' (and FreeBSD) systems inexplicably ship with -an extremely old GNU `readline' version (4.1, dated 21 March 2000). For -full interactive functionality, `readline' version 4.2 or later (16 -April 2001) is required. - - -File: asymptote.info, Node: Microsoft Windows, Next: Configuring, Prev: MacOS X binary distributions, Up: Installation - -2.3 Microsoft Windows -===================== - -Users of the `Microsoft Windows' operating system can install the -self-extracting `Asymptote' executable `asymptote-x.xx-setup.exe', -where `x.xx' denotes the latest version. - - A working TeX implementation (such as the one available at -`http://www.miktex.org') will be required to typeset labels. You will -also need to install `GPL Ghostscript' from -`http://sourceforge.net/projects/ghostscript/'. To view the default -`PostScript' output, you can install the program `gsview' available from -`http://www.cs.wisc.edu/~ghost/gsview/'. - - The `ImageMagick' package from - - `http://www.imagemagick.org/script/binary-releases.php' - -is required to support output formats other than EPS and PDF (*note -convert::). The `Python' 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 (by default, `.asy/config.asy' in the -user's home directory or `%USERPROFILE%\.asy\config.asy' under -`MSDOS'); *note configuration file::. Here are the default values of -several important configuration variables under `UNIX': - - - -import settings; -psviewer="gv"; -pdfviewer="acroread"; -gs="gs"; -python=""; - -The (installation-dependent) default values of these configuration -variables under `MSDOS' are determined automatically from the -`Microsoft Windows' registry. - - For PDF format output, the `gs' setting specifies the location of -the `PostScript'-to-PDF processor `Ghostscript', available from -`http://sourceforge.net/projects/ghostscript/'. - - The setting `pdfviewer' specifies the location of the PDF viewer. On -`UNIX' systems, to support automatic document reloading in `Adobe -Reader', we recommend copying the file `reload.js' from the `Asymptote' -system directory (by default, `/tmp/ainst/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 graphical user interface may also require setting the variable -`python' if `Python' is installed in a nonstandard location. - - The configuration variable `dir' can be used to adjust the search -path (*note Search paths::). - - By default, `Asymptote' attempts to center the figure on the page, -assuming that the paper type is `letter'. The default paper type may be -changed to `a4' with the configuration variable `papertype'. Alignment -to other paper sizes can be obtained by setting the configuration -variables `paperwidth' and `paperheight'. - - The following configuration variables normally do not require -adjustment: - -texpath -texcommand -texdvicommand -dvips -convert -display -animate -xasy - The `texdvicommand' is used for `3D' label typesetting, which requires -`dvips' output. An empty string indicates the default setting of -`latex'/`tex', depending on the setting of `texengine'. - - 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 `Properties' from the popup menu; - - 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' (separated by `:' under UNIX and `;' under `MSDOS'); - - 3. The directory `.asy' in the user's home directory - (`%USERPROFILE%\.asy' under `MSDOS'); - - 4. The `Asymptote' system directory (by default, - `/tmp/ainst/share/asymptote' under `UNIX' and `C:\Program - Files\Asymptote' under `MSDOS'). - - -File: asymptote.info, Node: Compiling from UNIX source, Next: Editing modes, Prev: Search paths, Up: Installation - -2.6 Compiling from UNIX source -============================== - -To compile and install a `UNIX' executable from a source release -`x.xx', first execute the commands: - -gunzip asymptote-x.xx.src.tgz -tar -xf asymptote-x.xx.src.tar -cd asymptote-x.xx - By default the system version of the Boehm garbage collector will be -used; if it is old we recommend first putting -`http://www.hpl.hp.com/personal/Hans_Boehm/gc/gc_source/gc-7.1.tar.gz' -in the `Asymptote' source directory. - -If your graphics card supports multisampling, we recommend using version -`2.6.0-rc1' (or later) of `freeglut' to support antialiasing in -`Asymptote''s adaptive `OpenGL' 3D renderer (`MacOS X' users can skip -this step since `Asymptote' is configured to use the native glut -library on that platform). Download - - `http://prdownloads.sourceforge.net/freeglut/freeglut-2.6.0-rc1.tar.gz' - and type (as the root user): - -tar -zxf freeglut-2.6.0-rc1.tar.gz -cd freeglut-2.6.0 -./configure --prefix=/usr -make install -cd .. - Then compile `Asymptote' with the commands - -./configure -make all -make install - Be sure to use GNU `make' (on non-GNU systems this command may be -called `gmake'). To build the documentation, you may need to install -the `texinfo-tex' package. If you get errors from a broken `texinfo' or -`pdftex' installation, simply put - - `http://asymptote.sourceforge.net/asymptote.pdf' - in the directory `doc' and repeat the command `make all'. - -For a (default) system-wide installation, the last command should be -done as the root user. To install without root privileges, change the -`./configure' command to - -./configure --prefix=$HOME/asymptote - One can disable use of the Boehm garbage collector by configuring with -`./configure --disable-gc'. For a list of other configuration options, -say `./configure --help'. For example, one can tell configure to look -for header files and libraries in nonstandard locations: - -./configure CFLAGS=-I/opt/usr/include LDFLAGS=-L/opt/usr/lib - - If you are compiling `Asymptote' with `gcc', you will need a -relatively recent version (e.g. 3.4.4 or later). For full interactive -functionality, you will need version 4.2 or later of the GNU `readline' -library. The file `gcc3.3.2curses.patch' in the `patches' directory can -be used to patch the broken curses.h header file (or a local copy -thereof in the current directory) on some `AIX' and `IRIX' systems. - - The `FFTW' library is only required if you want `Asymptote' to be -able to take Fourier transforms of data (say, to compute an audio power -spectrum). The `GSL' library is only required if you require the -special functions that it supports. - - If you don't want to install `Asymptote' system wide, just make sure -the compiled binary `asy' and GUI script `xasy' are in your path and -set the configuration variable `dir' to point to the directory `base' -(in the top level directory of the `Asymptote' source code). - - -File: asymptote.info, Node: Editing modes, Next: Subversion, Prev: Compiling from UNIX source, Up: Installation - -2.7 Editing modes -================= - -Users of `emacs' can edit `Asymptote' code with the mode `asy-mode', -after enabling it by putting the following lines in their `.emacs' -initialization file, replacing `ASYDIR' with the location of the -`Asymptote' system directory (by default, `/tmp/ainst/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 /tmp/ainst/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 `/tmp/ainst/share/asymptote' directory -and putting the generated `asymptote.xml' file in -`~/.kde/share/apps/katepart/syntax/'. - - -File: asymptote.info, Node: Subversion, Next: Uninstall, Prev: Editing modes, Up: Installation - -2.8 Subversion (SVN) -==================== - -The following commands are needed to install the latest development -version of `Asymptote' using `Subversion': - -svn co http://asymptote.svn.sourceforge.net/svnroot/asymptote/trunk/asymptote -cd asymptote -./autogen.sh -./configure -make all -make install - -To compile without optimization, use the command `make CFLAGS=-g'. - - -File: asymptote.info, Node: Uninstall, Prev: Subversion, Up: Installation - -2.9 Uninstall -============= - -To uninstall an `Linux i386' binary distribution, use the commands - -tar -zxvf asymptote-x.xx.i386.tgz | xargs --replace=% rm /% -texhash - -To uninstall all `Asymptote' files installed from a source -distribution, use the command - -make uninstall - - -File: asymptote.info, Node: Tutorial, Next: Drawing commands, Prev: Installation, Up: Top - -3 Tutorial -********** - -_An excellent user-written `Asymptote' tutorial is also available from_ - - `http://www.artofproblemsolving.com/Wiki/index.php/Asymptote:_Basics' - -To draw a line from coordinate (0,0) to coordinate (100,100) using -`Asymptote''s interactive mode, type at the command prompt: - -asy -draw((0,0)--(100,100)); - - - -The units here are `PostScript' "big points" (1 `bp' = 1/72 `inch'); -`--' means join with a linear segment. In `Asymptote' coordinates like -`(0,0)' and `(1000,100)' are called _pairs_. - - At this point you can type in further draw commands, which will be -added to the displayed figure, or type `quit' to exit interactive mode. -You can use the arrow keys in interactive mode to edit previous lines -(assuming that you have support for the GNU `readline' library -enabled). 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::. - - In batch mode, `Asymptote' reads commands directly from a file. To -try this out, type - -draw((0,0)--(100,100)); - into a file, say test.asy. Then execute this file with the `MSDOS' or -`UNIX' command - -asy -V test - `MSDOS' users can drag and drop the file onto the Desktop `asy' icon -or make `Asymptote' the default application for files with the -extension `asy'. - -The `-V' option opens up a `PostScript' viewer window so you can -immediately view the encapsulated `PostScript' output. By default the -output will be written to the file `test.eps'; the prefix of the output -file may be changed with the `-o' command-line option. - - One can draw a line with more than two points and create a cyclic -path like this square: - -draw((0,0)--(100,0)--(100,100)--(0,100)--cycle); - - - -It is often inconvenient to work directly with `PostScript' coordinates. -The next example draws a unit square scaled to width 101 bp and height -101 bp. The output is identical to that of the previous example. - -size(101,101); -draw((0,0)--(1,0)--(1,1)--(0,1)--cycle); - - For convenience, the path `(0,0)--(1,0)--(1,1)--(0,1)--cycle' may be -replaced with the predefined variable `unitsquare', or equivalently, -`box((0,0),(1,1))'. - - One can also specify the size in `pt' (1 `pt' = 1/72.27 `inch'), -`cm', `mm', or `inches'. 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(0,3cm); -draw(unitsquare); - - - -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(1cm,2cm); -draw(unitsquare); - - Adding labels is easy in `Asymptote'; one specifies the label as a -double-quoted `LaTeX' string, a coordinate, and an optional alignment -direction: - -size(0,3cm); -draw(unitsquare); -label("$A$",(0,0),SW); -label("$B$",(1,0),SE); -label("$C$",(1,1),NE); -label("$D$",(0,1),NW); - - - -`Asymptote' uses the standard compass directions `E=(1,0)', `N=(0,1)', -`NE=unit(N+E)', and `ENE=unit(E+NE)', etc., which along with the -directions `up', `down', `right', and `left' are defined as pairs in -the `Asymptote' base module `plain'. A user who has a local variable -named `E' may access the compass direction `E' by prefixing it with the -name of the module where it is defined: `plain.E'. - - This example draws a path that approximates a quarter circle: - -size(100,0); -draw((1,0){up}..{left}(0,1)); - - - -In general, a path is specified as a list of pairs (or other paths) -interconnected with `--', which denotes a straight line segment, or -`..', which denotes a cubic spline. - - Specifying a final node `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; - - Each interior node of a cubic spline may be given a direction prefix -or suffix `{dir}': the direction of the pair `dir' specifies the -direction of the incoming or outgoing tangent, respectively, to the -curve at that node. Exterior nodes may be given direction specifiers -only on their interior side. - - A cubic spline between the node z_0, with postcontrol point c_0, and -the node z_1, with precontrol point c_1, is computed as the Bezier curve - - - -As illustrated in the diagram below, the third-order midpoint (m_5) -constructed from two endpoints z_0 and z_1 and two control points c_0 -and c_1, is the point corresponding to t=1/2 on the Bezier curve formed -by the quadruple (z_0, c_0, c_1, z_1). This allows one to recursively -construct the desired curve, by using the newly extracted third-order -midpoint as an endpoint and the respective second- and first-order -midpoints as control points: - - - -Here m_0, m_1 and m_2 are the first-order midpoints, m_3 and m_4 are -the second-order midpoints, and m_5 is the third-order midpoint. The -curve is then constructed by recursively applying the algorithm to -(z_0, m_0, m_3, m_5) and (m_5, m_4, m_2, z_1). - - In fact, an analogous property holds for points located at any -fraction t in [0,1] of each segment, not just for midpoints (t=1/2). - - The Bezier curve constructed in this manner has the following -properties: - * It is entirely contained in the convex hull of the given four - points. - - * It starts heading from the first endpoint to the first control - point and finishes heading from the second control point to the - second endpoint. - - - The user can specify explicit control points between two nodes like -this: - -draw((0,0)..controls (0,100) and (100,100)..(100,0)); - - However, it is usually more convenient to just use the `..' -operator, which tells `Asymptote' to choose its own control points -using the algorithms described in Donald Knuth's monograph, The -MetaFontbook, Chapter 14. The user can still customize the guide (or -path) by specifying direction, tension, and curl values. - - The higher the tension, the straighter the curve is, and the more it -approximates a straight line. One can change the spline tension from -its default value of 1 to any real value greater than or equal to 0.75 -(cf. John D. Hobby, Discrete and Computational Geometry 1, 1986): - -draw((100,0)..tension 2 ..(100,100)..(0,100)); -draw((100,0)..tension 2 and 1 ..(100,100)..(0,100)); -draw((100,0)..tension atleast 1 ..(100,100)..(0,100)); - - The curl parameter specifies the curvature at the endpoints of a path -(0 means straight; the default value of 1 means approximately circular): - -draw((100,0){curl 0}..(100,100)..{curl 0}(0,100)); - - The `MetaPost ...' path connector, which requests, when possible, an -inflection-free curve confined to a triangle defined by the endpoints -and directions, is implemented in `Asymptote' as the convenient -abbreviation `::' for `..tension atleast 1 ..' (the ellipsis `...' is -used in `Asymptote' to indicate a variable number of arguments; *note -Rest arguments::). For example, compare - -draw((0,0){up}..(100,25){right}..(200,0){down}); - - -with - -draw((0,0){up}::(100,25){right}::(200,0){down}); - - - -The `---' connector is an abbreviation for `..tension atleast -infinity..' and the `&' connector concatenates two paths, after first -stripping off the last node of the first path (which normally should -coincide with the first node of the second path). - - An `Asymptote' path, being connected, is equivalent to a `Postscript -subpath'. The `^^' binary operator, which requests that the pen be -moved (without drawing or affecting endpoint curvatures) from the final -point of the left-hand path to the initial point of the right-hand -path, may be used to group several `Asymptote' paths into a `path[]' -array (equivalent to a `PostScript' path): - -size(0,100); -path unitcircle=E..N..W..S..cycle; -path g=scale(2)*unitcircle; -filldraw(unitcircle^^g,evenodd+yellow,black); - - - -The `PostScript' even-odd fill rule here specifies that only the region -bounded between the two unit circles is filled (*note fillrule::). In -this example, the same effect can be achieved by using the default zero -winding number fill rule, if one is careful to alternate the -orientation of the paths: - -filldraw(unitcircle^^reverse(g),yellow,black); - - The `^^' operator is used by the `box(triple, triple)' function in -`three.asy' to construct the edges of a cube `unitbox' without -retracing steps: - -import three; -dotgranularity=0; // Render dots as spheres. - -currentprojection=orthographic(5,4,2,center=true); - -size(5cm); -size3(3cm,5cm,8cm); - -draw(unitbox); - -dot(unitbox,red); - -label("$O$",(0,0,0),NW); -label("(1,0,0)",(1,0,0),S); -label("(0,1,0)",(0,1,0),E); -label("(0,0,1)",(0,0,1),Z); - - - -See section *Note graph:: (or the online `Asymptote' gallery and -external links posted at `http://asymptote.sourceforge.net') for -further examples, including two and three-dimensional scientific -graphs. Additional examples have been posted by Philippe Ivaldi at -`http://piprim.tuxfamily.org/asymptote/'. - - -File: asymptote.info, Node: Drawing commands, Next: Programming, Prev: Tutorial, Up: Top - -4 Drawing commands -****************** - -All of `Asymptote''s graphical capabilities are based on four primitive -commands. The three `PostScript' drawing commands `draw', `fill', and -`clip' add objects to a picture in the order in which they are -executed, with the most recently drawn object appearing on top. The -labeling command `label' can be used to add text labels and external -EPS images, which will appear on top of the `PostScript' objects (since -this is normally what one wants), but again in the relative order in -which they were executed. After drawing objects on a picture, the -picture can be output with the `shipout' function (*note shipout::). - - If you wish to draw `PostScript' objects on top of labels (or -verbatim `tex' commands; *note tex::), the `layer' command may be used -to start a new `PostScript/LaTeX' layer: - -void layer(picture pic=currentpicture); - - The `layer' function gives one full control over the order in which -objects are drawn. Layers are drawn sequentially, with the most recent -layer appearing on top. Within each layer, labels, images, and verbatim -`tex' commands are always drawn after the `PostScript' objects in that -layer. - - While some of these drawing commands take many options, they all -have sensible default values (for example, the picture argument -defaults to currentpicture). - -* Menu: - -* draw:: Draw a path on a picture or frame -* fill:: Fill a cyclic path on a picture or frame -* clip:: Clip a picture or frame to a cyclic path -* label:: Label a point on a picture - - -File: asymptote.info, Node: draw, Next: fill, Up: Drawing commands - -4.1 draw -======== - - -void draw(picture pic=currentpicture, Label L="", path g, - align align=NoAlign, pen p=currentpen, - arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin, - Label legend="", marker marker=nomarker); - -Draw the path `g' on the picture `pic' using pen `p' for drawing, with -optional drawing attributes (Label `L', explicit label alignment -`align', arrows and bars `arrow' and `bar', margins `margin', legend, -and markers `marker'). Only one parameter, the path, is required. For -convenience, the arguments `arrow' and `bar' may be specified in either -order. The argument `legend' is a Label to use in constructing an -optional legend entry. - - Bars are useful for indicating dimensions. The possible values of -`bar' are `None', `BeginBar', `EndBar' (or equivalently `Bar'), and -`Bars' (which draws a bar at both ends of the path). Each of these bar -specifiers (except for `None') will accept an optional real argument -that denotes the length of the bar in `PostScript' coordinates. The -default bar length is `barsize(pen)'. - - The possible values of `arrow' are `None', `Blank' (which draws no -arrows or path), `BeginArrow', `MidArrow', `EndArrow' (or equivalently -`Arrow'), and `Arrows' (which draws an arrow at both ends of the path). -All of the arrow specifiers except for `None' and `Blank' may be given -the optional arguments arrowhead `arrowhead' (one of the predefined -arrowhead styles `DefaultHead', `SimpleHead', `HookHead', `TeXHead'), -real `size' (arrowhead size in `PostScript' coordinates), real `angle' -(arrowhead angle in degrees), filltype `filltype' (one of `FillDraw', -`Fill', `NoFill', `UnFill', `Draw') and (except for `MidArrow' and -`Arrows') a relative real `position' along the path (an `arctime') 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, - pen penb, pair 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, - pen penb, pair b, real rb); - Illustrations of radial shading are provided in the example files -`shade.asy', `ring.asy', and `shadestroke.asy'. - - Gouraud shading using fill rule `fillrule' and the vertex colors in -the pen array `p' on a triangular lattice defined by the vertices `z' -and edge flags `edges' is implemented with - -void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, pair[] z, - int[] edges); -void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, int[] edges); - In the second form, the elements of `z' are taken to be successive -nodes of path `g'. The pens in `p' must belong to the same color space. -Illustrations of Gouraud shading are provided in the example file -`Gouraud.asy' and in the solid geometry module `solids.asy'. The edge -flags used in Gouraud shading are documented here: - - `http://partners.adobe.com/public/developer/en/ps/sdk/TN5600.SmoothShading.pdf'. - - Tensor product shading using fill rule `fillrule' on patches bounded -by the n cyclic paths of length 4 in path array `b', using the vertex -colors specified in the n \times 4 pen array `p' and internal control -points in the n \times 4 array `z', is implemented with - -void tensorshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[][] p, path[] b=g, - pair[][] z=new pair[][]); - If the array `z' is empty, Coons shading, in which the color control -points are calculated automatically, is used. The pens in `p' must -belong to the same color space. A simpler interface for the case of a -single patch (n=1) is also available: - -void tensorshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, path b=g, - pair[] z=new pair[]); - One can also smoothly shade the regions between consecutive paths of a -sequence using a given array of pens: - -void draw(picture pic=currentpicture, path[] g, pen[] p); - Illustrations of tensor product and Coons shading are provided in the -example files `tensor.asy', `Coons.asy', `BezierSurface.asy', and -`rainbow.asy'. - - More general shading possibilities are available with the `pdflatex', -`context', and `pdftex' TeX engines: the routine - -void functionshade(picture pic=currentpicture, path[] g, bool stroke=false, - pen fillrule=currentpen, string shader); - shades on picture `pic' the interior of path `g' according to fill -rule `fillrule' using the `PostScript' calculator routine specified by -the string `shader'; this routine takes 2 arguments, each in [0,1], and -returns `colors(fillrule).length' color components. Function shading -is illustrated in the example `functionshading.asy'. - - The following routine uses `evenodd' clipping together with the `^^' -operator to unfill a region: - - -void unfill(picture pic=currentpicture, path g); - - -File: asymptote.info, Node: clip, Next: label, Prev: fill, Up: Drawing commands - -4.3 clip -======== - - -void clip(picture pic=currentpicture, path g, stroke=false, - pen fillrule=currentpen); - -Clip the current contents of picture `pic' to the region bounded by the -path `g', using fill rule `fillrule' (*note fillrule::). If -`stroke=true', the clipped portion is the same as the region that would -be drawn with `draw(pic,g,fillrule+zerowinding)'; in this case the path -`g' need not be cyclic. For an illustration of picture clipping, see -the first example in *Note LaTeX usage::. - - -File: asymptote.info, Node: label, Prev: clip, Up: Drawing commands - -4.4 label -========= - - -void label(picture pic=currentpicture, Label L, pair position, - align align=NoAlign, pen p=nullpen, 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'. If `p' is `nullpen', the pen specified within the -Label, which defaults to `currentpen', will be used. - - 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'. 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=nullpen, filltype filltype=NoFill); - By default the label will be positioned at the midpoint of the path. -An alternative label location (an `arctime' value between 0 and -`length(g)' *note arctime::) may be specified as real value for -`position' in constructing the Label. The position `Relative(real)' -specifies a location relative to the total arclength of the path. These -convenient abbreviations are predefined: - -position BeginPoint=Relative(0); -position MidPoint=Relative(0.5); -position EndPoint=Relative(1); - - Path labels are aligned in the direction `align', which may be -specified as an absolute compass direction (pair) or a direction -`Relative(pair)' measured relative to a north axis in the local -direction of the path. For convenience `LeftSide', `Center', and -`RightSide' are defined as `Relative(W)', `Relative((0,0))', and -`Relative(E)', respectively. Multiplying `LeftSide', `Center', -`RightSide' on the left by a real scaling factor will move the label -further away from or closer to the path. - - A label with a fixed-size arrow of length `arrowlength' pointing to -`b' from direction `dir' can be produced with the routine - -void arrow(picture pic=currentpicture, Label L="", pair b, pair dir, - real length=arrowlength, align align=NoAlign, - pen p=currentpen, arrowbar arrow=Arrow, margin margin=EndMargin); - If no alignment is specified (either in the Label or as an explicit -argument), the optional Label will be aligned in the direction `dir', -using margin `margin'. - - The function `string graphic(string name, string options="")' -returns a string that can be used to include an encapsulated -`PostScript' (EPS) file. Here, `name' is the name of the file to -include and `options' is a string containing a comma-separated list of -optional bounding box (`bb=llx lly urx ury'), width (`width=value'), -height (`height=value'), rotation (`angle=value'), scaling -(`scale=factor'), clipping (`clip=bool'), and draft mode (`draft=bool') -parameters. The `layer()' function can be used to force future objects -to be drawn on top of the included image: - -label(graphic("file.eps","width=1cm"),(0,0),NE); -layer(); - - The `string baseline(string s, string template="\strut")' function -can be used to enlarge the bounding box of labels to match a given -template, so that their baselines will be typeset on a horizontal line. -See `Pythagoras.asy' for an example. - - One can prevent labels from overwriting one another with the -`overwrite' pen attribute (*note overwrite::). - - The structure `object' defined in `plain_Label.asy' allows Labels -and frames to be treated in a uniform manner. A group of objects may -be packed together into single frame with the routine - -frame pack(pair align=2S ... object inset[]); - To draw or fill a box (or ellipse or other path) around a Label and -return the bounding object, use one of the routines - -object draw(picture pic=currentpicture, Label L, envelope e, - real xmargin=0, real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); -object draw(picture pic=currentpicture, Label L, envelope e, pair position, - real xmargin=0, real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); - Here `envelope' is a boundary-drawing routine such as `box', -`roundbox', or `ellipse' defined in `plain_boxes.asy' (*note -envelope::). - - The function `path[] texpath(Label L)' returns the path array that -TeX would fill to draw the Label `L'. - - The `string minipage(string s, width=100pt)' function can be used to -format string `s' into a paragraph of width `width'. This example uses -`minipage', `clip', and `graphic' to produce a CD label: - - -size(11.7cm,11.7cm); -asy(nativeformat(),"logo"); -fill(unitcircle^^(scale(2/11.7)*unitcircle), - evenodd+rgb(124/255,205/255,124/255)); -label(scale(1.1)*minipage( -"\centering\scriptsize \textbf{\LARGE {\tt Asymptote}\\ -\smallskip -\small The Vector Graphics Language}\\ -\smallskip -\textsc{Andy Hammerlindl, John Bowman, and Tom Prince} -http://asymptote.sourceforge.net\\ -",8cm),(0,0.6)); -label(graphic("logo."+nativeformat(),"height=7cm"),(0,-0.22)); -clip(unitcircle^^(scale(2/11.7)*unitcircle),evenodd); - - -File: asymptote.info, Node: Programming, Next: LaTeX usage, Prev: Drawing commands, Up: Top - -5 Programming -************* - -Here is a short introductory example to the `Asymptote' programming -language that highlights the similarity of its control structures with -those of C, C++, and Java: - -// This is a comment. - -// Declaration: Declare x to be a real variable; -real x; - -// Assignment: Assign the real variable x the value 1. -x=1.0; - -// Conditional: Test if x equals 1 or not. -if(x == 1.0) { - write("x equals 1.0"); -} else { - write("x is not equal to 1.0"); -} - -// Loop: iterate 10 times -for(int i=0; i < 10; ++i) { - write(i); -} - - `Asymptote' supports `while', `do', `break', and `continue' -statements just as in C/C++. It also supports the Java-style shorthand -for iterating over all elements of an array: - - -// Iterate over an array -int[] array={1,1,2,3,5}; -for(int k : array) { - write(k); -} - In addition, it supports many features beyond the ones found in those -languages. - -* Menu: - -* Data types:: void, bool, int, real, pair, triple, string -* Paths and guides:: -* 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' packages -* Static:: Where to allocate your variable? - - -File: asymptote.info, Node: Data types, Next: Paths and guides, Up: Programming - -5.1 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'. - -`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(pair z, pair w)' - returns the dot product `z.x*w.x+z.y*w.y'; - - `pair minbound(pair z, pair w)' - returns `(min(z.x,w.x),min(z.y,w.y))'; - - `pair maxbound(pair z, pair w)' - returns `(max(z.x,w.x),max(z.y,w.y))'. - - -`triple' - an ordered triple of real components `(x,y,z)' used for - three-dimensional drawings. The respective components of a triple - `v' can read as `v.x', `v.y', and `v.z'. The implicit initializer - for triples is `(0.0,0.0,0.0)'. - - Here are the built-in functions for triples: - `real length(triple v)' - returns the length `|v|' of the vector `v'. A synonym for - `length(triple)' is `abs(triple)'; - - `real polar(triple v, bool warn=true)' - returns the colatitude of `v' measured from the z axis in - radians or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real azimuth(triple v, bool warn=true)' - returns the longitude of `v' measured from the x axis in - radians or `0' if `warn' is `false' and `v.x=v.y=0' (rather - than producing an error); - - `real colatitude(triple v, bool warn=true)' - returns the colatitude of `v' measured from the z axis in - degrees or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real latitude(triple v, bool warn=true)' - returns the latitude of `v' measured from the xy plane in - degrees or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real longitude(triple v, bool warn=true)' - returns the longitude of `v' measured from the x axis in - degrees or `0' if `warn' is `false' and `v.x=v.y=0' (rather - than producing an error); - - `triple unit(triple v)' - returns a unit triple in the direction of the triple `v'; - - `triple expi(real polar, real azimuth)' - returns a unit triple in the direction `(polar,azimuth)' - measured in radians; - - `triple dir(real colatitude, real longitude)' - returns a unit triple in the direction - `(colatitude,longitude)' measured in degrees; - - `real xpart(triple v)' - returns `v.x'; - - `real ypart(triple v)' - returns `v.y'; - - `real zpart(triple v)' - returns `v.z'; - - `real dot(triple u, triple v)' - returns the dot product `u.x*v.x+u.y*v.y+u.z*v.z'; - - `triple cross(triple u, triple v)' - returns the cross product - - `(u.y*v.z-u.z*v.y,u.z*v.x-u.x*v.z,u.x*v.y-v.x*u.y)'; - - `triple minbound(triple u, triple v)' - returns `(min(u.x,v.x),min(u.y,v.y),min(u.z,v.z))'; - - `triple maxbound(triple u, triple v)' - returns `(max(u.x,v.x),max(u.y,v.y),max(u.z,v.z)'). - - -`string' - a character string, implemented using the STL `string' class. - - Strings delimited by double quotes (`"') are subject to the - following mappings to allow the use of double quotes in TeX (e.g. - for using the `babel' package, *note babel::): - - * \" maps to " - - * \\ maps to \\ - - Strings delimited by single quotes (`'') have the same mappings as - character strings in ANSI `C': - - * \' maps to ' - - * \" maps to " - - * \? maps to ? - - * \\ maps to backslash - - * \a maps to alert - - * \b maps to backspace - - * \f maps to form feed - - * \n maps to newline - - * \r maps to carriage return - - * \t maps to tab - - * \v maps to vertical tab - - * \0-\377 map to corresponding octal byte - - * \x0-\xFF map to corresponding hexadecimal byte - - The implicit initializer for strings is the empty string `""'. - Strings may be concatenated with the `+' operator. In the following - string functions, position `0' denotes the start of the string: - `int length(string s)' - returns the length of the string `s'; - - `int find(string s, string t, int pos=0)' - returns the position of the first occurrence of string `t' in - string `s' at or after position `pos', or -1 if `t' is not a - substring of `s'; - - `int rfind(string s, string t, int pos=-1)' - returns the position of the last occurrence of string `t' in - string `s' at or before position `pos' (if `pos'=-1, at the - end of the string `s'), or -1 if `t' is not a substring of - `s'; - - `string insert(string s, int pos, string t)' - returns the string formed by inserting string `t' at position - `pos' in `s'; - - `string erase(string s, int pos, int n)' - returns the string formed by erasing the string of length `n' - (if `n'=-1, to the end of the string `s') at position `pos' - in `s'; - - `string substr(string s, int pos, int n=-1)' - returns the substring of `s' starting at position `pos' and - of length `n' (if `n'=-1, until the end of the string `s'); - - `string reverse(string s)' - returns the string formed by reversing string `s'; - - `string replace(string s, string before, string after)' - returns a string with all occurrences of the string `before' - in the string `s' changed to the string `after'; - - `string replace(string s, string[][] table)' - returns a string constructed by translating in string `s' all - occurrences of the string `before' in an array `table' of - string pairs {`before',`after'} to the corresponding string - `after'; - - `string[] split(string s, string delimiter)' - returns an array of strings obtained by splitting `s' into - substrings delimited by `delimiter'; - - `string format(string s, int n)' - returns a string containing `n' formatted according to the - C-style format string `s' using the current locale; - - `string format(string s=defaultformat, real x, string locale="")' - returns a string containing `x' formatted according to the - C-style format string `s' using locale `locale' (or the - current locale if an empty string is specified), following - the behaviour of the C function `fprintf'), except that only - one data field is allowed, trailing zeros are removed by - default (unless `#' is specified), and (if the format string - specifies math mode) TeX is used to typeset scientific - notation; - - `int hex(string s);' - casts a hexidecimal string `s' to an integer. - - `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); - - `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 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 - -5.2 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 - @cindex @code{ellipse} - path ellipse(pair c, real a, real b) - { - return shift(c)*scale(a,b)*unitcircle; - } - - This example illustrates the use of all five guide connectors - discussed in *Note Tutorial::: size(300,0); - pair[] z=new pair[10]; - - z[0]=(0,100); z[1]=(50,0); z[2]=(180,0); - - for(int n=3; n <= 9; ++n) - z[n]=z[n-3]+(200,0); - - path p=z[0]..z[1]---z[2]::{up}z[3] - &z[3]..z[4]--z[5]::{up}z[6] - &z[6]::z[7]---z[8]..{up}z[9]; - - draw(p,grey+linewidth(4mm)); - - dot(z); - - - - Here are some useful functions for paths: - - `int length(path p);' - This is the number of (linear or cubic) segments in path `p'. - If `p' is cyclic, this is the same as the number of nodes in - `p'. - - `int size(path p);' - This is the number of nodes in the path `p'. If `p' is - cyclic, this is the same as `length(p)'. - - `bool cyclic(path p);' - returns `true' iff path `p' is cyclic. - - `bool straight(path p, int i);' - returns `true' iff the segment of path `p' between node `i' - and node `i+1' is straight. - - `bool piecewisestraight(path p)' - returns `true' iff the path `p' is piecewise straight. - - `pair point(path p, int t);' - If `p' is cyclic, return the coordinates of node `t' mod - `length(p)'. Otherwise, return the coordinates of node `t', - unless `t' < 0 (in which case `point(0)' is returned) or `t' - > `length(p)' (in which case `point(length(p))' is returned). - - `pair point(path p, real t);' - This returns the coordinates of the point between node - `floor(t)' and `floor(t)+1' corresponding to the cubic spline - parameter `t-floor(t)' (*note Bezier::). 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::). - - `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'. - - `pair 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 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 the 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); - - - - 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 - -5.3 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); - - Various shades and mixtures of the grayscale primary colors - `black' and `white', RGB primary colors `red', `green', and - `blue', and RGB secondary colors `cyan', `magenta', and `yellow' - are defined as named colors, along with the CMYK primary colors - `Cyan', `Magenta', `Yellow', and `Black', in the module `plain': - - - - The standard 140 RGB `X11' colors can be imported with the command - import x11colors; - and the standard 68 CMYK TeX colors can be imported with the - command - import texcolors; - Note that there is some overlap between these two standards and - the definitions of some colors (e.g. `Green') actually disagree. - - `Asymptote' also comes with a `asycolors.sty' `LaTeX' package that - defines to `LaTeX' CMYK versions of `Asymptote''s predefined - colors, so that they can be used directly within `LaTeX' strings. - Normally, such colors are passed to `LaTeX' via a pen argument; - however, to change the color of only a portion of a string, say - for a slide presentation, (*note slide::) it may be desirable to - specify the color directly to `LaTeX'. This file can be passed to - `LaTeX' with the `Asymptote' command - usepackage("asycolors"); - - The structure `hsv' defined in `plain_pens.asy' may be used to - convert between HSV and RGB spaces, where the hue `h' is an angle - in [0,360) and the saturation `s' and value `v' lie in `[0,1]': - pen p=hsv(180,0.5,0.75); - write(p); // ([default], red=0.375, green=0.75, blue=0.75) - hsv q=p; - write(q.h,q.s,q.v); // 180 0.5 0.75 - - * Line types are specified with the function `pen linetype(string s, - real offset=0, bool scale=true, bool adjust=true)', where `s' is a - string of integer or real numbers separated by spaces. 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(""); - pen dotted=linetype("0 4"); - pen dashed=linetype("8 8"); - pen longdashed=linetype("24 8"); - pen dashdotted=linetype("8 8 0 8"); - pen longdashdotted=linetype("24 8 0 8"); - pen Dotted=dotted+1.0; - pen Dotted(pen p=currentpen) {return dotted+2*linewidth(p);} - - - - The default line type is `solid'; this may be changed with - `defaultpen(pen)'. The line type of a pen is returned by `int - linetype(pen p=currentpen)'. - - * 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' we define - static void defaultpen(real w) {defaultpen(linewidth(w));} - static pen operator +(pen p, real w) {return p+linewidth(w);} - static 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 `fix-cm' package - available from - - `http://www.ctan.org/tex-archive/help/Catalogue/entries/fix-cm' - and included in recent `LaTeX' distributions). The font size and - line skip of a pen can be examined with the routines `real - fontsize(pen p=currentpen)' and `real lineskip(pen p=currentpen)', - respectively. - - * A pen using a specific `LaTeX' `NFSS' font is returned by calling - the function `pen font(string encoding, string family, string - series, string shape)'. The default setting, - `font("OT1","cmr","m","n")', corresponds to 12pt Computer Modern - Roman; this may be changed with `defaultpen(pen)'. The font - setting of a pen is returned by `string font(pen p=currentpen)'. - Support for standardized international characters is provided by - the `unicode' package (*note unicode::). - - Alternatively, one may select a fixed-size TeX font (on which - `fontsize' has no effect) like `"cmr12"' (12pt Computer Modern - Roman) or `"pcrr"' (Courier) using the function `pen font(string - name)'. An optional size argument can also be given to scale the - font to the requested size: `pen font(string name, real size)'. - - A nonstandard font command can be generated with `pen - fontcommand(string)'. - - A convenient interface to the following standard `PostScript' - fonts is also provided: - pen AvantGarde(string series="m", string shape="n"); - pen Bookman(string series="m", string shape="n"); - pen Courier(string series="m", string shape="n"); - pen Helvetica(string series="m", string shape="n"); - pen NewCenturySchoolBook(string series="m", string shape="n"); - pen Palatino(string series="m", string shape="n"); - pen TimesRoman(string series="m", string shape="n"); - pen ZapfChancery(string series="m", string shape="n"); - pen Symbol(string series="m", string shape="n"); - pen ZapfDingbats(string series="m", string shape="n"); - - * The transparency of a pen can be changed with the command: - pen opacity(real opacity=1, string blend="Compatible"); - The opacity can be varied from `0' (fully transparent) to the - default value of `1' (opaque), and `blend' specifies one of the - following foreground-background blending operations: - "Compatible","Normal","Multiply","Screen","Overlay","SoftLight", - "HardLight","ColorDodge","ColorBurn","Darken","Lighten","Difference", - "Exclusion","Hue","Saturation","Color","Luminosity", - as described in - - `http://partners.adobe.com/public/developer/en/pdf/PDFReference16.pdf'. - Since `PostScript' does not support transparency, this feature is - only effective with the `-f pdf' output format option; other - formats can be produced from the resulting PDF file with the - `ImageMagick' `convert' program. Labels are always drawn with an - `opacity' of 1. A simple example of transparent filling is - provided in the example file `transparency.asy'. - - * `PostScript' commands within a `picture' may be used to create a - tiling pattern, identified by the string `name', for `fill' and - `draw' operations by adding it to the global `PostScript' frame - `currentpatterns', with optional left-bottom margin `lb' and - right-top margin `rt'. - import patterns; - void add(string name, picture pic, pair lb=0, pair rt=0); - - To `fill' or `draw' using pattern `name', use the pen - `pattern("name")'. For example, rectangular tilings can be - constructed using the routines `picture tile(real Hx=5mm, real - Hy=0, pen p=currentpen, filltype filltype=NoFill)', `picture - checker(real Hx=5mm, real Hy=0, pen p=currentpen)', and `picture - brick(real Hx=5mm, real Hy=0, pen p=currentpen)' defined in - `patterns.asy': size(0,90); - import patterns; - - add("tile",tile()); - add("filledtilewithmargin",tile(6mm,4mm,red,Fill),(1mm,1mm),(1mm,1mm)); - add("checker",checker()); - add("brick",brick()); - - real s=2.5; - filldraw(unitcircle,pattern("tile")); - filldraw(shift(s,0)*unitcircle,pattern("filledtilewithmargin")); - filldraw(shift(2s,0)*unitcircle,pattern("checker")); - filldraw(shift(3s,0)*unitcircle,pattern("brick")); - - - - Hatch patterns can be generated with the routines `picture - hatch(real H=5mm, pair dir=NE, pen p=currentpen)', `picture - crosshatch(real H=5mm, pen p=currentpen)': size(0,100); - import patterns; - - add("hatch",hatch()); - add("hatchback",hatch(NW)); - add("crosshatch",crosshatch(3mm)); - - real s=1.25; - filldraw(unitsquare,pattern("hatch")); - filldraw(shift(s,0)*unitsquare,pattern("hatchback")); - filldraw(shift(2s,0)*unitsquare,pattern("crosshatch")); - - - - You may need to turn off aliasing in your `PostScript' viewer for - patterns to appear correctly. Custom patterns can easily be - constructed, following the examples in `patterns.asy'. The tiled - pattern can even incorporate shading (*note gradient shading::), - as illustrated in this example (not included in the manual because - not all printers support `PostScript' 3): size(0,100); - import patterns; - - real d=4mm; - picture tiling; - path square=scale(d)*unitsquare; - axialshade(tiling,square,white,(0,0),black,(d,d)); - fill(tiling,shift(d,d)*square,blue); - add("shadedtiling",tiling); - - filldraw(unitcircle,pattern("shadedtiling")); - - * One can specify a custom pen nib as an arbitrary polygonal path - with `pen makepen(path)'; this path represents the mark to be - drawn for paths containing a single point. This pen nib path can be - recovered from a pen with `path nib(pen)'. Unlike in `MetaPost', - the path need not be convex: - - size(200); - pen convex=makepen(scale(10)*polygon(8))+grey; - draw((1,0.4),convex); - draw((0,0)---(1,1)..(2,0)--cycle,convex); - - pen nonconvex=scale(10)* - makepen((0,0)--(0.25,-1)--(0.5,0.25)--(1,0)--(0.5,1.25)--cycle)+red; - draw((0.5,-1.5),nonconvex); - draw((0,-1.5)..(1,-0.5)..(2,-1.5),nonconvex); - - - - The value `nullpath' represents a circular pen nib (the default); - an elliptical pen can be achieved simply by multiplying the pen by - a transform: `yscale(2)*currentpen'. - - * One can prevent labels from overwriting one another by using the - pen attribute `overwrite', which takes a single argument: - - `Allow' - Allow labels to overwrite one another. This is the default - behaviour (unless overridden with `defaultpen(pen)'. - - `Suppress' - Suppress, with a warning, each label that would overwrite - another label. - - `SuppressQuiet' - Suppress, without warning, each label that would overwrite - another label. - - `Move' - Move a label that would overwrite another out of the way and - issue a warning. As this adjustment is during the final - output phase (in `PostScript' coordinates) it could result in - a larger figure than requested. - - `MoveQuiet' - Move a label that would overwrite another out of the way, - without warning. As this adjustment is during the final - output phase (in `PostScript' coordinates) it could result in - a larger figure than requested. - - - - The routine `defaultpen()' returns the current default pen -attributes. Calling the routine `resetdefaultpen()' resets all pen -default attributes to their initial values. - - -File: asymptote.info, Node: Transforms, Next: Frames and pictures, Prev: Pens, Up: Programming - -5.4 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 - -5.5 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="", - 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. - - - 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 of - pen `p' with 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 `PostScript' bounds that picture `pic' would have - if it were currently fit to a frame using its default size - specification. If `user' is `false' the returned value is in - `PostScript' coordinates, otherwise it is in user coordinates. - - The function - pair point(picture pic=currentpicture, pair dir, bool user=true); - is a convenient way of determining the point on the bounding box - of `pic' in the direction `dir' relative to its center, ignoring - the contributions from fixed-size objects (such as labels and - arrowheads). If `user' is `true' the returned value is in user - coordinates, otherwise it is in `PostScript' coordinates. - - The function - pair truepoint(picture pic=currentpicture, pair dir, bool user=true); - is identical to `point', except that it also accounts for - fixed-size objects, using the scaling transform that picture `pic' - would have if currently fit to a frame using its default size - specification. If `user' is `true' the returned value is in user - coordinates, otherwise it is in `PostScript' coordinates. - - Sometimes it is useful to draw objects on separate pictures and - add one picture to another using the `add' function: - void add(picture src, bool group=true, - filltype filltype=NoFill, bool above=true); - void add(picture dest, picture src, bool group=true, - filltype filltype=NoFill, bool above=true); - The first example adds `src' to `currentpicture'; the second one - adds `src' to `dest'. The `group' option specifies whether or not - the graphical user interface `xasy' should treat all of the - elements of `src' as a single entity (*note GUI::), `filltype' - requests optional background filling or clipping, and `above' - specifies whether to add `src' above or below existing objects. - - There are also routines to add a picture or frame `src' specified - in postscript coordinates to another picture `dest' (or - `currentpicture') about the user coordinate `position': - - - void add(picture src, pair position, bool group=true, - filltype filltype=NoFill, bool above=true); - void add(picture dest, picture src, pair position, - bool group=true, filltype filltype=NoFill, bool above=true); - void add(picture dest=currentpicture, frame src, pair position=0, - bool group=true, filltype filltype=NoFill, bool above=true); - void add(picture dest=currentpicture, frame src, pair position, - pair align, bool group=true, filltype filltype=NoFill, - bool above=true); - - The optional `align' argument in the last three forms specifies a - direction to use for aligning the frame, in a manner analogous to - the `align' argument of `label' (*note label::). However, one key - difference is that when `align' is not specified, labels are - centered, whereas frames and pictures are aligned so that their - origin is at `position'. Illustrations of frame alignment can be - found in the examples *Note errorbars:: and *Note image::. If you - want to align three or more subpictures, group them two at a time: - - picture pic1; - real size=50; - size(pic1,size); - fill(pic1,(0,0)--(50,100)--(100,0)--cycle,red); - - picture pic2; - size(pic2,size); - fill(pic2,unitcircle,green); - - picture pic3; - size(pic3,size); - fill(pic3,unitsquare,blue); - - picture pic; - add(pic,pic1.fit(),(0,0),N); - add(pic,pic2.fit(),(0,0),10S); - - add(pic.fit(),(0,0),N); - add(pic3.fit(),(0,0),10S); - - - - Alternatively, one can use `attach' to automatically increase the - size of picture `dest' to accommodate adding a frame `src' about - the user coordinate `position': - void attach(picture dest=currentpicture, frame src, - pair position=0, bool group=true, - filltype filltype=NoFill, bool above=true); - void attach(picture dest=currentpicture, frame src, - pair position, pair align, bool group=true, - filltype filltype=NoFill, bool above=true); - - To erase the contents of a picture (but not the size - specification), use the function - void erase(picture pic=currentpicture); - - To save a snapshot of `currentpicture', `currentpen', and - `currentprojection', use the function `save()'. - - To restore a snapshot of `currentpicture', `currentpen', and - `currentprojection', use the function `restore()'. - - Many further examples of picture and frame operations are provided - in the base module `plain'. - - It is possible to insert verbatim `PostScript' commands in a - picture with one of the routines - void postscript(picture pic=currentpicture, string s); - void postscript(picture pic=currentpicture, string s, pair min, - pair max) - Here `min' and `max' can be used to specify explicit bounds - associated with the resulting `PostScript' code. - - Verbatim TeX commands can be inserted in the intermediate `LaTeX' - output file with one of the functions - void tex(picture pic=currentpicture, string s); - void tex(picture pic=currentpicture, string s, pair min, pair max) - Here `min' and `max' can be used to specify explicit bounds - associated with the resulting TeX code. - - To issue a global TeX command (such as a TeX macro definition) in - the TeX preamble (valid for the remainder of the top-level module) - use: - void texpreamble(string s); - - The TeX environment can be reset to its initial state, clearing all - macro definitions, with the function - void texreset(); - - The routine - void usepackage(string s, string options=""); - provides a convenient abbreviation for - texpreamble("\usepackage["+options+"]{"+s+"}"); - that can be used for importing `LaTeX' packages. - - - -File: asymptote.info, Node: Files, Next: Variable initializers, Prev: Frames and pictures, Up: Programming - -5.6 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="#")'; 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. - - If the `-globalwrite' (or `-nosafe') option is enabled, one can -change the current working directory 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); - 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. - - 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), `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 also be opened with `xinput' or `xoutput', instead of -`input' or `output', to read or write double precision (64-bit) real -values and single precision (32-bit) integer values in Sun -Microsystem's XDR (External Data Representation) portable binary format -(available on all `UNIX' platforms). A file may also be opened with -`binput' or `boutput' to read or write double precision values in the -native (nonportable) machine binary format. The function `file -single(file,0.0)' may be used to set a file to read single precision -real XDR or binary values; calling `file single(file,0.0,false)' sets -it back to read doubles again. The functions `file single(file,0)' and -`file single(file,0,false)' can be used to change the default integer -precision (single). The functions `file single(file)' and `file -single(file,false)' may be used to set the precision for both real and -integer values. - - 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'. If the setting `safe' is false, then the -function `int system(string s)' can be used to call the arbitrary system -command `s'. - - -File: asymptote.info, Node: Variable initializers, Next: Structures, Prev: Files, Up: Programming - -5.7 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. - - -File: asymptote.info, Node: Structures, Next: Operators, Prev: Variable initializers, Up: Programming - -5.8 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=new T; -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; - - Here, the expression `new T' will produce a new instance of the -class, but will also cause `Tcount' to be incremented, so that it keeps -track of the number of instances produced. - - The expression `null' can be cast to any structure type to yield a -null reference, a reference that does not actually refer to any -instance of the structure. Trying to use a field of a null reference -will cause an error. - - The function `bool alias(T,T)' checks to see if two structure -references refer to the same instance of the structure (or both to -`null'). For example, in the example code at the start of the section, -`alias(foo,bar)' would return true, but `alias(foo,new T)' would return -false, as `new T' creates a new instance of the structure `T'. The -boolean operators `==' and `!=' are by default equivalent to `alias' and -`!alias' respectively, but may be overwritten for a particular type -(for example, to do a deep comparison). - - After the definition of a structure `T', a variable of type `T' is -initialized to a new instance (`new T') by default. During the -definition of the structure, however, variables of type `T' are -initialized to `null' by default. This special behaviour is to avoid -infinite recursion of creating new instances in code such as - - -struct tree { - int value; - tree left; - tree right; -} - - Here is a simple example that illustrates the use of structures: - - -struct S { - real a=1; - real f(real a) {return a+this.a;} -} - -S s; // Initializes s with new S; - -write(s.f(2)); // Outputs 3 - -S operator + (S s1, S s2) -{ - S result; - result.a=s1.a+s2.a; - return result; -} - -write((s+s).f(0)); // Outputs 2 - - It is often convenient to have functions that construct new -instances of a structure. Say we have a `Person' structure: - - -struct Person { - string firstname; - string lastname; -} - -Person joe=new Person; -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 - -5.9 Operators -============= - -* Menu: - -* Arithmetic & logical:: Basic mathematical operators -* Self & prefix operators:: Increment and decrement -* User-defined operators:: Overloading operators - - -File: asymptote.info, Node: Arithmetic & logical, Next: Self & prefix operators, Up: Operators - -5.9.1 Arithmetic & logical operators ------------------------------------- - -`Asymptote' uses the standard binary arithmetic operators. However, -when one integer is divided by another, both arguments are converted to -real values before dividing and a real quotient is returned (since this -is usually what is intended). The function `int quotient(int x, int y)' -returns the greatest integer less than or equal to `x/y'. In all other -cases both operands are promoted to the same type, which will also be -the type of the result: -`+' - addition - -`-' - subtraction - -`*' - multiplication - -`/' - division - -`%' - modulo; the result always has the same sign as the divisor. In - particular, this makes `q*quotient(p,q)+p%q == p' for all integers - `p' and nonzero integers `q'. - -`^' - power; if the exponent (second argument) is an int, recursive - multiplication is used; otherwise, logarithms and exponentials are - used (`**' is a synonym for `^'). - - - The usual boolean operators are also defined: -`==' - equals - -`!=' - not equals - -`<' - less than - -`<=' - less than or equals - -`>=' - greater than or equals - -`>' - greater than - -`&&' - and (with conditional evaluation of right-hand argument) - -`&' - and - -`||' - or (with conditional evaluation of right-hand argument) - -`|' - or - -`^' - xor - -`!' - not - - `Asymptote' also supports the C-like conditional syntax: - -bool positive=(pi >= 0) ? true : false; - - The function `T interp(T a, T b, real t)' returns `(1-t)*a+t*b' for -nonintegral built-in arithmetic types `T'. If `a' and `b' are pens, -they are first promoted to the same color space. - - `Asymptote' also defines bitwise functions `int AND(int,int)', `int -OR(int,int)', `int XOR(int,int)', and `int NOT(int)'. - - -File: asymptote.info, Node: Self & prefix operators, Next: User-defined operators, Prev: Arithmetic & logical, Up: Operators - -5.9.2 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 - -5.9.3 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 - -5.10 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 - -5.11 Functions -============== - -`Asymptote' functions are treated as variables with a signature -(non-function variables have null signatures). Variables with the same -name are allowed, so long as they have distinct signatures. - - Functions arguments are passed by value. To pass an argument by -reference, simply enclose it in a structure (*note Structures::). - - Here are some significant features of `Asymptote' functions: - - 1. Variables with signatures (functions) and without signatures - (nonfunction variables) are distinct: - int x, x(); - x=5; - x=new int() {return 17;}; - x=x(); // calls x() and puts the result, 17, in the scalar x - - 2. Traditional function definitions are allowed: - int sqr(int x) - { - return x*x; - } - sqr=null; // but the function is still just a variable. - - 3. Casting can be used to resolve ambiguities: - int a, a(), b, b(); // Valid: creates four variables. - a=b; // Invalid: assignment is ambiguous. - a=(int) b; // Valid: resolves ambiguity. - (int) (a=b); // Valid: resolves ambiguity. - (int) a=b; // Invalid: cast expressions cannot be L-values. - - int c(); - c=a; // Valid: only one possible assignment. - - 4. Anonymous (so-called "high-order") functions are also allowed: - typedef int intop(int); - intop adder(int m) - { - return new int(int n) {return m+n;}; - } - intop addby7=adder(7); - write(addby7(1)); // Writes 8. - - 5. One may redefine a function `f', even for calls to `f' in - previously declared functions, by assigning another (anonymous or - named) function to it. However, if `f' is overloaded by a new - function definition, previous calls will still access the original - version of `f', as illustrated in this example: - void f() { - write("hi"); - } - - void g() { - f(); - } - - g(); // writes "hi" - - f=new void() {write("bye");}; - - g(); // writes "bye" - - void f() {write("overloaded");}; - - f(); // writes "overloaded" - g(); // writes "bye" - - 6. Anonymous functions can be used to redefine a function variable - that has been declared (and implicitly initialized to the null - function) but not yet explicitly defined: - void f(bool b); - - void g(bool b) { - if(b) f(b); - else write(b); - } - - f=new void(bool b) { - write(b); - g(false); - }; - - g(true); // Writes true, then writes false. - - - `Asymptote' is the only language we know of that treats functions as -variables, but allows overloading by distinguishing variables based on -their signatures. - - Functions are allowed to call themselves recursively. As in C++, -infinite nested recursion will generate a stack overflow (reported as a -segmentation fault, unless a fully working version of the GNU library -`libsigsegv' (e.g. 2.4 or later) is installed at configuration time). - -* Menu: - -* Default arguments:: Default values can appear anywhere -* Named arguments:: Assigning function arguments by keyword -* Rest arguments:: Functions with a variable number of arguments -* Mathematical functions:: Standard libm functions - - -File: asymptote.info, Node: Default arguments, Next: Named arguments, Up: Functions - -5.11.1 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 - -5.11.2 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. - - 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 - -5.11.3 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. - - 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 - -5.11.4 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 `J(int n, real)' and second kind -`Y(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 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 - -5.12 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', - - * `void cyclic(bool b)', - - * `bool cyclicflag', - - * `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.cyclicflag' returns the current setting of the `cyclic' flag. - - 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 the array of integers from `0' to `n-1' inclusive. 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, `cyclic', `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. By default, if - `value' is itself an array, a deep copy of that array is made for - each entry in the new array. If `depth' is specified, this deep - copying only recurses to the number of levels specified. - -`int[] sequence(int n)' - if `n >= 1' returns the array `{0,1,...,n-1}' (otherwise returns a - null array); - -`int[] sequence(int n, int m)' - if `m >= n' returns an array `{n,n+1,...,m}' (otherwise returns a - null array); - -`T[] sequence(T f(int), int n)' - if `n >= 1' returns the sequence `{f_i :i=0,1,...n-1}' given a - function `T f(int)' and integer `int n' (otherwise returns a null - array); - -`T[] map(T f(T), T[] a)' - returns the array obtained by applying the function `f' to each - element of the array `a'. This is equivalent to `sequence(new - T(int i) {return f(a[i]);},a.length)'. - -`int[] reverse(int n)' - if `n >= 1' returns the array `{n-1,n-2,...,0}' (otherwise returns - a null array); - -`int[] complement(int[] a, int n)' - returns the complement of the integer array `a' in - `{0,1,2,...,n-1}', so that `b[complement(a,b.length)]' yields the - complement of `b[a]'. - -`real[] uniform(real a, real b, int n)' - if `n >= 1' returns a uniform partition of `[a,b]' into `n' - subintervals (otherwise returns a null array); - -`int find(bool[], int n=1)' - returns the index of the `n'th `true' value or -1 if not found. - If `n' is negative, search backwards from the end of the array for - the `-n'th value; - -`int search(T[] a, T key)' - For built-in ordered types `T', searches a sorted ordered array - `a' of `n' elements to find an interval containing `key', - returning `-1' if `key' is less than the first element, `n-1' if - `key' is greater than or equal to the last element, and otherwise - the index corresponding to the left-hand (smaller) endpoint. - -`T[] copy(T[] a)' - returns a deep copy of the array `a'; - -`T[][] copy(T[][] a)' - returns a deep copy of the array `a'; - -`T[][][] copy(T[][][] a)' - returns a deep copy of the array `a'; - -`T[] concat(... T[][] a)' - returns a new array formed by concatenating the 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 compare(T i, T j))' - returns a copy of `a' stably sorted in ascending order such that - element `i' precedes element `j' if `compare(i,j)' is true. - -`T[][] transpose(T[][] a)' - returns the transpose of `a'. - -`T[][][] transpose(T[][][] a, int[] perm)' - returns the 3D transpose of `a' obtained by applying the - permutation `perm' of `new int[]{0,1,2}' to the indices of each - entry. - -`T sum(T[] a)' - For arithmetic types `T', returns the sum of `a'. In the case - where `T' is `bool', the number of true elements in `a' is - returned. - -`T min(T[] a)' - -`T min(T[][] a)' - -`T min(T[][][] a)' - For built-in ordered types `T', returns the minimum element of `a'. - -`T max(T[] a)' - -`T max(T[][] a)' - -`T max(T[][][] a)' - For built-in ordered types `T', returns the maximum element of `a'. - -`T[] min(T[] a, T[] b)' - For built-in ordered types `T', and arrays `a' and `b' of the same - length, returns an array composed of the minimum of the - corresponding elements of `a' and `b'. - -`T[] max(T[] a, T[] b)' - For built-in ordered types `T', and arrays `a' and `b' of the same - length, returns an array composed of the maximum of the - corresponding elements of `a' and `b'. - -`pair[] pairs(real[] x, real[] y);' - For arrays `x' and `y' of the same length, returns the pair array - `sequence(new pair(int i) {return (x[i],y[i]);},x.length)'. - -`pair[] fft(pair[] a, int sign=1)' - returns the Fast Fourier Transform of `a' (if the optional `FFTW' - package is installed), using the given `sign'. Here is a simple - example: - int n=4; - pair[] f=sequence(n); - write(f); - pair[] g=fft(f,-1); - write(); - write(g); - f=fft(g,1); - write(); - write(f/n); - -`real dot(real[] a, real[] b)' - returns the dot product of the vectors `a' and `b'. - -`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 two 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). If line mode is set with `line(file)', then reading will -stop once the end of the line is reached instead (line mode may be -cleared with `line(file,false)'): - -file fin=input("test.txt"); -real[] A=line(fin); - - 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, set with -`word(file)' and cleared with `word(file,false)', which causes string -reads to respect white-space delimiters, instead of the default -end-of-line delimiter: - -file fin=word(line(input("test.txt"))); -real[] A=fin; - - Another useful mode is comma-separated-value mode, set with -`csv(file)' and cleared with `csv(file,false)', 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 `dimension(file,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=dimension(fin,2,3); -real[][][] B=dimension(fin,2,3,4); - Again, an integer limit of zero means no restriction. - - Sometimes the array dimensions are stored with the data as integer -fields at the beginning of an array. Such arrays can be read in with the -functions `read1', `read2', and `read3', respectively: - -file fin=input("test.txt"); -real[] A=read1(fin); -real[][] B=read2(fin); -real[][][] C=read3(fin); - - One, two, and three-dimensional arrays of the basic data types can be -output with the functions `write(file,T[])', `write(file,T[][])', -`write(file,T[][][])', respectively. - - -File: asymptote.info, Node: Slices, Up: Arrays - -5.12.1 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 - -5.13 Casts -========== - -`Asymptote' implicitly casts `int' to `real', `int' to `pair', `real' -to `pair', `pair' to `path', `pair' to `guide', `path' to `guide', -`guide' to `path', `real' to `pen', `pair[]' to `guide[]', `pair[]' to -`path[]', `path' to `path[]', and `guide' to `path[]', along with -various three-dimensional casts defined in `three.asy'. Implicit casts -are automatically attempted on assignment and when trying to match -function calls with possible function signatures. Implicit casting can -be inhibited by declaring individual arguments `explicit' in the -function signature, say to avoid an ambiguous function call in the -following example, which outputs 0: - - -int f(pair a) {return 0;} -int f(explicit real x) {return 1;} - -write(f(0)); - - Other conversions, say `real' to `int' or `real' to `string', -require an explicit cast: - -int i=(int) 2.5; -string s=(string) 2.5; - -real[] a={2.5,-3.5}; -int[] b=(int []) a; -write(stdout,b); // Outputs 2,-3 - - Casting to user-defined types is also possible using `operator cast': - -struct rpair { - real radius; - real angle; -} - -pair operator cast(rpair x) { - return (x.radius*cos(x.angle),x.radius*sin(x.angle)); -} - -rpair x; -x.radius=1; -x.angle=pi/6; - -write(x); // Outputs (0.866025403784439,0.5) - - One must use care when defining new cast operators. Suppose that in -some code one wants all integers to represent multiples of 100. To -convert them to reals, one would first want to multiply them by 100. -However, the straightforward implementation - -real operator cast(int x) {return x*100;} - is equivalent to an infinite recursion, since the result `x*100' needs -itself to be cast from an integer to a real. Instead, we want to use -the standard conversion of int to real: - -real convert(int x) {return x*100;} -real operator cast(int x)=convert; - - Explicit casts are implemented similarly, with `operator ecast'. - - -File: asymptote.info, Node: Import, Next: Static, Prev: Casts, Up: Programming - -5.14 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 "/tmp/ainst/share/asymptote/graph.asy" as graph;' - -`from "/tmp/ainst/share/asymptote/graph.asy" access axes;' - -`import "/tmp/ainst/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 a file `graph' verbatim (as if the -contents of the file were inserted at that point), use one of the forms: - -include graph; - -`include "/tmp/ainst/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 - -5.15 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 - -6 `LaTeX' usage -*************** - -`Asymptote' comes with a convenient `LaTeX' style file `asymptote.sty' -that makes `LaTeX' `Asymptote'-aware. Entering `Asymptote' code -directly into the `LaTeX' source file, at the point where it is needed, -keeps figures organized and avoids the need to invent new file names -for each figure. Simply add the line `\usepackage{asymptote}' at the -beginning of your file and enclose your `Asymptote' code within a -`\begin{asy}...\end{asy}' environment. As with the `LaTeX' `comment' -environment, the `\end{asy}' command must appear on a line by itself, -with no leading spaces or trailing commands/comments. - - The sample `LaTeX' file below, named `latexusage.tex', can be run as -follows: - -latex latexusage -asy latexusage -latex latexusage - -or - - -pdflatex latexusage -asy latexusage -pdflatex latexusage - - To switch between using `latex' and `pdflatex' you may first need to -remove the files `latexusage-*', `latexusage_.pre', and -`latexusage.aux'. - - One can specify `width', `height', `viewportwidth', -`viewportheight', and `attach' `keyval'-style options to the `asy' -environment. The current version (1.07) of `asymptote.sty' supports the -embedding of 3D PRC files, either inline or, using the `attach' option -with the `attachfile2' (or older `attachfile') `LaTeX' package, as -annotated (but printable) attachments. For many applications, the -annotated attachment method tends to be more convenient. The default -value of `viewportwidth' is `\the\linewidth' for inline 3D figures and -`0' for attachments. - - If the `inline' option is given to the `asymptote.sty' package, -inline `LaTeX' code is generated 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 `latex' is used with the `inline' option, the 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). - - An excellent tutorial by Dario Teixeira on integrating `Asymptote' -and `LaTeX' is available at `http://dario.dse.nl/projects/asylatex/'. - - 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: -%\usepackage[inline]{asymptote} - -% Enable this line to support PDF hyperlinks: -%\usepackage[setpagesize=false]{hyperref} - -% Enable this line for PDF attachments with asy environment option attach=true: -%\usepackage[dvips]{attachfile2} - -\begin{document} - -\begin{asydef} -// Global Asymptote definitions can be put here. -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. It is often desirable to embed such files as annotated attachments; -this requires the optional \verb+\usepackage{attachfile2}+ package and -the \verb+{attach=true}+ option: -\begin{center} -\begin{asy}[height=4cm,attach=false] -import three; -currentprojection=orthographic(5,4,2); -draw(unitcube,blue); -label("$V-E+F=2$",(0,1,0.5),3Y,blue+fontsize(17)); -\end{asy} -\end{center} - -One can also scale the figure to the full line width: -\begin{center} -\begin{asy}[width=\the\linewidth] -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(24)+blue); - -pair s=-0.2*I; -draw("$x$",z0+s--z1+s,N,red,Arrows,Bars,PenMargins); -s=-0.5*I; -draw("$\bar{x}$",z0+s--zf+s,blue,Arrows,Bars,PenMargins); -s=-0.95*I; -draw("$X$",z0+s--z2+s,darkgreen,Arrows,Bars,PenMargins); -\end{asy} -\end{center} -\end{document} - - -File: asymptote.info, Node: Base modules, Next: Options, Prev: LaTeX usage, Up: Top - -7 Base modules -************** - -`Asymptote' currently ships with the following base modules: - -* Menu: - -* plain:: Default `Asymptote' base file -* simplex:: Linear programming: simplex method -* math:: Extend `Asymptote''s math capabilities -* interpolate:: Interpolation routines -* geometry:: Geometry routines -* trembling:: Wavy lines -* stats:: Statistics routines and histograms -* patterns:: Custom fill and draw patterns -* markers:: Custom path marker routines -* tree:: Dynamic binary search tree -* binarytree:: Binary tree drawing module -* drawtree:: Tree drawing module -* syzygy:: Syzygy and braid drawing module -* feynman:: Feynman diagrams -* roundedpath:: Round the sharp corners of paths -* animation:: Embedded PDF and MPEG movies -* embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with `Asymptote' -* MetaPost:: `MetaPost' compatibility routines -* unicode:: Accept `unicode' (UTF-8) characters -* latin1:: Accept `ISO 8859-1' characters -* babel:: Interface to `LaTeX' `babel' package -* labelpath:: Drawing curved labels -* labelpath3:: Drawing curved labels in 3D -* annotate:: Annotate your PDF files -* CAD:: 2D CAD pen and measurement functions (DIN 15) -* graph:: 2D linear & logarithmic graphs -* palette:: Color density images and palettes -* three:: 3D vector graphics -* obj:: 3D obj files -* graph3:: 3D linear & logarithmic graphs -* grid3:: 3D grids -* solids:: 3D solid geometry -* tube:: 3D rotation minimizing tubes -* flowchart:: Flowchart drawing routines -* contour:: Contour lines -* contour3:: Contour surfaces -* slopefield:: Slope fields -* ode:: Ordinary differential equations - - -File: asymptote.info, Node: plain, Next: simplex, Up: Base modules - -7.1 `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 - -7.2 `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 - -7.3 `math' -========== - -This package extends `Asymptote''s mathematical capabilities with -intersection algorithms and matrix arithmetic: - -`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. - - - -File: asymptote.info, Node: interpolate, Next: geometry, Prev: math, Up: Base modules - -7.4 `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 - -7.5 `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://piprim.tuxfamily.org/asymptote/geometry/index.html', and an -index: - - `http://piprim.tuxfamily.org/asymptote/geometry/modules/geometry.asy.index.type.html' - - -File: asymptote.info, Node: trembling, Next: stats, Prev: geometry, Up: Base modules - -7.6 `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. -Further examples are posted at -`http://piprim.tuxfamily.org/asymptote/trembling/index.html' - - -File: asymptote.info, Node: stats, Next: patterns, Prev: trembling, Up: Base modules - -7.7 `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 - -7.8 `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 - -7.9 `markers' -============= - -This package implements specialized routines for marking paths and -angles. The principal mark routine provided by this package is - -markroutine markinterval(int n=1, frame f, bool rotated=false); - which centers `n' copies of frame `f' within uniformly space intervals -in arclength along the path, optionally rotated by the angle of the -local tangent. - - The `marker' (*note marker::) routine can be used to construct new -markers from these predefined frames: - - -frame stickframe(int n=1, real size=0, pair space=0, real angle=0, - pair offset=0, pen p=currentpen); - - -frame circlebarframe(int n=1, real barsize=0, - real radius=0,real angle=0, - pair offset=0, pen p=currentpen, - filltype filltype=NoFill, bool above=false); - - -frame crossframe(int n=3, real size=0, pair space=0, - real angle=0, pair offset=0, pen p=currentpen); - - -frame tildeframe(int n=1, real size=0, pair space=0, - real angle=0, pair offset=0, pen p=currentpen); - - For convenience, this module also constructs the markers -`StickIntervalMarker', `CrossIntervalMarker', -`CircleBarIntervalMarker', and `TildeIntervalMarker' from the above -frames. The example `markers1.asy' illustrates the use of these markers: - - - - -This package also provides a routine for marking an angle AOB: - -void markangle(picture pic=currentpicture, Label L="", - int n=1, real radius=0, real space=0, - pair A, pair O, pair B, arrowbar arrow=None, - pen p=currentpen, margin margin=NoMargin, - marker marker=nomarker); - as illustrated in the example `markers2.asy'. - - - - - -File: asymptote.info, Node: tree, Next: binarytree, Prev: markers, Up: Base modules - -7.10 `tree' -=========== - -This package implements an example of a dynamic binary search tree. - - -File: asymptote.info, Node: binarytree, Next: drawtree, Prev: tree, Up: Base modules - -7.11 `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); - -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); - -add(pic.fit(),(0,0),10N); -add(pic2.fit(),(0,0),10S); - - - - -File: asymptote.info, Node: drawtree, Next: syzygy, Prev: binarytree, Up: Base modules - -7.12 `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 - -7.13 `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 - -7.14 `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 - -7.15 `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 - -7.16 `animation' -================ - -This module allows one to generate animations, as illustrated by the -files `wheel.asy', `wavelet.asy', and `cube.asy' in the `animations' -subdirectory of the examples directory. These animations use the -`ImageMagick' `convert' program to `merge' multiple images into a GIF -or MPEG movie. - - The related `animate' module, derived from the `animation' module, -generates higher-quality portable clickable PDF movies, with optional -controls. This requires installing the package - - `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/animate.sty' - (version 2007/11/30 or later) in a new directory `animate' in the -local `LaTeX' directory (for example, in -`/usr/local/share/texmf/tex/latex/animate'). On `UNIX' systems, one -must then execute the command `texhash'. - - The example `pdfmovie.asy' in the `animations' directory, along with -the slide presentations `slidemovies.asy' and `intro.asy', illustrate -the use of embedded PDF movies. The examples `inlinemovie.tex' and -`inlinemovie3.tex' show how to generate and embed PDF movies directly -within a `LaTeX' file (*note LaTeX usage::). The member function - -string pdf(fit fit=NoBox, real delay=animationdelay, string options="", - bool keep=settings.keep, bool multipage=true); - of the `animate' structure accepts any of the `animate.sty' options, -as described here: - - `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/doc/animate.pdf' - - -File: asymptote.info, Node: embed, Next: slide, Prev: animation, Up: Base modules - -7.17 `embed' -============ - -This module provides an interface to the `LaTeX' package (included with -`MikTeX') - - `http://www.ctan.org/tex-archive/macros/latex/contrib/movie15' - for embedding movies, sounds, and 3D objects into a PDF document. However, -`XeLaTeX' users need to rename the modified version -`movie15_dvipdfmx.sty' from - - `http://asymptote.svn.sourceforge.net/viewvc/asymptote/trunk/asymptote/patches/' - to `movie15.sty' and place it in their `LaTeX' path. - - The latest version of the `movie15' package requires both `pdflatex' -version 1.20 or later and the file - - `http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/ifdraft.dtx' - which can be installed by placing it in a directory `ifdraft' in the -local `LaTeX' directory (e.g. -`/usr/local/share/texmf/tex/latex/ifdraft') and executing in that -directory the commands: - -tex ifdraft.dtx -texhash - - An example of embedding `U3D' code is provided in the file -`embeddedu3d.asy'. As of version 7.0.8, `Adobe Reader' supports the -`U3D' format under Linux. - - Unfortunately, Adobe has not yet made available an embedded movie -plugin for the Linux version of `Adobe Reader'. A portable method for -embedding movie files, which should work on any platform and does not -require the `movie15' or `ifdraft' packages, is provided by using the -`external' module instead of `embed'. An example of these interfaces is -provided in the file `embeddedmovie.asy' and `externalmovie.asy' in the -`animations' subdirectory of the examples directory. For a higher -quality movie generated directly by `Asymptote', use the `animate' -module along with the `animate.sty' package to embed a portable PDF -animation (*note animate::). - - -File: asymptote.info, Node: slide, Next: MetaPost, Prev: embed, Up: Base modules - -7.18 `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 - -7.19 `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 - -7.20 `unicode' -============== - -Import this package at the beginning of the file to instruct `LaTeX' to -accept `unicode' (UTF-8) standardized international characters. To use -Cyrillic fonts, you will need to change the font encoding: - -import unicode; -texpreamble("\usepackage{mathtext}\usepackage[russian]{babel}"); -defaultpen(font("T2A","cmr","m","n")); - Support for Chinese, Japanese, and Korean fonts is provided by the CJK -package: - - `http://www.ctan.org/tex-archive/languages/chinese/CJK/' - The following commands enable the CJK song family (within a label, -you can also temporarily switch to another family, say kai, by -prepending `"\CJKfamily{kai}"' to the label string): - -texpreamble("\usepackage{CJK} -\AtBeginDocument{\begin{CJK*}{GBK}{song}} -\AtEndDocument{\clearpage\end{CJK*}}"); - - -File: asymptote.info, Node: latin1, Next: babel, Prev: unicode, Up: Base modules - -7.21 `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 - -7.22 `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 - -7.23 `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 - -7.24 `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 - -7.25 `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 - -7.26 `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 - -7.27 `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. - Th 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. - - - - - - 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 the current picture unless - `above=true'. The axis placement is determined by one of the - following `axis' types: - - `YZero(bool extend=true)' - Request an x axis at y=0 (or y=1 on a logarithmic axis) - extending to the full dimensions of the picture, unless - `extend'=false. - - `YEquals(real Y, bool extend=true)' - Request an x axis at y=`Y' extending to the full dimensions - of the picture, unless `extend'=false. - - `Bottom(bool extend=false)' - Request a bottom axis. - - `Top(bool extend=false)' - Request a top axis. - - `BottomTop(bool extend=false)' - Request a bottom and top axis. - - - Custom axis types can be created by following the examples in - `graph.asy'. One can easily override the default values for the - standard axis types: - import graph; - - YZero=new axis(bool extend=true) { - return new void(picture pic, axisT axis) { - real y=pic.scale.x.scale.logarithmic ? 1 : 0; - axis.value=I*pic.scale.y.T(y); - axis.position=1; - axis.side=right; - axis.align=2.5E; - axis.value2=Infinity; - axis.extend=extend; - }; - }; - YZero=YZero(); - - The default tick option is `NoTicks'. The options `LeftTicks', - `RightTicks', or `Ticks' can be used to draw ticks on the left, - right, or both sides of the path, relative to the direction in - which the path is drawn. These tick routines accept a number of - optional arguments: - ticks LeftTicks(Label format="", ticklabel ticklabel=null, - bool beginlabel=true, bool endlabel=true, - int N=0, int n=0, real Step=0, real step=0, - bool begin=true, bool end=true, tickmodifier modify=None, - real Size=0, real size=0, bool extend=false, - pen pTick=nullpen, pen ptick=nullpen); - - If any of these parameters are omitted, reasonable defaults will - be chosen: - `Label format' - override the default tick label format (`defaultformat', - initially "$%.4g$"), rotation, pen, and alignment (for - example, `LeftSide', `Center', or `RightSide') relative to - the axis. To enable `LaTeX' math mode fonts, the format - string should begin and end with `$' *note format::. If the - format string is `trailingzero', trailing zeros will be added - to the tick labels; if the format string is `"%"', the tick - label will be suppressed; - - `ticklabel' - is a function `string(real x)' returning the label (by - default, format(format.s,x)) for each major tick value `x'; - - `bool beginlabel' - include the first label; - - `bool endlabel' - include the last label; - - `int N' - when automatic scaling is enabled (the default; *note - automatic scaling::), divide a linear axis evenly into this - many intervals, separated by major ticks; for a logarithmic - axis, this is the number of decades between labelled ticks; - - `int n' - divide each interval into this many subintervals, separated - by minor ticks; - - `real Step' - the tick value spacing between major ticks (if `N'=`0'); - - `real step' - the tick value spacing between minor ticks (if `n'=`0'); - - `bool begin' - include the first major tick; - - `bool end' - include the last major tick; - - `tickmodifier modify;' - an optional function that takes and returns a `tickvalue' - structure having real[] members `major' and `minor' - consisting of the tick values (to allow modification of the - automatically generated tick values); - - `real Size' - the size of the major ticks (in `PostScript' coordinates); - - `real size' - the size of the minor ticks (in `PostScript' coordinates); - - `bool extend;' - extend the ticks between two axes (useful for drawing a grid - on the graph); - - `pen pTick' - an optional pen used to draw the major ticks; - - `pen ptick' - an optional pen used to draw the minor ticks. - - - For convenience, the predefined tickmodifier `OmitTick(... real[] - x)' tickmodifier 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); - - Draw a y axis on picture `pic' from y=`ymin' to y=`ymax' using pen - `p', optionally labelling it with Label `L'. 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 the current picture 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="", - 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 the current picture 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 - the current picture 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=nullpen); - void labelx(picture pic=currentpicture, Label L="", real x, - align align=S, string format="", pen p=nullpen); - 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=nullpen); - void labely(picture pic=currentpicture, Label L="", real y, - align align=W, string format="", pen p=nullpen); - void labely(picture pic=currentpicture, Label L, - string format="", explicit pen p=nullpen); - - Here are some simple examples of two-dimensional graphs: - - 1. This example draws a textbook-style graph of y= exp(x), with the y - axis starting at y=0: import graph; - size(150,0); - - real f(real x) {return exp(x);} - pair F(real x) {return (x,f(x));} - - xaxis("$x$"); - yaxis("$y$",0); - - draw(graph(f,-4,2,operator ..),red); - - labely(1,E); - label("$e^x$",F(1),SE); - - - - 2. The next example draws a scientific-style graph with a legend. - The position of the legend can be adjusted either explicitly or by - using the graphical user interface `xasy' (*note GUI::). If an - `UnFill(real xmargin=0, real ymargin=xmargin)' or `Fill(pen)' - option is specified to `add', the legend will obscure any - underlying objects. Here we illustrate how to clip the portion of - the picture covered by a label: - - import graph; - - size(400,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\sin(2\pi x)$"); - draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$"); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - label("LABEL",point(0),UnFill(1mm)); - - add(legend(),point(E),20E,UnFill); - - - - To specify a fixed size for the graph proper, use `attach': import graph; - - size(250,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\sin(2\pi x)$"); - draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$"); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - label("LABEL",point(0),UnFill(1mm)); - - attach(legend(),truepoint(E),20E,UnFill); - A legend can have multiple entries per line: import graph; - size(8cm,6cm,IgnoreAspect); - - typedef real realfcn(real); - realfcn F(real p) { - return new real(real x) {return sin(p*x);}; - }; - - for(int i=1; i < 5; ++i) - draw(graph(F(i*pi),0,1),Pen(i), - "$\sin("+(i == 1 ? "" : (string) i)+"\pi x)$"); - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - attach(legend(2),(point(S).x,truepoint(S).y),10S,UnFill); - - - - 3. This example draws a graph of one array versus another (both of - the same size) using custom tick locations and a smaller font size - for the tick labels on the y axis. import graph; - - size(200,150,IgnoreAspect); - - real[] x={0,1,2,3}; - real[] y=x^2; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight, - RightTicks(Label(fontsize(8)),new real[]{0,4,9})); - - - - 4. This example shows how to graph columns of data read from a file. import graph; - - size(200,150,IgnoreAspect); - - file in=line(input("filegraph.dat")); - real[][] a=dimension(in,0,0); - a=transpose(a); - - real[] x=a[0]; - real[] y=a[1]; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - 5. The next example draws two graphs of an array of coordinate pairs, - using frame alignment and data markers. In the left-hand graph, the - markers, constructed with - marker marker(path g, markroutine markroutine=marknodes, - pen p=currentpen, filltype filltype=NoFill, - bool above=true); - using the path `unitcircle' (*note filltype::), are drawn below - each node. Any frame can be converted to a marker, using - - - marker marker(frame f, markroutine markroutine=marknodes, - bool above=true); - In the right-hand graph, the unit n-sided regular polygon - `polygon(int n)' and the unit n-point cyclic cross `cross(int n, - bool round=true, real r=0)' (where `r' is an optional "inner" - radius) are used to build a custom marker frame. - - Here `markuniform(bool centered=false, int n, bool rotated=false)' - adds this frame at `n' uniformly spaced points along the arclength - of the path, optionally rotated by the angle of the local tangent - to the path (if centered is true, the frames will be centered - within `n' evenly spaced arclength intervals). Alternatively, one - can use markroutine `marknodes' to request that the marks be - placed at each Bezier node of the path, or markroutine - `markuniform(pair z(real t), real a, real b, int n)' to place - marks at points `z(t)' for n evenly spaced values of `t' in - `[a,b]'. - - These markers are predefined: - marker[] Mark={ - marker(scale(circlescale)*unitcircle), - marker(polygon(3)),marker(polygon(4)), - marker(polygon(5)),marker(invert*polygon(3)), - marker(cross(4)),marker(cross(6)) - }; - - marker[] MarkFill={ - marker(scale(circlescale)*unitcircle,Fill),marker(polygon(3),Fill), - marker(polygon(4),Fill),marker(polygon(5),Fill), - marker(invert*polygon(3),Fill) - }; - - The example also illustrates the `errorbar' routines: - - - void errorbars(picture pic=currentpicture, pair[] z, pair[] dp, - pair[] dm={}, bool[] cond={}, pen p=currentpen, - real size=0); - - void errorbars(picture pic=currentpicture, real[] x, real[] y, - real[] dpx, real[] dpy, real[] dmx={}, real[] dmy={}, - bool[] cond={}, pen p=currentpen, real size=0); - - Here, the positive and negative extents of the error are given by - the absolute values of the elements of the pair array `dp' and the - optional pair array `dm'. If `dm' is not specified, the positive - and negative extents of the error are assumed to be equal. - - import graph; - - picture pic; - real xsize=200, ysize=140; - size(pic,xsize,ysize,IgnoreAspect); - - pair[] f={(5,5),(50,20),(90,90)}; - pair[] df={(0,0),(5,7),(0,5)}; - - errorbars(pic,f,df,red); - draw(pic,graph(pic,f),"legend", - marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false)); - - scale(pic,true); - - xaxis(pic,"$x$",BottomTop,LeftTicks); - yaxis(pic,"$y$",LeftRight,RightTicks); - add(pic,legend(pic),point(pic,NW),20SE,UnFill); - - picture pic2; - size(pic2,xsize,ysize,IgnoreAspect); - - frame mark; - filldraw(mark,scale(0.8mm)*polygon(6),green,green); - draw(mark,scale(0.8mm)*cross(6),blue); - - draw(pic2,graph(pic2,f),marker(mark,markuniform(5))); - - scale(pic2,true); - - xaxis(pic2,"$x$",BottomTop,LeftTicks); - yaxis(pic2,"$y$",LeftRight,RightTicks); - - yequals(pic2,55.0,red+Dotted); - xequals(pic2,70.0,red+Dotted); - - // Fit pic to W of origin: - add(pic.fit(),(0,0),W); - - // Fit pic2 to E of (5mm,0): - add(pic2.fit(),(5mm,0),E); - - - - 6. A custom mark routine can be also be specified: import graph; - - size(200,100,IgnoreAspect); - - markroutine marks() { - return new void(picture pic=currentpicture, frame f, path g) { - path p=scale(1mm)*unitcircle; - for(int i=0; i <= length(g); ++i) { - pair z=point(g,i); - frame f; - if(i % 4 == 0) { - fill(f,p); - add(pic,f,z); - } else { - if(z.y > 50) { - pic.add(new void(frame F, transform t) { - path q=shift(t*z)*p; - unfill(F,q); - draw(F,q); - }); - } else { - draw(f,p); - add(pic,f,z); - } - } - } - }; - } - - pair[] f={(5,5),(40,20),(55,51),(90,30)}; - - draw(graph(f),marker(marks())); - - scale(true); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - 7. This example shows how to label an axis with arbitrary strings. import graph; - - size(400,150,IgnoreAspect); - - real[] x=sequence(12); - real[] y=sin(2pi*x/12); - - scale(false); - - string[] month={"Jan","Feb","Mar","Apr","May","Jun", - "Jul","Aug","Sep","Oct","Nov","Dec"}; - - draw(graph(x,y),red,MarkFill[0]); - - xaxis(BottomTop,LeftTicks(new string(real x) { - return month[round(x % 12)];})); - yaxis("$y$",LeftRight,RightTicks(4)); - - - - 8. The next example draws a graph of a parametrized curve. The calls - to - xlimits(picture pic=currentpicture, real min=-infinity, - real max=infinity, bool crop=NoCrop); - and the analogous function `ylimits' can be uncommented to set - the respective axes limits for picture `pic' to the specified - `min' and `max' values. Alternatively, the function - void limits(picture pic=currentpicture, pair min, pair max, bool crop=NoCrop); - can be used to limit the axes to the box having opposite vertices - at the given pairs). Existing objects in picture `pic' will be - cropped to lie within the given limits if `crop'=`Crop'. The - function `crop(picture pic)' can be used to crop a graph to the - current graph limits. import graph; - - size(0,200); - - real x(real t) {return cos(2pi*t);} - real y(real t) {return sin(2pi*t);} - - draw(graph(x,y,0,1)); - - //xlimits(0,1,Crop); - //ylimits(-1,0,Crop); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - - - The next example illustrates how one can extract a common axis - scaling factor. import graph; - - axiscoverage=0.9; - size(200,IgnoreAspect); - - real[] x={-1e-11,1e-11}; - real[] y={0,1e6}; - - real xscale=round(log10(max(x))); - real yscale=round(log10(max(y)))-1; - - draw(graph(x*10^(-xscale),y*10^(-yscale)),red); - - xaxis("$x/10^{"+(string) xscale+"}$",BottomTop,LeftTicks); - yaxis("$y/10^{"+(string) yscale+"}$",LeftRight,RightTicks(trailingzero)); - - - - Axis scaling can be requested and/or automatic selection of the - axis limits can be inhibited with one of these `scale' routines: - void scale(picture pic=currentpicture, scaleT x, scaleT y); - - void scale(picture pic=currentpicture, bool xautoscale=true, - bool yautoscale=xautoscale, bool zautoscale=yautoscale); - - This sets the scalings for picture `pic'. The `graph' routines - accept an optional `picture' argument for determining the - appropriate scalings to use; if none is given, it uses those set - for `currentpicture'. - - Two frequently used scaling routines `Linear' and `Log' are - predefined in `graph'. - - All picture coordinates (including those in paths and those given - to the `label' and `limits' functions) are always treated as linear - (post-scaled) coordinates. Use - pair Scale(picture pic=currentpicture, pair z); - to convert a graph coordinate into a scaled picture coordinate. - - The x and y components can be individually scaled using the - analogous routines - real ScaleX(picture pic=currentpicture, real x); - real ScaleY(picture pic=currentpicture, real y); - - The predefined scaling routines can be given two optional boolean - arguments: `automin=false' and `automax=automin'. These default to - `false' but can be respectively set to `true' to enable automatic - selection of "nice" axis minimum and maximum values. The `Linear' - scaling can also take as optional final arguments a multiplicative - scaling factor and intercept (e.g. for a depth axis, `Linear(-1)' - requests axis reversal). - - For example, to draw a log/log graph of a function, use - `scale(Log,Log)': import graph; - - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - - draw(graph(f,0.1,10)); - - //xlimits(1,10,Crop); - //ylimits(0.1,1,Crop); - - dot(Label("(3,5)",align=S),Scale((3,5))); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - By extending the ticks, one can easily produce a logarithmic grid: import graph; - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - draw(graph(f,0.1,10),red); - pen thin=linewidth(0.5*linewidth()); - xaxis("$x$",BottomTop,LeftTicks(begin=false,end=false,extend=true, - ptick=thin)); - yaxis("$y$",LeftRight,RightTicks(begin=false,end=false,extend=true, - ptick=thin)); - - - - One can also specify custom tick locations and formats for - logarithmic axes: import graph; - - size(300,175,IgnoreAspect); - scale(Log,Log); - draw(graph(identity,5,20)); - xlimits(5,20); - ylimits(1,100); - xaxis("$M/M_\odot$",BottomTop,LeftTicks(DefaultFormat, - new real[] {6,10,12,14,16,18})); - yaxis("$\nu_{\rm upp}$ [Hz]",LeftRight,RightTicks(DefaultFormat)); - - - - It is easy to draw logarithmic graphs with respect to other bases: import graph; - size(200,IgnoreAspect); - - // Base-2 logarithmic scale on y-axis: - - real log2(real x) {static real log2=log(2); return log(x)/log2;} - real pow2(real x) {return 2^x;} - - scaleT yscale=scaleT(log2,pow2,logarithmic=true); - scale(Linear,yscale); - - real f(real x) {return 1+x^2;} - - draw(graph(f,-4,4)); - - yaxis("$y$",ymin=1,ymax=f(5),RightTicks(Label(Fill(white))),EndArrow); - xaxis("$x$",xmin=-5,xmax=5,LeftTicks,EndArrow); - - - - Here is an example of "broken" linear x and logarithmic y axes - that omit the segments [3,8] and [100,1000], respectively. In the - case of a logarithmic axis, the break endpoints are automatically - rounded to the nearest integral power of the base. import graph; - - size(200,150,IgnoreAspect); - - // Break the x axis at 3; restart at 8: - real a=3, b=8; - - // Break the y axis at 100; restart at 1000: - real c=100, d=1000; - - scale(Broken(a,b),BrokenLog(c,d)); - - real[] x={1,2,4,6,10}; - real[] y=x^4; - - draw(graph(x,y),red,MarkFill[0]); - - xaxis("$x$",BottomTop,LeftTicks(Break(a,b))); - yaxis("$y$",LeftRight,RightTicks(Break(c,d))); - - label(rotate(90)*Break,(a,point(S).y)); - label(rotate(90)*Break,(a,point(N).y)); - label(Break,(point(W).x,ScaleY(c))); - label(Break,(point(E).x,ScaleY(c))); - - - - 9. `Asymptote' can draw secondary axes with the routines - picture secondaryX(picture primary=currentpicture, void f(picture)); - picture secondaryY(picture primary=currentpicture, void f(picture)); - - In this example, `secondaryY' is used to draw a secondary linear y - axis against a primary logarithmic y axis: import graph; - texpreamble("\def\Arg{\mathop {\rm Arg}\nolimits}"); - - size(10cm,5cm,IgnoreAspect); - - real ampl(real x) {return 2.5/(1+x^2);} - real phas(real x) {return -atan(x)/pi;} - - scale(Log,Log); - draw(graph(ampl,0.01,10)); - ylimits(0.001,100); - - xaxis("$\omega\tau_0$",BottomTop,LeftTicks); - yaxis("$|G(\omega\tau_0)|$",Left,RightTicks); - - picture q=secondaryY(new void(picture pic) { - scale(pic,Log,Linear); - draw(pic,graph(pic,phas,0.01,10),red); - ylimits(pic,-1.0,1.5); - yaxis(pic,"$\Arg G/\pi$",Right,red, - LeftTicks("$% #.1f$", - begin=false,end=false)); - yequals(pic,1,Dotted); - }); - label(q,"(1,0)",Scale(q,(1,0)),red); - add(q); - - - - A secondary logarithmic y axis can be drawn like this: import graph; - - size(9cm,6cm,IgnoreAspect); - string data="secondaryaxis.csv"; - - file in=line(csv(input(data))); - - string[] titlelabel=in; - string[] columnlabel=in; - - real[][] a=dimension(in,0,0); - a=transpose(a); - real[] t=a[0], susceptible=a[1], infectious=a[2], dead=a[3], larvae=a[4]; - real[] susceptibleM=a[5], exposed=a[6],infectiousM=a[7]; - - scale(true); - - draw(graph(t,susceptible,t >= 10 & t <= 15)); - draw(graph(t,dead,t >= 10 & t <= 15),dashed); - - xaxis("Time ($\tau$)",BottomTop,LeftTicks); - yaxis(Left,RightTicks); - - picture secondary=secondaryY(new void(picture pic) { - scale(pic,Linear(true),Log(true)); - draw(pic,graph(pic,t,infectious,t >= 10 & t <= 15),red); - yaxis(pic,Right,red,LeftTicks(begin=false,end=false)); - }); - - add(secondary); - label(shift(5mm*N)*"Proportion of crows",point(NW),E); - - - - 10. Here is a histogram example, which uses the `stats' module. import graph; - import stats; - - size(400,200,IgnoreAspect); - - int n=10000; - real[] a=new real[n]; - for(int i=0; i < n; ++i) a[i]=Gaussrand(); - - draw(graph(Gaussian,min(a),max(a)),blue); - - // Optionally calculate "optimal" number of bins a la Shimazaki and Shinomoto. - int N=bins(a); - - histogram(a,min(a),max(a),N,normalize=true,low=0,lightred,black,bars=false); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$dP/dx$",LeftRight,RightTicks(trailingzero)); - - - - 11. Here is an example of reading column data in from a file and a - least-squares fit, using the `stats' module. size(400,200,IgnoreAspect); - - import graph; - import stats; - - file fin=line(input("leastsquares.dat")); - - real[][] a=dimension(fin,0,0); - a=transpose(a); - - real[] t=a[0], rho=a[1]; - - // Read in parameters from the keyboard: - //real first=getreal("first"); - //real step=getreal("step"); - //real last=getreal("last"); - - real first=100; - real step=50; - real last=700; - - // Remove negative or zero values of rho: - t=rho > 0 ? t : null; - rho=rho > 0 ? rho : null; - - scale(Log(true),Linear(true)); - - int n=step > 0 ? ceil((last-first)/step) : 0; - - real[] T,xi,dxi; - - for(int i=0; i <= n; ++i) { - real first=first+i*step; - real[] logrho=(t >= first & t <= last) ? log(rho) : null; - real[] logt=(t >= first & t <= last) ? -log(t) : null; - - if(logt.length < 2) break; - - // Fit to the line logt=L.m*logrho+L.b: - linefit L=leastsquares(logt,logrho); - - T.push(first); - xi.push(L.m); - dxi.push(L.dm); - } - - draw(graph(T,xi),blue); - errorbars(T,xi,dxi,red); - - crop(); - - ylimits(0); - - xaxis("$T$",BottomTop,LeftTicks); - yaxis("$\xi$",LeftRight,RightTicks); - - - - 12. Here is an example that illustrates the general `axis' routine. import graph; - size(0,100); - - path g=ellipse((0,0),1,2); - - scale(true); - - axis(Label("C",align=10W),g,LeftTicks(endlabel=false,8,end=false), - ticklocate(0,360,new real(real v) { - path h=(0,0)--max(abs(max(g)),abs(min(g)))*dir(v); - return intersect(g,h)[0];})); - - - - 13. To draw a vector field of `n' arrows evenly spaced along the - arclength of a path, use the routine - picture vectorfield(path vector(real), path g, int n, bool truesize=false, - pen p=currentpen, arrowbar arrow=Arrow); - as illustrated in this simple example of a flow field: import graph; - defaultpen(1.0); - - size(0,150,IgnoreAspect); - - real arrowsize=4mm; - real arrowlength=2arrowsize; - - typedef path vector(real); - - // Return a vector interpolated linearly between a and b. - vector vector(pair a, pair b) { - return new path(real x) { - return (0,0)--arrowlength*interp(a,b,x); - }; - } - - real f(real x) {return 1/x;} - - real epsilon=0.5; - path g=graph(f,epsilon,1/epsilon); - - int n=3; - draw(g); - xaxis("$x$"); - yaxis("$y$"); - - add(vectorfield(vector(W,W),g,n,true)); - add(vectorfield(vector(NE,NW),(0,0)--(point(E).x,0),n,true)); - add(vectorfield(vector(NE,NE),(0,0)--(0,point(N).y),n,true)); - - - - 14. To draw a vector field of `nx'\times`ny' arrows in `box(a,b)', use - the routine - picture vectorfield(path vector(pair), pair a, pair b, - int nx=nmesh, int ny=nx, bool truesize=false, - real maxlength=truesize ? 0 : maxlength(a,b,nx,ny), - bool cond(pair z)=null, pen p=currentpen, - arrowbar arrow=Arrow, margin margin=PenMargin) - as illustrated in this example: import graph; - size(100); - - pair a=(0,0); - pair b=(2pi,2pi); - - path vector(pair z) {return (0,0)--(sin(z.x),cos(z.y));} - - add(vectorfield(vector,a,b)); - - - - 15. The following scientific graphs, which illustrate many features of - `Asymptote''s graphics routines, were generated from the examples - `diatom.asy' and `westnile.asy', using the comma-separated data in - `diatom.csv' and `westnile.csv'. - - - -File: asymptote.info, Node: palette, Next: three, Prev: graph, Up: Base modules - -7.28 `palette' -============== - -`Asymptote' can also generate color density images and palettes. The -following palettes are predefined in `palette.asy': - -`pen[] Grayscale(int NColors=256)' - a grayscale palette; - -`pen[] Rainbow(int NColors=32766)' - a rainbow spectrum; - -`pen[] BWRainbow(int NColors=32761)' - a rainbow spectrum tapering off to black/white at the ends; - -`pen[] BWRainbow2(int NColors=32761)' - a double rainbow palette tapering off to black/white at the ends, - with a linearly scaled intensity. - -`pen[] Wheel(int NColors=32766)' - a full color wheel palette; - -`pen[] Gradient(int NColors=256 ... pen[] p)' - a palette varying linearly over the specified array of pens, using - NColors in each interpolation interval; - - - The function `cmyk(pen[] Palette)' may be used to convert any of -these palettes to the CMYK colorspace. - - A color density plot using palette `palette' can be generated from a -function `f'(x,y) and added to a picture `pic': - -bounds image(picture pic=currentpicture, real f(real,real), - range range=Full, pair initial, pair final, - int nx=ngraph, int ny=nx, pen[] palette, bool antialias=false) - The function `f' will be sampled at `nx' and `ny' evenly spaced points -over a rectangle defined by the points `initial' and `final', -respecting the current graphical scaling of `pic'. The color space is -scaled according to the z axis scaling (*note automatic scaling::). A -bounds structure for the function values is returned: - -struct bounds { - real min; - real max; - // Possible tick intervals: - int[] divisor; -} - This information can be used for generating an optional palette bar. -The palette color space corresponds to a range of values specified by -the argument `range', which can be `Full', `Automatic', or an explicit -range `Range(real min, real max)'. Here `Full' specifies a range -varying from the minimum to maximum values of the function over the -sampling interval, while `Automatic' selects "nice" limits. The -example `imagecontour.asy' illustrates how level sets (contour lines) -can be drawn on a color density plot (*note contour::). - - A color density plot can also be generated from an explicit real[][] -array `data': - -bounds image(picture pic=currentpicture, real[][] f, range range=Full, - pair initial, pair final, pen[] palette, - bool transpose=(initial.x < final.x && initial.y < final.y), - bool copy=true, bool antialias=false); - If the initial point is to the left and below the final point, by -default the array indices are interpreted according to the Cartesian -convention (first index: x, second index: y) rather than the usual -matrix convention (first index: -y, second index: x). - - To construct an image from an array of irregularly spaced points and -an array of values `f' at these points, use one of the routines - -bounds image(picture pic=currentpicture, pair[] z, real[] f, - range range=Full, pen[] palette) -bounds image(picture pic=currentpicture, real[] x, real[] y, real[] f, - range range=Full, pen[] palette) - - An optionally labelled palette bar may be generated with the routine - -void palette(picture pic=currentpicture, Label L="", bounds bounds, - pair initial, pair final, axis axis=Right, pen[] palette, - pen p=currentpen, paletteticks ticks=PaletteTicks, - bool copy=true, bool antialias=false); - The color space of `palette' is taken to be over bounds `bounds' with -scaling given by the z scaling of `pic'. The palette orientation is -specified by `axis', which may be one of `Right', `Left', `Top', or -`Bottom'. The bar is drawn over the rectangle from `initial' to -`final'. The argument `paletteticks' is a special tick type (*note -ticks::) that takes the following arguments: - -paletteticks PaletteTicks(Label format="", ticklabel ticklabel=null, - bool beginlabel=true, bool endlabel=true, - int N=0, int n=0, real Step=0, real step=0, - pen pTick=nullpen, pen ptick=nullpen); - - The image and palette bar can be fit to a frame and added and -optionally aligned to a picture at the desired location: - -size(12cm,12cm); - -import graph; -import palette; - -int n=256; -real ninv=2pi/n; -real[][] v=new real[n][n]; - -for(int i=0; i < n; ++i) - for(int j=0; j < n; ++j) - v[i][j]=sin(i*ninv)*cos(j*ninv); - -pen[] Palette=BWRainbow(); - -picture bar; - -bounds range=image(v,(0,0),(1,1),Palette); -palette(bar,"$A$",range,(0,0),(0.5cm,8cm),Right,Palette, - PaletteTicks("$%+#.1f$")); -add(bar.fit(),point(E),30E); - - - -Here is an example that uses logarithmic scaling of the function values: - -import graph; -import palette; - -size(10cm,10cm,IgnoreAspect); - -real f(real x, real y) { - return 0.9*pow10(2*sin(x/5+2*y^0.25)) + 0.1*(1+cos(10*log(y))); -} - -scale(Linear,Log,Log); - -pen[] Palette=BWRainbow(); - -bounds range=image(f,Automatic,(0,1),(100,100),nx=200,Palette); - -xaxis("$x$",BottomTop,LeftTicks,above=true); -yaxis("$y$",LeftRight,RightTicks,above=true); - -palette("$f(x,y)$",range,(0,200),(100,250),Top,Palette, - PaletteTicks(ptick=linewidth(0.5*linewidth()))); - - - -One can also draw an image directly from a two-dimensional pen array: - -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); - as illustrated in the following example: - -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)); - - - -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 - -7.29 `three' -============ - -This module fully extends the notion of guides and paths in `Asymptote' -to three dimensions. It introduces the new types guide3, path3, and -surface. Guides in three dimensions are specified with the same syntax -as in two dimensions except that triples `(x,y,z)' are used in place of -pairs `(x,y)' for the nodes and direction specifiers. This -generalization of John Hobby's spline algorithm is shape-invariant under -three-dimensional rotation, scaling, and shifting, and reduces in the -planar case to the two-dimensional algorithm used in `Asymptote', -`MetaPost', and `MetaFont' [cf. J. C. Bowman, Proceedings in Applied -Mathematics and Mechanics, 7:1, 2010021-2010022 (2007)]. - - For example, a unit circle in the XY plane may be filled and drawn -like this: - -import three; - -size(100); - -path3 g=(1,0,0)..(0,1,0)..(-1,0,0)..(0,-1,0)..cycle; -draw(g); -draw(O--Z,red+dashed,Arrow3); -draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle)); -dot(g,red); - - -and then distorted into a saddle: - -import three; - -size(100,0); -path3 g=(1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle; -draw(g); -draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle)); -dot(g,red); - - -Module `three' provides constructors for converting two-dimensional -paths to three-dimensional ones, and vice-versa: - -path3 path3(path p, triple plane(pair)=XYplane); -path path(path3 p, pair P(triple)=xypart); - - A Bezier surface, the natural two-dimensional generalization of -Bezier curves, is defined in `three_surface.asy' as a structure -containing an array of Bezier patches. Surfaces may drawn with one of -the routines - -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material surfacepen=currentpen, pen meshpen=nullpen, - light light=currentlight, light meshlight=light); -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material[] surfacepen, pen meshpen, - light light=currentlight, light meshlight=light); -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material[] surfacepen, pen[] meshpen=nullpens, - light light=currentlight, light meshlight=light); - The parameters `nu' and `nv' specify the number of subdivisions for -drawing optional mesh lines for each Bezier patch. Here material is a -structure defined in `three_light.asy': - -struct material { - pen[] p; // diffusepen,ambientpen,emissivepen,specularpen - real opacity; - real shininess; - real granularity; -... -} - 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 examples `elevation.asy' and `sphericalharmonic.asy' illustrate -how to draw a surface with patch-dependent colors. The examples -`vertexshading' and `smoothelevation' illustrate vertex-dependent -colors, which is supported for both `Asymptote''s native `OpenGL' -renderer and two-dimensional projections. Since the PRC output format -does not currently support vertex shading of Bezier surfaces, PRC -patches are shaded with the mean of the four vertex colors. - - A surface can be constructed from a cyclic `path3' with the -constructor - -surface surface(path3 external, triple[] internal=new triple[], - triple[] normals=new triple[], pen[] colors=new pen[], - bool3 planar=default); - and then filled: - -draw(surface(path3(polygon(5))),red,nolight); -draw(surface(unitcircle3),red,nolight); -draw(surface(unitcircle3,new pen[] {red,green,blue,black}),nolight); - The last example constructs a patch with vertex-specific colors. A -three-dimensional planar surface in the plane `plane' can be -constructed from a two-dimensional cyclic path `g' with the constructor - -surface surface(path p, triple plane(pair)=XYplane); - and then filled: - -draw(surface((0,0)--E+2N--2E--E+N..0.2E..cycle),red); - Planar Bezier surfaces patches are constructed using Orest Shardt's -`bezulate' routine, which decomposes (possibly nonsimply connected) -regions bounded by nonselfintersecting cyclic paths (according to the -`zerowinding' fill rule) into subregions bounded by cyclic paths of -length `4' or less. - - Arbitrary thick three-dimensional curves and line caps (which the -`OpenGL' standard does not require implementations to provide) are -constructed with the routine - -surface tube(path3 g, real width); - which returns a tube of diameter `width' centered on `g'. This can -make files 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, we recommend installing the latest SVN (antialiased) - version of the `freeglut' library (*note 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",""}; - 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 - - * Middle: menu - - * Wheel Up: zoom in - - * Wheel Down: zoom out - - * Right: zoom - - * 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 - - * +: expand - - * =: expand - - * -: 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' - beyond the screen dimensions (indicated by `maxtile=(0,0)'. 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'. Other `UNIX' graphics drivers may require - the command line setting `-glOptions=-indirect'. - - 3. Embed the 3D PRC format in a PDF file and view the resulting PDF - file with version `8.0' 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. Version 2008/10/08 or - later of the `movie15' 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'. 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. - - 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, - 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, - bool showtarget=true, bool center=false)' - This is equivalent to - `orthographic((x,y,z),up,target,showtarget,center)'. - -`perspective(triple camera, triple up=Z, triple target=O, - 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, - bool showtarget=true, bool autoadjust=true, - bool center=autoadjust)' - This is equivalent to `perspective((x,y,z),up,target,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, bool group=true, - filltype filltype=NoFill); - adds picture `pic' as seen with `FrontView' aligned above the -projection `TopView' and to the right of the projection `RightView'. -Alternatively, the function - -void addAllViews(picture dest=currentpicture, picture src, - real xmargin=0, real ymargin=xmargin, - bool group=true, filltype filltype=NoFill); - may be used to exhibit all six standard views, with FrontView, -TopView, RightView in the upper row and BackView, BottomView, LeftView -in the lower row. - - 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: - -`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'. - - Three-dimensional TeX Labels, which are by default drawn as Bezier -surfaces directly on the projection plane, can be transformed from the -`XY' plane by any of the above transforms or mapped to a specified -two-dimensional plane with the transform3 types `XY', `YZ', `ZX', `YX', -`ZY', `ZX'. There are also modified versions of these transforms that -take an optional argument `projection P=currentprojection' that rotate -and/or flip the label so that it is more readable from the initial -viewpoint. - - A transform3 that projects in the direction `dir' onto the plane -with normal `n' through point `O' is returned by - -transform3 planeproject(triple n, triple O=O, triple dir=n); - One can use - -triple normal(path3 p); - to find the unit normal vector to a planar three-dimensional path `p'. -As illustrated in the example `planeproject.asy', a transform3 that -projects in the direction `dir' onto the plane defined by a planar path -`p' is returned by - -transform3 planeproject(path3 p, triple dir=normal(p)); - - The functions - -surface extrude(path p, triple axis=Z); -surface extrude(Label L, triple axis=Z); - return the surface obtained by extruding path `p' or Label `L' along -`axis'. - - Three-dimensional versions of the path functions `length', `size', -`point', `dir', `accel', `radius', `precontrol', `postcontrol', -`arclength', `arctime', `reverse', `subpath', `intersect', -`intersections', `intersectionpoint', `intersectionpoints', `min', -`max', `cyclic', and `straight' are also defined. - - The routine - -real[][] intersections(path3 p, surface s, real fuzz=-1); - returns the intersection times of a path `p' with a surface `s' as a -sorted array of real arrays of length 2, and - -triple[] intersectionpoints(path3 p, surface s, real fuzz=-1); - returns the corresponding intersection points. Here, the computations -are performed to the absolute error specified by `fuzz', or if `fuzz < -0', to machine precision. - - Here is an example showing all five guide3 connectors: - -import graph3; - -size(200); - -currentprojection=orthographic(500,-500,500); - -triple[] z=new triple[10]; - -z[0]=(0,100,0); z[1]=(50,0,0); z[2]=(180,0,0); - -for(int n=3; n <= 9; ++n) - z[n]=z[n-3]+(200,0,0); - -path3 p=z[0]..z[1]---z[2]::{Y}z[3] -&z[3]..z[4]--z[5]::{Y}z[6] -&z[6]::z[7]---z[8]..{Y}z[9]; - -draw(p,grey+linewidth(4mm)+opacity(0.5)); - -xaxis3(Label(XY()*"$x$",align=-3Y),red,above=true); -yaxis3(Label(XY()*"$y$",align=-3X),red,above=true); - -dot(z); - - - -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'. - - Further three-dimensional examples are provided in the files -`near_earth.asy', `conicurv.asy', and (in the `animations' -subdirectory) `cube.asy'. - - Limited support for projected vector graphics (effectively -three-dimensional nonrendered `PostScript') is available with the -setting `render=0'. This currently only works for piecewise planar -surfaces, such as those produced by the parametric `surface' routines -in the `graph3' module. Surfaces produced by the `solids' package will -also be properly rendered if the parameter `nslices' is sufficiently -large. - - In the module `bsp', hidden surface removal of planar pictures is -implemented using a binary space partition and picture clipping. A -planar path is first converted to a structure `face' derived from -`picture'. A `face' may be given to a two-dimensional drawing routine -in place of any `picture' argument. An array of such faces may then be -drawn, removing hidden surfaces: - -void add(picture pic=currentpicture, face[] faces, - projection P=currentprojection); - Labels may be projected to two dimensions, using projection `P', onto -the plane passing through point `O' with normal `cross(u,v)' by -multiplying it on the left by the transform - -transform transform(triple u, triple v, triple O=O, - projection P=currentprojection); - - Here is an example that shows how a binary space partition may be -used to draw a two-dimensional vector graphics projection of three -orthogonal intersecting planes: - -size(6cm,0); -import bsp; - -real u=2.5; -real v=1; - -currentprojection=oblique; - -path3 y=plane((2u,0,0),(0,2v,0),(-u,-v,0)); -path3 l=rotate(90,Z)*rotate(90,Y)*y; -path3 g=rotate(90,X)*rotate(90,Y)*y; - -face[] faces; -filldraw(faces.push(y),project(y),yellow); -filldraw(faces.push(l),project(l),lightgrey); -filldraw(faces.push(g),project(g),green); - -add(faces); - - - - -File: asymptote.info, Node: obj, Next: graph3, Prev: three, Up: Base modules - -7.30 `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 - -7.31 `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="", - triple min=(-infinity,-infinity,-infinity), - triple max=(infinity,infinity,infinity), - pen p=currentpen, arrowbar3 arrow=None); - -The predefined three-dimensional axis types are - -axis YZEquals(real y, real z, triple align=O, bool extend=false); -axis XZEquals(real x, real z, triple align=O, bool extend=false); -axis XYEquals(real x, real y, triple align=O, bool extend=false); -axis YZZero(triple align=O, bool extend=false); -axis XZZero(triple align=O, bool extend=false); -axis XYZero(triple align=O, bool extend=false); -axis Bounds(int type=Both, int type2=Both, triple align=O, bool extend=false); - The optional `align' parameter to these routines can be used to -specify the default axis and tick label alignments. The `Bounds' axis -accepts two type parameters, each of which must be one of `Min', `Max', -or `Both'. These parameters specify which of the four possible -three-dimensional bounding box edges should be drawn. - - The three-dimensional tick options are `NoTicks3', `InTicks', -`OutTicks', and `InOutTicks'. These specify the tick directions for the -`Bounds' axis type; other axis types inherit the direction that would -be used for the `Bounds(Min,Min)' axis. - - Here is an example of a helix and bounding box axes with ticks and -axis labels, using orthographic projection: - -import graph3; - -size(0,200); -size3(200,IgnoreAspect); - -currentprojection=orthographic(4,6,3); - -real x(real t) {return cos(2pi*t);} -real y(real t) {return sin(2pi*t);} -real z(real t) {return t;} - -path3 p=graph(x,y,z,0,2.7,operator ..); - -draw(p,Arrow3); - -scale(true); - -xaxis3(XZ()*"$x$",Bounds(),red,InTicks(Label,2,2)); -yaxis3(YZ()*"$y$",Bounds(),red,InTicks(beginlabel=false,Label,2,2)); -zaxis3(XZ()*"$z$",Bounds(),red,InTicks); - - - -The next example illustrates three-dimensional x, y, and z axes, -without autoscaling of the axis limits: - -import graph3; - -size(0,200); -size3(200,IgnoreAspect); - -currentprojection=perspective(5,2,2); - -scale(Linear,Linear,Log); - -xaxis3("$x$",0,1,red,OutTicks(2,2)); -yaxis3("$y$",0,1,red,OutTicks(2,2)); -zaxis3("$z$",1,30,red,OutTicks(beginlabel=false)); - - - -One can also place ticks along a general three-dimensional axis: - -import graph3; - -size(0,100); - -path3 g=yscale3(2)*unitcircle3; -currentprojection=perspective(10,10,10); - -axis(Label("C",position=0,align=15X),g,InTicks(endlabel=false,8,end=false), - ticklocate(0,360,new real(real v) { - path3 h=O--max(abs(max(g)),abs(min(g)))*dir(90,v); - return intersect(g,h)[0];}, - new triple(real t) {return cross(dir(g,t),Z);})); - - - -Surface plots of matrices and functions over the region `box(a,b)' in -the XY plane are also implemented: - -surface surface(real[][] f, pair a, pair b, bool[][] cond={}); -surface surface(real[][] f, pair a, pair b, splinetype xsplinetype, - splinetype ysplinetype=xsplinetype, bool[][] cond={}); -surface surface(real[][] f, real[] x, real[] y, - splinetype xsplinetype=null, splinetype ysplinetype=xsplinetype, - bool[][] cond={}) -surface surface(triple[][] f, bool[][] cond={}); -surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx, - bool cond(pair z)=null); -surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx, - splinetype xsplinetype, splinetype ysplinetype=xsplinetype, - bool cond(pair z)=null); -surface surface(triple f(pair z), 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); - -label("$O$",O,-Z+Y,red); - - -A mesh can be drawn without surface filling by specifying `nullpen' for -the surfacepen. - - A vector field of `nu'\times`nv' arrows on a parametric surface `f' -over `box(a,b)' can be drawn with the routine - -picture vectorfield(path3 vector(pair v), triple f(pair z), pair a, pair b, - int nu=nmesh, int nv=nu, bool truesize=false, - real maxlength=truesize ? 0 : maxlength(f,a,b,nu,nv), - bool cond(pair z)=null, pen p=currentpen, - arrowbar3 arrow=Arrow3, margin3 margin=PenMargin3) - as illustrated in the examples `vectorfield3.asy' and -`vectorfieldsphere.asy'. - - -File: asymptote.info, Node: grid3, Next: solids, Prev: graph3, Up: Base modules - -7.32 `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://piprim.tuxfamily.org/asymptote/grid3/'): - -import grid3; - -size(8cm,0,IgnoreAspect); -currentprojection=orthographic(0.5,1,0.5); - -scale(Linear, Linear, Log); - -limits((-2,-2,1),(0,2,100)); - -grid3(XYZgrid); - -xaxis3(Label("$x$",position=EndPoint,align=S),Bounds(Min,Min), - OutTicks()); -yaxis3(Label("$y$",position=EndPoint,align=S),Bounds(Min,Min),OutTicks()); -zaxis3(Label("$z$",position=EndPoint,align=(-1,0.5)),Bounds(Min,Min), - OutTicks(beginlabel=false)); - - - - -File: asymptote.info, Node: solids, Next: tube, Prev: grid3, Up: Base modules - -7.33 `solids' -============= - -This solid geometry package defines a structure `revolution' that can -be used to fill and draw surfaces of revolution. The following example -uses it to display the outline of a circular cylinder of radius 1 with -axis `O--1.5unit(Y+Z)' with perspective projection: - -import solids; - -size(0,100); - -revolution r=cylinder(O,1,1.5,Y+Z); -draw(r,heavygreen); - - - -Further illustrations are provided in the example files `cylinder.asy', -`cones.asy', `hyperboloid.asy', and `torus.asy'. - - The structure `skeleton' contains the three-dimensional wireframe -used to visualize a volume of revolution: - -struct skeleton { - struct curve { - path3[] front; - path3[] back; - } - // transverse skeleton (perpendicular to axis of revolution) - curve transverse; - // longitudinal skeleton (parallel to axis of revolution) - curve longitudinal; -} - - -File: asymptote.info, Node: tube, Next: flowchart, Prev: solids, Up: Base modules - -7.34 `tube' -=========== - -This package extends the routine `tube' defined 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://piprim.tuxfamily.org/asymptote/tube/'. - - -File: asymptote.info, Node: flowchart, Next: contour, Prev: tube, Up: Base modules - -7.35 `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); - -"diamond-shaped flowchart 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 flowchart block:" - - block circle(object body, pair center=(0,0), pen fillpen=invisible, - pen drawpen=currentpen, real dr=3, - real mindiameter=mincirclediameter); - -"rectangular flowchart 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 flowchart 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: - -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) { - draw(pic,path(new pair[]{block1.right(t),block2.top(t)},Horizontal), - Arrow,PenMargin); - draw(pic,Label("Yes",0.5,NW),path(new pair[]{block2.left(t),block3.top(t)}, - Horizontal),Arrow,PenMargin); - draw(pic,Label("No",0.5,NE),path(new pair[]{block2.right(t),block4.top(t)}, - Horizontal),Arrow,PenMargin); - draw(pic,path(new pair[]{block3.bottom(t),block5.left(t)},Vertical), - Arrow,PenMargin); - draw(pic,path(new pair[]{block4.bottom(t),block5.right(t)},Vertical), - Arrow,PenMargin); - }); - - - - -File: asymptote.info, Node: contour, Next: contour3, Prev: flowchart, Up: Base modules - -7.36 `contour' -============== - -This package draws contour lines. To construct contours corresponding -to the values in an array `c' for a function `f' on `box(a,b)', use - -guide[][] contour(real f(real, real), pair a, pair b, - real[] c, int nx=ngraph, int ny=nx, - interpolate join=operator --); - 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. - - To construct contours for an array of data values on a uniform -two-dimensional lattice on `box(a,b)', use - -guide[][] contour(real[][] f, real[][] midpoint=new real[][], - pair a, pair b, real[] c, - interpolate join=operator --); - - To construct contours for an array of data values on a nonoverlapping -regular mesh specified by the two-dimensional array `z', optionally -specifying the values of `f' at the mesh midpoints, use - -guide[][] contour(pair[][] z, real[][] f, - real[][] midpoint=new real[][], real[] c, - interpolate join=operator --); - - To construct contours for an array of values `f' specified at -irregularly positioned points `z', use the routine - -guide[][] contour(pair[] z, real[] f, real[] c, - interpolate join=operator --); - The contours themselves can be drawn with one of the routines - -void draw(picture pic=currentpicture, Label[] L=new Label[], - guide[][] g, pen p=currentpen) - -void draw(picture pic=currentpicture, Label[] L=new Label[], - guide[][] g, pen[] p) - - The following simple example draws the contour at value `1' for the -function z=x^2+y^2, which is a unit circle: - -import contour; -size(75); - -real f(real a, real b) {return a^2+b^2;} -draw(contour(f,(-1,-1),(1,1),new real[] {1})); - - - -The next example draws and labels multiple contours for the function -z=x^2-y^2 with the resolution `100 x 100', using a dashed pen for -negative contours and a solid pen for positive (and zero) contours: - -import contour; - -size(200); - -real f(real x, real y) {return x^2-y^2;} -int n=10; -real[] c=new real[n]; -for(int i=0; i < n; ++i) c[i]=(i-n/2)/n; - -pen[] p=sequence(new pen(int i) { - return (c[i] >= 0 ? solid : dashed)+fontsize(6); - },c.length); - -Label[] Labels=sequence(new Label(int i) { - return Label(c[i] != 0 ? (string) c[i] : "",Relative(unitrand()),(0,0), - UnFill(1bp)); - },c.length); - -draw(Labels,contour(f,(-1,-1),(1,1),c),p); - - - -The next example illustrates how contour lines can be drawn on color -density images: - -import graph; -import palette; -import contour; - -size(10cm,10cm,IgnoreAspect); - -pair a=(0,0); -pair b=(2pi,2pi); - -real f(real x, real y) {return cos(x)*sin(y);} - -int N=200; -int Divs=10; -int divs=2; - -defaultpen(1bp); -pen Tickpen=black; -pen tickpen=gray+0.5*linewidth(currentpen); -pen[] Palette=BWRainbow(); - -scale(false); - -bounds range=image(f,Automatic,a,b,N,Palette); - -// Major contours - -real[] Cvals=uniform(range.min,range.max,Divs); -draw(contour(f,a,b,Cvals,N,operator --),Tickpen); - -// Minor contours -real[] cvals; -for(int i=0; i < Cvals.length-1; ++i) - cvals.append(uniform(Cvals[i],Cvals[i+1],divs)[1:divs]); -draw(contour(f,a,b,cvals,N,operator --),tickpen); - -xaxis("$x$",BottomTop,LeftTicks,above=true); -yaxis("$y$",LeftRight,RightTicks,above=true); - -palette("$f(x,y)$",range,point(NW)+(0,0.5),point(NE)+(0,1),Top,Palette, - PaletteTicks(N=Divs,n=divs,Tickpen,tickpen)); - - - -Finally, here is an example that illustrates the construction of -contours from irregularly spaced data: - -import contour; - -size(200); - -int n=100; - -pair[] points=new pair[n]; -real[] values=new real[n]; - -real f(real a, real b) {return a^2+b^2;} - -real r() {return 1.1*(rand()/randMax*2-1);} - -for(int i=0; i < n; ++i) { - points[i]=(r(),r()); - values[i]=f(points[i].x,points[i].y); -} - -draw(contour(points,values,new real[]{0.25,0.5,1},operator ..),blue); - - - -In the above example, the contours of irregularly spaced data are -constructed by first creating a triangular mesh from an array `z' of -pairs: - - -int[][] triangulate(pair[] z); - -size(200); -int np=100; -pair[] points; - -real r() {return 1.2*(rand()/randMax*2-1);} - -for(int i=0; i < np; ++i) - points.push((r(),r())); - -int[][] trn=triangulate(points); - -for(int i=0; i < trn.length; ++i) { - draw(points[trn[i][0]]--points[trn[i][1]]); - draw(points[trn[i][1]]--points[trn[i][2]]); - draw(points[trn[i][2]]--points[trn[i][0]]); -} - -for(int i=0; i < np; ++i) - dot(points[i],red); - - - -The example `Gouraudcontour' illustrates how to produce color density -images over such irregular triangular meshes. `Asymptote' uses a -robust version of Paul Bourke's Delaunay triangulation algorithm based -on the public-domain exact arithmetic predicates written by Jonathan -Shewchuk. - - -File: asymptote.info, Node: contour3, Next: slopefield, Prev: contour, Up: Base modules - -7.37 `contour3' -=============== - -This package draws surfaces described as the null space of real-valued -functions of (x,y,z) or real[][][] matrices. Its usage is illustrated -in the example file `magnetic.asy'. - - -File: asymptote.info, Node: slopefield, Next: ode, Prev: contour3, Up: Base modules - -7.38 `slopefield' -================= - -To draw a slope field for the differential equation dy/dx=f(x,y) (or -dy/dx=f(x)), use: - -picture slopefield(real f(real,real), pair a, pair b, - int nx=nmesh, int ny=nx, - real tickfactor=0.5, pen p=currentpen, - arrowbar arrow=None); - Here, the points `a' and `b' are the lower left and upper right -corners of the rectangle in which the slope field is to be drawn, `nx' -and `ny' are the respective number of ticks in the x and y directions, -`tickfactor' is the fraction of the minimum cell dimension to use for -drawing ticks, and `p' is the pen to use for drawing the slope fields. -The return value is a picture that can be added to `currentpicture' via -the `add(picture)' command. - - The function - -path curve(pair c, real f(real,real), pair a, pair b); - takes a point (`c') and a slope field-defining function `f' and -returns, as a path, the curve passing through that point. The points -`a' and `b' represent the rectangular boundaries over which the curve -is interpolated. - - Both `slopefield' and `curve' alternatively accept a function `real -f(real)' that depends on x only, as seen in this example: - -import slopefield; - -size(200); - -real func(real x) {return 2x;} -add(slopefield(func,(-3,-3),(3,3),20,Arrow)); -draw(curve((0,0),func,(-3,-3),(3,3)),red); - - - - -File: asymptote.info, Node: ode, Prev: slopefield, Up: Base modules - -7.39 `ode' -========== - -The `ode' module, illustrated in the example `odetest.asy', implements -a number of explicit numerical integration schemes for ordinary -differential equations. - - -File: asymptote.info, Node: Options, Next: Interactive mode, Prev: Base modules, Up: Top - -8 Options -********* - -Type `asy -h' to see the full list of command-line options supported by -`Asymptote': - -Usage: ../asy [options] [file ...] - -Options (negate by replacing - with -no): - --V,-View View output; command-line only --a,-align C|B|T|Z Center, Bottom, Top, or Zero page alignment [C] --antialias n Antialiasing width for rasterized output [2] --auto3D Automatically activate 3D scene [true] --autoimport string Module to automatically import --autoplain Enable automatic importing of plain [true] --autorotate Enable automatic PDF page rotation [false] --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] --embed Embed rendered preview image [true] --exitonEOF Exit interactive mode on EOF [true] --fitscreen Fit rendered image to screen [true] --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] --m,-mask Mask fpu exceptions; command-line only --maxtile pair Maximum rendering tile size [(0,0)] --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] --O,-offset pair PostScript offset [(0,0)] --f,-outformat format Convert each output file to specified format --o,-outname name Alternative output directory/filename --p,-parseonly Parse file [false] --pdfreload Automatically reload document in pdfviewer [false] --pdfreloaddelay usec Delay before attempting initial pdf reload [750000] --position pair Initial 3D rendering screen position [(0,0)] --prc Embed 3D PRC graphics in PDF output [true] --prompt string Prompt [> ] --prompt2 string Continuation prompt for multiline input [..] --q,-quiet Suppress welcome message [false] --render n Render 3D graphics using n pixels per bp (-1=auto) [-1] --rgb Convert cmyk colors to rgb [false] --safe Disable system call [true] --scroll n Scroll standard output n lines at a time [0] --tabcompletion Interactive prompt auto-completion [true] --tex engine latex|pdflatex|xelatex|tex|pdftex|context|none [latex] --thick Render thick 3D lines [true] --thin Render thin 3D lines [true] --threads Use POSIX threads for 3D rendering [true] --toolbar Show 3D toolbar in PDF output [true] --s,-translate Show translated virtual machine code [false] --twice Run LaTeX twice (to resolve references) [false] --twosided Use two-sided 3D lighting model for rendering [true] --u,-user string General purpose user string --v,-verbose Increase verbosity level (can specify multiple times) [0] --version Show version; command-line only --wait Wait for child processes to finish before exiting [false] --where Show where listed variables are declared [false] --xformat format GUI deconstruction format [png] - - 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. -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', `convertOptions', `gsOptions', -`psviewerOptions', `pdfviewerOptions', and `glOptions' allow -specialized options to be passed as a string to the respective -applications or libraries. - - If you insert - -import plain; -settings.autoplain=true; - at the beginning of the configuration file, it can contain arbitrary -`Asymptote' code. - - The default output format is EPS for the (default) `latex' and `tex' -tex engine and PDF for the `pdflatex', `xelatex', and `context' tex -engines. Alternative output formats may be produced using the `-f' -option (or `outformat' setting). 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. `Asymptote' can 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'). To give specific 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)' call, allowing one to execute -arbitrary shell commands. The default mode, `-safe', disables this call. - - A `PostScript' offset may be specified as a pair (in `bp' units) -with the `-O' option: - -asy -O 0,0 file - The default offset is zero. The default value of the page alignment -setting `align' is `Center'. - - The `-c' (`command') option may be used to execute arbitrary -`Asymptote' code on the command line as a string. It is not necessary -to terminate the string with a semicolon. Multiple `-c' options are -executed in the order they are given. For example - -asy -c 2+2 -c "sin(1)" -c "size(100); draw(unitsquare)" - produces the output - -4 -0.841470984807897 - and draws a unitsquare of size `100'. - - The `-u' (`user') option may be used to specify arbitrary -`Asymptote' settings on the command line as a string. It is not -necessary to terminate the string with a semicolon. Multiple `-u' -options are executed in the order they are given. Command-line code like -`-u x=sqrt(2)' can be executed within a module like this: - -real x; -usersetting(); -write(x); - - When the `-l' (`listvariables') option is used with file arguments, -only global functions and variables defined in the specified file(s) -are listed. - - Additional debugging output is produced with each additional `-v' -option: -`-v' - Display top-level module and final output file names. - -`-vv' - Also display imported and included module names and final `LaTeX' - and `dvips' processing information. - -`-vvv' - Also output `LaTeX' bidirectional pipe diagnostics. - -`-vvvv' - Also output knot guide solver diagnostics. - -`-vvvvv' - Also output `Asymptote' traceback diagnostics. - - -File: asymptote.info, Node: Interactive mode, Next: GUI, Prev: Options, Up: Top - -9 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'. - - The following special commands are supported only in interactive mode -and must be entered immediately after the prompt: - -`help' - view the manual; - -`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 - -10 Graphical User Interface -*************************** - -In the event that adjustments to the final figure are required, the -preliminary Graphical User Interface (GUI) `xasy' included with -`Asymptote' allows you to move graphical objects and draw new ones. -The modified figure can then be saved as a normal `Asymptote' file. - -* Menu: - -* GUI Installation:: Installing `xasy' -* GUI Usage:: - - -File: asymptote.info, Node: GUI Installation, Next: GUI Usage, Up: GUI - -10.1 GUI Installation -===================== - -As `xasy' is written in the interactive scripting language `Python/TK', -it requires `Python' (`http://www.python.org'), the `Python Imaging -Library' (`http://www.pythonware.com/products/pil/'), and the `tkinter' -package (included with `Python' under `Microsoft Windows') be -installed. `Fedora Linux' users can either install `tkinter' with the -commands - -yum install tkinter -yum install tk-devel - or manually install the `tkinter', `tix', `tk', and `tk-devel' -packages. - - Pictures are deconstructed into the PNG image format, which supports -full alpha channel transparency. Under `Microsoft Windows', this -requires `Python 2.6.2' and the `Python Imaging Library': - - `http://www.python.org/ftp/python/2.6.2/python-2.6.2.msi' - - `http://effbot.org/downloads/PIL-1.1.7b1.win32-py2.6.exe'. - On `UNIX' systems, place -`http://effbot.org/downloads/Imaging-1.1.7b1.tar.gz' in the `Asymptote' -source directory, and type (as the root user): - -tar -zxf Imaging-1.1.7b1.tar.gz -cd Imaging-1.1.7b1 -python setup.py install - - Alternatively, `xasy' can deconstruct pictures into the GIF image -format (not recommended as this is very slow), using white as the -transparent color. This requires the lines - -import settings; -xformat="gif"; - in the `Asymptote' configuration file (*note configuration file::), -along with the `ImageMagick' (*note convert::) program. - - -File: asymptote.info, Node: GUI Usage, Prev: GUI Installation, Up: GUI - -10.2 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 - -11 `PostScript' to `Asymptote' -****************************** - -The excellent `PostScript' editor `pstoedit' (version 3.45 or later; -available from `http://pstoedit.net') 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. - - For full functionality, the patch `pstoedit-3.45asy.patch' in the -`patches' directory should be applied. On `UNIX' systems, as the root -user, place - - `http://prdownloads.sourceforge.net/pstoedit/pstoedit-3.45.tar.gz' - in the `Asymptote' source directory, and type: - - -tar -zxf pstoedit-3.45.tar.gz -cd pstoedit-3.45 -patch -p1 < ../patches/pstoedit-3.45asy.patch -autoconf -./configure --prefix=/usr -make install - -Then try: - -`asy -V /tmp/ainst/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 - -12 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/forum/forum.php?forum_id=409349' - Including an example that illustrates what you are trying to do will -help you get useful feedback. `LaTeX' problems can often be diagnosed -with the `-vv' or `-vvv' command-line options. Contributions in the -form of patches or `Asymptote' modules can be posted here: - - `http://sourceforge.net/tracker/?atid=685685&group_id=120000' - To receive announcements of upcoming releases, please subscribe to -`Asymptote' at - - `http://freshmeat.net/projects/asy' - If you find a bug in `Asymptote', please check (if possible) whether -the bug is still present in the latest `Subversion' developmental code -(*note Subversion::) before submitting a bug report. New bugs can be -submitted using the Bug Tracking System at - - `http://sourceforge.net/projects/asymptote' - To see if the bug has already been fixed, check bugs with Status -`Closed' and recent lines in - - `http://asymptote.sourceforge.net/ChangeLog' - `Asymptote' can be configured with the optional GNU library -`libsigsegv', available from `http://libsigsegv.sourceforge.net', which -allows one to distinguish user-generated `Asymptote' stack overflows -(*note stack overflow::) from true segmentation faults (due to internal -C++ programming errors; please submit the `Asymptote' code that -generates such segmentation faults along with your bug report). - - -File: asymptote.info, Node: Debugger, Next: Credits, Prev: Help, Up: Top - -13 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 - -14 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 Radoslav Marinov, Orest Shardt, Chris Savage, -Philippe Ivaldi, Olivier Guibe', Jacques Pienaar, Mark Henning, Steve -Melenchuk, Martin Wiebusch, and Stefan Knorr. - - -File: asymptote.info, Node: Index, Prev: Credits, Up: Top - -Index -***** - - -* Menu: - -* !: Arithmetic & logical. - (line 68) -* != <1>: Arithmetic & logical. - (line 38) -* !=: Structures. (line 56) -* %: Arithmetic & logical. - (line 23) -* %=: Self & prefix operators. - (line 6) -* & <1>: Arithmetic & logical. - (line 56) -* &: Tutorial. (line 203) -* &&: Arithmetic & logical. - (line 53) -* * <1>: Arithmetic & logical. - (line 17) -* *: Pens. (line 15) -* **: Arithmetic & logical. - (line 31) -* *=: Self & prefix operators. - (line 6) -* + <1>: Arithmetic & logical. - (line 13) -* +: Pens. (line 15) -* ++: Self & prefix operators. - (line 6) -* +=: Self & prefix operators. - (line 6) -* -: Arithmetic & logical. - (line 14) -* -- <1>: Self & prefix operators. - (line 6) -* --: Tutorial. (line 114) -* ---: Tutorial. (line 203) -* -=: Self & prefix operators. - (line 6) -* -c: Options. (line 158) -* -l: Options. (line 180) -* -u: Options. (line 170) -* -V <1>: Tutorial. (line 43) -* -V: Configuring. (line 6) -* ..: Tutorial. (line 114) -* .asy: Search paths. (line 13) -* /: Arithmetic & logical. - (line 20) -* /=: Self & prefix operators. - (line 6) -* 2D graphs: graph. (line 6) -* 3D graphs: graph3. (line 6) -* 3D grids: grid3. (line 6) -* 3D rendering: Compiling from UNIX source. - (line 17) -* :: Arithmetic & logical. - (line 73) -* ::: Tutorial. (line 187) -* <: Arithmetic & logical. - (line 41) -* <=: Arithmetic & logical. - (line 44) -* == <1>: Arithmetic & logical. - (line 37) -* ==: Structures. (line 56) -* >: Arithmetic & logical. - (line 50) -* >=: Arithmetic & logical. - (line 47) -* ?: Arithmetic & logical. - (line 73) -* ^: Arithmetic & logical. - (line 28) -* ^=: Self & prefix operators. - (line 6) -* ^^: Tutorial. (line 208) -* a4: Configuring. (line 64) -* abort: Data types. (line 326) -* abs <1>: Mathematical functions. - (line 35) -* abs: Data types. (line 62) -* accel <1>: three. (line 469) -* accel: Paths and guides. (line 117) -* access: Import. (line 6) -* acknowledgments: Credits. (line 6) -* aCos: Mathematical functions. - (line 20) -* acos: Mathematical functions. - (line 6) -* acosh: Mathematical functions. - (line 6) -* add: Frames and pictures. (line 215) -* Ai: Mathematical functions. - (line 48) -* Ai_deriv: Mathematical functions. - (line 48) -* Airy: Mathematical functions. - (line 48) -* alias <1>: Arrays. (line 192) -* alias: Structures. (line 56) -* align: Options. (line 151) -* Align: label. (line 13) -* all: Arrays. (line 342) -* Allow: Pens. (line 338) -* AND: Arithmetic & logical. - (line 81) -* and: Tutorial. (line 174) -* angle: Data types. (line 70) -* animate <1>: animation. (line 12) -* animate <2>: Files. (line 155) -* animate: Configuring. (line 70) -* animation: animation. (line 6) -* annotate: annotate. (line 6) -* antialias <1>: Options. (line 130) -* antialias: three. (line 198) -* antialiasing: Compiling from UNIX source. - (line 17) -* append <1>: Arrays. (line 42) -* append: Files. (line 37) -* arc: three. (line 266) -* Arc: Paths and guides. (line 37) -* arc: Paths and guides. (line 24) -* ArcArrow: draw. (line 27) -* ArcArrow3: three. (line 514) -* ArcArrows: draw. (line 27) -* ArcArrows3: three. (line 514) -* arclength <1>: three. (line 469) -* arclength: Paths and guides. (line 144) -* arctime <1>: three. (line 469) -* arctime: Paths and guides. (line 148) -* arguments: Default arguments. (line 6) -* arithmetic operators: Arithmetic & logical. - (line 6) -* array: Arrays. (line 130) -* array iteration: Programming. (line 34) -* arrays: Arrays. (line 6) -* arrow: label. (line 77) -* Arrow: draw. (line 27) -* arrow: Drawing commands. (line 32) -* arrow keys: Tutorial. (line 22) -* Arrow3: three. (line 514) -* Arrows: draw. (line 27) -* Arrows3: three. (line 514) -* as: Import. (line 78) -* aSin: Mathematical functions. - (line 20) -* asin: Mathematical functions. - (line 6) -* asinh: Mathematical functions. - (line 6) -* Aspect: Frames and pictures. (line 60) -* assignment: Programming. (line 8) -* asy: Import. (line 117) -* asy-mode: Editing modes. (line 6) -* asy.vim: Editing modes. (line 34) -* asymptote.sty: LaTeX usage. (line 6) -* asymptote.xml: Editing modes. (line 52) -* ASYMPTOTE_CONFIG: Options. (line 101) -* aTan: Mathematical functions. - (line 20) -* atan: Mathematical functions. - (line 6) -* atan2: Mathematical functions. - (line 6) -* atanh: Mathematical functions. - (line 6) -* atleast: Tutorial. (line 174) -* attach <1>: graph. (line 423) -* attach: LaTeX usage. (line 34) -* autoadjust: three. (line 341) -* autoimport: Options. (line 97) -* automatic scaling: graph. (line 702) -* axialshade: fill. (line 49) -* axis <1>: graph3. (line 69) -* axis: graph. (line 904) -* azimuth: Data types. (line 126) -* babel: babel. (line 6) -* background color: Frames and pictures. (line 183) -* BackView: three. (line 366) -* Bar: draw. (line 20) -* Bar3: three. (line 514) -* Bars: draw. (line 20) -* Bars3: three. (line 514) -* barsize: draw. (line 20) -* base modules: Base modules. (line 6) -* basealign: Pens. (line 175) -* baseline: label. (line 99) -* batch mode: Tutorial. (line 31) -* beep: Data types. (line 340) -* BeginArcArrow: draw. (line 27) -* BeginArcArrow3: three. (line 514) -* BeginArrow: draw. (line 27) -* BeginArrow3: three. (line 514) -* BeginBar: draw. (line 20) -* BeginBar3: three. (line 514) -* BeginDotMargin: draw. (line 43) -* BeginDotMargin3: three. (line 530) -* BeginMargin: draw. (line 43) -* BeginMargin3: three. (line 530) -* BeginPenMargin: draw. (line 43) -* BeginPenMargin2: three. (line 530) -* BeginPenMargin3: three. (line 530) -* BeginPoint: label. (line 61) -* Bessel: Mathematical functions. - (line 48) -* bevel: flowchart. (line 75) -* beveljoin: Pens. (line 143) -* bezulate: three. (line 105) -* Bi: Mathematical functions. - (line 48) -* Bi_deriv: Mathematical functions. - (line 48) -* binary format: Files. (line 75) -* binary operators: Arithmetic & logical. - (line 6) -* binarytree: binarytree. (line 6) -* binput: Files. (line 75) -* Blank: draw. (line 27) -* block.bottom: flowchart. (line 20) -* block.bottomleft: flowchart. (line 20) -* block.bottomright: flowchart. (line 20) -* block.center: flowchart. (line 28) -* block.draw: flowchart. (line 34) -* block.left: flowchart. (line 20) -* block.position: flowchart. (line 26) -* block.right: flowchart. (line 20) -* block.top: flowchart. (line 20) -* block.topleft: flowchart. (line 20) -* block.topright: flowchart. (line 20) -* bool: Data types. (line 14) -* bool3: Data types. (line 25) -* boolean operators: Arithmetic & logical. - (line 6) -* Bottom: graph. (line 136) -* BottomTop: graph. (line 142) -* BottomView: three. (line 366) -* bounding box: Frames and pictures. (line 183) -* Bounds: graph3. (line 22) -* boutput: Files. (line 75) -* box <1>: three. (line 291) -* box: Frames and pictures. (line 25) -* bp: Tutorial. (line 18) -* break: Programming. (line 30) -* breakpoints: Debugger. (line 24) -* brick: Pens. (line 264) -* broken axis: graph. (line 806) -* bug reports: Help. (line 23) -* buildcycle: Paths and guides. (line 259) -* Button-1: GUI. (line 6) -* Button-2: GUI. (line 6) -* BWRainbow: palette. (line 15) -* BWRainbow2: palette. (line 18) -* C string: Data types. (line 191) -* CAD: CAD. (line 6) -* calculateTransform: Frames and pictures. (line 123) -* casts: Casts. (line 6) -* cbrt: Mathematical functions. - (line 6) -* cd: Files. (line 25) -* ceil: Mathematical functions. - (line 26) -* center: three. (line 326) -* Center: label. (line 67) -* checker: Pens. (line 264) -* Chinese: unicode. (line 13) -* choose: Mathematical functions. - (line 39) -* Ci: Mathematical functions. - (line 48) -* circle <1>: flowchart. (line 62) -* circle: three. (line 261) -* Circle: Paths and guides. (line 18) -* circle: Paths and guides. (line 10) -* circlebarframe: markers. (line 20) -* CJK: unicode. (line 13) -* clear <1>: Debugger. (line 27) -* clear: Files. (line 90) -* clip: fill. (line 124) -* cm: Tutorial. (line 66) -* cmyk: Pens. (line 34) -* colatitude: Data types. (line 131) -* color: Pens. (line 23) -* coloredNodes: tube. (line 27) -* coloredpath: tube. (line 19) -* coloredSegments: tube. (line 27) -* colorless: Pens. (line 54) -* colors: Pens. (line 51) -* comma: Files. (line 62) -* comma-separated-value mode: Arrays. (line 376) -* command-line options <1>: Options. (line 6) -* command-line options: Configuring. (line 85) -* comment character: Files. (line 16) -* compass directions: Tutorial. (line 99) -* Compiling from UNIX source: Compiling from UNIX source. - (line 6) -* complement: Arrays. (line 158) -* concat: Arrays. (line 188) -* conditional <1>: Arithmetic & logical. - (line 73) -* conditional: Programming. (line 8) -* config: Options. (line 101) -* configuration file: Configuring. (line 21) -* configuring: Configuring. (line 6) -* conj: Data types. (line 59) -* constructors: Structures. (line 99) -* context: Options. (line 130) -* continue <1>: Debugger. (line 37) -* continue: Programming. (line 30) -* contour: contour. (line 9) -* contour3: contour3. (line 6) -* controls <1>: three. (line 6) -* controls: Tutorial. (line 162) -* controlSpecifier: Paths and guides. (line 385) -* convert <1>: Options. (line 130) -* convert <2>: animation. (line 6) -* convert <3>: Files. (line 155) -* convert: Configuring. (line 70) -* convertOptions: Options. (line 117) -* Coons shading: fill. (line 83) -* copy: Arrays. (line 179) -* Cos: Mathematical functions. - (line 20) -* cos: Mathematical functions. - (line 6) -* cosh: Mathematical functions. - (line 6) -* cputime: Structures. (line 185) -* crop: graph. (line 654) -* cropping graphs: graph. (line 654) -* cross <1>: graph. (line 492) -* cross: Data types. (line 169) -* crossframe: markers. (line 26) -* crosshatch: Pens. (line 280) -* csv: Arrays. (line 376) -* cubicroots: Arrays. (line 330) -* curl <1>: three. (line 6) -* curl: Tutorial. (line 182) -* curlSpecifier: Paths and guides. (line 397) -* currentpen: Pens. (line 6) -* currentprojection: three. (line 363) -* curve: slopefield. (line 21) -* custom axis types: graph. (line 146) -* custom mark routine: graph. (line 594) -* custom tick locations: graph. (line 251) -* cut: Paths and guides. (line 240) -* cycle <1>: three. (line 6) -* cycle: Tutorial. (line 48) -* cyclic <1>: three. (line 469) -* cyclic <2>: Arrays. (line 42) -* cyclic: Paths and guides. (line 82) -* cyclicflag: Arrays. (line 42) -* Cyrillic: unicode. (line 7) -* dashdotted: Pens. (line 97) -* dashed: Pens. (line 97) -* data types: Data types. (line 6) -* date: Data types. (line 293) -* Debian: UNIX binary distributions. - (line 21) -* debugger: Debugger. (line 6) -* declaration: Programming. (line 8) -* deconstruct: GUI Usage. (line 6) -* default arguments: Default arguments. (line 6) -* defaultformat: graph. (line 179) -* DefaultHead: draw. (line 27) -* DefaultHead3: three. (line 514) -* defaultpen: Pens. (line 46) -* deferred drawing: simplex. (line 6) -* Degrees: Mathematical functions. - (line 17) -* degrees <1>: Mathematical functions. - (line 17) -* degrees: Data types. (line 75) -* delete <1>: Arrays. (line 42) -* delete: Files. (line 150) -* description: Description. (line 6) -* diagonal: Arrays. (line 315) -* diamond: flowchart. (line 54) -* dimension: Arrays. (line 383) -* dir <1>: three. (line 469) -* dir <2>: Paths and guides. (line 106) -* dir <3>: Data types. (line 87) -* dir: Search paths. (line 10) -* direction specifier: Tutorial. (line 123) -* directory: Files. (line 25) -* dirSpecifier: Paths and guides. (line 379) -* dirtime: Paths and guides. (line 154) -* display: Configuring. (line 70) -* do: Programming. (line 30) -* dot <1>: Data types. (line 100) -* dot: draw. (line 85) -* DotMargin: draw. (line 43) -* DotMargin3: three. (line 530) -* DotMargins: draw. (line 43) -* DotMargins3: three. (line 530) -* dotted: Pens. (line 97) -* double: Files. (line 75) -* double deferred drawing: three. (line 240) -* Draw: Frames and pictures. (line 166) -* draw: draw. (line 114) -* Draw: draw. (line 27) -* draw: Drawing commands. (line 32) -* drawing commands: Drawing commands. (line 6) -* drawline: math. (line 9) -* drawtree: drawtree. (line 9) -* dvips: Configuring. (line 70) -* dvipsOptions: Options. (line 117) -* E <1>: Mathematical functions. - (line 48) -* E: Tutorial. (line 99) -* Editing modes: Editing modes. (line 6) -* Ei: Mathematical functions. - (line 48) -* ellipse: Frames and pictures. (line 25) -* elliptic functions: Mathematical functions. - (line 48) -* else: Programming. (line 8) -* emacs: Editing modes. (line 6) -* embed: embed. (line 6) -* empty: Frames and pictures. (line 7) -* EndArcArrow: draw. (line 27) -* EndArcArrow3: three. (line 514) -* EndArrow: draw. (line 27) -* EndArrow3: three. (line 514) -* EndBar: draw. (line 20) -* EndBar3: three. (line 514) -* EndDotMargin: draw. (line 43) -* EndDotMargin3: three. (line 530) -* endl: Files. (line 62) -* EndMargin: draw. (line 43) -* EndMargin3: three. (line 530) -* EndPenMargin: draw. (line 43) -* EndPenMargin2: three. (line 530) -* EndPenMargin3: three. (line 530) -* EndPoint: label. (line 61) -* envelope: Frames and pictures. (line 25) -* environment variables: Configuring. (line 90) -* eof <1>: Arrays. (line 358) -* eof: Files. (line 90) -* eol <1>: Arrays. (line 358) -* eol: Files. (line 90) -* EPS: label. (line 86) -* erase <1>: Frames and pictures. (line 7) -* erase: Data types. (line 241) -* erf: Mathematical functions. - (line 6) -* erfc: Mathematical functions. - (line 6) -* error: Files. (line 16) -* errorbars: graph. (line 492) -* eval: Import. (line 112) -* evenodd <1>: Pens. (line 158) -* evenodd: Tutorial. (line 222) -* exit <1>: Debugger. (line 63) -* exit <2>: Interactive mode. (line 37) -* exit: Data types. (line 331) -* exp: Mathematical functions. - (line 6) -* expi: Data types. (line 83) -* explicit: Casts. (line 6) -* explicit casts: Casts. (line 23) -* expm1: Mathematical functions. - (line 6) -* exponential integral: Mathematical functions. - (line 48) -* extendcap: Pens. (line 133) -* extension <1>: MetaPost. (line 10) -* extension: Paths and guides. (line 235) -* external: embed. (line 29) -* extrude: three. (line 462) -* F: Mathematical functions. - (line 48) -* fabs: Mathematical functions. - (line 6) -* face: three. (line 549) -* factorial: Mathematical functions. - (line 39) -* Fedora: UNIX binary distributions. - (line 16) -* feynman: feynman. (line 6) -* fft: Arrays. (line 259) -* FFTW: Compiling from UNIX source. - (line 63) -* file <1>: Debugger. (line 51) -* file: Files. (line 6) -* Fill: Frames and pictures. (line 152) -* fill <1>: fill. (line 19) -* fill: draw. (line 121) -* Fill: draw. (line 27) -* FillDraw: Frames and pictures. (line 142) -* filldraw: fill. (line 12) -* FillDraw: draw. (line 27) -* filloutside: fill. (line 31) -* fillrule: Pens. (line 158) -* find <1>: Arrays. (line 167) -* find: Data types. (line 226) -* firstcut: Paths and guides. (line 251) -* fit: Frames and pictures. (line 118) -* fix-cm: Pens. (line 186) -* fixedscaling: Frames and pictures. (line 84) -* floor: Mathematical functions. - (line 26) -* flowchart: flowchart. (line 6) -* flush: Files. (line 62) -* fmod: Mathematical functions. - (line 6) -* font: Pens. (line 201) -* font command: Pens. (line 201) -* fontcommand: Pens. (line 216) -* fontsize: Pens. (line 186) -* for: Programming. (line 8) -* format <1>: Options. (line 130) -* format: Data types. (line 268) -* forum: Help. (line 6) -* frame: Frames and pictures. (line 7) -* freeglut: Compiling from UNIX source. - (line 17) -* from: Import. (line 18) -* FrontView: three. (line 366) -* function declarations: Functions. (line 72) -* function shading: fill. (line 107) -* Function shading: fill. (line 107) -* functions <1>: Mathematical functions. - (line 6) -* functions: Functions. (line 6) -* functionshade: fill. (line 107) -* gamma: Mathematical functions. - (line 6) -* Gaussrand: Mathematical functions. - (line 39) -* geometry: geometry. (line 6) -* getc: Files. (line 31) -* getpair: Files. (line 115) -* getreal: Files. (line 115) -* getstring: Files. (line 115) -* gettriple: Files. (line 115) -* glOptions <1>: Options. (line 117) -* glOptions: three. (line 198) -* GNU Scientific Library: Mathematical functions. - (line 48) -* gouraudshade: fill. (line 66) -* Gradient: palette. (line 25) -* gradient shading: fill. (line 37) -* graph: graph. (line 6) -* graph3: graph3. (line 6) -* graphic: label. (line 86) -* graphical user interface: GUI. (line 6) -* gray: Pens. (line 25) -* Grayscale: palette. (line 9) -* grayscale: Pens. (line 25) -* grid <1>: graph. (line 757) -* grid: Pens. (line 264) -* grid3: grid3. (line 6) -* gs: Configuring. (line 6) -* gsl: Mathematical functions. - (line 48) -* GSL: Compiling from UNIX source. - (line 63) -* gsOptions: Options. (line 117) -* GUI: GUI. (line 6) -* GUI installation: GUI Installation. (line 6) -* GUI usage: GUI Usage. (line 6) -* guide: Paths and guides. (line 304) -* guide3: three. (line 6) -* hatch: Pens. (line 280) -* height: LaTeX usage. (line 34) -* help <1>: Debugger. (line 36) -* help <2>: Help. (line 6) -* help: Interactive mode. (line 25) -* Hermite: graph. (line 38) -* Hermite(splinetype splinetype: graph. (line 38) -* hex: Data types. (line 281) -* hexidecimal <1>: Pens. (line 59) -* hexidecimal: Data types. (line 281) -* hidden surface removal: three. (line 549) -* histogram: Mathematical functions. - (line 39) -* history: Files. (line 142) -* historylines: Interactive mode. (line 42) -* HookHead: draw. (line 27) -* HookHead3: three. (line 514) -* Horizontal: flowchart. (line 82) -* hypot: Mathematical functions. - (line 6) -* I: Mathematical functions. - (line 48) -* i_scaled: Mathematical functions. - (line 48) -* iconic: three. (line 198) -* identity <1>: Arrays. (line 312) -* identity <2>: Mathematical functions. - (line 6) -* identity: Transforms. (line 25) -* if: Programming. (line 8) -* IgnoreAspect: Frames and pictures. (line 64) -* image: palette. (line 34) -* ImageMagick <1>: Options. (line 130) -* ImageMagick <2>: animation. (line 6) -* ImageMagick: Configuring. (line 70) -* implicit casts: Casts. (line 6) -* implicit linear solver: MetaPost. (line 10) -* implicit scaling: Implicit scaling. (line 6) -* import: Import. (line 54) -* inches: Tutorial. (line 66) -* including images: label. (line 86) -* inheritance: Structures. (line 198) -* initialized: Arrays. (line 42) -* initializers: Variable initializers. - (line 6) -* InOutTicks: graph3. (line 37) -* input <1>: Interactive mode. (line 31) -* input: Files. (line 11) -* insert <1>: Arrays. (line 42) -* insert: Data types. (line 237) -* inside: Paths and guides. (line 283) -* inst: Debugger. (line 42) -* installation: Installation. (line 6) -* int: Data types. (line 30) -* integer division: Arithmetic & logical. - (line 6) -* interactive mode: Interactive mode. (line 6) -* interior: Paths and guides. (line 279) -* international characters: unicode. (line 6) -* interp: Arithmetic & logical. - (line 77) -* interpolate: interpolate. (line 6) -* intersect <1>: three. (line 469) -* intersect <2>: math. (line 13) -* intersect: Paths and guides. (line 183) -* intersectionpoint <1>: three. (line 469) -* intersectionpoint <2>: math. (line 17) -* intersectionpoint: Paths and guides. (line 227) -* intersectionpoints <1>: three. (line 469) -* intersectionpoints: Paths and guides. (line 231) -* intersections <1>: three. (line 469) -* intersections: Paths and guides. (line 194) -* InTicks: graph3. (line 37) -* intMax: Data types. (line 30) -* intMin: Data types. (line 30) -* inverse <1>: Arrays. (line 318) -* inverse: Transforms. (line 17) -* invert: three. (line 395) -* invisible: Pens. (line 39) -* J: Mathematical functions. - (line 6) -* Japanese: unicode. (line 13) -* K: Mathematical functions. - (line 48) -* k_scaled: Mathematical functions. - (line 48) -* Kate: Editing modes. (line 52) -* KDE editor: Editing modes. (line 52) -* keyboard bindings:: three. (line 167) -* keys: Arrays. (line 42) -* keywords: Named arguments. (line 6) -* Korean: unicode. (line 13) -* Label: graph. (line 349) -* label: clip. (line 17) -* Label: draw. (line 101) -* labelpath: labelpath. (line 6) -* labelpath3: labelpath3. (line 6) -* labelx: graph. (line 349) -* labely: graph. (line 349) -* Landscape: Frames and pictures. (line 109) -* lastcut: Paths and guides. (line 255) -* lasy-mode: Editing modes. (line 6) -* latex: Options. (line 130) -* LaTeX fonts: Pens. (line 201) -* LaTeX usage: LaTeX usage. (line 6) -* latin1: latin1. (line 6) -* latitude: Data types. (line 136) -* latticeshade: fill. (line 37) -* layer: Drawing commands. (line 16) -* leastsquares <1>: graph. (line 926) -* leastsquares: stats. (line 6) -* Left: graph. (line 286) -* LeftRight: graph. (line 292) -* LeftSide: label. (line 67) -* LeftTicks: graph. (line 164) -* LeftView: three. (line 366) -* legend <1>: graph. (line 439) -* legend <2>: draw. (line 65) -* legend: Drawing commands. (line 32) -* Legendre: Mathematical functions. - (line 48) -* length <1>: three. (line 469) -* length <2>: Arrays. (line 42) -* length <3>: Paths and guides. (line 73) -* length: Data types. (line 62) -* letter: Configuring. (line 64) -* libm routines: Mathematical functions. - (line 6) -* libsigsegv <1>: Help. (line 33) -* libsigsegv: Functions. (line 94) -* limits: graph. (line 654) -* line: Arrays. (line 358) -* line mode: Arrays. (line 358) -* Linear: graph. (line 702) -* linecap: Pens. (line 133) -* linejoin: Pens. (line 143) -* lineskip: Pens. (line 186) -* linewidth: Pens. (line 121) -* locale: Data types. (line 288) -* Log: graph. (line 702) -* log: Mathematical functions. - (line 6) -* log-log graph: graph. (line 736) -* log10: Mathematical functions. - (line 6) -* log1p: Mathematical functions. - (line 6) -* log2 graph: graph. (line 786) -* logarithmic graph: graph. (line 736) -* logical operators: Arithmetic & logical. - (line 6) -* longdashdotted: Pens. (line 97) -* longdashed: Pens. (line 97) -* longitude: Data types. (line 141) -* loop: Programming. (line 8) -* MacOS X binary distributions: MacOS X binary distributions. - (line 6) -* makepen: Pens. (line 313) -* map: Arrays. (line 149) -* Margin: draw. (line 43) -* Margin3: three. (line 530) -* margins: three. (line 247) -* Margins: draw. (line 43) -* Margins3: three. (line 530) -* mark: graph. (line 492) -* markangle: markers. (line 43) -* marker: graph. (line 492) -* markers: markers. (line 6) -* marknodes: graph. (line 492) -* markuniform: graph. (line 492) -* math: math. (line 6) -* mathematical functions: Mathematical functions. - (line 6) -* max <1>: three. (line 469) -* max <2>: Arrays. (line 238) -* max <3>: Frames and pictures. (line 7) -* max: Paths and guides. (line 268) -* maxbound: Data types. (line 106) -* maxtile: three. (line 198) -* maxtimes: Paths and guides. (line 222) -* maxviewport: three. (line 198) -* merge: animation. (line 6) -* MetaPost: MetaPost. (line 6) -* MetaPost ... : Tutorial. (line 187) -* MetaPost cutafter: Paths and guides. (line 256) -* MetaPost cutbefore: Paths and guides. (line 252) -* MetaPost pickup: Pens. (line 6) -* MetaPost whatever: MetaPost. (line 10) -* Microsoft Windows: Microsoft Windows. (line 6) -* MidArcArrow: draw. (line 27) -* MidArcArrow3: three. (line 514) -* MidArrow: draw. (line 27) -* MidArrow3: three. (line 514) -* midpoint: Paths and guides. (line 168) -* MidPoint: label. (line 61) -* min <1>: three. (line 469) -* min <2>: Arrays. (line 231) -* min <3>: Frames and pictures. (line 7) -* min: Paths and guides. (line 264) -* minbound: Data types. (line 103) -* minipage: label. (line 128) -* mintimes: Paths and guides. (line 217) -* miterjoin: Pens. (line 143) -* miterlimit: Pens. (line 153) -* mm: Tutorial. (line 66) -* mouse: GUI. (line 6) -* mouse bindings: three. (line 137) -* Move: Pens. (line 350) -* MoveQuiet: Pens. (line 356) -* multisample: three. (line 127) -* multisampling: Compiling from UNIX source. - (line 17) -* N: Tutorial. (line 99) -* named arguments: Named arguments. (line 6) -* new <1>: Arrays. (line 117) -* new: Structures. (line 6) -* newframe: Frames and pictures. (line 7) -* newl: Files. (line 62) -* newton: Mathematical functions. - (line 66) -* next: Debugger. (line 48) -* NFSS: Pens. (line 201) -* nobasealign: Pens. (line 175) -* NoFill <1>: Frames and pictures. (line 160) -* NoFill: draw. (line 27) -* NoMargin: draw. (line 43) -* NoMargin3: three. (line 530) -* none: Files. (line 62) -* None: draw. (line 20) -* normal: three. (line 452) -* nosafe: Options. (line 147) -* NOT: Arithmetic & logical. - (line 81) -* NoTicks: graph. (line 164) -* NoTicks3: graph3. (line 37) -* null: Structures. (line 6) -* nullpen <1>: Frames and pictures. (line 146) -* nullpen: label. (line 15) -* NURBS: three. (line 344) -* O: three. (line 255) -* obj: obj. (line 9) -* oblique: three. (line 307) -* obliqueX: three. (line 315) -* obliqueY: three. (line 322) -* obliqueZ: three. (line 307) -* ode: ode. (line 9) -* offset: Options. (line 151) -* opacity: Pens. (line 232) -* open: Files. (line 11) -* OpenGL: three. (line 127) -* operator: User-defined operators. - (line 6) -* operator --: graph. (line 32) -* operator ..: graph. (line 35) -* operator cast: Casts. (line 33) -* operator ecast: Casts. (line 63) -* operator init <1>: Structures. (line 148) -* operator init: Variable initializers. - (line 6) -* operators: Operators. (line 6) -* options: Options. (line 6) -* OR: Arithmetic & logical. - (line 81) -* orientation: Frames and pictures. (line 109) -* orthographic: three. (line 326) -* outformat: three. (line 127) -* outprefix: Frames and pictures. (line 96) -* output <1>: Options. (line 130) -* output: Files. (line 37) -* OutTicks: graph3. (line 37) -* overloading functions: Functions. (line 48) -* overwrite: Pens. (line 335) -* P: Mathematical functions. - (line 48) -* pack: label. (line 109) -* packing: Rest arguments. (line 31) -* pair <1>: Data types. (line 43) -* pair: Tutorial. (line 18) -* pairs: Arrays. (line 255) -* paperheight: Configuring. (line 64) -* papertype: Configuring. (line 64) -* paperwidth: Configuring. (line 64) -* parametric surface: graph3. (line 103) -* parametrized curve: graph. (line 654) -* patch-dependent colors: three. (line 78) -* path <1>: flowchart. (line 82) -* path <2>: three. (line 43) -* path: Paths and guides. (line 7) -* path3: three. (line 6) -* path[]: Tutorial. (line 208) -* patterns <1>: patterns. (line 6) -* patterns: Pens. (line 250) -* pdflatex: Options. (line 130) -* pdfviewer: Configuring. (line 6) -* pdfviewerOptions: Options. (line 117) -* pen: Pens. (line 6) -* PenMargin: draw. (line 43) -* PenMargin2: three. (line 530) -* PenMargin3: three. (line 530) -* PenMargins: draw. (line 43) -* PenMargins2: three. (line 530) -* PenMargins3: three. (line 530) -* perpendicular: geometry. (line 6) -* perspective: three. (line 344) -* picture: Frames and pictures. (line 39) -* picture alignment: Frames and pictures. (line 231) -* piecewisestraight: Paths and guides. (line 89) -* Pl: Mathematical functions. - (line 48) -* plain: plain. (line 6) -* planar: three. (line 86) -* plane: three. (line 286) -* planeproject: three. (line 448) -* point <1>: three. (line 469) -* point: Paths and guides. (line 92) -* polar: Data types. (line 121) -* polargraph: graph. (line 95) -* polygon: graph. (line 492) -* pop: Arrays. (line 42) -* Portrait: Frames and pictures. (line 109) -* postcontrol <1>: three. (line 469) -* postcontrol: Paths and guides. (line 137) -* postfix operators: Self & prefix operators. - (line 21) -* postscript: Frames and pictures. (line 296) -* PostScript fonts: Pens. (line 219) -* PostScript subpath: Tutorial. (line 208) -* pow10: Mathematical functions. - (line 6) -* prc: three. (line 215) -* precision: Files. (line 90) -* precontrol <1>: three. (line 469) -* precontrol: Paths and guides. (line 130) -* prefix operators: Self & prefix operators. - (line 6) -* private: Structures. (line 6) -* programming: Programming. (line 6) -* pstoedit: PostScript to Asymptote. - (line 6) -* psviewer: Configuring. (line 6) -* psviewerOptions: Options. (line 117) -* pt: Tutorial. (line 66) -* public: Structures. (line 6) -* push: Arrays. (line 42) -* python: Configuring. (line 27) -* Python usage: Interactive mode. (line 58) -* quadraticroots: Arrays. (line 321) -* quarticroots: math. (line 22) -* quit <1>: Debugger. (line 60) -* quit: Interactive mode. (line 37) -* quote: Import. (line 133) -* quotient: Arithmetic & logical. - (line 6) -* RadialShade: Frames and pictures. (line 178) -* radialshade: fill. (line 56) -* radians: Mathematical functions. - (line 17) -* radius <1>: three. (line 469) -* radius: Paths and guides. (line 126) -* Rainbow: palette. (line 12) -* rand: Mathematical functions. - (line 39) -* randMax: Mathematical functions. - (line 39) -* read1: Arrays. (line 403) -* read2: Arrays. (line 403) -* read3: Arrays. (line 403) -* reading: Files. (line 11) -* reading string arrays: Arrays. (line 366) -* readline: Files. (line 133) -* 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 97) -* rectangle: flowchart. (line 40) -* recursion: Functions. (line 94) -* reflect: Transforms. (line 52) -* Relative: label. (line 56) -* relpoint: Paths and guides. (line 164) -* reltime: Paths and guides. (line 160) -* remainder: Mathematical functions. - (line 6) -* rename: Files. (line 152) -* render <1>: Options. (line 130) -* render: three. (line 127) -* replace: Data types. (line 254) -* resetdefaultpen: Pens. (line 364) -* rest arguments: Rest arguments. (line 6) -* restore: Frames and pictures. (line 290) -* restricted: Structures. (line 6) -* return: Debugger. (line 54) -* reverse <1>: three. (line 469) -* reverse <2>: Arrays. (line 154) -* reverse <3>: Paths and guides. (line 171) -* reverse: Data types. (line 250) -* rewind: Files. (line 90) -* rfind: Data types. (line 231) -* rgb: Pens. (line 30) -* Riemann zeta function: Mathematical functions. - (line 48) -* Right: graph. (line 289) -* RightSide: label. (line 67) -* RightTicks: graph. (line 164) -* RightView: three. (line 366) -* Rotate: label. (line 40) -* Rotate(pair z): label. (line 43) -* round: Mathematical functions. - (line 26) -* roundcap: Pens. (line 133) -* roundedpath: roundedpath. (line 6) -* roundjoin: Pens. (line 143) -* roundrectangle: flowchart. (line 68) -* RPM: UNIX binary distributions. - (line 6) -* runtime imports: Import. (line 112) -* Russian: unicode. (line 7) -* S: Tutorial. (line 99) -* safe: Options. (line 147) -* save: Frames and pictures. (line 287) -* saveline: Files. (line 133) -* scale: three. (line 427) -* Scale: graph. (line 719) -* scale <1>: graph. (line 702) -* scale: Transforms. (line 40) -* Scale: label. (line 49) -* scale3: three. (line 424) -* scaled graph: graph. (line 683) -* scientific graph: graph. (line 404) -* scroll: Files. (line 106) -* search: Arrays. (line 172) -* search paths: Search paths. (line 6) -* Seascape: Frames and pictures. (line 115) -* secondary axis: graph. (line 836) -* secondaryX: graph. (line 836) -* secondaryY: graph. (line 836) -* seconds: Data types. (line 302) -* seek: Files. (line 90) -* seekeof: Files. (line 90) -* segmentation fault: Help. (line 33) -* self operators: Self & prefix operators. - (line 6) -* sequence: Arrays. (line 136) -* settings <1>: Options. (line 101) -* settings: Configuring. (line 21) -* sgn: Mathematical functions. - (line 26) -* shading: fill. (line 37) -* shift <1>: three. (line 412) -* shift: Transforms. (line 28) -* Shift: label. (line 37) -* shiftless: Transforms. (line 54) -* shipout: Frames and pictures. (line 96) -* showtarget: three. (line 326) -* Si: Mathematical functions. - (line 48) -* SimpleHead: draw. (line 27) -* simplex: simplex. (line 6) -* simpson: Mathematical functions. - (line 82) -* Sin: Mathematical functions. - (line 20) -* sin: Mathematical functions. - (line 6) -* single: Files. (line 75) -* sinh: Mathematical functions. - (line 6) -* size <1>: Options. (line 130) -* size <2>: three. (line 469) -* size <3>: Frames and pictures. (line 48) -* size: Paths and guides. (line 78) -* size3: three. (line 243) -* slant: Transforms. (line 46) -* Slant: label. (line 46) -* sleep: Data types. (line 334) -* slice: Paths and guides. (line 240) -* slices: Slices. (line 6) -* slide: slide. (line 6) -* slopefield: slopefield. (line 6) -* solid: Pens. (line 97) -* solids: solids. (line 9) -* solve: Arrays. (line 273) -* sort: Arrays. (line 195) -* Spline <1>: graph3. (line 103) -* Spline: graph. (line 35) -* split: Data types. (line 263) -* sqrt: Mathematical functions. - (line 6) -* squarecap: Pens. (line 133) -* srand: Mathematical functions. - (line 39) -* stack overflow <1>: Help. (line 33) -* stack overflow: Functions. (line 94) -* static: Static. (line 6) -* stats: stats. (line 6) -* stdin: Files. (line 48) -* stdout: Files. (line 48) -* step: Debugger. (line 45) -* stickframe: markers. (line 17) -* stop: Debugger. (line 10) -* straight: three. (line 469) -* Straight: graph. (line 32) -* straight: Paths and guides. (line 85) -* strftime: Data types. (line 293) -* string: Data types. (line 181) -* stroke: fill. (line 42) -* strokepath: Paths and guides. (line 298) -* strptime: Data types. (line 302) -* struct: Structures. (line 6) -* structures: Structures. (line 6) -* subpath <1>: three. (line 469) -* subpath: Paths and guides. (line 174) -* subpictures: Frames and pictures. (line 118) -* substr: Data types. (line 246) -* Subversion: Subversion. (line 6) -* sum: Arrays. (line 226) -* superpath: Tutorial. (line 208) -* Suppress: Pens. (line 342) -* SuppressQuiet: Pens. (line 346) -* surface <1>: graph3. (line 103) -* surface: three. (line 48) -* SVN: Subversion. (line 6) -* system <1>: Options. (line 147) -* system: Files. (line 161) -* syzygy: syzygy. (line 6) -* tab: Files. (line 62) -* tab completion: Tutorial. (line 22) -* Tan: Mathematical functions. - (line 20) -* tan: Mathematical functions. - (line 6) -* tanh: Mathematical functions. - (line 6) -* target: three. (line 326) -* tell: Files. (line 90) -* tension <1>: three. (line 6) -* tension: Tutorial. (line 174) -* tensionSpecifier: Paths and guides. (line 391) -* tensor product shading: fill. (line 83) -* tensorshade: fill. (line 83) -* tex <1>: Options. (line 130) -* tex: Frames and pictures. (line 304) -* TeX fonts: Pens. (line 210) -* TeX string: Data types. (line 181) -* texcommand: Configuring. (line 70) -* texdvicommand: Configuring. (line 70) -* TeXHead: draw. (line 27) -* TeXHead3: three. (line 514) -* texpath <1>: label. (line 125) -* texpath: Configuring. (line 70) -* texpreamble: Frames and pictures. (line 313) -* texreset: Frames and pictures. (line 317) -* textbook graph: graph. (line 379) -* tgz: UNIX binary distributions. - (line 6) -* thick: three. (line 111) -* thin: three. (line 111) -* this: Structures. (line 6) -* three: three. (line 6) -* tick: graph. (line 349) -* Ticks: graph. (line 164) -* ticks: graph. (line 164) -* tildeframe: markers. (line 30) -* tile: Pens. (line 264) -* tilings: Pens. (line 250) -* time: Data types. (line 293) -* times: Paths and guides. (line 209) -* Top: graph. (line 139) -* TopView: three. (line 366) -* trace: Debugger. (line 57) -* trailingzero: graph. (line 179) -* transform <1>: three. (line 439) -* transform: Transforms. (line 6) -* transform3: three. (line 408) -* transparency: Pens. (line 232) -* transpose: Arrays. (line 218) -* tree: tree. (line 9) -* trembling: trembling. (line 6) -* triangle: geometry. (line 6) -* triangulate: contour. (line 161) -* tridiagonal: Arrays. (line 276) -* trigonometric integrals: Mathematical functions. - (line 48) -* triple: Data types. (line 110) -* TrueMargin: draw. (line 43) -* TrueMargin3: three. (line 530) -* tube <1>: tube. (line 6) -* tube: three. (line 111) -* tutorial: Tutorial. (line 6) -* typedef <1>: Functions. (line 39) -* typedef: Data types. (line 344) -* undefined: Paths and guides. (line 272) -* UnFill: Frames and pictures. (line 171) -* unfill: fill. (line 118) -* UnFill: draw. (line 27) -* unicode: unicode. (line 6) -* uniform: Arrays. (line 163) -* Uninstall: Uninstall. (line 6) -* unit: Data types. (line 80) -* unitbox <1>: three. (line 294) -* unitbox: Tutorial. (line 230) -* unitcircle <1>: three. (line 255) -* unitcircle: Tutorial. (line 117) -* unitrand: Mathematical functions. - (line 39) -* unitsize <1>: Frames and pictures. (line 72) -* unitsize: Tutorial. (line 76) -* UNIX binary distributions: UNIX binary distributions. - (line 6) -* unpacking: Rest arguments. (line 42) -* unravel: Import. (line 35) -* up: three. (line 326) -* update: Files. (line 37) -* UpsideDown: Frames and pictures. (line 109) -* usepackage: Frames and pictures. (line 320) -* user coordinates: Tutorial. (line 76) -* user-defined operators: User-defined operators. - (line 6) -* usleep: Data types. (line 337) -* variable initializers: Variable initializers. - (line 6) -* vectorfield: graph. (line 999) -* vectorfield3: graph3. (line 160) -* vectorization: Arrays. (line 335) -* verbatim: Frames and pictures. (line 296) -* vertex-dependent colors: three. (line 78) -* Vertical: flowchart. (line 82) -* viewportheight: LaTeX usage. (line 34) -* viewportmargin: three. (line 247) -* viewportsize: three. (line 247) -* viewportwidth: LaTeX usage. (line 34) -* views: three. (line 215) -* vim: Editing modes. (line 34) -* virtual functions: Structures. (line 198) -* void: Data types. (line 10) -* W: Tutorial. (line 99) -* whatever: Paths and guides. (line 235) -* Wheel: palette. (line 22) -* wheel mouse: GUI. (line 6) -* while: Programming. (line 30) -* white-space string delimiter mode: Arrays. (line 366) -* width: LaTeX usage. (line 34) -* windingnumber: Paths and guides. (line 272) -* word: Arrays. (line 366) -* write <1>: Arrays. (line 412) -* write: Files. (line 53) -* X: three. (line 255) -* xasy <1>: GUI. (line 6) -* xasy: Configuring. (line 70) -* xaxis3: graph3. (line 7) -* xelatex <1>: Options. (line 130) -* xelatex: embed. (line 10) -* xequals: graph. (line 296) -* XEquals: graph. (line 282) -* xinput: Files. (line 75) -* xlimits: graph. (line 654) -* XOR: Arithmetic & logical. - (line 81) -* xoutput: Files. (line 75) -* xpart: Data types. (line 91) -* xscale: Transforms. (line 34) -* xscale3: three. (line 415) -* xtick: graph. (line 349) -* XYEquals: graph3. (line 22) -* XYZero: graph3. (line 22) -* XZEquals: graph3. (line 22) -* XZero: graph. (line 277) -* XZZero: graph3. (line 22) -* Y <1>: three. (line 255) -* Y: Mathematical functions. - (line 6) -* yaxis3: graph3. (line 7) -* yequals: graph. (line 296) -* YEquals: graph. (line 132) -* ylimits: graph. (line 654) -* ypart: Data types. (line 94) -* yscale: Transforms. (line 37) -* yscale3: three. (line 418) -* ytick: graph. (line 349) -* YZEquals: graph3. (line 22) -* YZero: graph. (line 127) -* YZZero: graph3. (line 22) -* Z: three. (line 255) -* zaxis3: graph3. (line 7) -* zero_Ai: Mathematical functions. - (line 48) -* zero_Ai_deriv: Mathematical functions. - (line 48) -* zero_Bi: Mathematical functions. - (line 48) -* zero_Bi_deriv: Mathematical functions. - (line 48) -* zero_J: Mathematical functions. - (line 48) -* zerowinding: Pens. (line 158) -* zeta: Mathematical functions. - (line 48) -* zpart: Data types. (line 163) -* zscale3: three. 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Vector graphics language. -END-INFO-DIR-ENTRY - - -File: asymptote.info, Node: Top, Next: Description, Up: (dir) - -Asymptote -********* - -This file documents `Asymptote', version 1.75. - - `http://asymptote.sourceforge.net' - - Copyright (C) 2004-9 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 -* Programming:: The `Asymptote' vector graphics language -* LaTeX usage:: Embedding `Asymptote' commands within `LaTeX' -* Base modules:: Base modules shipped with `Asymptote' -* Options:: Command-line options -* Interactive mode:: Typing `Asymptote' commands interactively -* GUI:: Graphical user interface -* PostScript to Asymptote:: `Asymptote' backend to `pstoedit' -* Help:: Where to get help and submit bug reports -* Debugger:: Squish those bugs! -* Credits:: Contributions and acknowledgments -* Index:: General index - - --- The Detailed Node Listing --- - -Installation - -* UNIX binary distributions:: Prebuilt `UNIX' binaries -* MacOS X binary distributions:: Prebuilt `MacOS X' binaries -* Microsoft Windows:: Prebuilt `Microsoft Windows' binary -* Configuring:: Configuring `Asymptote' for your system -* Search paths:: Where `Asymptote' looks for your files -* Compiling from UNIX source:: Building `Asymptote' from scratch -* Editing modes:: Convenient `emacs' and `vim' modes -* Subversion:: -* Uninstall:: Goodbye, `Asymptote'! - -Drawing commands - -* draw:: Draw a path on a picture or frame -* fill:: Fill a cyclic path on a picture or frame -* clip:: Clip a picture or frame to a cyclic path -* label:: Label a point on a picture - -Programming - -* Data types:: void, bool, int, real, pair, triple, string -* Paths and guides:: -* 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' packages -* Static:: Where to allocate your variable? - -Operators - -* Arithmetic & logical:: Basic mathematical operators -* Self & prefix operators:: Increment and decrement -* User-defined operators:: Overloading operators - -Functions - -* Default arguments:: Default values can appear anywhere -* Named arguments:: Assigning function arguments by keyword -* Rest arguments:: Functions with a variable number of arguments -* Mathematical functions:: Standard libm functions - - -Arrays - -* Slices:: Python-style array slices - -Base modules - -* plain:: Default `Asymptote' base file -* simplex:: Linear programming: simplex method -* math:: Extend `Asymptote''s math capabilities -* interpolate:: Interpolation routines -* geometry:: Geometry routines -* trembling:: Wavy lines -* stats:: Statistics routines and histograms -* patterns:: Custom fill and draw patterns -* markers:: Custom path marker routines -* tree:: Dynamic binary search tree -* binarytree:: Binary tree drawing module -* drawtree:: Tree drawing module -* syzygy:: Syzygy and braid drawing module -* feynman:: Feynman diagrams -* roundedpath:: Round the sharp corners of paths -* animation:: Embedded PDF and MPEG movies -* embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with `Asymptote' -* MetaPost:: `MetaPost' compatibility routines -* unicode:: Accept `unicode' (UTF-8) characters -* latin1:: Accept `ISO 8859-1' characters -* babel:: Interface to `LaTeX' `babel' package -* labelpath:: Drawing curved labels -* labelpath3:: Drawing curved labels in 3D -* annotate:: Annotate your PDF files -* CAD:: 2D CAD pen and measurement functions (DIN 15) -* graph:: 2D linear & logarithmic graphs -* palette:: Color density images and palettes -* three:: 3D vector graphics -* obj:: 3D obj files -* graph3:: 3D linear & logarithmic graphs -* grid3:: 3D grids -* solids:: 3D solid geometry -* tube:: 3D rotation minimizing tubes -* flowchart:: Flowchart drawing routines -* contour:: Contour lines -* contour3:: Contour surfaces -* slopefield:: Slope fields - - -Graphical User Interface - -* GUI Installation:: Installing `xasy' -* GUI Usage:: - - -File: asymptote.info, Node: Description, Next: Installation, Prev: Top, Up: Top - -1 Description -************* - -`Asymptote' is a powerful descriptive vector graphics language that -provides a mathematical coordinate-based framework for technical -drawings. Labels and equations are typeset with `LaTeX', for overall -document consistency, yielding the same high-quality level of -typesetting that `LaTeX' provides for scientific text. By default it -produces `PostScript' output, but it can also generate any format that -the `ImageMagick' package can produce. - - A major advantage of `Asymptote' over other graphics packages is -that it is a high-level programming language, as opposed to just a -graphics program: it can therefore exploit the best features of the -script (command-driven) and graphical-user-interface (GUI) methods for -producing figures. The rudimentary GUI `xasy' included with the package -allows one to move script-generated objects around. To make `Asymptote' -accessible to the average user, this GUI is currently being developed -into a full-fledged interface that can generate objects directly. -However, the script portion of the language is now ready for general -use by users who are willing to learn a few simple `Asymptote' graphics -commands (*note Drawing commands::). - - `Asymptote' is mathematically oriented (e.g. one can use complex -multiplication to rotate a vector) and uses `LaTeX' to do the -typesetting of labels. This is an important feature for scientific -applications. It was inspired by an earlier drawing program (with a -weaker syntax and capabilities) called `MetaPost'. - - The `Asymptote' vector graphics language provides: - - * a standard for typesetting mathematical figures, just as - TeX/`LaTeX' is the de-facto standard for typesetting equations. - - * `LaTeX' typesetting of labels, for overall document consistency; - - * a natural coordinate-based framework for technical drawings, - inspired by `MetaPost', with a much cleaner, powerful C++-like - programming syntax; - - * compilation of figures into virtual machine code for speed, without - sacrificing portability; - - * the power of a script-based language coupled to the convenience of - a GUI; - - * customization using its own C++-like graphics programming language; - - * sensible defaults for graphical features, with the ability to - override; - - * a high-level mathematically oriented interface to the `PostScript' - language for vector graphics, including affine transforms and - complex variables; - - * functions that can create new (anonymous) functions; - - * deferred drawing that uses the simplex method to solve overall size - constraint issues between fixed-sized objects (labels and - arrowheads) and objects that should scale with figure size; - - - Many of the features of `Asymptote' are written in the `Asymptote' -language itself. While the stock version of `Asymptote' is designed for -mathematics typesetting needs, one can write `Asymptote' modules that -tailor it to specific applications. A scientific graphing module has -already been written (*note graph::). Examples of `Asymptote' code and -output, including animations, are available at - - `http://asymptote.sourceforge.net/gallery/'. - Links to many external resources, including an excellent user-written -`Asymptote' tutorial can be found at - - `http://asymptote.sourceforge.net/links.html'. - - -File: asymptote.info, Node: Installation, Next: Tutorial, Prev: Description, Up: Top - -2 Installation -************** - -* Menu: - -* UNIX binary distributions:: Prebuilt `UNIX' binaries -* MacOS X binary distributions:: Prebuilt `MacOS X' binaries -* Microsoft Windows:: Prebuilt `Microsoft Windows' binary -* Configuring:: Configuring `Asymptote' for your system -* Search paths:: Where `Asymptote' looks for your files -* Compiling from UNIX source:: Building `Asymptote' from scratch -* Editing modes:: Convenient `emacs' and `vim' modes -* Subversion:: -* Uninstall:: Goodbye, `Asymptote'! - - After following the instructions for your specific distribution, -please see also *note Configuring::. - -We recommend subscribing to new release announcements at - - `http://freshmeat.net/projects/asy' - Users may also wish to monitor the `Asymptote' forum: - - `http://sourceforge.net/forum/monitor.php?forum_id=409349' - - -File: asymptote.info, Node: UNIX binary distributions, Next: MacOS X binary distributions, Up: Installation - -2.1 UNIX binary distributions -============================= - -We release both `tgz' and RPM binary distributions of `Asymptote'. The -root user can install the `Linux i386' `tgz' distribution of version -`x.xx' of `Asymptote' with the commands: -tar -C / -zxf asymptote-x.xx.i386.tgz -texhash - The `texhash' command, which installs LaTeX style files, is optional. -The executable file will be `/usr/local/bin/asy') and example code will -be installed by default in `/usr/local/share/doc/asymptote/examples'. - -Fedora users can easily install the most recent version of `Asymptote' -with the command -yum --enablerepo=rawhide install asymptote - -To install the latest version of `Asymptote' on a Debian-based -distribution (e.g. Ubuntu, Mepis, Linspire) follow the instructions for -compiling from `UNIX' source (*note Compiling from UNIX source::). -Alternatively, Debian users can install one of Hubert Chan's prebuilt -`Asymptote' binaries from - - `http://ftp.debian.org/debian/pool/main/a/asymptote' - - -File: asymptote.info, Node: MacOS X binary distributions, Next: Microsoft Windows, Prev: UNIX binary distributions, Up: Installation - -2.2 MacOS X binary distributions -================================ - -`MacOS X' users can either compile the `UNIX' source code (*note -Compiling from UNIX source::) or install the contributed `Asymptote' -binary available at - -`http://www.hmug.org/pub/MacOS_X/X/Applications/Publishing/asymptote/' - -Because these preconfigured binary distributions have strict -architecture and library dependencies that many installations do not -satisfy, we recommend installing `Asymptote' directly from the official -source: - - `http://sourceforge.net/project/showfiles.php?group_id=120000' - -Note that many `MacOS X' (and FreeBSD) systems inexplicably ship with -an extremely old GNU `readline' version (4.1, dated 21 March 2000). For -full interactive functionality, `readline' version 4.2 or later (16 -April 2001) is required. - - -File: asymptote.info, Node: Microsoft Windows, Next: Configuring, Prev: MacOS X binary distributions, Up: Installation - -2.3 Microsoft Windows -===================== - -Users of the `Microsoft Windows' operating system can install the -self-extracting `Asymptote' executable `asymptote-x.xx-setup.exe', -where `x.xx' denotes the latest version. - - A working TeX implementation (such as the one available at -`http://www.miktex.org') will be required to typeset labels. You will -also need to install `GPL Ghostscript' from -`http://sourceforge.net/projects/ghostscript/'. To view the default -`PostScript' output, you can install the program `gsview' available from -`http://www.cs.wisc.edu/~ghost/gsview/'. - - The `ImageMagick' package from - - `http://www.imagemagick.org/script/binary-releases.php' - -is required to support output formats other than EPS and PDF (*note -convert::). The `Python' 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 the configuration file (by default, `.asy/config.asy' in the user's -home directory or `%USERPROFILE%\.asy\config.asy' under `MSDOS'); *note -configuration file::. Here are the default values of several important -configuration variables under `UNIX': - - -import settings; -psviewer="gv"; -pdfviewer="acroread"; -gs="gs"; -python=""; - -The (installation-dependent) default values of these configuration -variables under `MSDOS' are determined automatically from the -`Microsoft Windows' registry. - - For PDF format output, the `gs' setting specifies the location of -the `PostScript'-to-PDF processor `Ghostscript', available from -`http://sourceforge.net/projects/ghostscript/'. - - The setting `pdfviewer' specifies the location of the PDF viewer. On -`UNIX' systems, to support automatic document reloading in `Adobe -Reader', we recommend copying the file `reload.js' from the `Asymptote' -system directory (by default, `/usr/local/share/asymptote' under `UNIX' -to `~/.adobe/Acrobat/x.x/JavaScripts/', where `x.x' represents the -appropriate `Adobe Reader' version number. The automatic document -reload feature must then be explicitly enabled by putting -import settings; -pdfreload=true; -pdfreloadOptions="-tempFile"; - in the `Asymptote' configuration file. This reload feature is not -useful under `MSDOS' since the document cannot be updated anyway on -that operating system until it is first closed by `Adobe Reader'. - - The graphical user interface may also require setting the variable -`python' if `Python' is installed in a nonstandard location. - - The configuration variable `dir' can be used to adjust the search -path (*note Search paths::). - - By default, `Asymptote' attempts to center the figure on the page, -assuming that the paper type is `letter'. The default paper type may be -changed to `a4' with the configuration variable `papertype'. Alignment -to other paper sizes can be obtained by setting the configuration -variables `paperwidth' and `paperheight'. - - The following configuration variables normally do not require -adjustment: -texpath -texcommand -texdvicommand -dvips -convert -display -animate -xasy - The `texdvicommand' is used for `3D' label typesetting, which requires -`dvips' output. An empty string indicates the default setting of -`latex'/`tex', depending on the setting of `texengine'. - - 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 `Properties' from the popup menu; - - 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' (separated by `:' under UNIX and `;' under `MSDOS'); - - 3. The directory `.asy' in the user's home directory - (`%USERPROFILE%\.asy' under `MSDOS'); - - 4. The `Asymptote' system directory (by default, - `/usr/local/share/asymptote' under `UNIX' and `C:\Program - Files\Asymptote' under `MSDOS'). - - -File: asymptote.info, Node: Compiling from UNIX source, Next: Editing modes, Prev: Search paths, Up: Installation - -2.6 Compiling from UNIX source -============================== - -To compile and install a `UNIX' executable from a source release -`x.xx', first execute the commands: -gunzip asymptote-x.xx.src.tgz -tar -xf asymptote-x.xx.src.tar -cd asymptote-x.xx - By default the system version of the Boehm garbage collector will be -used; if it is old we recommend first putting -`http://www.hpl.hp.com/personal/Hans_Boehm/gc/gc_source/gc-7.1.tar.gz' -in the `Asymptote' source directory. - -If your graphics card supports multisampling, we recommend using SVN -revision 761 (or later) of `freeglut' to support antialiasing in -`Asymptote''s adaptive `OpenGL' 3D renderer (`MacOS X' users can skip -this step since `Asymptote' is configured to use the native glut -library on that platform). Download - - `http://freeglut.svn.sourceforge.net/viewvc/freeglut/trunk/freeglut/freeglut.tar.gz' - and type (as the root user): -tar -zxf freeglut.tar.gz -cd freeglut -sh autogen.sh -./configure --prefix=/usr -make install -cd .. - Then compile `Asymptote' with the commands -./configure -make all -make install - Be sure to use GNU `make' (on non-GNU systems this command may be -called `gmake'). To build the documentation, you may need to install -the `texinfo-tex' package. If you get errors from a broken `texinfo' or -`pdftex' installation, simply put - - `http://asymptote.sourceforge.net/asymptote.pdf' - in the directory `doc' and repeat the command `make all'. - -For a (default) system-wide installation, the last command should be -done as the root user. To install without root privileges, change the -`./configure' command to -./configure --prefix=$HOME/asymptote - One can disable use of the Boehm garbage collector by configuring with -`./configure --disable-gc'. For a list of other configuration options, -say `./configure --help'. For example, one can tell configure to look -for header files and libraries in nonstandard locations: -./configure CFLAGS=-I/opt/usr/include LDFLAGS=-L/opt/usr/lib - - If you are compiling `Asymptote' with `gcc', you will need a -relatively recent version (e.g. 3.4.4 or later). For full interactive -functionality, you will need version 4.2 or later of the GNU `readline' -library. The file `gcc3.3.2curses.patch' in the `patches' directory can -be used to patch the broken curses.h header file (or a local copy -thereof in the current directory) on some `AIX' and `IRIX' systems. - - The `FFTW' library is only required if you want `Asymptote' to be -able to take Fourier transforms of data (say, to compute an audio power -spectrum). The `GSL' library is only required if you require the -special functions that it supports. - - If you don't want to install `Asymptote' system wide, just make sure -the compiled binary `asy' and GUI script `xasy' are in your path and -set the configuration variable `dir' to point to the directory `base' -(in the top level directory of the `Asymptote' source code). - - -File: asymptote.info, Node: Editing modes, Next: Subversion, Prev: Compiling from UNIX source, Up: Installation - -2.7 Editing modes -================= - -Users of `emacs' can edit `Asymptote' code with the mode `asy-mode', -after enabling it by putting the following lines in their `.emacs' -initialization file, replacing `ASYDIR' with the location of the -`Asymptote' system directory (by default, `/usr/local/share/asymptote' -or `C:\Program Files\Asymptote' under `MSDOS'): -(add-to-list 'load-path "ASYDIR") -(autoload 'asy-mode "asy-mode.el" "Asymptote major mode." t) -(autoload 'lasy-mode "asy-mode.el" "hybrid Asymptote/Latex major mode." t) -(autoload 'asy-insinuate-latex "asy-mode.el" "Asymptote insinuate LaTeX." t) -(add-to-list 'auto-mode-alist '("\\.asy$" . asy-mode)) - - Particularly useful key bindings in this mode are `C-c C-c', which -compiles and displays the current buffer, and the key binding `C-c ?', -which shows the available function prototypes for the command at the -cursor. For full functionality you should also install the Apache -Software Foundation package `two-mode-mode': - - `http://www.dedasys.com/freesoftware/files/two-mode-mode.el' - Once installed, you can use the hybrid mode `lasy-mode' to edit a -LaTeX file containing embedded `Asymptote' code (*note LaTeX usage::). -This mode can be enabled within `latex-mode' with the key sequence `M-x -lasy-mode <RET>'. On `UNIX' systems, additional keywords will be -generated from all `asy' files in the space-separated list of -directories specified by the environment variable `ASYMPTOTE_SITEDIR'. -Further documentation of `asy-mode' is available within `emacs' by -pressing the sequence keys `C-h f asy-mode <RET>'. - - Fans of `vim' can customize `vim' for `Asymptote' with - -`cp /usr/local/share/asymptote/asy.vim ~/.vim/syntax/asy.vim' - -and add the following to their `~/.vimrc' file: -augroup filetypedetect -au BufNewFile,BufRead *.asy setf asy -augroup END -filetype plugin on - - If any of these directories or files don't exist, just create them. -To set `vim' up to run the current asymptote script using `:make' just -add to `~/.vim/ftplugin/asy.vim': -setlocal makeprg=asy\ % -setlocal errorformat=%f:\ %l.%c:\ %m - - -File: asymptote.info, Node: Subversion, Next: Uninstall, Prev: Editing modes, Up: Installation - -2.8 Subversion (SVN) -==================== - -The following commands are needed to install the latest development -version of `Asymptote' using Subversion: -svn co http://asymptote.svn.sourceforge.net/svnroot/asymptote/trunk/asymptote -cd asymptote -./autogen.sh -./configure -make all -make install - -To compile without optimization, use the command `make CFLAGS=-g'. - - -File: asymptote.info, Node: Uninstall, Prev: Subversion, Up: Installation - -2.9 Uninstall -============= - -To uninstall an `Linux i386' binary distribution, use the commands -tar -zxvf asymptote-x.xx.i386.tgz | xargs --replace=% rm /% -texhash - -To uninstall all `Asymptote' files installed from a source -distribution, use the command -make uninstall - - -File: asymptote.info, Node: Tutorial, Next: Drawing commands, Prev: Installation, Up: Top - -3 Tutorial -********** - -_An excellent user-written `Asymptote' tutorial is also available from_ - - `http://www.artofproblemsolving.com/Wiki/index.php/Asymptote:_Basics' - -To draw a line from coordinate (0,0) to coordinate (100,100) using -`Asymptote''s interactive mode, type at the command prompt: -asy -draw((0,0)--(100,100)); - - - -The units here are `PostScript' "big points" (1 `bp' = 1/72 `inch'); -`--' means join with a linear segment. In `Asymptote' coordinates like -`(0,0)' and `(1000,100)' are called _pairs_. - - At this point you can type in further draw commands, which will be -added to the displayed figure, or type `quit' to exit interactive mode. -You can use the arrow keys in interactive mode to edit previous lines -(assuming that you have support for the GNU `readline' library -enabled). 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::. - - In batch mode, `Asymptote' reads commands directly from a file. To -try this out, type - -draw((0,0)--(100,100)); - into a file, say test.asy. Then execute this file with the `MSDOS' or -`UNIX' command -asy -V test - `MSDOS' users can drag and drop the file onto the Desktop `asy' icon -or make `Asymptote' the default application for files with the -extension `asy'. - -The `-V' option opens up a `PostScript' viewer window so you can -immediately view the encapsulated `PostScript' output. By default the -output will be written to the file `test.eps'; the prefix of the output -file may be changed with the `-o' command-line option. - - One can draw a line with more than two points and create a cyclic -path like this square: - -draw((0,0)--(100,0)--(100,100)--(0,100)--cycle); - - - -It is often inconvenient to work directly with `PostScript' coordinates. -The next example draws a unit square scaled to width 101 bp and height -101 bp. The output is identical to that of the previous example. -size(101,101); -draw((0,0)--(1,0)--(1,1)--(0,1)--cycle); - - For convenience, the path `(0,0)--(1,0)--(1,1)--(0,1)--cycle' may be -replaced with the predefined variable `unitsquare', or equivalently, -`box((0,0),(1,1))'. - - One can also specify the size in `pt' (1 `pt' = 1/72.27 `inch'), -`cm', `mm', or `inches'. 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(0,3cm); -draw(unitsquare); - - - -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(1cm,2cm); -draw(unitsquare); - - Adding labels is easy in `Asymptote'; one specifies the label as a -double-quoted `LaTeX' string, a coordinate, and an optional alignment -direction: - -size(0,3cm); -draw(unitsquare); -label("$A$",(0,0),SW); -label("$B$",(1,0),SE); -label("$C$",(1,1),NE); -label("$D$",(0,1),NW); - - - -`Asymptote' uses the standard compass directions `E=(1,0)', `N=(0,1)', -`NE=unit(N+E)', and `ENE=unit(E+NE)', etc., which along with the -directions `up', `down', `right', and `left' are defined as pairs in -the `Asymptote' base module `plain'. A user who has a local variable -named `E' may access the compass direction `E' by prefixing it with the -name of the module where it is defined: `plain.E'. - - This example draws a path that approximates a quarter circle: - -size(100,0); -draw((1,0){up}..{left}(0,1)); - - - -In general, a path is specified as a list of pairs (or other paths) -interconnected with `--', which denotes a straight line segment, or -`..', which denotes a cubic spline. Specifying a final node `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; - - Each interior node of a cubic spline may be given a direction prefix -or suffix `{dir}': the direction of the pair `dir' specifies the -direction of the incoming or outgoing tangent, respectively, to the -curve at that node. Exterior nodes may be given direction specifiers -only on their interior side. - - A cubic spline between the node z_0, with postcontrol point c_0, and -the node z_1, with precontrol point c_1, is computed as the Bezier curve - - - -As illustrated in the diagram below, the third-order midpoint (m_5) -constructed from two endpoints z_0 and z_1 and two control points c_0 -and c_1, is the point corresponding to t=1/2 on the Bezier curve formed -by the quadruple (z_0, c_0, c_1, z_1). This allows one to recursively -construct the desired curve, by using the newly extracted third-order -midpoint as an endpoint and the respective second- and first-order -midpoints as control points: - - - -Here m_0, m_1 and m_2 are the first-order midpoints, m_3 and m_4 are -the second-order midpoints, and m_5 is the third-order midpoint. The -curve is then constructed by recursively applying the algorithm to -(z_0, m_0, m_3, m_5) and (m_5, m_4, m_2, z_1). - - In fact, an analogous property holds for points located at any -fraction t in [0,1] of each segment, not just for midpoints (t=1/2). - - The Bezier curve constructed in this manner has the following -properties: - * It is entirely contained in the convex hull of the given four - points. - - * It starts heading from the first endpoint to the first control - point and finishes heading from the second control point to the - second endpoint. - - - The user can specify explicit control points between two nodes like -this: -draw((0,0)..controls (0,100) and (100,100)..(100,0)); - - However, it is usually more convenient to just use the `..' -operator, which tells `Asymptote' to choose its own control points -using the algorithms described in Donald Knuth's monograph, The -MetaFontbook, Chapter 14. The user can still customize the guide (or -path) by specifying direction, tension, and curl values. - - The higher the tension, the straighter the curve is, and the more it -approximates a straight line. One can change the spline tension from -its default value of 1 to any real value greater than or equal to 0.75 -(cf. John D. Hobby, Discrete and Computational Geometry 1, 1986): -draw((100,0)..tension 2 ..(100,100)..(0,100)); -draw((100,0)..tension 2 and 1 ..(100,100)..(0,100)); -draw((100,0)..tension atleast 1 ..(100,100)..(0,100)); - - The curl parameter specifies the curvature at the endpoints of a path -(0 means straight; the default value of 1 means approximately circular): -draw((100,0){curl 0}..(100,100)..{curl 0}(0,100)); - - The `MetaPost ...' path connector, which requests, when possible, an -inflection-free curve confined to a triangle defined by the endpoints -and directions, is implemented in `Asymptote' as the convenient -abbreviation `::' for `..tension atleast 1 ..' (the ellipsis `...' is -used in `Asymptote' to indicate a variable number of arguments; *note -Rest arguments::). For example, compare - -draw((0,0){up}..(100,25){right}..(200,0){down}); - - -with - -draw((0,0){up}::(100,25){right}::(200,0){down}); - - - -The `---' connector is an abbreviation for `..tension atleast -infinity..' and the `&' connector concatenates two paths, after first -stripping off the last node of the first path (which normally should -coincide with the first node of the second path). - - An `Asymptote' path, being connected, is equivalent to a `Postscript -subpath'. The `^^' binary operator, which requests that the pen be -moved (without drawing or affecting endpoint curvatures) from the final -point of the left-hand path to the initial point of the right-hand -path, may be used to group several `Asymptote' paths into a `path[]' -array (equivalent to a `PostScript' path): - -size(0,100); -path unitcircle=E..N..W..S..cycle; -path g=scale(2)*unitcircle; -filldraw(unitcircle^^g,evenodd+yellow,black); - - - -The `PostScript' even-odd fill rule here specifies that only the region -bounded between the two unit circles is filled (*note fillrule::). In -this example, the same effect can be achieved by using the default zero -winding number fill rule, if one is careful to alternate the -orientation of the paths: -filldraw(unitcircle^^reverse(g),yellow,black); - - The `^^' operator is used by the `box(triple, triple)' function in -`three.asy' to construct the edges of a cube `unitbox' without -retracing steps: - -import three; -dotgranularity=0; // Render dots as spheres. - -currentprojection=orthographic(5,4,2,center=true); - -size(5cm); -size3(3cm,5cm,8cm); - -draw(unitbox); - -dot(unitbox,red); - -label("$O$",(0,0,0),NW); -label("(1,0,0)",(1,0,0),S); -label("(0,1,0)",(0,1,0),E); -label("(0,0,1)",(0,0,1),Z); - - - -See section *note graph:: (or the online `Asymptote' gallery and -external links posted at `http://asymptote.sourceforge.net') for -further examples, including two and three-dimensional scientific -graphs. Additional examples have been posted by Philippe Ivaldi at -`http://piprim.tuxfamily.org/asymptote/'. - - -File: asymptote.info, Node: Drawing commands, Next: Programming, Prev: Tutorial, Up: Top - -4 Drawing commands -****************** - -All of `Asymptote''s graphical capabilities are based on four primitive -commands. The three `PostScript' drawing commands `draw', `fill', and -`clip' add objects to a picture in the order in which they are -executed, with the most recently drawn object appearing on top. The -labeling command `label' can be used to add text labels and external -EPS images, which will appear on top of the `PostScript' objects (since -this is normally what one wants), but again in the relative order in -which they were executed. After drawing objects on a picture, the -picture can be output with the `shipout' function (*note shipout::). - - If you wish to draw `PostScript' objects on top of labels (or -verbatim `tex' commands; *note tex::), the `layer' command may be used -to start a new `PostScript/LaTeX' layer: -void layer(picture pic=currentpicture); - - The `layer' function gives one full control over the order in which -objects are drawn. Layers are drawn sequentially, with the most recent -layer appearing on top. Within each layer, labels, images, and verbatim -`tex' commands are always drawn after the `PostScript' objects in that -layer. - - While some of these drawing commands take many options, they all -have sensible default values (for example, the picture argument -defaults to currentpicture). - -* Menu: - -* draw:: Draw a path on a picture or frame -* fill:: Fill a cyclic path on a picture or frame -* clip:: Clip a picture or frame to a cyclic path -* label:: Label a point on a picture - - -File: asymptote.info, Node: draw, Next: fill, Up: Drawing commands - -4.1 draw -======== - -void draw(picture pic=currentpicture, Label L="", path g, - align align=NoAlign, pen p=currentpen, - arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin, - Label legend="", marker marker=nomarker); - -Draw the path `g' on the picture `pic' using pen `p' for drawing, with -optional drawing attributes (Label `L', explicit label alignment -`align', arrows and bars `arrow' and `bar', margins `margin', legend, -and markers `marker'). Only one parameter, the path, is required. For -convenience, the arguments `arrow' and `bar' may be specified in either -order. The argument `legend' is a Label to use in constructing an -optional legend entry. - - Bars are useful for indicating dimensions. The possible values of -`bar' are `None', `BeginBar', `EndBar' (or equivalently `Bar'), and -`Bars' (which draws a bar at both ends of the path). Each of these bar -specifiers (except for `None') will accept an optional real argument -that denotes the length of the bar in `PostScript' coordinates. The -default bar length is `barsize(pen)'. - - The possible values of `arrow' are `None', `Blank' (which draws no -arrows or path), `BeginArrow', `MidArrow', `EndArrow' (or equivalently -`Arrow'), and `Arrows' (which draws an arrow at both ends of the path). -All of the arrow specifiers except for `None' and `Blank' may be given -the optional arguments arrowhead `arrowhead' (one of the predefined -arrowhead styles `DefaultHead', `SimpleHead', `HookHead', `TeXHead'), -real `size' (arrowhead size in `PostScript' coordinates), real `angle' -(arrowhead angle in degrees), filltype `filltype' (one of `FillDraw', -`Fill', `NoFill', `UnFill', `Draw') and (except for `MidArrow' and -`Arrows') a relative real `position' along the path (an `arctime') 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, - pen penb, pair 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, - pen penb, pair b, real rb); - Illustrations of radial shading are provided in the example files -`shade.asy', `ring.asy', and `shadestroke.asy'. - - Gouraud shading using fill rule `fillrule' and the vertex colors in -the pen array `p' on a triangular lattice defined by the vertices `z' -and edge flags `edges' is implemented with -void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, pair[] z, - int[] edges); -void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, int[] edges); - In the second form, the elements of `z' are taken to be successive -nodes of path `g'. The pens in `p' must belong to the same color space. -Illustrations of Gouraud shading are provided in the example file -`Gouraud.asy' and in the solid geometry module `solids.asy'. The edge -flags used in Gouraud shading are documented here: - - `http://partners.adobe.com/public/developer/en/ps/sdk/TN5600.SmoothShading.pdf'. - - Tensor product shading using fill rule `fillrule' on patches bounded -by the n cyclic paths of length 4 in path array `b', using the vertex -colors specified in the n \times 4 pen array `p' and internal control -points in the n \times 4 array `z', is implemented with -void tensorshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[][] p, path[] b=g, - pair[][] z=new pair[][]); - If the array `z' is empty, Coons shading, in which the color control -points are calculated automatically, is used. The pens in `p' must -belong to the same color space. A simpler interface for the case of a -single patch (n=1) is also available: -void tensorshade(picture pic=currentpicture, path g, bool stroke=false, - pen fillrule=currentpen, pen[] p, path b=g, - pair[] z=new pair[]); - One can also smoothly shade the regions between consecutive paths of a -sequence using a given array of pens: -void draw(picture pic=currentpicture, path[] g, pen[] p); - Illustrations of tensor product and Coons shading are provided in the -example files `tensor.asy', `Coons.asy', `BezierSurface.asy', and -`rainbow.asy'. - - More general shading possibilities are available with the `pdflatex', -`context', and `pdftex' TeX engines: the routine -void functionshade(picture pic=currentpicture, path[] g, bool stroke=false, - pen fillrule=currentpen, string shader); - shades on picture `pic' the interior of path `g' according to fill -rule `fillrule' using the `PostScript' calculator routine specified by -the string `shader'; this routine takes 2 arguments, each in [0,1], and -returns `colors(fillrule).length' color components. Function shading -is illustrated in the example `functionshading.asy'. - - The following routine uses `evenodd' clipping together with the `^^' -operator to unfill a region: - -void unfill(picture pic=currentpicture, path g); - - -File: asymptote.info, Node: clip, Next: label, Prev: fill, Up: Drawing commands - -4.3 clip -======== - -void clip(picture pic=currentpicture, path g, stroke=false, - pen fillrule=currentpen); - -Clip the current contents of picture `pic' to the region bounded by the -path `g', using fill rule `fillrule' (*note fillrule::). If -`stroke=true', the clipped portion is the same as the region that would -be drawn with `draw(pic,g,fillrule+zerowinding)'; in this case the path -`g' need not be cyclic. For an illustration of picture clipping, see -the first example in *note LaTeX usage::. - - -File: asymptote.info, Node: label, Prev: clip, Up: Drawing commands - -4.4 label -========= - -void label(picture pic=currentpicture, Label L, pair position, - align align=NoAlign, pen p=nullpen, 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'. If `p' is `nullpen', the pen specified within the -Label, which defaults to `currentpen', will be used. 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'. 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=nullpen, filltype filltype=NoFill); - By default the label will be positioned at the midpoint of the path. -An alternative label location (an `arctime' value between 0 and -`length(g)' *note arctime::) may be specified as real value for -`position' in constructing the Label. The position `Relative(real)' -specifies a location relative to the total arclength of the path. These -convenient abbreviations are predefined: -position BeginPoint=Relative(0); -position MidPoint=Relative(0.5); -position EndPoint=Relative(1); - - Path labels are aligned in the direction `align', which may be -specified as an absolute compass direction (pair) or a direction -`Relative(pair)' measured relative to a north axis in the local -direction of the path. For convenience `LeftSide', `Center', and -`RightSide' are defined as `Relative(W)', `Relative((0,0))', and -`Relative(E)', respectively. Multiplying `LeftSide', `Center', -`RightSide' on the left by a real scaling factor will move the label -further away from or closer to the path. - - A label with a fixed-size arrow of length `arrowlength' pointing to -`b' from direction `dir' can be produced with the routine -void arrow(picture pic=currentpicture, Label L="", pair b, pair dir, - real length=arrowlength, align align=NoAlign, - pen p=currentpen, arrowbar arrow=Arrow, margin margin=EndMargin); - If no alignment is specified (either in the Label or as an explicit -argument), the optional Label will be aligned in the direction `dir', -using margin `margin'. - - The function `string graphic(string name, string options="")' -returns a string that can be used to include an encapsulated -`PostScript' (EPS) file. Here, `name' is the name of the file to -include and `options' is a string containing a comma-separated list of -optional bounding box (`bb=llx lly urx ury'), width (`width=value'), -height (`height=value'), rotation (`angle=value'), scaling -(`scale=factor'), clipping (`clip=bool'), and draft mode (`draft=bool') -parameters. The `layer()' function can be used to force future objects -to be drawn on top of the included image: -label(graphic("file.eps","width=1cm"),(0,0),NE); -layer(); - - The `string baseline(string s, string template="\strut")' function -can be used to enlarge the bounding box of labels to match a given -template, so that their baselines will be typeset on a horizontal line. -See `Pythagoras.asy' for an example. - - One can prevent labels from overwriting one another with the -`overwrite' pen attribute (*note overwrite::). - - The structure `object' defined in `plain_Label.asy' allows Labels -and frames to be treated in a uniform manner. A group of objects may -be packed together into single frame with the routine -frame pack(pair align=2S ... object inset[]); - To draw or fill a box (or ellipse or other path) around a Label and -return the bounding object, use one of the routines -object draw(picture pic=currentpicture, Label L, envelope e, - real xmargin=0, real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); -object draw(picture pic=currentpicture, Label L, envelope e, pair position, - real xmargin=0, real ymargin=xmargin, pen p=currentpen, - filltype filltype=NoFill, bool above=true); - Here `envelope' is a boundary-drawing routine such as `box', -`roundbox', or `ellipse' defined in `plain_boxes.asy' (*note -envelope::). - - The function `path[] texpath(Label L)' returns the path array that -TeX would fill to draw the Label `L'. - - The `string minipage(string s, width=100pt)' function can be used to -format string `s' into a paragraph of width `width'. This example uses -`minipage', `clip', and `graphic' to produce a CD label: - - -size(11.7cm,11.7cm); -asy(nativeformat(),"logo"); -fill(unitcircle^^(scale(2/11.7)*unitcircle), - evenodd+rgb(124/255,205/255,124/255)); -label(scale(1.1)*minipage( -"\centering\scriptsize \textbf{\LARGE {\tt Asymptote}\\ -\smallskip -\small The Vector Graphics Language}\\ -\smallskip -\textsc{Andy Hammerlindl, John Bowman, and Tom Prince} -http://asymptote.sourceforge.net\\ -",8cm),(0,0.6)); -label(graphic("logo."+nativeformat(),"height=7cm"),(0,-0.22)); -clip(unitcircle^^(scale(2/11.7)*unitcircle),evenodd); - - -File: asymptote.info, Node: Programming, Next: LaTeX usage, Prev: Drawing commands, Up: Top - -5 Programming -************* - -Here is a short introductory example to the `Asymptote' programming -language that highlights the similarity of its control structures with -those of C, C++, and Java: -// This is a comment. - -// Declaration: Declare x to be a real variable; -real x; - -// Assignment: Assign the real variable x the value 1. -x=1.0; - -// Conditional: Test if x equals 1 or not. -if(x == 1.0) { - write("x equals 1.0"); -} else { - write("x is not equal to 1.0"); -} - -// Loop: iterate 10 times -for(int i=0; i < 10; ++i) { - write(i); -} - - `Asymptote' supports `while', `do', `break', and `continue' -statements just as in C/C++. It also supports the Java-style shorthand -for iterating over all elements of an array: - -// Iterate over an array -int[] array={1,1,2,3,5}; -for(int k : array) { - write(k); -} - In addition, it supports many features beyond the ones found in those -languages. - -* Menu: - -* Data types:: void, bool, int, real, pair, triple, string -* Paths and guides:: -* 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' packages -* Static:: Where to allocate your variable? - - -File: asymptote.info, Node: Data types, Next: Paths and guides, Up: Programming - -5.1 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'. - -`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(pair z, pair w)' - returns the dot product `z.x*w.x+z.y*w.y'; - - `pair minbound(pair z, pair w)' - returns `(min(z.x,w.x),min(z.y,w.y))'; - - `pair maxbound(pair z, pair w)' - returns `(max(z.x,w.x),max(z.y,w.y))'. - - -`triple' - an ordered triple of real components `(x,y,z)' used for - three-dimensional drawings. The respective components of a triple - `v' can read as `v.x', `v.y', and `v.z'. The implicit initializer - for triples is `(0.0,0.0,0.0)'. - - Here are the built-in functions for triples: - `real length(triple v)' - returns the length `|v|' of the vector `v'. A synonym for - `length(triple)' is `abs(triple)'; - - `real polar(triple v, bool warn=true)' - returns the colatitude of `v' measured from the z axis in - radians or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real azimuth(triple v, bool warn=true)' - returns the longitude of `v' measured from the x axis in - radians or `0' if `warn' is `false' and `v.x=v.y=0' (rather - than producing an error); - - `real colatitude(triple v, bool warn=true)' - returns the colatitude of `v' measured from the z axis in - degrees or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real latitude(triple v, bool warn=true)' - returns the latitude of `v' measured from the xy plane in - degrees or `0' if `warn' is `false' and `v=O' (rather than - producing an error); - - `real longitude(triple v, bool warn=true)' - returns the longitude of `v' measured from the x axis in - degrees or `0' if `warn' is `false' and `v.x=v.y=0' (rather - than producing an error); - - `triple unit(triple v)' - returns a unit triple in the direction of the triple `v'; - - `triple expi(real polar, real azimuth)' - returns a unit triple in the direction `(polar,azimuth)' - measured in radians; - - `triple dir(real colatitude, real longitude)' - returns a unit triple in the direction - `(colatitude,longitude)' measured in degrees; - - `real xpart(triple v)' - returns `v.x'; - - `real ypart(triple v)' - returns `v.y'; - - `real zpart(triple v)' - returns `v.z'; - - `real dot(triple u, triple v)' - returns the dot product `u.x*v.x+u.y*v.y+u.z*v.z'; - - `triple cross(triple u, triple v)' - returns the cross product - - `(u.y*v.z-u.z*v.y,u.z*v.x-u.x*v.z,u.x*v.y-v.x*u.y)'; - - `triple minbound(triple u, triple v)' - returns `(min(u.x,v.x),min(u.y,v.y),min(u.z,v.z))'; - - `triple maxbound(triple u, triple v)' - returns `(max(u.x,v.x),max(u.y,v.y),max(u.z,v.z)'). - - -`string' - a character string, implemented using the STL `string' class. - - Strings delimited by double quotes (`"') are subject to the - following mappings to allow the use of double quotes in TeX (e.g. - for using the `babel' package, *note babel::): - - * \" maps to " - - * \\ maps to \\ - - Strings delimited by single quotes (`'') have the same mappings as - character strings in ANSI `C': - - * \' maps to ' - - * \" maps to " - - * \? maps to ? - - * \\ maps to backslash - - * \a maps to alert - - * \b maps to backspace - - * \f maps to form feed - - * \n maps to newline - - * \r maps to carriage return - - * \t maps to tab - - * \v maps to vertical tab - - * \0-\377 map to corresponding octal byte - - * \x0-\xFF map to corresponding hexadecimal byte - - The implicit initializer for strings is the empty string `""'. - Strings may be concatenated with the `+' operator. In the following - string functions, position `0' denotes the start of the string: - `int length(string s)' - returns the length of the string `s'; - - `int find(string s, string t, int pos=0)' - returns the position of the first occurrence of string `t' in - string `s' at or after position `pos', or -1 if `t' is not a - substring of `s'; - - `int rfind(string s, string t, int pos=-1)' - returns the position of the last occurrence of string `t' in - string `s' at or before position `pos' (if `pos'=-1, at the - end of the string `s'), or -1 if `t' is not a substring of - `s'; - - `string insert(string s, int pos, string t)' - returns the string formed by inserting string `t' at position - `pos' in `s'; - - `string erase(string s, int pos, int n)' - returns the string formed by erasing the string of length `n' - (if `n'=-1, to the end of the string `s') at position `pos' - in `s'; - - `string substr(string s, int pos, int n=-1)' - returns the substring of `s' starting at position `pos' and - of length `n' (if `n'=-1, until the end of the string `s'); - - `string reverse(string s)' - returns the string formed by reversing string `s'; - - `string replace(string s, string before, string after)' - returns a string with all occurrences of the string `before' - in the string `s' changed to the string `after'; - - `string replace(string s, string[][] table)' - returns a string constructed by translating in string `s' all - occurrences of the string `before' in an array `table' of - string pairs {`before',`after'} to the corresponding string - `after'; - - `string[] split(string s, string delimiter)' - returns an array of strings obtained by splitting `s' into - substrings delimited by `delimiter'; - - `string format(string s, int n)' - returns a string containing `n' formatted according to the - C-style format string `s' using the current locale; - - `string format(string s, 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 TeX is used to typeset - scientific notation; - - `int hex(string s);' - casts a hexidecimal string `s' to an integer. - - `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); - - `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 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 - -5.2 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 @cindex @code{ellipse} - path ellipse(pair c, real a, real b) - { - return shift(c)*scale(a,b)*unitcircle; - } - - This example illustrates the use of all five guide connectors - discussed in *note Tutorial::: size(300,0); - pair[] z=new pair[10]; - - z[0]=(0,100); z[1]=(50,0); z[2]=(180,0); - - for(int n=3; n <= 9; ++n) - z[n]=z[n-3]+(200,0); - - path p=z[0]..z[1]---z[2]::{up}z[3] - &z[3]..z[4]--z[5]::{up}z[6] - &z[6]::z[7]---z[8]..{up}z[9]; - - draw(p,grey+linewidth(4mm)); - - dot(z); - - - - Here are some useful functions for paths: - - `int length(path p);' - This is the number of (linear or cubic) segments in path `p'. - If `p' is cyclic, this is the same as the number of nodes in - `p'. - - `int size(path p);' - This is the number of nodes in the path `p'. If `p' is - cyclic, this is the same as `length(p)'. - - `bool cyclic(path p);' - returns `true' iff path `p' is cyclic. - - `bool straight(path p, int i);' - returns `true' iff the segment of path `p' between node `i' - and node `i+1' is straight. - - `bool piecewisestraight(path p)' - returns `true' iff the path `p' is piecewise straight. - - `pair point(path p, int t);' - If `p' is cyclic, return the coordinates of node `t' mod - `length(p)'. Otherwise, return the coordinates of node `t', - unless `t' < 0 (in which case `point(0)' is returned) or `t' - > `length(p)' (in which case `point(length(p))' is returned). - - `pair point(path p, real t);' - This returns the coordinates of the point between node - `floor(t)' and `floor(t)+1' corresponding to the cubic spline - parameter `t-floor(t)' (*note Bezier::). 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::). - - `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'. - - `pair 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 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 the 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 inside(path p, pair z, pen fillrule=currentpen);' - returns `true' iff the point `z' is 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); - - - - 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 - -5.3 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); - - Various shades and mixtures of the grayscale primary colors - `black' and `white', RGB primary colors `red', `green', and - `blue', and RGB secondary colors `cyan', `magenta', and `yellow' - are defined as named colors, along with the CMYK primary colors - `Cyan', `Magenta', `Yellow', and `Black', in the module `plain': - - - - The standard 140 RGB `X11' colors can be imported with the command import x11colors; - and the standard 68 CMYK TeX colors can be imported with the - command import texcolors; - Note that there is some overlap between these two standards and - the definitions of some colors (e.g. `Green') actually disagree. - - `Asymptote' also comes with a `asycolors.sty' `LaTeX' package that - defines to `LaTeX' CMYK versions of `Asymptote''s predefined - colors, so that they can be used directly within `LaTeX' strings. - Normally, such colors are passed to `LaTeX' via a pen argument; - however, to change the color of only a portion of a string, say - for a slide presentation, (*note slide::) it may be desirable to - specify the color directly to `LaTeX'. This file can be passed to - `LaTeX' with the `Asymptote' command usepackage("asycolors"); - - The structure `hsv' defined in `plain_pens.asy' may be used to - convert between HSV and RGB spaces, where the hue `h' is an angle - in [0,360) and the saturation `s' and value `v' lie in `[0,1]': pen p=hsv(180,0.5,0.75); - write(p); // ([default], red=0.375, green=0.75, blue=0.75) - hsv q=p; - write(q.h,q.s,q.v); // 180 0.5 0.75 - - * Line types are specified with the function `pen linetype(string s, - real offset=0, bool scale=true, bool adjust=true)', where `s' is a - string of integer or real numbers separated by spaces. 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(""); - pen dotted=linetype("0 4"); - pen dashed=linetype("8 8"); - pen longdashed=linetype("24 8"); - pen dashdotted=linetype("8 8 0 8"); - pen longdashdotted=linetype("24 8 0 8"); - pen Dotted=dotted+1.0; - pen Dotted(pen p=currentpen) {return dotted+2*linewidth(p);} - - - - The default line type is `solid'; this may be changed with - `defaultpen(pen)'. The line type of a pen is returned by `int - linetype(pen p=currentpen)'. - - * 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' we define static void defaultpen(real w) {defaultpen(linewidth(w));} - static pen operator +(pen p, real w) {return p+linewidth(w);} - static 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 `fix-cm' package - available from - - `http://www.ctan.org/tex-archive/help/Catalogue/entries/fix-cm' - and included in recent `LaTeX' distributions). The font size and - line skip of a pen can be examined with the routines `real - fontsize(pen p=currentpen)' and `real lineskip(pen p=currentpen)', - respectively. - - * A pen using a specific `LaTeX' `NFSS' font is returned by calling - the function `pen font(string encoding, string family, string - series, string shape)'. The default setting, - `font("OT1","cmr","m","n")', corresponds to 12pt Computer Modern - Roman; this may be changed with `defaultpen(pen)'. The font - setting of a pen is returned by `string font(pen p=currentpen)'. - Support for standardized international characters is provided by - the `unicode' package (*note unicode::). - - Alternatively, one may select a fixed-size TeX font (on which - `fontsize' has no effect) like `"cmr12"' (12pt Computer Modern - Roman) or `"pcrr"' (Courier) using the function `pen font(string - name)'. An optional size argument can also be given to scale the - font to the requested size: `pen font(string name, real size)'. - - A nonstandard font command can be generated with `pen - fontcommand(string)'. - - A convenient interface to the following standard `PostScript' - fonts is also provided: pen AvantGarde(string series="m", string shape="n"); - pen Bookman(string series="m", string shape="n"); - pen Courier(string series="m", string shape="n"); - pen Helvetica(string series="m", string shape="n"); - pen NewCenturySchoolBook(string series="m", string shape="n"); - pen Palatino(string series="m", string shape="n"); - pen TimesRoman(string series="m", string shape="n"); - pen ZapfChancery(string series="m", string shape="n"); - pen Symbol(string series="m", string shape="n"); - pen ZapfDingbats(string series="m", string shape="n"); - - * The transparency of a pen can be changed with the command: pen opacity(real opacity=1, string blend="Compatible"); - The opacity can be varied from `0' (fully transparent) to the - default value of `1' (opaque), and `blend' specifies one of the - following foreground-background blending operations: "Compatible","Normal","Multiply","Screen","Overlay","SoftLight", - "HardLight","ColorDodge","ColorBurn","Darken","Lighten","Difference", - "Exclusion","Hue","Saturation","Color","Luminosity", - as described in - - `http://partners.adobe.com/public/developer/en/pdf/PDFReference16.pdf'. - Since `PostScript' does not support transparency, this feature is - only effective with the `-f pdf' output format option; other - formats can be produced from the resulting PDF file with the - `ImageMagick' `convert' program. Labels are always drawn with an - `opacity' of 1. A simple example of transparent filling is - provided in the example file `transparency.asy'. - - * `PostScript' commands within a `picture' may be used to create a - tiling pattern, identified by the string `name', for `fill' and - `draw' operations by adding it to the global `PostScript' frame - `currentpatterns', with optional left-bottom margin `lb' and - right-top margin `rt'. import patterns; - void add(string name, picture pic, pair lb=0, pair rt=0); - - To `fill' or `draw' using pattern `name', use the pen - `pattern("name")'. For example, rectangular tilings can be - constructed using the routines `picture tile(real Hx=5mm, real - Hy=0, pen p=currentpen, filltype filltype=NoFill)', `picture - checker(real Hx=5mm, real Hy=0, pen p=currentpen)', and `picture - brick(real Hx=5mm, real Hy=0, pen p=currentpen)' defined in - `patterns.asy': size(0,90); - import patterns; - - add("tile",tile()); - add("filledtilewithmargin",tile(6mm,4mm,red,Fill),(1mm,1mm),(1mm,1mm)); - add("checker",checker()); - add("brick",brick()); - - real s=2.5; - filldraw(unitcircle,pattern("tile")); - filldraw(shift(s,0)*unitcircle,pattern("filledtilewithmargin")); - filldraw(shift(2s,0)*unitcircle,pattern("checker")); - filldraw(shift(3s,0)*unitcircle,pattern("brick")); - - - - Hatch patterns can be generated with the routines `picture - hatch(real H=5mm, pair dir=NE, pen p=currentpen)', `picture - crosshatch(real H=5mm, pen p=currentpen)': size(0,100); - import patterns; - - add("hatch",hatch()); - add("hatchback",hatch(NW)); - add("crosshatch",crosshatch(3mm)); - - real s=1.25; - filldraw(unitsquare,pattern("hatch")); - filldraw(shift(s,0)*unitsquare,pattern("hatchback")); - filldraw(shift(2s,0)*unitsquare,pattern("crosshatch")); - - - - You may need to turn off aliasing in your `PostScript' viewer for - patterns to appear correctly. Custom patterns can easily be - constructed, following the examples in `patterns.asy'. The tiled - pattern can even incorporate shading (*note gradient shading::), - as illustrated in this example (not included in the manual because - not all printers support `PostScript' 3): size(0,100); - import patterns; - - real d=4mm; - picture tiling; - path square=scale(d)*unitsquare; - axialshade(tiling,square,white,(0,0),black,(d,d)); - fill(tiling,shift(d,d)*square,blue); - add("shadedtiling",tiling); - - filldraw(unitcircle,pattern("shadedtiling")); - - - - * One can specify a custom pen nib as an arbitrary polygonal path - with `pen makepen(path)'; this path represents the mark to be - drawn for paths containing a single point. This pen nib path can be - recovered from a pen with `path nib(pen)'. Unlike in `MetaPost', - the path need not be convex: - - size(200); - pen convex=makepen(scale(10)*polygon(8))+grey; - draw((1,0.4),convex); - draw((0,0)---(1,1)..(2,0)--cycle,convex); - - pen nonconvex=scale(10)* - makepen((0,0)--(0.25,-1)--(0.5,0.25)--(1,0)--(0.5,1.25)--cycle)+red; - draw((0.5,-1.5),nonconvex); - draw((0,-1.5)..(1,-0.5)..(2,-1.5),nonconvex); - - - - The value `nullpath' represents a circular pen nib (the default); - an elliptical pen can be achieved simply by multiplying the pen by - a transform: `yscale(2)*currentpen'. - - * One can prevent labels from overwriting one another by using the - pen attribute `overwrite', which takes a single argument: - - `Allow' - Allow labels to overwrite one another. This is the default - behaviour (unless overridden with `defaultpen(pen)'. - - `Suppress' - Suppress, with a warning, each label that would overwrite - another label. - - `SuppressQuiet' - Suppress, without warning, each label that would overwrite - another label. - - `Move' - Move a label that would overwrite another out of the way and - issue a warning. As this adjustment is during the final - output phase (in `PostScript' coordinates) it could result in - a larger figure than requested. - - `MoveQuiet' - Move a label that would overwrite another out of the way, - without warning. As this adjustment is during the final - output phase (in `PostScript' coordinates) it could result in - a larger figure than requested. - - - - The routine `defaultpen()' returns the current default pen -attributes. Calling the routine `resetdefaultpen()' resets all pen -default attributes to their initial values. - - -File: asymptote.info, Node: Transforms, Next: Frames and pictures, Prev: Pens, Up: Programming - -5.4 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 - -5.5 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="", - 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. - - 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. - - - 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 of - pen `p' with 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 `PostScript' bounds that picture `pic' would have - if it were currently fit to a frame using its default size - specification. If `user' is `false' the returned value is in - `PostScript' coordinates, otherwise it is in user coordinates. - - The function pair point(picture pic=currentpicture, pair dir, bool user=true); - is a convenient way of determining the point on the bounding box - of `pic' in the direction `dir' relative to its center, ignoring - the contributions from fixed-size objects (such as labels and - arrowheads). If `user' is `true' the returned value is in user - coordinates, otherwise it is in `PostScript' coordinates. - - The function pair truepoint(picture pic=currentpicture, pair dir, bool user=true); - is identical to `point', except that it also accounts for - fixed-size objects, using the scaling transform that picture `pic' - would have if currently fit to a frame using its default size - specification. If `user' is `true' the returned value is in user - coordinates, otherwise it is in `PostScript' coordinates. - - Sometimes it is useful to draw objects on separate pictures and - add one picture to another using the `add' function: void add(picture src, bool group=true, - filltype filltype=NoFill, bool above=true); - void add(picture dest, picture src, bool group=true, - filltype filltype=NoFill, bool above=true); - The first example adds `src' to `currentpicture'; the second one - adds `src' to `dest'. The `group' option specifies whether or not - the graphical user interface `xasy' should treat all of the - elements of `src' as a single entity (*note GUI::), `filltype' - requests optional background filling or clipping, and `above' - specifies whether to add `src' above or below existing objects. - - There are also routines to add a picture or frame `src' specified - in postscript coordinates to another picture `dest' (or - `currentpicture') about the user coordinate `position': void add(picture src, pair position, bool group=true, - filltype filltype=NoFill, bool above=true); - void add(picture dest, picture src, pair position, - bool group=true, filltype filltype=NoFill, bool above=true); - void add(picture dest=currentpicture, frame src, pair position=0, - bool group=true, filltype filltype=NoFill, bool above=true); - void add(picture dest=currentpicture, frame src, pair position, - pair align, bool group=true, filltype filltype=NoFill, - bool above=true); - - The optional `align' argument in the last three forms specifies a - direction to use for aligning the frame, in a manner analogous to - the `align' argument of `label' (*note label::). However, one key - difference is that when `align' is not specified, labels are - centered, whereas frames and pictures are aligned so that their - origin is at `position'. Illustrations of frame alignment can be - found in the examples *note errorbars:: and *note image::. If you - want to align three or more subpictures, group them two at a time: - - picture pic1; - real size=50; - size(pic1,size); - fill(pic1,(0,0)--(50,100)--(100,0)--cycle,red); - - picture pic2; - size(pic2,size); - fill(pic2,unitcircle,green); - - picture pic3; - size(pic3,size); - fill(pic3,unitsquare,blue); - - picture pic; - add(pic,pic1.fit(),(0,0),N); - add(pic,pic2.fit(),(0,0),10S); - - add(pic.fit(),(0,0),N); - add(pic3.fit(),(0,0),10S); - - - - Alternatively, one can use `attach' to automatically increase the - size of picture `dest' to accommodate adding a frame `src' about - the user coordinate `position': void attach(picture dest=currentpicture, frame src, - pair position=0, bool group=true, - filltype filltype=NoFill, bool above=true); - void attach(picture dest=currentpicture, frame src, - pair position, pair align, bool group=true, - filltype filltype=NoFill, bool above=true); - - To erase the contents of a picture (but not the size - specification), use the function void erase(picture pic=currentpicture); - - To save a snapshot of `currentpicture', `currentpen', and - `currentprojection', use the function `save()'. - - To restore a snapshot of `currentpicture', `currentpen', and - `currentprojection', use the function `restore()'. - - Many further examples of picture and frame operations are provided - in the base module `plain'. - - It is possible to insert verbatim `PostScript' commands in a - picture with one of the routines void postscript(picture pic=currentpicture, string s); - void postscript(picture pic=currentpicture, string s, pair min, - pair max) - Here `min' and `max' can be used to specify explicit bounds - associated with the resulting `PostScript' code. - - Verbatim TeX commands can be inserted in the intermediate `LaTeX' - output file with one of the functions void tex(picture pic=currentpicture, string s); - void tex(picture pic=currentpicture, string s, pair min, pair max) - Here `min' and `max' can be used to specify explicit bounds - associated with the resulting TeX code. - - To issue a global TeX command (such as a TeX macro definition) in - the TeX preamble (valid for the remainder of the top-level module) - use: void texpreamble(string s); - - The TeX environment can be reset to its initial state, clearing all - macro definitions, with the function void texreset(); - - The routine void usepackage(string s, string options=""); - provides a convenient abbreviation for texpreamble("\usepackage["+options+"]{"+s+"}"); - that can be used for importing `LaTeX' packages. - - - -File: asymptote.info, Node: Files, Next: Variable initializers, Prev: Frames and pictures, Up: Programming - -5.6 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="#")'; 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. - - If the `-globalwrite' (or `-nosafe') option is enabled, one can -change the current working directory 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); - 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. - - 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), `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 also be opened with `xinput' or `xoutput', instead of -`input' or `output', to read or write double precision (64-bit) real -values and single precision (32-bit) integer values in Sun -Microsystem's XDR (External Data Representation) portable binary format -(available on all `UNIX' platforms). A file may also be opened with -`binput' or `boutput' to read or write double precision values in the -native (nonportable) machine binary format. The function `file -single(file,0.0)' may be used to set a file to read single precision -real XDR or binary values; calling `file single(file,0.0,false)' sets -it back to read doubles again. The functions `file single(file,0)' and -`file single(file,0,false)' can be used to change the default integer -precision (single). The functions `file single(file)' and `file -single(file,false)' may be used to set the precision for both real and -integer values. - - 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'. If the setting `safe' is false, then the -function `int system(string s)' can be used to call the arbitrary system -command `s'. - - -File: asymptote.info, Node: Variable initializers, Next: Structures, Prev: Files, Up: Programming - -5.7 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. - - -File: asymptote.info, Node: Structures, Next: Operators, Prev: Variable initializers, Up: Programming - -5.8 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=new T; -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; - - Here, the expression `new T' will produce a new instance of the -class, but will also cause `Tcount' to be incremented, so that it keeps -track of the number of instances produced. - - The expression `null' can be cast to any structure type to yield a -null reference, a reference that does not actually refer to any -instance of the structure. Trying to use a field of a null reference -will cause an error. - - The function `bool alias(T,T)' checks to see if two structure -references refer to the same instance of the structure (or both to -`null'). For example, in the example code at the start of the section, -`alias(foo,bar)' would return true, but `alias(foo,new T)' would return -false, as `new T' creates a new instance of the structure `T'. The -boolean operators `==' and `!=' are by default equivalent to `alias' and -`!alias' respectively, but may be overwritten for a particular type -(for example, to do a deep comparison). - - After the definition of a structure `T', a variable of type `T' is -initialized to a new instance (`new T') by default. During the -definition of the structure, however, variables of type `T' are -initialized to `null' by default. This special behaviour is to avoid -infinite recursion of creating new instances in code such as - -struct tree { - int value; - tree left; - tree right; -} - - Here is a simple example that illustrates the use of structures: - -struct S { - real a=1; - real f(real a) {return a+this.a;} -} - -S s; // Initializes s with new S; - -write(s.f(2)); // Outputs 3 - -S operator + (S s1, S s2) -{ - S result; - result.a=s1.a+s2.a; - return result; -} - -write((s+s).f(0)); // Outputs 2 - - It is often convenient to have functions that construct new -instances of a structure. Say we have a `Person' structure: - -struct Person { - string firstname; - string lastname; -} - -Person joe=new Person; -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=1; - void virtual(int) {write (0);} - void f() {virtual(1);} -} - -void write(parent p) {write(p.x);} - -struct child { - parent parent; - real y=2; - void virtual(int x) {write (x);} - parent.virtual=virtual; - void f()=parent.f; -} - -parent operator cast(child child) {return child.parent;} - -parent p; -child c; - -write(c); // Outputs 1; - -p.f(); // Outputs 0; -c.f(); // Outputs 1; - -write(c.parent.x); // Outputs 1; -write(c.y); // Outputs 2; - - 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 - -5.9 Operators -============= - -* Menu: - -* Arithmetic & logical:: Basic mathematical operators -* Self & prefix operators:: Increment and decrement -* User-defined operators:: Overloading operators - - -File: asymptote.info, Node: Arithmetic & logical, Next: Self & prefix operators, Up: Operators - -5.9.1 Arithmetic & logical operators ------------------------------------- - -`Asymptote' uses the standard binary arithmetic operators. However, -when one integer is divided by another, both arguments are converted to -real values before dividing and a real quotient is returned (since this -is usually what is intended). The function `int quotient(int x, int y)' -returns the greatest integer less than or equal to `x/y'. In all other -cases both operands are promoted to the same type, which will also be -the type of the result: -`+' - addition - -`-' - subtraction - -`*' - multiplication - -`/' - division - -`%' - modulo; the result always has the same sign as the divisor. In - particular, this makes `q*quotient(p,q)+p%q == p' for all integers - `p' and nonzero integers `q'. - -`^' - power; if the exponent (second argument) is an int, recursive - multiplication is used; otherwise, logarithms and exponentials are - used (`**' is a synonym for `^'). - - - The usual boolean operators are also defined: -`==' - equals - -`!=' - not equals - -`<' - less than - -`<=' - less than or equals - -`>=' - greater than or equals - -`>' - greater than - -`&&' - and (with conditional evaluation of right-hand argument) - -`&' - and - -`||' - or (with conditional evaluation of right-hand argument) - -`|' - or - -`^' - xor - -`!' - not - - `Asymptote' also supports the C-like conditional syntax: -bool positive=(pi >= 0) ? true : false; - - The function `T interp(T a, T b, real t)' returns `(1-t)*a+t*b' for -nonintegral built-in arithmetic types `T'. If `a' and `b' are pens, -they are first promoted to the same color space. - - `Asymptote' also defines bitwise functions `int AND(int,int)', `int -OR(int,int)', `int XOR(int,int)', and `int NOT(int)'. - - -File: asymptote.info, Node: Self & prefix operators, Next: User-defined operators, Prev: Arithmetic & logical, Up: Operators - -5.9.2 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 - -5.9.3 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 - -5.10 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 - -5.11 Functions -============== - -`Asymptote' functions are treated as variables with a signature -(non-function variables have null signatures). Variables with the same -name are allowed, so long as they have distinct signatures. - - Functions arguments are passed by value. To pass an argument by -reference, simply enclose it in a structure (*note Structures::). - - Here are some significant features of `Asymptote' functions: - - 1. Variables with signatures (functions) and without signatures - (nonfunction variables) are distinct: int x, x(); - x=5; - x=new int() {return 17;}; - x=x(); // calls x() and puts the result, 17, in the scalar x - - 2. Traditional function definitions are allowed: int sqr(int x) - { - return x*x; - } - sqr=null; // but the function is still just a variable. - - 3. Casting can be used to resolve ambiguities: int a, a(), b, b(); // Valid: creates four variables. - a=b; // Invalid: assignment is ambiguous. - a=(int) b; // Valid: resolves ambiguity. - (int) (a=b); // Valid: resolves ambiguity. - (int) a=b; // Invalid: cast expressions cannot be L-values. - - int c(); - c=a; // Valid: only one possible assignment. - - 4. Anonymous (so-called "high-order") functions are also allowed: typedef int intop(int); - intop adder(int m) - { - return new int(int n) {return m+n;}; - } - intop addby7=adder(7); - write(addby7(1)); // Writes 8. - - 5. One may redefine a function `f', even for calls to `f' in - previously declared functions, by assigning another (anonymous or - named) function to it. However, if `f' is overloaded by a new - function definition, previous calls will still access the original - version of `f', as illustrated in this example: void f() { - write("hi"); - } - - void g() { - f(); - } - - g(); // writes "hi" - - f=new void() {write("bye");}; - - g(); // writes "bye" - - void f() {write("overloaded");}; - - f(); // writes "overloaded" - g(); // writes "bye" - - 6. Anonymous functions can be used to redefine a function variable - that has been declared (and implicitly initialized to the null - function) but not yet explicitly defined: void f(bool b); - - void g(bool b) { - if(b) f(b); - else write(b); - } - - f=new void(bool b) { - write(b); - g(false); - }; - - g(true); // Writes true, then writes false. - - - `Asymptote' is the only language we know of that treats functions as -variables, but allows overloading by distinguishing variables based on -their signatures. - - Functions are allowed to call themselves recursively. As in C++, -infinite nested recursion will generate a stack overflow (reported as a -segmentation fault, unless a fully working version of the GNU library -`libsigsegv' (e.g. 2.4 or later) is installed at configuration time). - -* Menu: - -* Default arguments:: Default values can appear anywhere -* Named arguments:: Assigning function arguments by keyword -* Rest arguments:: Functions with a variable number of arguments -* Mathematical functions:: Standard libm functions - - -File: asymptote.info, Node: Default arguments, Next: Named arguments, Up: Functions - -5.11.1 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 - -5.11.2 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. - - 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 - -5.11.3 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. - - 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 - -5.11.4 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 `J(int n, real)' and second kind -`Y(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 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 - -5.12 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', - - * `void cyclic(bool b)', - - * `bool cyclicflag', - - * `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.cyclicflag' returns the current setting of the `cyclic' flag. - - 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 the array of integers from `0' to `n-1' inclusive. 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, `cyclic', `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. By default, if - `value' is itself an array, a deep copy of that array is made for - each entry in the new array. If `depth' is specified, this deep - copying only recurses to the number of levels specified. - -`int[] sequence(int n)' - if `n >= 1' returns the array `{0,1,...,n-1}' (otherwise returns a - null array); - -`int[] sequence(int n, int m)' - if `m >= n' returns an array `{n,n+1,...,m}' (otherwise returns a - null array); - -`T[] sequence(T f(int), int n)' - if `n >= 1' returns the sequence `{f_i :i=0,1,...n-1}' given a - function `T f(int)' and integer `int n' (otherwise returns a null - array); - -`T[] map(T f(T), T[] a)' - returns the array obtained by applying the function `f' to each - element of the array `a'. This is equivalent to `sequence(new - T(int i) {return f(a[i]);},a.length)'. - -`int[] reverse(int n)' - if `n >= 1' returns the array `{n-1,n-2,...,0}' (otherwise returns - a null array); - -`int[] complement(int[] a, int n)' - returns the complement of the integer array `a' in - `{0,1,2,...,n-1}', so that `b[complement(a,b.length)]' yields the - complement of `b[a]'. - -`real[] uniform(real a, real b, int n)' - if `n >= 1' returns a uniform partition of `[a,b]' into `n' - subintervals (otherwise returns a null array); - -`int find(bool[], int n=1)' - returns the index of the `n'th `true' value or -1 if not found. - If `n' is negative, search backwards from the end of the array for - the `-n'th value; - -`int search(T[] a, T key)' - For built-in ordered types `T', searches a sorted ordered array - `a' of `n' elements to find an interval containing `key', - returning `-1' if `key' is less than the first element, `n-1' if - `key' is greater than or equal to the last element, and otherwise - the index corresponding to the left-hand (smaller) endpoint. - -`T[] copy(T[] a)' - returns a deep copy of the array `a'; - -`T[][] copy(T[][] a)' - returns a deep copy of the array `a'; - -`T[][][] copy(T[][][] a)' - returns a deep copy of the array `a'; - -`T[] concat(... T[][] a)' - returns a new array formed by concatenating the 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 compare(T i, T j))' - returns a copy of `a' stably sorted in ascending order such that - element `i' precedes element `j' if `compare(i,j)' is true. - -`T[][] transpose(T[][] a)' - returns the transpose of `a'. - -`T[][][] transpose(T[][][] a, int[] perm)' - returns the 3D transpose of `a' obtained by applying the - permutation `perm' of `new int[]{0,1,2}' to the indices of each - entry. - -`T sum(T[] a)' - For arithmetic types `T', returns the sum of `a'. In the case - where `T' is `bool', the number of true elements in `a' is - returned. - -`T min(T[] a)' - -`T min(T[][] a)' - -`T min(T[][][] a)' - For built-in ordered types `T', returns the minimum element of `a'. - -`T max(T[] a)' - -`T max(T[][] a)' - -`T max(T[][][] a)' - For built-in ordered types `T', returns the maximum element of `a'. - -`T[] min(T[] a, T[] b)' - For built-in ordered types `T', and arrays `a' and `b' of the same - length, returns an array composed of the minimum of the - corresponding elements of `a' and `b'. - -`T[] max(T[] a, T[] b)' - For built-in ordered types `T', and arrays `a' and `b' of the same - length, returns an array composed of the maximum of the - corresponding elements of `a' and `b'. - -`pair[] pairs(real[] x, real[] y);' - For arrays `x' and `y' of the same length, returns the pair array - `sequence(new pair(int i) {return (x[i],y[i]);},x.length)'. - -`pair[] fft(pair[] a, int sign=1)' - returns the Fast Fourier Transform of `a' (if the optional `FFTW' - package is installed), using the given `sign'. Here is a simple - example: int n=4; - pair[] f=sequence(n); - write(f); - pair[] g=fft(f,-1); - write(); - write(g); - f=fft(g,1); - write(); - write(f/n); - -`real dot(real[] a, real[] b)' - returns the dot product of the vectors `a' and `b'. - -`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 two 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). If line mode is set with `line(file)', then reading will -stop once the end of the line is reached instead (line mode may be -cleared with `line(file,false)'): -file fin=input("test.txt"); -real[] A=line(fin); - - 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, set with -`word(file)' and cleared with `word(file,false)', which causes string -reads to respect white-space delimiters, instead of the default -end-of-line delimiter: -file fin=word(line(input("test.txt"))); -real[] A=fin; - - Another useful mode is comma-separated-value mode, set with -`csv(file)' and cleared with `csv(file,false)', 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 `dimension(file,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=dimension(fin,2,3); -real[][][] B=dimension(fin,2,3,4); - Again, an integer limit of zero means no restriction. - - Sometimes the array dimensions are stored with the data as integer -fields at the beginning of an array. Such arrays can be read in with the -functions `read1', `read2', and `read3', respectively: -file fin=input("test.txt"); -real[] A=read1(fin); -real[][] B=read2(fin); -real[][][] C=read3(fin); - - One, two, and three-dimensional arrays of the basic data types can be -output with the functions `write(file,T[])', `write(file,T[][])', -`write(file,T[][][])', respectively. - - -File: asymptote.info, Node: Slices, Up: Arrays - -5.12.1 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 - -5.13 Casts -========== - -`Asymptote' implicitly casts `int' to `real', `int' to `pair', `real' -to `pair', `pair' to `path', `pair' to `guide', `path' to `guide', -`guide' to `path', `real' to `pen', `pair[]' to `guide[]', `pair[]' to -`path[]', `path' to `path[]', and `guide' to `path[]', along with -various three-dimensional casts defined in `three.asy'. Implicit casts -are automatically attempted on assignment and when trying to match -function calls with possible function signatures. Implicit casting can -be inhibited by declaring individual arguments `explicit' in the -function signature, say to avoid an ambiguous function call in the -following example, which outputs 0: - -int f(pair a) {return 0;} -int f(explicit real x) {return 1;} - -write(f(0)); - - Other conversions, say `real' to `int' or `real' to `string', -require an explicit cast: -int i=(int) 2.5; -string s=(string) 2.5; - -real[] a={2.5,-3.5}; -int[] b=(int []) a; -write(stdout,b); // Outputs 2,-3 - - Casting to user-defined types is also possible using `operator cast': -struct rpair { - real radius; - real angle; -} - -pair operator cast(rpair x) { - return (x.radius*cos(x.angle),x.radius*sin(x.angle)); -} - -rpair x; -x.radius=1; -x.angle=pi/6; - -write(x); // Outputs (0.866025403784439,0.5) - - One must use care when defining new cast operators. Suppose that in -some code one wants all integers to represent multiples of 100. To -convert them to reals, one would first want to multiply them by 100. -However, the straightforward implementation -real operator cast(int x) {return x*100;} - is equivalent to an infinite recursion, since the result `x*100' needs -itself to be cast from an integer to a real. Instead, we want to use -the standard conversion of int to real: -real convert(int x) {return x*100;} -real operator cast(int x)=convert; - - Explicit casts are implemented similarly, with `operator ecast'. - - -File: asymptote.info, Node: Import, Next: Static, Prev: Casts, Up: Programming - -5.14 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 a 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 - -5.15 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 - -6 `LaTeX' usage -*************** - -`Asymptote' comes with a convenient `LaTeX' style file `asymptote.sty' -that makes `LaTeX' `Asymptote'-aware. Entering `Asymptote' code -directly into the `LaTeX' source file, at the point where it is needed, -keeps figures organized and avoids the need to invent new file names -for each figure. Simply add the line `\usepackage{asymptote}' at the -beginning of your file and enclose your `Asymptote' code within a -`\begin{asy}...\end{asy}' environment. As with the `LaTeX' `comment' -environment, the `\end{asy}' command must appear on a line by itself, -with no leading spaces or trailing commands/comments. - - The sample `LaTeX' file below, named `latexusage.tex', can be run as -follows: -latex latexusage -asy latexusage -latex latexusage - -or - -pdflatex latexusage -asy latexusage -pdflatex latexusage - - To switch between using `latex' and `pdflatex' you may first need to -remove the files `latexusage-*', `latexusage_.pre', and -`latexusage.aux'. - - One can specify `width', `height', `viewportwidth', -`viewportheight', and `attach' `keyval'-style options to the `asy' -environment. The current version (1.06) of `asymptote.sty' supports the -embedding of 3D PRC files, either inline or, using the `attach' option -with the `attachfile2' (or older `attachfile') `LaTeX' package, as -annotated (but printable) attachments. For many applications, the -annotated attachment method tends to be more convenient. The default -value of `viewportwidth' is `\the\linewidth' for inline 3D figures and -`0' for attachments. - - If the `inline' option is given to the `asymptote.sty' package, -inline `LaTeX' code is generated instead of EPS or PDF files. This -makes LaTeX symbols visible to the `\begin{asy}...\end{asy}' -environment. In this mode, Asymptote correctly aligns 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 `latex' is used with the `inline' option, the 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). - - An excellent tutorial by Dario Teixeira on integrating `Asymptote' -and `LaTeX' is available at `http://dario.dse.nl/projects/asylatex/'. - - 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: -%\usepackage[inline]{asymptote} - -% Enable this line to support PDF hyperlinks: -%\usepackage[setpagesize=false]{hyperref} - -% Enable this line for PDF attachments with asy environment option attach=true: -%\usepackage[dvips]{attachfile2} - -\begin{document} - -\begin{asydef} -// Global Asymptote definitions can be put here. -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. It is often desirable to embed such files as annotated attachments; -this requires the optional \verb+\usepackage{attachfile2}+ package and -the \verb+{attach=true}+ option: -\begin{center} -\begin{asy}[height=4cm,attach=false] -import three; -currentprojection=orthographic(5,4,2); -draw(unitcube,blue); -label("$V-E+F=2$",(0,1,0.5),3Y,blue+fontsize(17)); -\end{asy} -\end{center} - -One can also scale the figure to the full line width: -\begin{center} -\begin{asy}[width=\the\linewidth] -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(24)+blue); - -pair s=-0.2*I; -draw("$x$",z0+s--z1+s,N,red,Arrows,Bars,PenMargins); -s=-0.5*I; -draw("$\bar{x}$",z0+s--zf+s,blue,Arrows,Bars,PenMargins); -s=-0.95*I; -draw("$X$",z0+s--z2+s,darkgreen,Arrows,Bars,PenMargins); -\end{asy} -\end{center} -\end{document} - - - -File: asymptote.info, Node: Base modules, Next: Options, Prev: LaTeX usage, Up: Top - -7 Base modules -************** - -`Asymptote' currently ships with the following base modules: - -* Menu: - -* plain:: Default `Asymptote' base file -* simplex:: Linear programming: simplex method -* math:: Extend `Asymptote''s math capabilities -* interpolate:: Interpolation routines -* geometry:: Geometry routines -* trembling:: Wavy lines -* stats:: Statistics routines and histograms -* patterns:: Custom fill and draw patterns -* markers:: Custom path marker routines -* tree:: Dynamic binary search tree -* binarytree:: Binary tree drawing module -* drawtree:: Tree drawing module -* syzygy:: Syzygy and braid drawing module -* feynman:: Feynman diagrams -* roundedpath:: Round the sharp corners of paths -* animation:: Embedded PDF and MPEG movies -* embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with `Asymptote' -* MetaPost:: `MetaPost' compatibility routines -* unicode:: Accept `unicode' (UTF-8) characters -* latin1:: Accept `ISO 8859-1' characters -* babel:: Interface to `LaTeX' `babel' package -* labelpath:: Drawing curved labels -* labelpath3:: Drawing curved labels in 3D -* annotate:: Annotate your PDF files -* CAD:: 2D CAD pen and measurement functions (DIN 15) -* graph:: 2D linear & logarithmic graphs -* palette:: Color density images and palettes -* three:: 3D vector graphics -* obj:: 3D obj files -* graph3:: 3D linear & logarithmic graphs -* grid3:: 3D grids -* solids:: 3D solid geometry -* tube:: 3D rotation minimizing tubes -* flowchart:: Flowchart drawing routines -* contour:: Contour lines -* contour3:: Contour surfaces -* slopefield:: Slope fields - - -File: asymptote.info, Node: plain, Next: simplex, Up: Base modules - -7.1 `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 - -7.2 `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 - -7.3 `math' -========== - -This package extends `Asymptote''s mathematical capabilities with -intersection algorithms and matrix arithmetic: - -`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. - - - -File: asymptote.info, Node: interpolate, Next: geometry, Prev: math, Up: Base modules - -7.4 `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 - -7.5 `geometry' -============== - -This module, written by Philippe Ivaldi, provides an extensive set of -geometry routines, including `perpendicular' symbols and a `triangle' -structure. It is documented here: -`http://asymptote.sourceforge.net/geometry_en.pdf', including an -extensive set of examples, -`http://piprim.tuxfamily.org/asymptote/geometry/index.html', and an -index: - - `http://piprim.tuxfamily.org/asymptote/geometry/modules/geometry.asy.index.type.html' - - -File: asymptote.info, Node: trembling, Next: stats, Prev: geometry, Up: Base modules - -7.6 `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. -Further examples are posted at -`http://piprim.tuxfamily.org/asymptote/trembling/index.html' - - -File: asymptote.info, Node: stats, Next: patterns, Prev: trembling, Up: Base modules - -7.7 `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 - -7.8 `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 - -7.9 `markers' -============= - -This package implements specialized routines for marking paths and -angles. The principal mark routine provided by this package is -markroutine markinterval(int n=1, frame f, bool rotated=false); - which centers `n' copies of frame `f' within uniformly space intervals -in arclength along the path, optionally rotated by the angle of the -local tangent. - - The `marker' (*note marker::) routine can be used to construct new -markers from these predefined frames: - -frame stickframe(int n=1, real size=0, pair space=0, real angle=0, - pair offset=0, pen p=currentpen); - -frame circlebarframe(int n=1, real barsize=0, - real radius=0,real angle=0, - pair offset=0, pen p=currentpen, - filltype filltype=NoFill, bool above=false); - -frame crossframe(int n=3, real size=0, pair space=0, - real angle=0, pair offset=0, pen p=currentpen); - -frame tildeframe(int n=1, real size=0, pair space=0, - real angle=0, pair offset=0, pen p=currentpen); - - For convenience, this module also constructs the markers -`StickIntervalMarker', `CrossIntervalMarker', -`CircleBarIntervalMarker', and `TildeIntervalMarker' from the above -frames. The example `markers1.asy' illustrates the use of these markers: - - - - -This package also provides a routine for marking an angle AOB: -void markangle(picture pic=currentpicture, Label L="", - int n=1, real radius=0, real space=0, - pair A, pair O, pair B, arrowbar arrow=None, - pen p=currentpen, margin margin=NoMargin, - marker marker=nomarker); - as illustrated in the example `markers2.asy'. - - - - - -File: asymptote.info, Node: tree, Next: binarytree, Prev: markers, Up: Base modules - -7.10 `tree' -=========== - -This package implements an example of a dynamic binary search tree. - - -File: asymptote.info, Node: binarytree, Next: drawtree, Prev: tree, Up: Base modules - -7.11 `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); - -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); - -add(pic.fit(),(0,0),10N); -add(pic2.fit(),(0,0),10S); - - - - -File: asymptote.info, Node: drawtree, Next: syzygy, Prev: binarytree, Up: Base modules - -7.12 `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 - -7.13 `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 - -7.14 `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 - -7.15 `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 - -7.16 `animation' -================ - -This module allows one to generate animations, as illustrated by the -files `wheel.asy', `wavelet.asy', and `cube.asy' in the `animations' -subdirectory of the examples directory. These animations use the -`ImageMagick' `convert' program to `merge' multiple images into a GIF -or MPEG movie. - - The related `animate' module, derived from the `animation' module, -generates higher-quality portable clickable PDF movies, with optional -controls. This requires installing the package - - `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/animate.sty' - (version 2007/11/30 or later) in a new directory `animate' in the -local `LaTeX' directory (for example, in -`/usr/local/share/texmf/tex/latex/animate'). On `UNIX' systems, one -must then execute the command `texhash'. - - The example `pdfmovie.asy' in the `animations' directory, along with -the slide presentations `slidemovies.asy' and `intro.asy', illustrate -the use of embedded PDF movies. The examples `inlinemovie.tex' and -`inlinemovie3.tex' show how to generate and embed PDF movies directly -within a `LaTeX' file (*note LaTeX usage::). The member function -string pdf(fit fit=NoBox, real delay=animationdelay, string options="", - bool keep=settings.keep, bool multipage=true); - of the `animate' structure accepts any of the `animate.sty' options, -as described here: - - `http://www.ctan.org/tex-archive/macros/latex/contrib/animate/doc/animate.pdf' - - -File: asymptote.info, Node: embed, Next: slide, Prev: animation, Up: Base modules - -7.17 `embed' -============ - -This module provides an interface to the `LaTeX' package (included with -`MikTeX') - - `http://www.ctan.org/tex-archive/macros/latex/contrib/movie15' - for embedding movies, sounds, and 3D objects into a PDF document. However, -`XeLaTeX' users need to rename the modified version -`movie15_dvipdfmx.sty' from - - `http://asymptote.svn.sourceforge.net/viewvc/asymptote/trunk/asymptote/patches/' - to `movie15.sty' and place it in their `LaTeX' path. - - The latest version (2008/10/08) of the `movie15' package requires -both `pdflatex' version 1.20 or later and the file - - `http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/ifdraft.dtx' - which can be installed by placing it in a directory `ifdraft' in the -local `LaTeX' directory (e.g. -`/usr/local/share/texmf/tex/latex/ifdraft') and executing in that -directory the commands: -tex ifdraft.dtx -texhash - - An example of embedding `U3D' code is provided in the file -`embeddedu3d.asy'. As of version 7.0.8, `Adobe Reader' supports the -`U3D' format under Linux. - - Unfortunately, Adobe has not yet made available an embedded movie -plugin for the Linux version of `Adobe Reader'. A portable method for -embedding movie files, which should work on any platform and does not -require the `movie15' or `ifdraft' packages, is provided by using the -`external' module instead of `embed'. An example of these interfaces is -provided in the file `embeddedmovie.asy' and `externalmovie.asy' in the -`animations' subdirectory of the examples directory. For a higher -quality movie generated directly by `Asymptote', use the `animate' -module along with the `animate.sty' package to embed a portable PDF -animation (*note animate::). - - -File: asymptote.info, Node: slide, Next: MetaPost, Prev: embed, Up: Base modules - -7.18 `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 - -7.19 `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 - -7.20 `unicode' -============== - -Import this package at the beginning of the file to instruct `LaTeX' to -accept `unicode' (UTF-8) standardized international characters. To use -Cyrillic fonts, you will need to change the font encoding: -import unicode; -texpreamble("\usepackage{mathtext}\usepackage[russian]{babel}"); -defaultpen(font("T2A","cmr","m","n")); - Support for Chinese, Japanese, and Korean fonts is provided by the CJK -package: - - `http://www.ctan.org/tex-archive/languages/chinese/CJK/' - The following commands enable the CJK song family (within a label, -you can also temporarily switch to another family, say kai, by -prepending `"\CJKfamily{kai}"' to the label string): -texpreamble("\usepackage{CJK} -\AtBeginDocument{\begin{CJK*}{GBK}{song}} -\AtEndDocument{\clearpage\end{CJK*}}"); - - -File: asymptote.info, Node: latin1, Next: babel, Prev: unicode, Up: Base modules - -7.21 `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 - -7.22 `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 - -7.23 `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 - -7.24 `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 - -7.25 `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 - -7.26 `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 - -7.27 `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. - Th 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. - - - - - 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 the current picture unless - `above=true'. The axis placement is determined by one of the - following `axis' types: - - `YZero(bool extend=true)' - Request an x axis at y=0 (or y=1 on a logarithmic axis) - extending to the full dimensions of the picture, unless - `extend'=false. - - `YEquals(real Y, bool extend=true)' - Request an x axis at y=`Y' extending to the full dimensions - of the picture, unless `extend'=false. - - `Bottom(bool extend=false)' - Request a bottom axis. - - `Top(bool extend=false)' - Request a top axis. - - `BottomTop(bool extend=false)' - Request a bottom and top axis. - - - Custom axis types can be created by following the examples in - `graph.asy'. One can easily override the default values for the - standard axis types: import graph; - - YZero=new axis(bool extend=true) { - return new void(picture pic, axisT axis) { - real y=pic.scale.x.scale.logarithmic ? 1 : 0; - axis.value=I*pic.scale.y.T(y); - axis.position=1; - axis.side=right; - axis.align=2.5E; - axis.value2=Infinity; - axis.extend=extend; - }; - }; - YZero=YZero(); - - The default tick option is `NoTicks'. The options `LeftTicks', - `RightTicks', or `Ticks' can be used to draw ticks on the left, - right, or both sides of the path, relative to the direction in - which the path is drawn. These tick routines accept a number of - optional arguments: ticks LeftTicks(Label format="", ticklabel ticklabel=null, - bool beginlabel=true, bool endlabel=true, - int N=0, int n=0, real Step=0, real step=0, - bool begin=true, bool end=true, tickmodifier modify=None, - real Size=0, real size=0, bool extend=false, - pen pTick=nullpen, pen ptick=nullpen); - - If any of these parameters are omitted, reasonable defaults will - be chosen: - `Label format' - override the default tick label format (`defaultformat', - initially "$%.4g$"), rotation, pen, and alignment (for - example, `LeftSide', `Center', or `RightSide') relative to - the axis. To enable `LaTeX' math mode fonts, the format - string should begin and end with `$' *note format::. If the - format string is `trailingzero', trailing zeros will be added - to the tick labels; if the format string is `"%"', the tick - label will be suppressed; - - `ticklabel' - is a function `string(real x)' returning the label (by - default, format(format.s,x)) for each major tick value `x'; - - `bool beginlabel' - include the first label; - - `bool endlabel' - include the last label; - - `int N' - when automatic scaling is enabled (the default; *note - automatic scaling::), divide a linear axis evenly into this - many intervals, separated by major ticks; for a logarithmic - axis, this is the number of decades between labelled ticks; - - `int n' - divide each interval into this many subintervals, separated - by minor ticks; - - `real Step' - the tick value spacing between major ticks (if `N'=`0'); - - `real step' - the tick value spacing between minor ticks (if `n'=`0'); - - `bool begin' - include the first major tick; - - `bool end' - include the last major tick; - - `tickmodifier modify;' - an optional function that takes and returns a `tickvalue' - structure having real[] members `major' and `minor' - consisting of the tick values (to allow modification of the - automatically generated tick values); - - `real Size' - the size of the major ticks (in `PostScript' coordinates); - - `real size' - the size of the minor ticks (in `PostScript' coordinates); - - `bool extend;' - extend the ticks between two axes (useful for drawing a grid - on the graph); - - `pen pTick' - an optional pen used to draw the major ticks; - - `pen ptick' - an optional pen used to draw the minor ticks. - - - For convenience, the predefined tickmodifier `OmitTick(... real[] - x)' tickmodifier 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); - - Draw a y axis on picture `pic' from y=`ymin' to y=`ymax' using pen - `p', optionally labelling it with Label `L'. 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 the current picture 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="", - 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 the current picture 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 - the current picture 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=nullpen); - void labelx(picture pic=currentpicture, Label L="", real x, - align align=S, string format="", pen p=nullpen); - 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=nullpen); - void labely(picture pic=currentpicture, Label L="", real y, - align align=W, string format="", pen p=nullpen); - void labely(picture pic=currentpicture, Label L, - string format="", explicit pen p=nullpen); - - Here are some simple examples of two-dimensional graphs: - - 1. This example draws a textbook-style graph of y= exp(x), with the y - axis starting at y=0: import graph; - size(150,0); - - real f(real x) {return exp(x);} - pair F(real x) {return (x,f(x));} - - xaxis("$x$"); - yaxis("$y$",0); - - draw(graph(f,-4,2,operator ..),red); - - labely(1,E); - label("$e^x$",F(1),SE); - - - - 2. The next example draws a scientific-style graph with a legend. - The position of the legend can be adjusted either explicitly or by - using the graphical user interface `xasy' (*note GUI::). If an - `UnFill(real xmargin=0, real ymargin=xmargin)' or `Fill(pen)' - option is specified to `add', the legend will obscure any - underlying objects. Here we illustrate how to clip the portion of - the picture covered by a label: - - import graph; - - size(400,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\sin(2\pi x)$"); - draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$"); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - label("LABEL",point(0),UnFill(1mm)); - - add(legend(),point(E),20E,UnFill); - - - - To specify a fixed size for the graph proper, use `attach': import graph; - - size(250,200,IgnoreAspect); - - real Sin(real t) {return sin(2pi*t);} - real Cos(real t) {return cos(2pi*t);} - - draw(graph(Sin,0,1),red,"$\sin(2\pi x)$"); - draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$"); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - label("LABEL",point(0),UnFill(1mm)); - - attach(legend(),truepoint(E),20E,UnFill); - A legend can have multiple entries per line: import graph; - size(8cm,6cm,IgnoreAspect); - - typedef real realfcn(real); - realfcn F(real p) { - return new real(real x) {return sin(p*x);}; - }; - - for(int i=1; i < 5; ++i) - draw(graph(F(i*pi),0,1),Pen(i), - "$\sin("+(i == 1 ? "" : (string) i)+"\pi x)$"); - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - attach(legend(2),(point(S).x,truepoint(S).y),10S,UnFill); - - - - 3. This example draws a graph of one array versus another (both of - the same size) using custom tick locations and a smaller font size - for the tick labels on the y axis. import graph; - - size(200,150,IgnoreAspect); - - real[] x={0,1,2,3}; - real[] y=x^2; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight, - RightTicks(Label(fontsize(8)),new real[]{0,4,9})); - - - - 4. This example shows how to graph columns of data read from a file. import graph; - - size(200,150,IgnoreAspect); - - file in=line(input("filegraph.dat")); - real[][] a=dimension(in,0,0); - a=transpose(a); - - real[] x=a[0]; - real[] y=a[1]; - - draw(graph(x,y),red); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - 5. The next example draws two graphs of an array of coordinate pairs, - using frame alignment and data markers. In the left-hand graph, the - markers, constructed with marker marker(path g, markroutine markroutine=marknodes, - pen p=currentpen, filltype filltype=NoFill, - bool above=true); - using the path `unitcircle' (*note filltype::), are drawn below - each node. Any frame can be converted to a marker, using marker marker(frame f, markroutine markroutine=marknodes, - bool above=true); - In the right-hand graph, the unit n-sided regular polygon - `polygon(int n)' and the unit n-point cyclic cross `cross(int n, - bool round=true, real r=0)' (where `r' is an optional "inner" - radius) are used to build a custom marker frame. Here - `markuniform(bool centered=false, int n, bool rotated=false)' adds - this frame at `n' uniformly spaced points along the arclength of - the path, optionally rotated by the angle of the local tangent to - the path (if centered is true, the frames will be centered within - `n' evenly spaced arclength intervals). Alternatively, one can use - markroutine `marknodes' to request that the marks be placed at each - Bezier node of the path, or markroutine `markuniform(pair z(real - t), real a, real b, int n)' to place marks at points `z(t)' for n - evenly spaced values of `t' in `[a,b]'. - - These markers are predefined: marker[] Mark={ - marker(scale(circlescale)*unitcircle), - marker(polygon(3)),marker(polygon(4)), - marker(polygon(5)),marker(invert*polygon(3)), - marker(cross(4)),marker(cross(6)) - }; - - marker[] MarkFill={ - marker(scale(circlescale)*unitcircle,Fill),marker(polygon(3),Fill), - marker(polygon(4),Fill),marker(polygon(5),Fill), - marker(invert*polygon(3),Fill) - }; - - The example also illustrates the `errorbar' routines: - - void errorbars(picture pic=currentpicture, pair[] z, pair[] dp, - pair[] dm={}, bool[] cond={}, pen p=currentpen, - real size=0); - - void errorbars(picture pic=currentpicture, real[] x, real[] y, - real[] dpx, real[] dpy, real[] dmx={}, real[] dmy={}, - bool[] cond={}, pen p=currentpen, real size=0); - - Here, the positive and negative extents of the error are given by - the absolute values of the elements of the pair array `dp' and the - optional pair array `dm'. If `dm' is not specified, the positive - and negative extents of the error are assumed to be equal. import graph; - - picture pic; - real xsize=200, ysize=140; - size(pic,xsize,ysize,IgnoreAspect); - - pair[] f={(5,5),(50,20),(90,90)}; - pair[] df={(0,0),(5,7),(0,5)}; - - errorbars(pic,f,df,red); - draw(pic,graph(pic,f),"legend", - marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false)); - - scale(pic,true); - - xaxis(pic,"$x$",BottomTop,LeftTicks); - yaxis(pic,"$y$",LeftRight,RightTicks); - add(pic,legend(pic),point(pic,NW),20SE,UnFill); - - picture pic2; - size(pic2,xsize,ysize,IgnoreAspect); - - frame mark; - filldraw(mark,scale(0.8mm)*polygon(6),green,green); - draw(mark,scale(0.8mm)*cross(6),blue); - - draw(pic2,graph(pic2,f),marker(mark,markuniform(5))); - - scale(pic2,true); - - xaxis(pic2,"$x$",BottomTop,LeftTicks); - yaxis(pic2,"$y$",LeftRight,RightTicks); - - yequals(pic2,55.0,red+Dotted); - xequals(pic2,70.0,red+Dotted); - - // Fit pic to W of origin: - add(pic.fit(),(0,0),W); - - // Fit pic2 to E of (5mm,0): - add(pic2.fit(),(5mm,0),E); - - - - 6. A custom mark routine can be also be specified: import graph; - - size(200,100,IgnoreAspect); - - markroutine marks() { - return new void(picture pic=currentpicture, frame f, path g) { - path p=scale(1mm)*unitcircle; - for(int i=0; i <= length(g); ++i) { - pair z=point(g,i); - frame f; - if(i % 4 == 0) { - fill(f,p); - add(pic,f,z); - } else { - if(z.y > 50) { - pic.add(new void(frame F, transform t) { - path q=shift(t*z)*p; - unfill(F,q); - draw(F,q); - }); - } else { - draw(f,p); - add(pic,f,z); - } - } - } - }; - } - - pair[] f={(5,5),(40,20),(55,51),(90,30)}; - - draw(graph(f),marker(marks())); - - scale(true); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - 7. This example shows how to label an axis with arbitrary strings. import graph; - - size(400,150,IgnoreAspect); - - real[] x=sequence(12); - real[] y=sin(2pi*x/12); - - scale(false); - - string[] month={"Jan","Feb","Mar","Apr","May","Jun", - "Jul","Aug","Sep","Oct","Nov","Dec"}; - - draw(graph(x,y),red,MarkFill[0]); - - xaxis(BottomTop,LeftTicks(new string(real x) { - return month[round(x % 12)];})); - yaxis("$y$",LeftRight,RightTicks(4)); - - - - 8. The next example draws a graph of a parametrized curve. The calls - to xlimits(picture pic=currentpicture, real min=-infinity, - real max=infinity, bool crop=NoCrop); - and the analogous function `ylimits' can be uncommented to set - the respective axes limits for picture `pic' to the specified - `min' and `max' values. Alternatively, the function void limits(picture pic=currentpicture, pair min, pair max, bool crop=NoCrop); - can be used to limit the axes to the box having opposite vertices - at the given pairs). Existing objects in picture `pic' will be - cropped to lie within the given limits if `crop'=`Crop'. The - function `crop(picture pic)' can be used to crop a graph to the - current graph limits. import graph; - - size(0,200); - - real x(real t) {return cos(2pi*t);} - real y(real t) {return sin(2pi*t);} - - draw(graph(x,y,0,1)); - - //xlimits(0,1,Crop); - //ylimits(-1,0,Crop); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks(trailingzero)); - - - - The next example illustrates how one can extract a common axis - scaling factor. import graph; - - axiscoverage=0.9; - size(200,IgnoreAspect); - - real[] x={-1e-11,1e-11}; - real[] y={0,1e6}; - - real xscale=round(log10(max(x))); - real yscale=round(log10(max(y)))-1; - - draw(graph(x*10^(-xscale),y*10^(-yscale)),red); - - xaxis("$x/10^{"+(string) xscale+"}$",BottomTop,LeftTicks); - yaxis("$y/10^{"+(string) yscale+"}$",LeftRight,RightTicks(trailingzero)); - - - - Axis scaling can be requested and/or automatic selection of the - axis limits can be inhibited with one of these `scale' routines: void scale(picture pic=currentpicture, scaleT x, scaleT y); - - void scale(picture pic=currentpicture, bool xautoscale=true, - bool yautoscale=xautoscale, bool zautoscale=yautoscale); - - This sets the scalings for picture `pic'. The `graph' routines - accept an optional `picture' argument for determining the - appropriate scalings to use; if none is given, it uses those set - for `currentpicture'. - - Two frequently used scaling routines `Linear' and `Log' are - predefined in `graph'. - - All picture coordinates (including those in paths and those given - to the `label' and `limits' functions) are always treated as linear - (post-scaled) coordinates. Use pair Scale(picture pic=currentpicture, pair z); - to convert a graph coordinate into a scaled picture coordinate. - - The x and y components can be individually scaled using the - analogous routines real ScaleX(picture pic=currentpicture, real x); - real ScaleY(picture pic=currentpicture, real y); - - The predefined scaling routines can be given two optional boolean - arguments: `automin=false' and `automax=automin'. These default to - `false' but can be respectively set to `true' to enable automatic - selection of "nice" axis minimum and maximum values. The `Linear' - scaling can also take as optional final arguments a multiplicative - scaling factor and intercept (e.g. for a depth axis, `Linear(-1)' - requests axis reversal). - - For example, to draw a log/log graph of a function, use - `scale(Log,Log)': import graph; - - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - - draw(graph(f,0.1,10)); - - //xlimits(1,10); - //ylimits(0.1,1); - - dot(Label("(3,5)",align=S),Scale((3,5))); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$y$",LeftRight,RightTicks); - - - - By extending the ticks, one can easily produce a logarithmic grid: import graph; - size(200,200,IgnoreAspect); - - real f(real t) {return 1/t;} - - scale(Log,Log); - draw(graph(f,0.1,10),red); - pen thin=linewidth(0.5*linewidth()); - xaxis("$x$",BottomTop,LeftTicks(begin=false,end=false,extend=true, - ptick=thin)); - yaxis("$y$",LeftRight,RightTicks(begin=false,end=false,extend=true, - ptick=thin)); - - - - One can also specify custom tick locations and formats for - logarithmic axes: import graph; - - size(300,175,IgnoreAspect); - scale(Log,Log); - draw(graph(identity,5,20)); - xlimits(5,20); - ylimits(1,100); - xaxis("$M/M_\odot$",BottomTop,LeftTicks(DefaultFormat, - new real[] {6,10,12,14,16,18})); - yaxis("$\nu_{\rm upp}$ [Hz]",LeftRight,RightTicks(DefaultFormat)); - - - - It is easy to draw logarithmic graphs with respect to other bases: import graph; - size(200,IgnoreAspect); - - // Base-2 logarithmic scale on y-axis: - - real log2(real x) {static real log2=log(2); return log(x)/log2;} - real pow2(real x) {return 2^x;} - - scaleT yscale=scaleT(log2,pow2,logarithmic=true); - scale(Linear,yscale); - - real f(real x) {return 1+x^2;} - - draw(graph(f,-4,4)); - - yaxis("$y$",ymin=1,ymax=f(5),RightTicks(Label(Fill(white))),EndArrow); - xaxis("$x$",xmin=-5,xmax=5,LeftTicks,EndArrow); - - - - Here is an example of "broken" linear x and logarithmic y axes - that omit the segments [3,8] and [100,1000], respectively. In the - case of a logarithmic axis, the break endpoints are automatically - rounded to the nearest integral power of the base. import graph; - - size(200,150,IgnoreAspect); - - // Break the x axis at 3; restart at 8: - real a=3, b=8; - - // Break the y axis at 100; restart at 1000: - real c=100, d=1000; - - scale(Broken(a,b),BrokenLog(c,d)); - - real[] x={1,2,4,6,10}; - real[] y=x^4; - - draw(graph(x,y),red,MarkFill[0]); - - xaxis("$x$",BottomTop,LeftTicks(Break(a,b))); - yaxis("$y$",LeftRight,RightTicks(Break(c,d))); - - label(rotate(90)*Break,(a,point(S).y)); - label(rotate(90)*Break,(a,point(N).y)); - label(Break,(point(W).x,ScaleY(c))); - label(Break,(point(E).x,ScaleY(c))); - - - - 9. `Asymptote' can draw secondary axes with the routines picture secondaryX(picture primary=currentpicture, void f(picture)); - picture secondaryY(picture primary=currentpicture, void f(picture)); - - In this example, `secondaryY' is used to draw a secondary linear y - axis against a primary logarithmic y axis: import graph; - texpreamble("\def\Arg{\mathop {\rm Arg}\nolimits}"); - - size(10cm,5cm,IgnoreAspect); - - real ampl(real x) {return 2.5/(1+x^2);} - real phas(real x) {return -atan(x)/pi;} - - scale(Log,Log); - draw(graph(ampl,0.01,10)); - ylimits(0.001,100); - - xaxis("$\omega\tau_0$",BottomTop,LeftTicks); - yaxis("$|G(\omega\tau_0)|$",Left,RightTicks); - - picture q=secondaryY(new void(picture pic) { - scale(pic,Log,Linear); - draw(pic,graph(pic,phas,0.01,10),red); - ylimits(pic,-1.0,1.5); - yaxis(pic,"$\Arg G/\pi$",Right,red, - LeftTicks("$% #.1f$", - begin=false,end=false)); - yequals(pic,1,Dotted); - }); - label(q,"(1,0)",Scale(q,(1,0)),red); - add(q); - - - - A secondary logarithmic y axis can be drawn like this: import graph; - - size(9cm,6cm,IgnoreAspect); - string data="secondaryaxis.csv"; - - file in=line(csv(input(data))); - - string[] titlelabel=in; - string[] columnlabel=in; - - real[][] a=dimension(in,0,0); - a=transpose(a); - real[] t=a[0], susceptible=a[1], infectious=a[2], dead=a[3], larvae=a[4]; - real[] susceptibleM=a[5], exposed=a[6],infectiousM=a[7]; - - scale(true); - - draw(graph(t,susceptible,t >= 10 & t <= 15)); - draw(graph(t,dead,t >= 10 & t <= 15),dashed); - - xaxis("Time ($\tau$)",BottomTop,LeftTicks); - yaxis(Left,RightTicks); - - picture secondary=secondaryY(new void(picture pic) { - scale(pic,Linear(true),Log(true)); - draw(pic,graph(pic,t,infectious,t >= 10 & t <= 15),red); - yaxis(pic,Right,red,LeftTicks(begin=false,end=false)); - }); - - add(secondary); - label(shift(5mm*N)*"Proportion of crows",point(NW),E); - - - - 10. Here is a histogram example, which uses the `stats' module. import graph; - import stats; - - size(400,200,IgnoreAspect); - - int n=10000; - real[] a=new real[n]; - for(int i=0; i < n; ++i) a[i]=Gaussrand(); - - draw(graph(Gaussian,min(a),max(a)),blue); - - // Optionally calculate "optimal" number of bins a la Shimazaki and Shinomoto. - int N=bins(a); - - histogram(a,min(a),max(a),N,normalize=true,low=0,lightred,black,bars=false); - - xaxis("$x$",BottomTop,LeftTicks); - yaxis("$dP/dx$",LeftRight,RightTicks(trailingzero)); - - - - 11. Here is an example of reading column data in from a file and a - least-squares fit, using the `stats' module. size(400,200,IgnoreAspect); - - import graph; - import stats; - - file fin=line(input("leastsquares.dat")); - - real[][] a=dimension(fin,0,0); - a=transpose(a); - - real[] t=a[0], rho=a[1]; - - // Read in parameters from the keyboard: - //real first=getreal("first"); - //real step=getreal("step"); - //real last=getreal("last"); - - real first=100; - real step=50; - real last=700; - - // Remove negative or zero values of rho: - t=rho > 0 ? t : null; - rho=rho > 0 ? rho : null; - - scale(Log(true),Linear(true)); - - int n=step > 0 ? ceil((last-first)/step) : 0; - - real[] T,xi,dxi; - - for(int i=0; i <= n; ++i) { - real first=first+i*step; - real[] logrho=(t >= first & t <= last) ? log(rho) : null; - real[] logt=(t >= first & t <= last) ? -log(t) : null; - - if(logt.length < 2) break; - - // Fit to the line logt=L.m*logrho+L.b: - linefit L=leastsquares(logt,logrho); - - T.push(first); - xi.push(L.m); - dxi.push(L.dm); - } - - draw(graph(T,xi),blue); - errorbars(T,xi,dxi,red); - - crop(); - - ylimits(0); - - xaxis("$T$",BottomTop,LeftTicks); - yaxis("$\xi$",LeftRight,RightTicks); - - - - 12. Here is an example that illustrates the general `axis' routine. import graph; - size(0,100); - - path g=ellipse((0,0),1,2); - - scale(true); - - axis(Label("C",align=10W),g,LeftTicks(endlabel=false,8,end=false), - ticklocate(0,360,new real(real v) { - path h=(0,0)--max(abs(max(g)),abs(min(g)))*dir(v); - return intersect(g,h)[0];})); - - - - 13. To draw a vector field of `n' arrows evenly spaced along the - arclength of a path, use the routine picture vectorfield(path vector(real), path g, int n, bool truesize=false, - pen p=currentpen, arrowbar arrow=Arrow); - as illustrated in this simple example of a flow field: import graph; - defaultpen(1.0); - - size(0,150,IgnoreAspect); - - real arrowsize=4mm; - real arrowlength=2arrowsize; - - typedef path vector(real); - - // Return a vector interpolated linearly between a and b. - vector vector(pair a, pair b) { - return new path(real x) { - return (0,0)--arrowlength*interp(a,b,x); - }; - } - - real f(real x) {return 1/x;} - - real epsilon=0.5; - path g=graph(f,epsilon,1/epsilon); - - int n=3; - draw(g); - xaxis("$x$"); - yaxis("$y$"); - - add(vectorfield(vector(W,W),g,n,true)); - add(vectorfield(vector(NE,NW),(0,0)--(point(E).x,0),n,true)); - add(vectorfield(vector(NE,NE),(0,0)--(0,point(N).y),n,true)); - - - - 14. To draw a vector field of `nx'\times`ny' arrows in `box(a,b)', use - the routine picture vectorfield(path vector(pair), pair a, pair b, - int nx=nmesh, int ny=nx, bool truesize=false, - real maxlength=truesize ? 0 : maxlength(a,b,nx,ny), - bool cond(pair z)=null, pen p=currentpen, - arrowbar arrow=Arrow, margin margin=PenMargin) - as illustrated in this example: import graph; - size(100); - - pair a=(0,0); - pair b=(2pi,2pi); - - path vector(pair z) {return (0,0)--(sin(z.x),cos(z.y));} - - add(vectorfield(vector,a,b)); - - - - 15. The following scientific graphs, which illustrate many features of - `Asymptote''s graphics routines, were generated from the examples - `diatom.asy' and `westnile.asy', using the comma-separated data in - `diatom.csv' and `westnile.csv'. - - - - - - - -File: asymptote.info, Node: palette, Next: three, Prev: graph, Up: Base modules - -7.28 `palette' -============== - -`Asymptote' can also generate color density images and palettes. The -following palettes are predefined in `palette.asy': - -`pen[] Grayscale(int NColors=256)' - a grayscale palette; - -`pen[] Rainbow(int NColors=32766)' - a rainbow spectrum; - -`pen[] BWRainbow(int NColors=32761)' - a rainbow spectrum tapering off to black/white at the ends; - -`pen[] BWRainbow2(int NColors=32761)' - a double rainbow palette tapering off to black/white at the ends, - with a linearly scaled intensity. - -`pen[] Wheel(int NColors=32766)' - a full color wheel palette; - -`pen[] Gradient(int NColors=256 ... pen[] p)' - a palette varying linearly over the specified array of pens, using - NColors in each interpolation interval; - - - The function `cmyk(pen[] Palette)' may be used to convert any of -these palettes to the CMYK colorspace. - - A color density plot using palette `palette' can be generated from a -function `f'(x,y) and added to a picture `pic': -bounds image(picture pic=currentpicture, real f(real,real), - range range=Full, pair initial, pair final, - int nx=ngraph, int ny=nx, pen[] palette, bool antialias=false) - The function `f' will be sampled at `nx' and `ny' evenly spaced points -over a rectangle defined by the points `initial' and `final', -respecting the current graphical scaling of `pic'. The color space is -scaled according to the z axis scaling (*note automatic scaling::). A -bounds structure for the function values is returned: -struct bounds { - real min; - real max; - // Possible tick intervals: - int[] divisor; -} - This information can be used for generating an optional palette bar. -The palette color space corresponds to a range of values specified by -the argument `range', which can be `Full', `Automatic', or an explicit -range `Range(real min, real max)'. Here `Full' specifies a range -varying from the minimum to maximum values of the function over the -sampling interval, while `Automatic' selects "nice" limits. The -example `imagecontour.asy' illustrates how level sets (contour lines) -can be drawn on a color density plot (*note contour::). - - A color density plot can also be generated from an explicit real[][] -array `data': -bounds image(picture pic=currentpicture, real[][] f, range range=Full, - pair initial, pair final, pen[] palette, - bool transpose=(initial.x < final.x && initial.y < final.y), - bool copy=true, bool antialias=false); - If the initial point is to the left and below the final point, by -default the array indices are interpreted according to the Cartesian -convention (first index: x, second index: y) rather than the usual -matrix convention (first index: -y, second index: x). - - To construct an image from an array of irregularly spaced points and -an array of values `f' at these points, use one of the routines -bounds image(picture pic=currentpicture, pair[] z, real[] f, - range range=Full, pen[] palette) -bounds image(picture pic=currentpicture, real[] x, real[] y, real[] f, - range range=Full, pen[] palette) - - An optionally labelled palette bar may be generated with the routine -void palette(picture pic=currentpicture, Label L="", bounds bounds, - pair initial, pair final, axis axis=Right, pen[] palette, - pen p=currentpen, paletteticks ticks=PaletteTicks, - bool copy=true, bool antialias=false); - The color space of `palette' is taken to be over bounds `bounds' with -scaling given by the z scaling of `pic'. The palette orientation is -specified by `axis', which may be one of `Right', `Left', `Top', or -`Bottom'. The bar is drawn over the rectangle from `initial' to -`final'. The argument `paletteticks' is a special tick type (*note -ticks::) that takes the following arguments: -paletteticks PaletteTicks(Label format="", ticklabel ticklabel=null, - bool beginlabel=true, bool endlabel=true, - int N=0, int n=0, real Step=0, real step=0, - pen pTick=nullpen, pen ptick=nullpen); - - The image and palette bar can be fit to a frame and added and -optionally aligned to a picture at the desired location: - -size(12cm,12cm); - -import graph; -import palette; - -int n=256; -real ninv=2pi/n; -real[][] v=new real[n][n]; - -for(int i=0; i < n; ++i) - for(int j=0; j < n; ++j) - v[i][j]=sin(i*ninv)*cos(j*ninv); - -pen[] Palette=BWRainbow(); - -picture bar; - -bounds range=image(v,(0,0),(1,1),Palette); -palette(bar,"$A$",range,(0,0),(0.5cm,8cm),Right,Palette, - PaletteTicks("$%+#.1f$")); -add(bar.fit(),point(E),30E); - - - -Here is an example that uses logarithmic scaling of the function values: - -import graph; -import palette; - -size(10cm,10cm,IgnoreAspect); - -real f(real x, real y) { - return 0.9*pow10(2*sin(x/5+2*y^0.25)) + 0.1*(1+cos(10*log(y))); -} - -scale(Linear,Log,Log); - -pen[] Palette=BWRainbow(); - -bounds range=image(f,Automatic,(0,1),(100,100),nx=200,Palette); - -xaxis("$x$",BottomTop,LeftTicks,above=true); -yaxis("$y$",LeftRight,RightTicks,above=true); - -palette("$f(x,y)$",range,(0,200),(100,250),Top,Palette, - PaletteTicks(ptick=linewidth(0.5*linewidth()))); - - - -One can also draw an image directly from a two-dimensional pen array: -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); - as illustrated in the following example: - -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)); - - - -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 - -7.29 `three' -============ - -This module fully extends the notion of guides and paths in `Asymptote' -to three dimensions. It introduces the new types guide3, path3, and -surface. Guides in three dimensions are specified with the same syntax -as in two dimensions except that triples `(x,y,z)' are used in place of -pairs `(x,y)' for the nodes and direction specifiers. This -generalization of John Hobby's spline algorithm is shape-invariant under -three-dimensional rotation, scaling, and shifting, and reduces in the -planar case to the two-dimensional algorithm used in `Asymptote', -`MetaPost', and `MetaFont' [cf. J. C. Bowman, Proceedings in Applied -Mathematics and Mechanics, 7:1, 2010021-2010022 (2007)]. - - For example, a unit circle in the XY plane may be filled and drawn -like this: - -import three; - -size(100); - -path3 g=(1,0,0)..(0,1,0)..(-1,0,0)..(0,-1,0)..cycle; -draw(g); -draw(O--Z,red+dashed,Arrow3); -draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle)); -dot(g,red); - - -and then distorted into a saddle: - -import three; - -size(100,0); -path3 g=(1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle; -draw(g); -draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle)); -dot(g,red); - - -Module `three' provides constructors for converting two-dimensional -paths to three-dimensional ones, and vice-versa: -path3 path3(path p, triple plane(pair)=XYplane); -path path(path3 p, pair P(triple)=xypart); - - A Bezier surface, the natural two-dimensional generalization of -Bezier curves, is defined in `three_surface.asy' as a structure -containing an array of Bezier patches. Surfaces may drawn with one of -the routines -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material surfacepen=currentpen, pen meshpen=nullpen, - light light=currentlight, light meshlight=light); -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material[] surfacepen, pen meshpen, - light light=currentlight, light meshlight=light); -void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, - material[] surfacepen, pen[] meshpen=nullpens, - light light=currentlight, light meshlight=light); - The parameters `nu' and `nv' specify the number of subdivisions for -drawing optional mesh lines for each Bezier patch. Here material is a -structure defined in `three_light.asy': -struct material { - pen[] p; // diffusepen,ambientpen,emissivepen,specularpen - real opacity; - real shininess; - real granularity; -... -} - 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 examples `elevation.asy' and `sphericalharmonic.asy' illustrate -how to draw a surface with patch-dependent colors. The examples -`vertexshading' and `smoothelevation' illustrate vertex-dependent -colors, which is supported for both `Asymptote''s native `OpenGL' -renderer and two-dimensional projections. Since the PRC output format -does not currently support vertex shading of Bezier surfaces, PRC -patches are shaded with the mean of the four vertex colors. - - A surface can be constructed from a cyclic `path3' with the -constructor -surface surface(path3 external, triple[] internal=new triple[], - triple[] normals=new triple[], pen[] colors=new pen[], - bool3 planar=default); - and then filled: -draw(surface(path3(polygon(5))),red); -draw(surface(unitcircle3),red); -draw(surface(unitcircle3,new pen[] {red,green,blue,black})); - 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 by nonselfintersecting cyclic paths (according to the -`zerowinding' fill rule) into subregions bounded by cyclic paths of -length `4' or less. - - Arbitrary thick three-dimensional curves and line caps (which the -`OpenGL' standard does not require implementations to provide) are -constructed with the routine -surface tube(path3 g, real width); - which returns a tube of diameter `width' centered on `g'. This can -make files 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, we recommend installing the latest SVN (antialiased) - version of the `freeglut' library (*note 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 mouse bindings are: - * Left: rotate - - * shift Left: zoom - - * ctrl Left: shift - - * Middle: menu - - * Wheel: zoom - - * Right: zoom - - * 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 - - * +: expand - - * =: expand - - * -: 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' - beyond the screen dimensions (indicated by `maxtile=(0,0)'. 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'. Other `UNIX' graphics drivers may require - the command line setting `-glOptions=-indirect'. - - 3. Embed the 3D PRC format in a PDF file and view the resulting PDF - file with version `8.0' 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. Version 2008/10/08 or - later of the `movie15' 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'. 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. - - 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, - 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, - bool showtarget=true, bool center=false)' - This is equivalent to - `orthographic((x,y,z),up,target,showtarget,center)'. - -`perspective(triple camera, triple up=Z, triple target=O, - 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, - bool showtarget=true, bool autoadjust=true, - bool center=autoadjust)' - This is equivalent to `perspective((x,y,z),up,target,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, bool group=true, - filltype filltype=NoFill, bool above=true); - adds picture `pic' as seen with `FrontView' aligned above the -projection `TopView' and to the right of the projection `RightView'. - - 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: - -`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'. - - Three-dimensional TeX Labels, which are by default drawn as Bezier -surfaces directly on the projection plane, can be transformed from the -`XY' plane by any of the above transforms or mapped to a specified -two-dimensional plane with the transform3 types `XY', `YZ', `ZX', `YX', -`ZY', `ZX'. There are also modified versions of these transforms that -take an optional argument `projection P=currentprojection' that rotate -and/or flip the label so that it is more readable from the initial -viewpoint. - - A transform3 that projects in the direction `dir' onto the plane -with normal `n' through point `O' is returned by -transform3 planeproject(triple n, triple O=O, triple dir=n); - One can use -triple normal(path3 p); - to find the unit normal vector to a planar three-dimensional path `p'. -As illustrated in the example `planeproject.asy', a transform3 that -projects in the direction `dir' onto the plane defined by a planar path -`p' is returned by -transform3 planeproject(path3 p, triple dir=normal(p)); - - The functions -surface extrude(path p, triple axis=Z); -surface extrude(Label L, triple axis=Z); - return the surface obtained by extruding path `p' or Label `L' along -`axis'. - - Three-dimensional versions of the path functions `length', `size', -`point', `dir', `accel', `radius', `precontrol', `postcontrol', -`arclength', `arctime', `reverse', `subpath', `intersect', -`intersections', `intersectionpoint', `intersectionpoints', `min', -`max', `cyclic', and `straight' are also defined. - - The routine -real[][] intersections(path3 p, surface s, real fuzz=-1); - returns the intersection times of a path `p' with a surface `s' as a -sorted array of real arrays of length 2, and -triple[] intersectionpoints(path3 p, surface s, real fuzz=-1); - returns the corresponding intersection points. Here, the computations -are performed to the absolute error specified by `fuzz', or if `fuzz < -0', to machine precision. - - Here is an example showing all five guide3 connectors: - -import graph3; - -size(200); - -currentprojection=orthographic(500,-500,500); - -triple[] z=new triple[10]; - -z[0]=(0,100,0); z[1]=(50,0,0); z[2]=(180,0,0); - -for(int n=3; n <= 9; ++n) - z[n]=z[n-3]+(200,0,0); - -path3 p=z[0]..z[1]---z[2]::{Y}z[3] -&z[3]..z[4]--z[5]::{Y}z[6] -&z[6]::z[7]---z[8]..{Y}z[9]; - -draw(p,grey+linewidth(4mm)+opacity(0.5)); - -xaxis3(Label(XY()*"$x$",align=-3Y),red,above=true); -yaxis3(Label(XY()*"$y$",align=-3X),red,above=true); - -dot(z); - - - -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'. - - Further three-dimensional examples are provided in the files -`near_earth.asy', `conicurv.asy', and (in the `animations' -subdirectory) `cube.asy'. - - Limited support for projected vector graphics (effectively -three-dimensional nonrendered `PostScript') is available with the -setting `render=0'. This currently only works for piecewise planar -surfaces, such as those produced by the parametric `surface' routines -in the `graph3' module. Surfaces produced by the `solids' package will -also be properly rendered if the parameter `nslices' is sufficiently -large. - - In the module `bsp', hidden surface removal of planar pictures is -implemented using a binary space partition and picture clipping. A -planar path is first converted to a structure `face' derived from -`picture'. A `face' may be given to a two-dimensional drawing routine -in place of any `picture' argument. An array of such faces may then be -drawn, removing hidden surfaces: -void add(picture pic=currentpicture, face[] faces, - projection P=currentprojection); - Labels may be projected to two dimensions, using projection `P', onto -the plane passing through point `O' with normal `cross(u,v)' by -multiplying it on the left by the transform -transform transform(triple u, triple v, triple O=O, - projection P=currentprojection); - - Here is an example that shows how a binary space partition may be -used to draw a two-dimensional vector graphics projection of three -orthogonal intersecting planes: - -size(6cm,0); -import bsp; - -real u=2.5; -real v=1; - -currentprojection=oblique; - -path3 y=plane((2u,0,0),(0,2v,0),(-u,-v,0)); -path3 l=rotate(90,Z)*rotate(90,Y)*y; -path3 g=rotate(90,X)*rotate(90,Y)*y; - -face[] faces; -filldraw(faces.push(y),project(y),yellow); -filldraw(faces.push(l),project(l),lightgrey); -filldraw(faces.push(g),project(g),green); - -add(faces); - - - - -File: asymptote.info, Node: obj, Next: graph3, Prev: three, Up: Base modules - -7.30 `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 - -7.31 `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="", - triple min=(-infinity,-infinity,-infinity), - triple max=(infinity,infinity,infinity), - pen p=currentpen, arrowbar3 arrow=None); - -The predefined three-dimensional axis types are -axis YZEquals(real y, real z, triple align=O, bool extend=false); -axis XZEquals(real x, real z, triple align=O, bool extend=false); -axis XYEquals(real x, real y, triple align=O, bool extend=false); -axis YZZero(triple align=O, bool extend=false); -axis XZZero(triple align=O, bool extend=false); -axis XYZero(triple align=O, bool extend=false); -axis Bounds(int type=Both, int type2=Both, triple align=O, bool extend=false); - The optional `align' parameter to these routines can be used to -specify the default axis and tick label alignments. The `Bounds' axis -accepts two type parameters, each of which must be one of `Min', `Max', -or `Both'. These parameters specify which of the four possible -three-dimensional bounding box edges should be drawn. - - The three-dimensional tick options are `NoTicks3', `InTicks', -`OutTicks', and `InOutTicks'. These specify the tick directions for the -`Bounds' axis type; other axis types inherit the direction that would -be used for the `Bounds(Min,Min)' axis. - - Here is an example of a helix and bounding box axes with ticks and -axis labels, using orthographic projection: - -import graph3; - -size(0,200); -size3(200,IgnoreAspect); - -currentprojection=orthographic(4,6,3); - -real x(real t) {return cos(2pi*t);} -real y(real t) {return sin(2pi*t);} -real z(real t) {return t;} - -path3 p=graph(x,y,z,0,2.7,operator ..); - -draw(p,Arrow3); - -scale(true); - -xaxis3(XZ()*"$x$",Bounds(),red,InTicks(Label,2,2)); -yaxis3(YZ()*"$y$",Bounds(),red,InTicks(beginlabel=false,Label,2,2)); -zaxis3(XZ()*"$z$",Bounds(),red,InTicks); - - - -The next example illustrates three-dimensional x, y, and z axes, -without autoscaling of the axis limits: - -import graph3; - -size(0,200); -size3(200,IgnoreAspect); - -currentprojection=perspective(5,2,2); - -scale(Linear,Linear,Log); - -xaxis3("$x$",0,1,red,OutTicks(2,2)); -yaxis3("$y$",0,1,red,OutTicks(2,2)); -zaxis3("$z$",1,30,red,OutTicks(beginlabel=false)); - - - -One can also place ticks along a general three-dimensional axis: - -import graph3; - -size(0,100); - -path3 g=yscale3(2)*unitcircle3; -currentprojection=perspective(10,10,10); - -axis(Label("C",position=0,align=15X),g,InTicks(endlabel=false,8,end=false), - ticklocate(0,360,new real(real v) { - path3 h=O--max(abs(max(g)),abs(min(g)))*dir(90,v); - return intersect(g,h)[0];}, - new triple(real t) {return cross(dir(g,t),Z);})); - - - -Surface plots of matrices and functions over the region `box(a,b)' in -the XY plane are also implemented: -surface surface(real[][] f, pair a, pair b, bool[][] cond={}); -surface surface(real[][] f, pair a, pair b, splinetype splinetype, - bool[][] cond={}); -surface surface(real[][] f, real[] x, real[] y, - splinetype splinetype=null, 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 splinetype, 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); - The final version draws a parametric surface for a function f(u,v) -over the parameter space `box(a,b)', as illustrated in the example -`parametricsurface.asy'. 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); - -label("$O$",O,-Z+Y,red); - - -A mesh can be drawn without surface filling by specifying `nullpen' for -the surfacepen. - - A vector field of `nu'\times`nv' arrows on a parametric surface `f' -over `box(a,b)' can be drawn with the routine -picture vectorfield(path3 vector(pair v), triple f(pair z), pair a, pair b, - int nu=nmesh, int nv=nu, bool truesize=false, - real maxlength=truesize ? 0 : maxlength(f,a,b,nu,nv), - bool cond(pair z)=null, pen p=currentpen, - arrowbar3 arrow=Arrow3, margin3 margin=PenMargin3) - as illustrated in the examples `vectorfield3.asy' and -`vectorfieldsphere.asy'. - - -File: asymptote.info, Node: grid3, Next: solids, Prev: graph3, Up: Base modules - -7.32 `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://piprim.tuxfamily.org/asymptote/grid3/'): - -import grid3; - -size(8cm,0,IgnoreAspect); -currentprojection=orthographic(0.5,1,0.5); - -scale(Linear, Linear, Log); - -limits((-2,-2,1),(0,2,100)); - -grid3(XYZgrid); - -xaxis3(Label("$x$",position=EndPoint,align=S),Bounds(Min,Min), - OutTicks()); -yaxis3(Label("$y$",position=EndPoint,align=S),Bounds(Min,Min),OutTicks()); -zaxis3(Label("$z$",position=EndPoint,align=(-1,0.5)),Bounds(Min,Min), - OutTicks(beginlabel=false)); - - - - -File: asymptote.info, Node: solids, Next: tube, Prev: grid3, Up: Base modules - -7.33 `solids' -============= - -This solid geometry package defines a structure `revolution' that can -be used to fill and draw surfaces of revolution. The following example -uses it to display the outline of a circular cylinder of radius 1 with -axis `O--1.5unit(Y+Z)' with perspective projection: - -import solids; - -size(0,100); - -revolution r=cylinder(O,1,1.5,Y+Z); -draw(r,heavygreen); - - - -Further illustrations are provided in the example files `cylinder.asy', -`cones.asy', `hyperboloid.asy', and `torus.asy'. - - The structure `skeleton' contains the three-dimensional wireframe -used to visualize a volume of revolution: -struct skeleton { - struct curve { - path3[] front; - path3[] back; - } - // transverse skeleton (perpendicular to axis of revolution) - curve transverse; - // longitudinal skeleton (parallel to axis of revolution) - curve longitudinal; -} - - -File: asymptote.info, Node: tube, Next: flowchart, Prev: solids, Up: Base modules - -7.34 `tube' -=========== - -This package extends the routine `tube' defined 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://piprim.tuxfamily.org/asymptote/tube/'. - - -File: asymptote.info, Node: flowchart, Next: contour, Prev: tube, Up: Base modules - -7.35 `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); - -"diamond-shaped flowchart 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 flowchart block:" - block circle(object body, pair center=(0,0), pen fillpen=invisible, - pen drawpen=currentpen, real dr=3, - real mindiameter=mincirclediameter); - -"rectangular flowchart 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 flowchart 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: - -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) { - draw(pic,path(new pair[]{block1.right(t),block2.top(t)},Horizontal), - Arrow,PenMargin); - draw(pic,Label("Yes",0.5,NW),path(new pair[]{block2.left(t),block3.top(t)}, - Horizontal),Arrow,PenMargin); - draw(pic,Label("No",0.5,NE),path(new pair[]{block2.right(t),block4.top(t)}, - Horizontal),Arrow,PenMargin); - draw(pic,path(new pair[]{block3.bottom(t),block5.left(t)},Vertical), - Arrow,PenMargin); - draw(pic,path(new pair[]{block4.bottom(t),block5.right(t)},Vertical), - Arrow,PenMargin); - }); - - - - -File: asymptote.info, Node: contour, Next: contour3, Prev: flowchart, Up: Base modules - -7.36 `contour' -============== - -This package draws contour lines. To construct contours corresponding -to the values in an array `c' for a function `f' on `box(a,b)', use -guide[][] contour(real f(real, real), pair a, pair b, - real[] c, int nx=ngraph, int ny=nx, - interpolate join=operator --); - 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. - - To construct contours for an array of data values on a uniform -two-dimensional lattice on `box(a,b)', use -guide[][] contour(real[][] f, real[][] midpoint=new real[][], - pair a, pair b, real[] c, - interpolate join=operator --); - - To construct contours for an array of data values on a nonoverlapping -regular mesh specified by the two-dimensional array `z', optionally -specifying the values of `f' at the mesh midpoints, use -guide[][] contour(pair[][] z, real[][] f, - real[][] midpoint=new real[][], real[] c, - interpolate join=operator --); - - To construct contours for an array of values `f' specified at -irregularly positioned points `z', use the routine -guide[][] contour(pair[] z, real[] f, real[] c, - interpolate join=operator --); - The contours themselves can be drawn with one of the routines -void draw(picture pic=currentpicture, Label[] L=new Label[], - guide[][] g, pen p=currentpen) - -void draw(picture pic=currentpicture, Label[] L=new Label[], - guide[][] g, pen[] p) - - The following simple example draws the contour at value `1' for the -function z=x^2+y^2, which is a unit circle: - -import contour; -size(75); - -real f(real a, real b) {return a^2+b^2;} -draw(contour(f,(-1,-1),(1,1),new real[] {1})); - - - -The next example draws and labels multiple contours for the function -z=x^2-y^2 with the resolution `100 x 100', using a dashed pen for -negative contours and a solid pen for positive (and zero) contours: - -import contour; - -size(200); - -real f(real x, real y) {return x^2-y^2;} -int n=10; -real[] c=new real[n]; -for(int i=0; i < n; ++i) c[i]=(i-n/2)/n; - -pen[] p=sequence(new pen(int i) { - return (c[i] >= 0 ? solid : dashed)+fontsize(6); - },c.length); - -Label[] Labels=sequence(new Label(int i) { - return Label(c[i] != 0 ? (string) c[i] : "",Relative(unitrand()),(0,0), - UnFill(1bp)); - },c.length); - -draw(Labels,contour(f,(-1,-1),(1,1),c),p); - - - -The next example illustrates how contour lines can be drawn on color -density images: - -import graph; -import palette; -import contour; - -size(10cm,10cm,IgnoreAspect); - -pair a=(0,0); -pair b=(2pi,2pi); - -real f(real x, real y) {return cos(x)*sin(y);} - -int N=200; -int Divs=10; -int divs=2; - -defaultpen(1bp); -pen Tickpen=black; -pen tickpen=gray+0.5*linewidth(currentpen); -pen[] Palette=BWRainbow(); - -scale(false); - -bounds range=image(f,Automatic,a,b,N,Palette); - -// Major contours - -real[] Cvals=uniform(range.min,range.max,Divs); -draw(contour(f,a,b,Cvals,N,operator --),Tickpen); - -// Minor contours -real[] cvals; -for(int i=0; i < Cvals.length-1; ++i) - cvals.append(uniform(Cvals[i],Cvals[i+1],divs)[1:divs]); -draw(contour(f,a,b,cvals,N,operator --),tickpen); - -xaxis("$x$",BottomTop,LeftTicks,above=true); -yaxis("$y$",LeftRight,RightTicks,above=true); - -palette("$f(x,y)$",range,point(NW)+(0,0.5),point(NE)+(0,1),Top,Palette, - PaletteTicks(N=Divs,n=divs,Tickpen,tickpen)); - - - -Finally, here is an example that illustrates the construction of -contours from irregularly spaced data: - -import contour; - -size(200); - -int n=100; - -pair[] points=new pair[n]; -real[] values=new real[n]; - -real f(real a, real b) {return a^2+b^2;} - -real r() {return 1.1*(rand()/randMax*2-1);} - -for(int i=0; i < n; ++i) { - points[i]=(r(),r()); - values[i]=f(points[i].x,points[i].y); -} - -draw(contour(points,values,new real[]{0.25,0.5,1},operator ..),blue); - - - -In the above example, the contours of irregularly spaced data are -constructed by first creating a triangular mesh from an array `z' of -pairs: - -int[][] triangulate(pair[] z); - -size(200); -int np=100; -pair[] points; - -real r() {return 1.2*(rand()/randMax*2-1);} - -for(int i=0; i < np; ++i) - points.push((r(),r())); - -int[][] trn=triangulate(points); - -for(int i=0; i < trn.length; ++i) { - draw(points[trn[i][0]]--points[trn[i][1]]); - draw(points[trn[i][1]]--points[trn[i][2]]); - draw(points[trn[i][2]]--points[trn[i][0]]); -} - -for(int i=0; i < np; ++i) - dot(points[i],red); - - - -The example `Gouraudcontour' illustrates how to produce color density -images over such irregular triangular meshes. `Asymptote' uses a -robust version of Paul Bourke's Delaunay triangulation algorithm based -on the public-domain exact arithmetic predicates written by Jonathan -Shewchuk. - - -File: asymptote.info, Node: contour3, Next: slopefield, Prev: contour, Up: Base modules - -7.37 `contour3' -=============== - -This package draws surfaces described as the null space of real-valued -functions of (x,y,z) or real[][][] matrices. Its usage is illustrated -in the example file `magnetic.asy'. - - -File: asymptote.info, Node: slopefield, Prev: contour3, Up: Base modules - -7.38 `slopefield' -================= - -To draw a slope field for the differential equation dy/dx=f(x,y) (or -dy/dx=f(x)), use: -picture slopefield(real f(real,real), pair a, pair b, - int nx=nmesh, int ny=nx, - real tickfactor=0.5, pen p=currentpen, - arrowbar arrow=None); - Here, the points `a' and `b' are the lower left and upper right -corners of the rectangle in which the slope field is to be drawn, `nx' -and `ny' are the respective number of ticks in the x and y directions, -`tickfactor' is the fraction of the minimum cell dimension to use for -drawing ticks, and `p' is the pen to use for drawing the slope fields. -The return value is a picture that can be added to `currentpicture' via -the `add(picture)' command. - - The function -path curve(pair c, real f(real,real), pair a, pair b); - takes a point (`c') and a slope field-defining function `f' and -returns, as a path, the curve passing through that point. The points -`a' and `b' represent the rectangular boundaries over which the curve -is interpolated. - - Both `slopefield' and `curve' alternatively accept a function `real -f(real)' that depends on x only, as seen in this example: - -import slopefield; - -size(200); - -real func(real x) {return 2x;} -add(slopefield(func,(-3,-3),(3,3),20,Arrow)); -draw(curve((0,0),func,(-3,-3),(3,3)),red); - - diff --git a/Build/source/utils/asymptote/doc/png/asymptote.info-2 b/Build/source/utils/asymptote/doc/png/asymptote.info-2 deleted file mode 100644 index 749689f2d00..00000000000 --- a/Build/source/utils/asymptote/doc/png/asymptote.info-2 +++ /dev/null @@ -1,1795 +0,0 @@ -This is asymptote.info, produced by makeinfo version 4.13 from -../asymptote.texi. - -This file documents `Asymptote', version 1.75. - - `http://asymptote.sourceforge.net' - - Copyright (C) 2004-9 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). Vector graphics language. -END-INFO-DIR-ENTRY - - - -File: asymptote.info, Node: Options, Next: Interactive mode, Prev: Base modules, Up: Top - -8 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 [Center] --antialias n Antialiasing width for rasterized output [2] --auto3D Automatically activate 3D scene [true] --autoimport string Module to automatically import --autoplain Enable automatic importing of plain [true] --autorotate Enable automatic PDF page rotation [false] --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] --embed Embed rendered preview image [true] --exitonEOF Exit interactive mode on EOF [true] --fitscreen Fit rendered image to screen [true] --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] --m,-mask Mask fpu exceptions; command-line only --maxtile pair Maximum rendering tile size [(0,0)] --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] --O,-offset pair PostScript offset [(0,0)] --f,-outformat format Convert each output file to specified format --o,-outname name Alternative output directory/filename --p,-parseonly Parse file [false] --pdfreload Automatically reload document in pdfviewer [false] --pdfreloaddelay usec Delay before attempting initial pdf reload [750000] --position pair Initial 3D rendering screen position [(0,0)] --prc Embed 3D PRC graphics in PDF output [true] --prompt string Prompt [> ] --prompt2 string Continuation prompt for multiline input [..] --q,-quiet Suppress welcome message [false] --render n Render 3D graphics using n pixels per bp (-1=auto) [-1] --rgb Convert cmyk colors to rgb [false] --safe Disable system call [true] --scroll n Scroll standard output n lines at a time [0] --tabcompletion Interactive prompt auto-completion [true] --tex engine latex|pdflatex|xelatex|tex|pdftex|context|none [latex] --thick Render thick 3D lines [true] --thin Render thin 3D lines [true] --threads Use POSIX threads for 3D rendering [true] --toolbar Show 3D toolbar in PDF output [true] --s,-translate Show translated virtual machine code [false] --twice Run LaTeX twice (to resolve references) [false] --twosided Use two-sided 3D lighting model for rendering [true] --u,-user string General purpose user string --v,-verbose Increase verbosity level (can specify multiple times) [0] --version Show version; command-line only --wait Wait for child processes to finish before exiting [false] --where Show where listed variables are declared [false] --xformat format GUI deconstruction format [png] - - 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. -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', `convertOptions', `gsOptions', -`psviewerOptions', `pdfviewerOptions', and `glOptions' allow -specialized options to be passed as a string to the respective -applications or libraries. - - If you insert -import plain; -settings.autoplain=true; - at the beginning of the configuration file, it can contain arbitrary -`Asymptote' code. - - The default output format is EPS for the (default) `latex' and `tex' -tex engine and PDF for the `pdflatex', `xelatex', and `context' tex -engines. Alternative output formats may be produced using the `-f' -option (or `outformat' setting). 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. `Asymptote' can 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'). To give specific 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)' call, allowing one to execute -arbitrary shell commands. The default mode, `-safe', disables this call. - - A `PostScript' offset may be specified as a pair (in `bp' units) -with the `-O' option: -asy -O 0,0 file - The default offset is zero. The default value of the page alignment -setting `align' is `Center'. - - The `-c' (`command') option may be used to execute arbitrary -`Asymptote' code on the command line as a string. It is not necessary -to terminate the string with a semicolon. Multiple `-c' options are -executed in the order they are given. For example -asy -c 2+2 -c "sin(1)" -c "size(100); draw(unitsquare)" - produces the output -4 -0.841470984807897 - and draws a unitsquare of size `100'. - - The `-u' (`user') option may be used to specify arbitrary -`Asymptote' settings on the command line as a string. It is not -necessary to terminate the string with a semicolon. Multiple `-u' -options are executed in the order they are given. Command-line code like -`-u x=sqrt(2)' can be executed within a module like this: -real x; -usersetting(); -write(x); - - When the `-l' (`listvariables') option is used with file arguments, -only global functions and variables defined in the specified file(s) -are listed. - - Additional debugging output is produced with each additional `-v' -option: -`-v' - Display top-level module and final output file names. - -`-vv' - Also display imported and included module names and final `LaTeX' - and `dvips' processing information. - -`-vvv' - Also output `LaTeX' bidirectional pipe diagnostics. - -`-vvvv' - Also output knot guide solver diagnostics. - -`-vvvvv' - Also output `Asymptote' traceback diagnostics. - - -File: asymptote.info, Node: Interactive mode, Next: GUI, Prev: Options, Up: Top - -9 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'. - - The following special commands are supported only in interactive mode -and must be entered immediately after the prompt: - -`help' - view the manual; - -`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 - -10 Graphical User Interface -*************************** - -In the event that adjustments to the final figure are required, the -preliminary Graphical User Interface (GUI) `xasy' included with -`Asymptote' allows you to move graphical objects and draw new ones. -The modified figure can then be saved as a normal `Asymptote' file. - -* Menu: - -* GUI Installation:: Installing `xasy' -* GUI Usage:: - - -File: asymptote.info, Node: GUI Installation, Next: GUI Usage, Up: GUI - -10.1 GUI Installation -===================== - -As `xasy' is written in the interactive scripting language `Python/TK', -it requires `Python' (`http://www.python.org'), the Python Imaging -Library (`http://www.pythonware.com/products/pil/'), and the `tkinter' -package (included with s`Python' under `Microsoft Windows') be -installed. `Fedora Linux' users can either install `tkinter' with the -commands -yum install tkinter -yum install tk-devel - or manually install the `tkinter', `tix', `tk', and `tk-devel' -packages. - - Pictures are deconstructed into the PNG image format, which supports -full alpha channel transparency. Under `Microsoft Windows', this -requires `Python 2.5 (or 2.5.1)' and the `Python Imaging Library': - - `http://www.python.org/ftp/python/2.5.1/python-2.5.1.msi' - - `http://effbot.org/downloads/PIL-1.1.6.win32-py2.5.exe'. - On `UNIX' systems, place -`http://effbot.org/downloads/Imaging-1.1.6.tar.gz' in the `Asymptote' -source directory, and type (as the root user): -tar -zxf Imaging-1.1.6.tar.gz -cd Imaging-1.1.6 -patch -p1 < ../patches/TkAlpha-Imaging-1.1.6.patch -python setup.py install - - Alternatively, `xasy' can deconstruct pictures into the GIF image -format (not recommended as this is very slow), using white as the -transparent color. This requires the lines -import settings; -xformat="gif"; - in the `Asymptote' configuration file (*note configuration file::), -along with the `ImageMagick' (*note convert::) program. - - -File: asymptote.info, Node: GUI Usage, Prev: GUI Installation, Up: GUI - -10.2 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 - -11 `PostScript' to `Asymptote' -****************************** - -The excellent `PostScript' editor `pstoedit' (version 3.45 or later; -available from `http://pstoedit.net') 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. - - For full functionality, the patch `pstoedit-3.45asy.patch' in the -`patches' directory should be applied. On `UNIX' systems, as the root -user, place - - `http://prdownloads.sourceforge.net/pstoedit/pstoedit-3.45.tar.gz' - in the `Asymptote' source directory, and type: - -tar -zxf pstoedit-3.45.tar.gz -cd pstoedit-3.45 -patch -p1 < ../patches/pstoedit-3.45asy.patch -autoconf -./configure --prefix=/usr -make install - -Then try: - -`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 - -12 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/forum/forum.php?forum_id=409349' - Including an example that illustrates what you are trying to do will -help you get useful feedback. `LaTeX' problems can often be diagnosed -with the `-vv' or `-vvv' command-line options. Contributions in the -form of patches or `Asymptote' modules can be posted here: - - `http://sourceforge.net/tracker/?atid=685685&group_id=120000' - To receive announcements of upcoming releases, please subscribe to -`Asymptote' at - - `http://freshmeat.net/projects/asy' - If you find a bug in `Asymptote', please check (if possible) whether -the bug is still present in the latest Subversion developmental code -(*note Subversion::) before submitting a bug report. New bugs can be -submitted using the Bug Tracking System at - - `http://sourceforge.net/projects/asymptote' - To see if the bug has already been fixed, check bugs with Status -`Closed' and recent lines in - - `http://asymptote.sourceforge.net/ChangeLog' - `Asymptote' can be configured with the optional GNU library -`libsigsegv', available from `http://libsigsegv.sourceforge.net', which -allows one to distinguish user-generated `Asymptote' stack overflows -(*note stack overflow::) from true segmentation faults (due to internal -C++ programming errors; please submit the `Asymptote' code that -generates such segmentation faults along with your bug report). - - -File: asymptote.info, Node: Debugger, Next: Credits, Prev: Help, Up: Top - -13 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 - -14 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 Radoslav Marinov, Orest Shardt, Chris Savage, -Philippe Ivaldi, Olivier Guibe', Jacques Pienaar, Mark Henning, Steve -Melenchuk, Martin Wiebusch, and Stefan Knorr. - - -File: asymptote.info, Node: Index, Prev: Credits, Up: Top - -Index -***** - - -* Menu: - -* !: Arithmetic & logical. - (line 68) -* != <1>: Arithmetic & logical. - (line 38) -* !=: Structures. (line 54) -* %: Arithmetic & logical. - (line 23) -* %=: Self & prefix operators. - (line 6) -* & <1>: Arithmetic & logical. - (line 56) -* &: Tutorial. (line 192) -* &&: Arithmetic & logical. - (line 53) -* * <1>: Arithmetic & logical. - (line 17) -* *: Pens. (line 15) -* **: Arithmetic & logical. - (line 31) -* *=: Self & prefix operators. - (line 6) -* + <1>: Arithmetic & logical. - (line 13) -* +: Pens. (line 15) -* ++: Self & prefix operators. - (line 6) -* +=: Self & prefix operators. - (line 6) -* -: Arithmetic & logical. - (line 14) -* -- <1>: Self & prefix operators. - (line 6) -* --: Tutorial. (line 109) -* ---: Tutorial. (line 192) -* -=: Self & prefix operators. - (line 6) -* -c: Options. (line 155) -* -l: Options. (line 174) -* -u: Options. (line 165) -* -V <1>: Tutorial. (line 41) -* -V: Configuring. (line 6) -* ..: Tutorial. (line 109) -* .asy: Search paths. (line 13) -* /: Arithmetic & logical. - (line 20) -* /=: Self & prefix operators. - (line 6) -* 2D graphs: graph. (line 6) -* 3D graphs: graph3. (line 6) -* 3D grids: grid3. (line 6) -* 3D rendering: Compiling from UNIX source. - (line 16) -* :: Arithmetic & logical. - (line 73) -* ::: Tutorial. (line 176) -* <: Arithmetic & logical. - (line 41) -* <=: Arithmetic & logical. - (line 44) -* == <1>: Arithmetic & logical. - (line 37) -* ==: Structures. (line 54) -* >: Arithmetic & logical. - (line 50) -* >=: Arithmetic & logical. - (line 47) -* ?: Arithmetic & logical. - (line 73) -* ^: Arithmetic & logical. - (line 28) -* ^=: Self & prefix operators. - (line 6) -* ^^: Tutorial. (line 197) -* a4: Configuring. (line 62) -* abort: Data types. (line 320) -* abs <1>: Mathematical functions. - (line 35) -* abs: Data types. (line 60) -* accel <1>: three. (line 426) -* accel: Paths and guides. (line 110) -* access: Import. (line 6) -* acknowledgments: Credits. (line 6) -* aCos: Mathematical functions. - (line 20) -* acos: Mathematical functions. - (line 6) -* acosh: Mathematical functions. - (line 6) -* add: Frames and pictures. (line 190) -* Ai: Mathematical functions. - (line 48) -* Ai_deriv: Mathematical functions. - (line 48) -* Airy: Mathematical functions. - (line 48) -* alias <1>: Arrays. (line 187) -* alias: Structures. (line 54) -* align: Options. (line 149) -* Align: label. (line 12) -* all: Arrays. (line 331) -* Allow: Pens. (line 323) -* AND: Arithmetic & logical. - (line 80) -* and: Tutorial. (line 165) -* angle: Data types. (line 68) -* animate <1>: animation. (line 12) -* animate <2>: Files. (line 148) -* animate: Configuring. (line 68) -* animation: animation. (line 6) -* annotate: annotate. (line 6) -* antialias <1>: Options. (line 129) -* antialias: three. (line 180) -* antialiasing: Compiling from UNIX source. - (line 16) -* append <1>: Arrays. (line 39) -* append: Files. (line 36) -* arc: three. (line 245) -* Arc: Paths and guides. (line 32) -* arc: Paths and guides. (line 22) -* ArcArrow: draw. (line 26) -* ArcArrow3: three. (line 469) -* ArcArrows: draw. (line 26) -* ArcArrows3: three. (line 469) -* arclength <1>: three. (line 426) -* arclength: Paths and guides. (line 137) -* arctime <1>: three. (line 426) -* arctime: Paths and guides. (line 141) -* arguments: Default arguments. (line 6) -* arithmetic operators: Arithmetic & logical. - (line 6) -* array: Arrays. (line 125) -* array iteration: Programming. (line 33) -* arrays: Arrays. (line 6) -* arrow: label. (line 72) -* Arrow: draw. (line 26) -* arrow: Drawing commands. (line 31) -* arrow keys: Tutorial. (line 21) -* Arrow3: three. (line 469) -* Arrows: draw. (line 26) -* Arrows3: three. (line 469) -* as: Import. (line 70) -* aSin: Mathematical functions. - (line 20) -* asin: Mathematical functions. - (line 6) -* asinh: Mathematical functions. - (line 6) -* Aspect: Frames and pictures. (line 54) -* assignment: Programming. (line 8) -* asy: Import. (line 105) -* asy-mode: Editing modes. (line 6) -* asy.vim: Editing modes. (line 33) -* asymptote.sty: LaTeX usage. (line 6) -* ASYMPTOTE_CONFIG: Options. (line 102) -* aTan: Mathematical functions. - (line 20) -* atan: Mathematical functions. - (line 6) -* atan2: Mathematical functions. - (line 6) -* atanh: Mathematical functions. - (line 6) -* atleast: Tutorial. (line 165) -* attach <1>: graph. (line 405) -* attach: LaTeX usage. (line 32) -* autoadjust: three. (line 315) -* autoimport: Options. (line 98) -* automatic scaling: graph. (line 672) -* axialshade: fill. (line 43) -* axis <1>: graph3. (line 66) -* axis: graph. (line 870) -* azimuth: Data types. (line 124) -* babel: babel. (line 6) -* background color: Frames and pictures. (line 162) -* BackView: three. (line 340) -* Bar: draw. (line 19) -* Bar3: three. (line 469) -* Bars: draw. (line 19) -* Bars3: three. (line 469) -* barsize: draw. (line 19) -* base modules: Base modules. (line 6) -* basealign: Pens. (line 164) -* baseline: label. (line 92) -* batch mode: Tutorial. (line 30) -* beep: Data types. (line 334) -* BeginArcArrow: draw. (line 26) -* BeginArcArrow3: three. (line 469) -* BeginArrow: draw. (line 26) -* BeginArrow3: three. (line 469) -* BeginBar: draw. (line 19) -* BeginBar3: three. (line 469) -* BeginDotMargin: draw. (line 42) -* BeginDotMargin3: three. (line 485) -* BeginMargin: draw. (line 42) -* BeginMargin3: three. (line 485) -* BeginPenMargin: draw. (line 42) -* BeginPenMargin2: three. (line 485) -* BeginPenMargin3: three. (line 485) -* BeginPoint: label. (line 57) -* Bessel: Mathematical functions. - (line 48) -* bevel: flowchart. (line 68) -* beveljoin: Pens. (line 134) -* bezulate: three. (line 98) -* Bi: Mathematical functions. - (line 48) -* Bi_deriv: Mathematical functions. - (line 48) -* binary format: Files. (line 71) -* binary operators: Arithmetic & logical. - (line 6) -* binarytree: binarytree. (line 6) -* binput: Files. (line 71) -* Blank: draw. (line 26) -* block.bottom: flowchart. (line 19) -* block.bottomleft: flowchart. (line 19) -* block.bottomright: flowchart. (line 19) -* block.center: flowchart. (line 26) -* block.draw: flowchart. (line 31) -* block.left: flowchart. (line 19) -* block.position: flowchart. (line 24) -* block.right: flowchart. (line 19) -* block.top: flowchart. (line 19) -* block.topleft: flowchart. (line 19) -* block.topright: flowchart. (line 19) -* bool: Data types. (line 14) -* bool3: Data types. (line 23) -* boolean operators: Arithmetic & logical. - (line 6) -* Bottom: graph. (line 128) -* BottomTop: graph. (line 134) -* BottomView: three. (line 340) -* bounding box: Frames and pictures. (line 162) -* Bounds: graph3. (line 20) -* boutput: Files. (line 71) -* box <1>: three. (line 267) -* box: Frames and pictures. (line 22) -* bp: Tutorial. (line 17) -* break: Programming. (line 29) -* breakpoints: Debugger. (line 21) -* brick: Pens. (line 247) -* broken axis: graph. (line 773) -* bug reports: Help. (line 23) -* buildcycle: Paths and guides. (line 251) -* Button-1: GUI. (line 6) -* Button-2: GUI. (line 6) -* BWRainbow: palette. (line 15) -* BWRainbow2: palette. (line 18) -* C string: Data types. (line 189) -* CAD: CAD. (line 6) -* calculateTransform: Frames and pictures. (line 105) -* casts: Casts. (line 6) -* cbrt: Mathematical functions. - (line 6) -* cd: Files. (line 24) -* ceil: Mathematical functions. - (line 26) -* center: three. (line 300) -* Center: label. (line 62) -* checker: Pens. (line 247) -* Chinese: unicode. (line 12) -* choose: Mathematical functions. - (line 39) -* Ci: Mathematical functions. - (line 48) -* circle <1>: flowchart. (line 57) -* circle: three. (line 241) -* Circle: Paths and guides. (line 17) -* circle: Paths and guides. (line 10) -* circlebarframe: markers. (line 18) -* CJK: unicode. (line 12) -* clear <1>: Debugger. (line 23) -* clear: Files. (line 86) -* clip: fill. (line 110) -* cm: Tutorial. (line 63) -* cmyk: Pens. (line 34) -* colatitude: Data types. (line 129) -* color: Pens. (line 23) -* coloredNodes: tube. (line 25) -* coloredpath: tube. (line 18) -* coloredSegments: tube. (line 25) -* colorless: Pens. (line 54) -* colors: Pens. (line 51) -* comma: Files. (line 59) -* comma-separated-value mode: Arrays. (line 362) -* command-line options <1>: Options. (line 7) -* command-line options: Configuring. (line 82) -* comment character: Files. (line 15) -* compass directions: Tutorial. (line 94) -* Compiling from UNIX source: Compiling from UNIX source. - (line 6) -* complement: Arrays. (line 153) -* concat: Arrays. (line 183) -* conditional <1>: Arithmetic & logical. - (line 73) -* conditional: Programming. (line 8) -* config: Options. (line 102) -* configuration file: Configuring. (line 21) -* configuring: Configuring. (line 6) -* conj: Data types. (line 57) -* constructors: Structures. (line 95) -* context: Options. (line 129) -* continue <1>: Debugger. (line 31) -* continue: Programming. (line 29) -* contour: contour. (line 7) -* contour3: contour3. (line 6) -* controls <1>: three. (line 6) -* controls: Tutorial. (line 154) -* controlSpecifier: Paths and guides. (line 371) -* convert <1>: Options. (line 129) -* convert <2>: animation. (line 6) -* convert <3>: Files. (line 148) -* convert: Configuring. (line 68) -* convertOptions: Options. (line 117) -* Coons shading: fill. (line 74) -* copy: Arrays. (line 174) -* Cos: Mathematical functions. - (line 20) -* cos: Mathematical functions. - (line 6) -* cosh: Mathematical functions. - (line 6) -* cputime: Structures. (line 177) -* crop: graph. (line 626) -* cropping graphs: graph. (line 626) -* cross <1>: graph. (line 474) -* cross: Data types. (line 167) -* crossframe: markers. (line 23) -* crosshatch: Pens. (line 263) -* csv: Arrays. (line 362) -* cubicroots: Arrays. (line 320) -* curl <1>: three. (line 6) -* curl: Tutorial. (line 172) -* curlSpecifier: Paths and guides. (line 383) -* currentpen: Pens. (line 6) -* currentprojection: three. (line 337) -* curve: slopefield. (line 20) -* custom axis types: graph. (line 138) -* custom mark routine: graph. (line 566) -* custom tick locations: graph. (line 241) -* cut: Paths and guides. (line 233) -* cycle <1>: three. (line 6) -* cycle: Tutorial. (line 46) -* cyclic <1>: three. (line 426) -* cyclic <2>: Arrays. (line 39) -* cyclic: Paths and guides. (line 75) -* cyclicflag: Arrays. (line 39) -* Cyrillic: unicode. (line 7) -* dashdotted: Pens. (line 92) -* dashed: Pens. (line 92) -* data types: Data types. (line 6) -* date: Data types. (line 290) -* Debian: UNIX binary distributions. - (line 19) -* debugger: Debugger. (line 6) -* declaration: Programming. (line 8) -* deconstruct: GUI Usage. (line 6) -* default arguments: Default arguments. (line 6) -* defaultformat: graph. (line 169) -* DefaultHead: draw. (line 26) -* DefaultHead3: three. (line 469) -* defaultpen: Pens. (line 46) -* deferred drawing: simplex. (line 6) -* Degrees: Mathematical functions. - (line 17) -* degrees <1>: Mathematical functions. - (line 17) -* degrees: Data types. (line 73) -* delete <1>: Arrays. (line 39) -* delete: Files. (line 143) -* description: Description. (line 6) -* diagonal: Arrays. (line 305) -* diamond: flowchart. (line 50) -* dimension: Arrays. (line 368) -* dir <1>: three. (line 426) -* dir <2>: Paths and guides. (line 99) -* dir <3>: Data types. (line 85) -* dir: Search paths. (line 10) -* direction specifier: Tutorial. (line 115) -* directory: Files. (line 24) -* dirSpecifier: Paths and guides. (line 365) -* dirtime: Paths and guides. (line 147) -* display: Configuring. (line 68) -* do: Programming. (line 29) -* dot <1>: Data types. (line 98) -* dot: draw. (line 83) -* DotMargin: draw. (line 42) -* DotMargin3: three. (line 485) -* DotMargins: draw. (line 42) -* DotMargins3: three. (line 485) -* dotted: Pens. (line 92) -* double: Files. (line 71) -* double deferred drawing: three. (line 222) -* Draw: Frames and pictures. (line 145) -* draw: draw. (line 110) -* Draw: draw. (line 26) -* draw: Drawing commands. (line 31) -* drawing commands: Drawing commands. (line 6) -* drawline: math. (line 9) -* drawtree: drawtree. (line 7) -* dvips: Configuring. (line 68) -* dvipsOptions: Options. (line 117) -* E <1>: Mathematical functions. - (line 48) -* E: Tutorial. (line 94) -* Editing modes: Editing modes. (line 6) -* Ei: Mathematical functions. - (line 48) -* ellipse: Frames and pictures. (line 22) -* elliptic functions: Mathematical functions. - (line 48) -* else: Programming. (line 8) -* emacs: Editing modes. (line 6) -* embed: embed. (line 6) -* empty: Frames and pictures. (line 7) -* EndArcArrow: draw. (line 26) -* EndArcArrow3: three. (line 469) -* EndArrow: draw. (line 26) -* EndArrow3: three. (line 469) -* EndBar: draw. (line 19) -* EndBar3: three. (line 469) -* EndDotMargin: draw. (line 42) -* EndDotMargin3: three. (line 485) -* endl: Files. (line 59) -* EndMargin: draw. (line 42) -* EndMargin3: three. (line 485) -* EndPenMargin: draw. (line 42) -* EndPenMargin2: three. (line 485) -* EndPenMargin3: three. (line 485) -* EndPoint: label. (line 57) -* envelope: Frames and pictures. (line 22) -* environment variables: Configuring. (line 86) -* eof <1>: Arrays. (line 346) -* eof: Files. (line 86) -* eol <1>: Arrays. (line 346) -* eol: Files. (line 86) -* EPS: label. (line 80) -* erase <1>: Frames and pictures. (line 7) -* erase: Data types. (line 239) -* erf: Mathematical functions. - (line 6) -* erfc: Mathematical functions. - (line 6) -* error: Files. (line 15) -* errorbars: graph. (line 474) -* eval: Import. (line 101) -* evenodd <1>: Pens. (line 148) -* evenodd: Tutorial. (line 211) -* exit <1>: Debugger. (line 57) -* exit <2>: Interactive mode. (line 37) -* exit: Data types. (line 325) -* exp: Mathematical functions. - (line 6) -* expi: Data types. (line 81) -* explicit: Casts. (line 6) -* explicit casts: Casts. (line 22) -* expm1: Mathematical functions. - (line 6) -* exponential integral: Mathematical functions. - (line 48) -* extendcap: Pens. (line 125) -* extension <1>: MetaPost. (line 10) -* extension: Paths and guides. (line 228) -* external: embed. (line 28) -* extrude: three. (line 420) -* F: Mathematical functions. - (line 48) -* fabs: Mathematical functions. - (line 6) -* face: three. (line 504) -* factorial: Mathematical functions. - (line 39) -* Fedora: UNIX binary distributions. - (line 15) -* feynman: feynman. (line 6) -* fft: Arrays. (line 252) -* FFTW: Compiling from UNIX source. - (line 59) -* file <1>: Debugger. (line 45) -* file: Files. (line 6) -* Fill: Frames and pictures. (line 131) -* fill <1>: fill. (line 17) -* fill: draw. (line 116) -* Fill: draw. (line 26) -* FillDraw: Frames and pictures. (line 121) -* filldraw: fill. (line 11) -* FillDraw: draw. (line 26) -* filloutside: fill. (line 27) -* fillrule: Pens. (line 148) -* find <1>: Arrays. (line 162) -* find: Data types. (line 224) -* firstcut: Paths and guides. (line 243) -* fit: Frames and pictures. (line 101) -* fix-cm: Pens. (line 174) -* fixedscaling: Frames and pictures. (line 74) -* floor: Mathematical functions. - (line 26) -* flowchart: flowchart. (line 6) -* flush: Files. (line 59) -* fmod: Mathematical functions. - (line 6) -* font: Pens. (line 188) -* font command: Pens. (line 188) -* fontcommand: Pens. (line 203) -* fontsize: Pens. (line 174) -* for: Programming. (line 8) -* format <1>: Options. (line 129) -* format: Data types. (line 266) -* forum: Help. (line 6) -* frame: Frames and pictures. (line 7) -* freeglut: Compiling from UNIX source. - (line 16) -* from: Import. (line 17) -* FrontView: three. (line 340) -* function declarations: Functions. (line 67) -* function shading: fill. (line 95) -* Function shading: fill. (line 95) -* functions <1>: Mathematical functions. - (line 6) -* functions: Functions. (line 6) -* functionshade: fill. (line 95) -* gamma: Mathematical functions. - (line 6) -* Gaussrand: Mathematical functions. - (line 39) -* geometry: geometry. (line 6) -* getc: Files. (line 30) -* getpair: Files. (line 111) -* getreal: Files. (line 111) -* getstring: Files. (line 111) -* gettriple: Files. (line 111) -* glOptions <1>: Options. (line 117) -* glOptions: three. (line 180) -* GNU Scientific Library: Mathematical functions. - (line 48) -* gouraudshade: fill. (line 58) -* Gradient: palette. (line 25) -* gradient shading: fill. (line 32) -* graph: graph. (line 6) -* graph3: graph3. (line 6) -* graphic: label. (line 80) -* graphical user interface: GUI. (line 6) -* gray: Pens. (line 25) -* Grayscale: palette. (line 9) -* grayscale: Pens. (line 25) -* grid <1>: graph. (line 724) -* grid: Pens. (line 247) -* grid3: grid3. (line 6) -* gs: Configuring. (line 6) -* gsl: Mathematical functions. - (line 48) -* GSL: Compiling from UNIX source. - (line 59) -* gsOptions: Options. (line 117) -* GUI: GUI. (line 6) -* GUI installation: GUI Installation. (line 6) -* GUI usage: GUI Usage. (line 6) -* guide: Paths and guides. (line 292) -* guide3: three. (line 6) -* hatch: Pens. (line 263) -* height: LaTeX usage. (line 32) -* help <1>: Debugger. (line 30) -* help <2>: Help. (line 6) -* help: Interactive mode. (line 25) -* Hermite: graph. (line 37) -* Hermite(splinetype splinetype: graph. (line 37) -* hex: Data types. (line 278) -* hexidecimal <1>: Pens. (line 59) -* hexidecimal: Data types. (line 278) -* hidden surface removal: three. (line 504) -* histogram: Mathematical functions. - (line 39) -* history: Files. (line 136) -* historylines: Interactive mode. (line 42) -* HookHead: draw. (line 26) -* HookHead3: three. (line 469) -* Horizontal: flowchart. (line 74) -* hypot: Mathematical functions. - (line 6) -* I: Mathematical functions. - (line 48) -* i_scaled: Mathematical functions. - (line 48) -* iconic: three. (line 180) -* identity <1>: Arrays. (line 302) -* identity <2>: Mathematical functions. - (line 6) -* identity: Transforms. (line 24) -* if: Programming. (line 8) -* IgnoreAspect: Frames and pictures. (line 58) -* image: palette. (line 34) -* ImageMagick <1>: Options. (line 129) -* ImageMagick <2>: animation. (line 6) -* ImageMagick: Configuring. (line 68) -* implicit casts: Casts. (line 6) -* implicit linear solver: MetaPost. (line 10) -* implicit scaling: Implicit scaling. (line 6) -* import: Import. (line 48) -* inches: Tutorial. (line 63) -* including images: label. (line 80) -* inheritance: Structures. (line 189) -* initialized: Arrays. (line 39) -* initializers: Variable initializers. - (line 6) -* InOutTicks: graph3. (line 34) -* input <1>: Interactive mode. (line 31) -* input: Files. (line 11) -* insert <1>: Arrays. (line 39) -* insert: Data types. (line 235) -* inside: Paths and guides. (line 271) -* inst: Debugger. (line 36) -* installation: Installation. (line 6) -* int: Data types. (line 28) -* integer division: Arithmetic & logical. - (line 6) -* interactive mode: Interactive mode. (line 6) -* international characters: unicode. (line 6) -* interp: Arithmetic & logical. - (line 76) -* interpolate: interpolate. (line 6) -* intersect <1>: three. (line 426) -* intersect <2>: math. (line 13) -* intersect: Paths and guides. (line 176) -* intersectionpoint <1>: three. (line 426) -* intersectionpoint <2>: math. (line 17) -* intersectionpoint: Paths and guides. (line 220) -* intersectionpoints <1>: three. (line 426) -* intersectionpoints: Paths and guides. (line 224) -* intersections <1>: three. (line 426) -* intersections: Paths and guides. (line 187) -* InTicks: graph3. (line 34) -* intMax: Data types. (line 28) -* intMin: Data types. (line 28) -* inverse <1>: Arrays. (line 308) -* inverse: Transforms. (line 16) -* invert: three. (line 359) -* invisible: Pens. (line 39) -* J: Mathematical functions. - (line 6) -* Japanese: unicode. (line 12) -* K: Mathematical functions. - (line 48) -* k_scaled: Mathematical functions. - (line 48) -* keyboard bindings:: three. (line 149) -* keys: Arrays. (line 39) -* keywords: Named arguments. (line 6) -* Korean: unicode. (line 12) -* Label: graph. (line 332) -* label: clip. (line 16) -* Label: draw. (line 98) -* labelpath: labelpath. (line 6) -* labelpath3: labelpath3. (line 6) -* labelx: graph. (line 332) -* labely: graph. (line 332) -* Landscape: Frames and pictures. (line 93) -* lastcut: Paths and guides. (line 247) -* lasy-mode: Editing modes. (line 6) -* latex: Options. (line 129) -* LaTeX fonts: Pens. (line 188) -* LaTeX usage: LaTeX usage. (line 6) -* latin1: latin1. (line 6) -* latitude: Data types. (line 134) -* latticeshade: fill. (line 32) -* layer: Drawing commands. (line 16) -* leastsquares <1>: graph. (line 892) -* leastsquares: stats. (line 6) -* Left: graph. (line 274) -* LeftRight: graph. (line 280) -* LeftSide: label. (line 62) -* LeftTicks: graph. (line 155) -* LeftView: three. (line 340) -* legend <1>: graph. (line 421) -* legend <2>: draw. (line 64) -* legend: Drawing commands. (line 31) -* Legendre: Mathematical functions. - (line 48) -* length <1>: three. (line 426) -* length <2>: Arrays. (line 39) -* length <3>: Paths and guides. (line 66) -* length: Data types. (line 60) -* letter: Configuring. (line 62) -* libm routines: Mathematical functions. - (line 6) -* libsigsegv <1>: Help. (line 33) -* libsigsegv: Functions. (line 88) -* limits: graph. (line 626) -* line: Arrays. (line 346) -* line mode: Arrays. (line 346) -* Linear: graph. (line 672) -* linecap: Pens. (line 125) -* linejoin: Pens. (line 134) -* lineskip: Pens. (line 174) -* linewidth: Pens. (line 115) -* locale: Data types. (line 285) -* Log: graph. (line 672) -* log: Mathematical functions. - (line 6) -* log-log graph: graph. (line 703) -* log10: Mathematical functions. - (line 6) -* log1p: Mathematical functions. - (line 6) -* log2 graph: graph. (line 753) -* logarithmic graph: graph. (line 703) -* logical operators: Arithmetic & logical. - (line 6) -* longdashdotted: Pens. (line 92) -* longdashed: Pens. (line 92) -* longitude: Data types. (line 139) -* loop: Programming. (line 8) -* MacOS X binary distributions: MacOS X binary distributions. - (line 6) -* makepen: Pens. (line 296) -* map: Arrays. (line 144) -* Margin: draw. (line 42) -* Margin3: three. (line 485) -* margins: three. (line 228) -* Margins: draw. (line 42) -* Margins3: three. (line 485) -* mark: graph. (line 474) -* markangle: markers. (line 38) -* marker: graph. (line 474) -* markers: markers. (line 6) -* marknodes: graph. (line 474) -* markuniform: graph. (line 474) -* math: math. (line 6) -* mathematical functions: Mathematical functions. - (line 6) -* max <1>: three. (line 426) -* max <2>: Arrays. (line 231) -* max <3>: Frames and pictures. (line 7) -* max: Paths and guides. (line 260) -* maxbound: Data types. (line 104) -* maxtile: three. (line 180) -* maxtimes: Paths and guides. (line 215) -* maxviewport: three. (line 180) -* merge: animation. (line 6) -* MetaPost: MetaPost. (line 6) -* MetaPost ... : Tutorial. (line 176) -* MetaPost cutafter: Paths and guides. (line 248) -* MetaPost cutbefore: Paths and guides. (line 244) -* MetaPost pickup: Pens. (line 6) -* MetaPost whatever: MetaPost. (line 10) -* Microsoft Windows: Microsoft Windows. (line 6) -* MidArcArrow: draw. (line 26) -* MidArcArrow3: three. (line 469) -* MidArrow: draw. (line 26) -* MidArrow3: three. (line 469) -* midpoint: Paths and guides. (line 161) -* MidPoint: label. (line 57) -* min <1>: three. (line 426) -* min <2>: Arrays. (line 224) -* min <3>: Frames and pictures. (line 7) -* min: Paths and guides. (line 256) -* minbound: Data types. (line 101) -* minipage: label. (line 119) -* mintimes: Paths and guides. (line 210) -* miterjoin: Pens. (line 134) -* miterlimit: Pens. (line 143) -* mm: Tutorial. (line 63) -* mouse: GUI. (line 6) -* mouse bindings: three. (line 129) -* Move: Pens. (line 335) -* MoveQuiet: Pens. (line 341) -* multisample: three. (line 119) -* multisampling: Compiling from UNIX source. - (line 16) -* N: Tutorial. (line 94) -* named arguments: Named arguments. (line 6) -* new <1>: Arrays. (line 112) -* new: Structures. (line 6) -* newframe: Frames and pictures. (line 7) -* newl: Files. (line 59) -* newton: Mathematical functions. - (line 65) -* next: Debugger. (line 42) -* NFSS: Pens. (line 188) -* nobasealign: Pens. (line 164) -* NoFill <1>: Frames and pictures. (line 139) -* NoFill: draw. (line 26) -* NoMargin: draw. (line 42) -* NoMargin3: three. (line 485) -* none: Files. (line 59) -* None: draw. (line 19) -* normal: three. (line 412) -* nosafe: Options. (line 145) -* NOT: Arithmetic & logical. - (line 80) -* NoTicks: graph. (line 155) -* NoTicks3: graph3. (line 34) -* null: Structures. (line 6) -* nullpen <1>: Frames and pictures. (line 125) -* nullpen: label. (line 14) -* NURBS: three. (line 318) -* O: three. (line 236) -* obj: obj. (line 7) -* oblique: three. (line 281) -* obliqueX: three. (line 289) -* obliqueY: three. (line 296) -* obliqueZ: three. (line 281) -* offset: Options. (line 149) -* opacity: Pens. (line 218) -* open: Files. (line 11) -* OpenGL: three. (line 119) -* operator: User-defined operators. - (line 6) -* operator --: graph. (line 31) -* operator ..: graph. (line 34) -* operator cast: Casts. (line 31) -* operator ecast: Casts. (line 58) -* operator init <1>: Structures. (line 141) -* operator init: Variable initializers. - (line 6) -* operators: Operators. (line 6) -* options: Options. (line 7) -* OR: Arithmetic & logical. - (line 80) -* orientation: Frames and pictures. (line 93) -* orthographic: three. (line 300) -* outformat: three. (line 119) -* output <1>: Options. (line 129) -* output: Files. (line 36) -* OutTicks: graph3. (line 34) -* overloading functions: Functions. (line 44) -* overwrite: Pens. (line 320) -* P: Mathematical functions. - (line 48) -* pack: label. (line 102) -* packing: Rest arguments. (line 30) -* pair <1>: Data types. (line 41) -* pair: Tutorial. (line 17) -* pairs: Arrays. (line 248) -* paperheight: Configuring. (line 62) -* papertype: Configuring. (line 62) -* paperwidth: Configuring. (line 62) -* parametrized curve: graph. (line 626) -* patch-dependent colors: three. (line 75) -* path <1>: flowchart. (line 74) -* path <2>: three. (line 43) -* path: Paths and guides. (line 7) -* path3: three. (line 6) -* path[]: Tutorial. (line 197) -* patterns <1>: patterns. (line 6) -* patterns: Pens. (line 234) -* pdflatex: Options. (line 129) -* pdfviewer: Configuring. (line 6) -* pdfviewerOptions: Options. (line 117) -* pen: Pens. (line 6) -* PenMargin: draw. (line 42) -* PenMargin2: three. (line 485) -* PenMargin3: three. (line 485) -* PenMargins: draw. (line 42) -* PenMargins2: three. (line 485) -* PenMargins3: three. (line 485) -* perpendicular: geometry. (line 6) -* perspective: three. (line 318) -* picture: Frames and pictures. (line 35) -* picture alignment: Frames and pictures. (line 203) -* piecewisestraight: Paths and guides. (line 82) -* Pl: Mathematical functions. - (line 48) -* plain: plain. (line 6) -* planar: three. (line 83) -* plane: three. (line 263) -* planeproject: three. (line 409) -* point <1>: three. (line 426) -* point: Paths and guides. (line 85) -* polar: Data types. (line 119) -* polargraph: graph. (line 90) -* polygon: graph. (line 474) -* pop: Arrays. (line 39) -* Portrait: Frames and pictures. (line 93) -* postcontrol <1>: three. (line 426) -* postcontrol: Paths and guides. (line 130) -* postfix operators: Self & prefix operators. - (line 19) -* postscript: Frames and pictures. (line 265) -* PostScript fonts: Pens. (line 206) -* PostScript subpath: Tutorial. (line 197) -* pow10: Mathematical functions. - (line 6) -* prc: three. (line 197) -* precision: Files. (line 86) -* precontrol <1>: three. (line 426) -* precontrol: Paths and guides. (line 123) -* 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 117) -* pt: Tutorial. (line 63) -* public: Structures. (line 6) -* push: Arrays. (line 39) -* python: Configuring. (line 27) -* Python usage: Interactive mode. (line 58) -* quadraticroots: Arrays. (line 311) -* quarticroots: math. (line 22) -* quit <1>: Debugger. (line 54) -* quit: Interactive mode. (line 37) -* quote: Import. (line 119) -* quotient: Arithmetic & logical. - (line 6) -* RadialShade: Frames and pictures. (line 157) -* radialshade: fill. (line 49) -* radians: Mathematical functions. - (line 17) -* radius <1>: three. (line 426) -* radius: Paths and guides. (line 119) -* Rainbow: palette. (line 12) -* rand: Mathematical functions. - (line 39) -* randMax: Mathematical functions. - (line 39) -* read1: Arrays. (line 386) -* read2: Arrays. (line 386) -* read3: Arrays. (line 386) -* reading: Files. (line 11) -* reading string arrays: Arrays. (line 353) -* readline: Files. (line 128) -* real: Data types. (line 33) -* realDigits: Data types. (line 33) -* realEpsilon: Data types. (line 33) -* realMax: Data types. (line 33) -* realMin: Data types. (line 33) -* realmult: Data types. (line 95) -* rectangle: flowchart. (line 37) -* recursion: Functions. (line 88) -* reflect: Transforms. (line 51) -* Relative: label. (line 52) -* relpoint: Paths and guides. (line 157) -* reltime: Paths and guides. (line 153) -* remainder: Mathematical functions. - (line 6) -* rename: Files. (line 145) -* render <1>: Options. (line 129) -* render: three. (line 119) -* replace: Data types. (line 252) -* resetdefaultpen: Pens. (line 349) -* rest arguments: Rest arguments. (line 6) -* restore: Frames and pictures. (line 259) -* restricted: Structures. (line 6) -* return: Debugger. (line 48) -* reverse <1>: three. (line 426) -* reverse <2>: Arrays. (line 149) -* reverse <3>: Paths and guides. (line 164) -* reverse: Data types. (line 248) -* rewind: Files. (line 86) -* rfind: Data types. (line 229) -* rgb: Pens. (line 30) -* Riemann zeta function: Mathematical functions. - (line 48) -* Right: graph. (line 277) -* RightSide: label. (line 62) -* RightTicks: graph. (line 155) -* RightView: three. (line 340) -* Rotate: label. (line 37) -* Rotate(pair z): label. (line 40) -* round: Mathematical functions. - (line 26) -* roundcap: Pens. (line 125) -* roundedpath: roundedpath. (line 6) -* roundjoin: Pens. (line 134) -* roundrectangle: flowchart. (line 62) -* RPM: UNIX binary distributions. - (line 6) -* runtime imports: Import. (line 101) -* Russian: unicode. (line 7) -* S: Tutorial. (line 94) -* safe: Options. (line 145) -* save: Frames and pictures. (line 256) -* saveline: Files. (line 128) -* scale: three. (line 388) -* Scale: graph. (line 688) -* scale <1>: graph. (line 672) -* scale: Transforms. (line 39) -* Scale: label. (line 46) -* scale3: three. (line 385) -* scaled graph: graph. (line 653) -* scientific graph: graph. (line 386) -* scroll: Files. (line 102) -* search: Arrays. (line 167) -* search paths: Search paths. (line 6) -* Seascape: Frames and pictures. (line 98) -* secondary axis: graph. (line 803) -* secondaryX: graph. (line 803) -* secondaryY: graph. (line 803) -* seconds: Data types. (line 298) -* seek: Files. (line 86) -* seekeof: Files. (line 86) -* segmentation fault: Help. (line 33) -* self operators: Self & prefix operators. - (line 6) -* sequence: Arrays. (line 131) -* settings <1>: Options. (line 102) -* settings: Configuring. (line 21) -* sgn: Mathematical functions. - (line 26) -* shading: fill. (line 32) -* shift <1>: three. (line 373) -* shift: Transforms. (line 27) -* Shift: label. (line 34) -* shiftless: Transforms. (line 53) -* shipout: Frames and pictures. (line 83) -* showtarget: three. (line 300) -* Si: Mathematical functions. - (line 48) -* SimpleHead: draw. (line 26) -* simplex: simplex. (line 6) -* simpson: Mathematical functions. - (line 81) -* Sin: Mathematical functions. - (line 20) -* sin: Mathematical functions. - (line 6) -* single: Files. (line 71) -* sinh: Mathematical functions. - (line 6) -* size <1>: Options. (line 129) -* size <2>: three. (line 426) -* size <3>: Frames and pictures. (line 43) -* size: Paths and guides. (line 71) -* size3: three. (line 225) -* slant: Transforms. (line 45) -* Slant: label. (line 43) -* sleep: Data types. (line 328) -* slice: Paths and guides. (line 233) -* slices: Slices. (line 6) -* slide: slide. (line 6) -* slopefield: slopefield. (line 6) -* solid: Pens. (line 92) -* solids: solids. (line 7) -* solve: Arrays. (line 265) -* sort: Arrays. (line 190) -* Spline: graph. (line 34) -* split: Data types. (line 261) -* sqrt: Mathematical functions. - (line 6) -* squarecap: Pens. (line 125) -* srand: Mathematical functions. - (line 39) -* stack overflow <1>: Help. (line 33) -* stack overflow: Functions. (line 88) -* static: Static. (line 6) -* stats: stats. (line 6) -* stdin: Files. (line 46) -* stdout: Files. (line 46) -* step: Debugger. (line 39) -* stickframe: markers. (line 16) -* stop: Debugger. (line 10) -* straight: three. (line 426) -* Straight: graph. (line 31) -* straight: Paths and guides. (line 78) -* strftime: Data types. (line 290) -* string: Data types. (line 179) -* stroke: fill. (line 36) -* strokepath: Paths and guides. (line 286) -* strptime: Data types. (line 298) -* struct: Structures. (line 6) -* structures: Structures. (line 6) -* subpath <1>: three. (line 426) -* subpath: Paths and guides. (line 167) -* subpictures: Frames and pictures. (line 101) -* substr: Data types. (line 244) -* Subversion: Subversion. (line 6) -* sum: Arrays. (line 219) -* superpath: Tutorial. (line 197) -* Suppress: Pens. (line 327) -* SuppressQuiet: Pens. (line 331) -* surface: three. (line 47) -* SVN: Subversion. (line 6) -* system <1>: Options. (line 145) -* system: Files. (line 153) -* syzygy: syzygy. (line 6) -* tab: Files. (line 59) -* tab completion: Tutorial. (line 21) -* Tan: Mathematical functions. - (line 20) -* tan: Mathematical functions. - (line 6) -* tanh: Mathematical functions. - (line 6) -* target: three. (line 300) -* tell: Files. (line 86) -* tension <1>: three. (line 6) -* tension: Tutorial. (line 165) -* tensionSpecifier: Paths and guides. (line 377) -* tensor product shading: fill. (line 74) -* tensorshade: fill. (line 74) -* tex <1>: Options. (line 129) -* tex: Frames and pictures. (line 272) -* TeX fonts: Pens. (line 197) -* TeX string: Data types. (line 179) -* texcommand: Configuring. (line 68) -* texdvicommand: Configuring. (line 68) -* TeXHead: draw. (line 26) -* TeXHead3: three. (line 469) -* texpath <1>: label. (line 116) -* texpath: Configuring. (line 68) -* texpreamble: Frames and pictures. (line 280) -* texreset: Frames and pictures. (line 283) -* textbook graph: graph. (line 361) -* tgz: UNIX binary distributions. - (line 6) -* thick: three. (line 104) -* thin: three. (line 104) -* this: Structures. (line 6) -* three: three. (line 6) -* tick: graph. (line 332) -* Ticks: graph. (line 155) -* ticks: graph. (line 155) -* tildeframe: markers. (line 26) -* tile: Pens. (line 247) -* tilings: Pens. (line 234) -* time: Data types. (line 290) -* times: Paths and guides. (line 202) -* Top: graph. (line 131) -* TopView: three. (line 340) -* trace: Debugger. (line 51) -* trailingzero: graph. (line 169) -* transform <1>: three. (line 400) -* transform: Transforms. (line 6) -* transform3: three. (line 369) -* transparency: Pens. (line 218) -* transpose: Arrays. (line 211) -* tree: tree. (line 7) -* trembling: trembling. (line 6) -* triangle: geometry. (line 6) -* triangulate: contour. (line 154) -* tridiagonal: Arrays. (line 268) -* trigonometric integrals: Mathematical functions. - (line 48) -* triple: Data types. (line 108) -* TrueMargin: draw. (line 42) -* TrueMargin3: three. (line 485) -* tube <1>: tube. (line 6) -* tube: three. (line 104) -* tutorial: Tutorial. (line 6) -* typedef <1>: Functions. (line 36) -* typedef: Data types. (line 338) -* undefined: Paths and guides. (line 264) -* UnFill: Frames and pictures. (line 150) -* unfill: fill. (line 105) -* UnFill: draw. (line 26) -* unicode: unicode. (line 6) -* uniform: Arrays. (line 158) -* Uninstall: Uninstall. (line 6) -* unit: Data types. (line 78) -* unitbox <1>: three. (line 269) -* unitbox: Tutorial. (line 218) -* unitcircle <1>: three. (line 236) -* unitcircle: Tutorial. (line 110) -* unitrand: Mathematical functions. - (line 39) -* unitsize <1>: Frames and pictures. (line 64) -* unitsize: Tutorial. (line 73) -* UNIX binary distributions: UNIX binary distributions. - (line 6) -* unpacking: Rest arguments. (line 39) -* unravel: Import. (line 31) -* up: three. (line 300) -* update: Files. (line 36) -* UpsideDown: Frames and pictures. (line 93) -* usepackage: Frames and pictures. (line 285) -* user coordinates: Tutorial. (line 73) -* user-defined operators: User-defined operators. - (line 6) -* usleep: Data types. (line 331) -* variable initializers: Variable initializers. - (line 6) -* vectorfield: graph. (line 965) -* vectorfield3: graph3. (line 150) -* vectorization: Arrays. (line 325) -* verbatim: Frames and pictures. (line 265) -* vertex-dependent colors: three. (line 75) -* Vertical: flowchart. (line 74) -* viewportheight: LaTeX usage. (line 32) -* viewportmargin: three. (line 228) -* viewportsize: three. (line 228) -* viewportwidth: LaTeX usage. (line 32) -* views: three. (line 197) -* vim: Editing modes. (line 33) -* virtual functions: Structures. (line 189) -* void: Data types. (line 10) -* W: Tutorial. (line 94) -* whatever: Paths and guides. (line 228) -* Wheel: palette. (line 22) -* wheel mouse: GUI. (line 6) -* while: Programming. (line 29) -* white-space string delimiter mode: Arrays. (line 353) -* width: LaTeX usage. (line 32) -* windingnumber: Paths and guides. (line 264) -* word: Arrays. (line 353) -* write <1>: Arrays. (line 394) -* write: Files. (line 51) -* X: three. (line 236) -* xasy <1>: GUI. (line 6) -* xasy: Configuring. (line 68) -* xaxis: graph3. (line 7) -* xelatex <1>: Options. (line 129) -* xelatex: embed. (line 10) -* xequals: graph. (line 284) -* XEquals: graph. (line 270) -* xinput: Files. (line 71) -* xlimits: graph. (line 626) -* XOR: Arithmetic & logical. - (line 80) -* xoutput: Files. (line 71) -* xpart: Data types. (line 89) -* xscale: Transforms. (line 33) -* xscale3: three. (line 376) -* xtick: graph. (line 332) -* XYEquals: graph3. (line 20) -* XYZero: graph3. (line 20) -* XZEquals: graph3. (line 20) -* XZero: graph. (line 265) -* XZZero: graph3. (line 20) -* Y <1>: three. (line 236) -* Y: Mathematical functions. - (line 6) -* yaxis: graph3. (line 7) -* yequals: graph. (line 284) -* YEquals: graph. (line 124) -* ylimits: graph. (line 626) -* ypart: Data types. (line 92) -* yscale: Transforms. (line 36) -* yscale3: three. (line 379) -* ytick: graph. (line 332) -* YZEquals: graph3. (line 20) -* YZero: graph. (line 119) -* YZZero: graph3. (line 20) -* Z: three. (line 236) -* zaxis: graph3. (line 7) -* zero_Ai: Mathematical functions. - (line 48) -* zero_Ai_deriv: Mathematical functions. - (line 48) -* zero_Bi: Mathematical functions. - (line 48) -* zero_Bi_deriv: Mathematical functions. - (line 48) -* zero_J: Mathematical functions. - (line 48) -* zerowinding: Pens. (line 148) -* zeta: Mathematical functions. - (line 48) -* zpart: Data types. (line 161) -* zscale3: three. (line 382) -* |: Arithmetic & logical. - (line 62) -* ||: Arithmetic & logical. - (line 59) - - diff --git a/Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6.patch b/Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6.patch deleted file mode 100644 index 30ee1ffa31a..00000000000 --- a/Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6.patch +++ /dev/null @@ -1,156 +0,0 @@ -diff -ru Imaging-1.1.6/Tk/tkImaging.c Imaging-1.1.6J/Tk/tkImaging.c ---- Imaging-1.1.6/Tk/tkImaging.c 2006-12-03 04:37:29.000000000 -0700 -+++ Imaging-1.1.6J/Tk/tkImaging.c 2007-11-14 20:22:02.000000000 -0700 -@@ -48,6 +48,9 @@ - for the Tcl_CreateCommand command. */ - #define USE_COMPAT_CONST - -+#define CONST84 const -+#define CONST84_RETURN const -+ - #include "tk.h" - - #include "Imaging.h" -@@ -76,6 +79,13 @@ - Imaging im; - Tk_PhotoHandle photo; - Tk_PhotoImageBlock block; -+ int renderalpha; -+ char *max_alpha_area; -+ int maxarea; -+ Tk_PhotoImageBlock run; -+ -+ unsigned char back[3]={255,255,255}; -+ char *background=getenv("PIL_BACKGROUND"); - - if (argc != 3) { - Tcl_AppendResult(interp, "usage: ", argv[0], -@@ -117,6 +127,15 @@ - - /* Mode */ - -+#ifndef MAX_ALPHA_AREA -+#define MAX_ALPHA_AREA 10000; -+#endif -+ -+ maxarea=MAX_ALPHA_AREA; -+ max_alpha_area=getenv("PIL_MAX_ALPHA_AREA"); -+ if(max_alpha_area != NULL) maxarea=atoi(max_alpha_area); -+ renderalpha=(maxarea < 0) ? 1 : (im->xsize*im->ysize < maxarea); -+ - if (strcmp(im->mode, "1") == 0 || strcmp(im->mode, "L") == 0) { - block.pixelSize = 1; - block.offset[0] = block.offset[1] = block.offset[2] = 0; -@@ -125,7 +144,10 @@ - block.offset[0] = 0; - block.offset[1] = 1; - block.offset[2] = 2; -- block.offset[3] = 0; /* no alpha (or reserved, under 8.2) */ -+ if(renderalpha && strcmp(im->mode,"RGBA") == 0) -+ block.offset[3] = 3; /* alpha (or reserved, under 8.2) */ -+ else -+ block.offset[3] = 0; /* no alpha */ - } else { - Tcl_AppendResult(interp, "Bad mode", (char*) NULL); - return TCL_ERROR; -@@ -140,15 +162,30 @@ - src_yoffset * im->linesize + - src_xoffset * im->pixelsize; - #endif -- -- if (strcmp(im->mode, "RGBA") == 0) { -- /* Copy non-transparent pixels to photo image */ -+ if (!renderalpha && strcmp(im->mode, "RGBA") == 0) { -+ int bytes =block.height*block.pitch; -+ unsigned char *pixelPtr; - int x, y; -- Tk_PhotoImageBlock run; -+ int j; -+ -+ /* Buffer image block for pseudo-antialiasing */ -+ if (bytes <= 0) -+ bytes=1; -+ pixelPtr=(unsigned char *) malloc(bytes); -+ if (!pixelPtr) { -+ Tcl_AppendResult(interp, "bad display memory", (char*) NULL); -+ return TCL_ERROR; -+ } - -- /* Clear current contents */ -- Tk_PhotoBlank(photo); -+ /* Copy non-transparent pixels to photo image */ - -+ if(background && strlen(background) == 6) { -+ for(j=0; j < 3; ++j) { -+ char h[3]={background[2*j],background[2*j+1],0}; -+ back[j]=strtol(h,NULL,16); -+ } -+ } -+ - /* Setup run descriptor */ - run.height = 1; - run.pitch = block.pitch; -@@ -161,13 +198,19 @@ - /* Copy opaque runs to photo image */ - for (y = 0; y < block.height; y++) { - unsigned char* p = block.pixelPtr + y*block.pitch; -- unsigned char* s = p; -+ unsigned char* q = pixelPtr + y*block.pitch; -+ unsigned char* s = q; - int w = 0; - for (x = 0; x < block.width; x++) { - if (p[3]) { - /* opaque: add pixel to current run */ -- if (w == 0) -- s = p; -+ double opacity=p[3]/255.0; -+ double transparency=1.0-opacity; -+ q[0]=(int) (opacity*p[0]+transparency*back[0]); -+ q[1]=(int) (opacity*p[1]+transparency*back[1]); -+ q[2]=(int) (opacity*p[2]+transparency*back[2]); -+ if (w == 0) -+ s = q; - w = w + 1; - } else if (s) { - /* copy run to photo image */ -@@ -179,6 +222,7 @@ - w = 0; - } - p += block.pixelSize; -+ q += block.pixelSize; - } - if (w > 0) { - /* copy final run, if any */ -@@ -188,10 +232,15 @@ - } - } - -- } else -- -- /* Copy opaque block to photo image, and leave the rest to TK */ -- Tk_PhotoPutBlock(photo, &block, 0, 0, block.width, block.height); -+ } else { -+ /* Copy block to photo image, and leave the rest to TK */ -+ Tk_PhotoPutBlock(photo, &block, 0, 0, block.width, block.height); -+ -+ if (strcmp(im->mode, "RGBA") == 0) -+ /* Tk workaround: we need apply ToggleComplexAlphaIfNeeded */ -+ /* (fixed in Tk 8.5a3) */ -+ Tk_PhotoSetSize(photo, block.width, block.height); -+ } - - return TCL_OK; - } -diff -ru Imaging-1.1.6/_imagingtk.c Imaging-1.1.6J/_imagingtk.c ---- Imaging-1.1.6/_imagingtk.c 2006-12-03 04:51:25.000000000 -0700 -+++ Imaging-1.1.6J/_imagingtk.c 2007-11-14 17:42:54.000000000 -0700 -@@ -17,6 +17,9 @@ - #include "Python.h" - #include "Imaging.h" - -+#define CONST84 const -+#define CONST84_RETURN const -+ - #include "tk.h" - - /* must link with Tk/tkImaging.c */ diff --git a/Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6msdos.patch b/Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6msdos.patch deleted file mode 100644 index 8e946963685..00000000000 --- a/Build/source/utils/asymptote/patches/TkAlpha-Imaging-1.1.6msdos.patch +++ /dev/null @@ -1,52 +0,0 @@ ---- Imaging-1.1.6/Tk/tkImaging.c.orig 2006-12-03 04:37:29.000000000 -0700 -+++ Imaging-1.1.6/Tk/tkImaging.c 2007-05-15 11:37:54.000000000 -0600 -@@ -39,10 +39,7 @@ - * See the README file for information on usage and redistribution. - */ - --/* This is needed for (at least) Tk 8.4.1, otherwise the signature of --** Tk_PhotoPutBlock changes. --*/ --#define USE_COMPOSITELESS_PHOTO_PUT_BLOCK -+#define TKMAJORMINOR (TK_MAJOR_VERSION*1000 + TK_MINOR_VERSION) - - /* This is needed for (at least) Tk 8.4.6 and later, to avoid warnings - for the Tcl_CreateCommand command. */ -@@ -125,7 +122,10 @@ - block.offset[0] = 0; - block.offset[1] = 1; - block.offset[2] = 2; -- block.offset[3] = 0; /* no alpha (or reserved, under 8.2) */ -+ if(strcmp(im->mode,"RGBA")==0) -+ block.offset[3] = 3; /*alpha (or reserved, under 8.2)*/ -+ else -+ block.offset[3] = 0; /* no alpha */ - } else { - Tcl_AppendResult(interp, "Bad mode", (char*) NULL); - return TCL_ERROR; -@@ -140,7 +140,7 @@ - src_yoffset * im->linesize + - src_xoffset * im->pixelsize; - #endif -- -+#if TKMAJORMINOR < 8004 /* Tk < 8.4.0 */ - if (strcmp(im->mode, "RGBA") == 0) { - /* Copy non-transparent pixels to photo image */ - int x, y; -@@ -193,6 +193,16 @@ - /* Copy opaque block to photo image, and leave the rest to TK */ - Tk_PhotoPutBlock(photo, &block, 0, 0, block.width, block.height); - -+#else /* Tk >= 8.4.0 */ -+ Tk_PhotoPutBlock(photo, &block, 0, 0, block.width, block.height, -+ TK_PHOTO_COMPOSITE_SET); -+ if (strcmp(im->mode, "RGBA") == 0) -+ /* Tk workaround: we need apply ToggleComplexAlphaIfNeeded */ -+ /* (fixed in Tk 8.5a3) */ -+ Tk_PhotoSetSize(photo, block.width, block.height); -+#endif -+ -+ - return TCL_OK; - } - diff --git a/Build/source/utils/asymptote/patches/movie15_20090323.patch b/Build/source/utils/asymptote/patches/movie15_20090323.patch deleted file mode 100644 index 953b0214c89..00000000000 --- a/Build/source/utils/asymptote/patches/movie15_20090323.patch +++ /dev/null @@ -1,11 +0,0 @@ ---- old/movie15.sty 2009-05-14 16:21:46.437500000 -0700 -+++ movie15.sty 2009-05-14 17:09:00.984375000 -0700 -@@ -2796,7 +2796,7 @@ - var spc=String.fromCharCode(32);% - var nl=String.fromCharCode(10);% - var charht=2;% -- var res='VIEW\%={<insert descriptive name here (optional)>}'+nl;% -+ var res='VIEW\%={<insert\ descriptive\ name\ here\ (optional)>}'+nl;% - var x = (Math.abs(coo.x) < 1e-12 ? 0 : coo.x);% - var y = (Math.abs(coo.y) < 1e-12 ? 0 : coo.y);% - var z = (Math.abs(coo.z) < 1e-12 ? 0 : coo.z);% |