Introduction to MetaPost
Contents
1. but specifically designed for producing PostScript graphics Preliminary comments on MetaPost appeared in 2 Since MetaPost is based on the public domain META FONT source code given in 6 MetaPost has been able to inherit all the features of METAFONT that make it a powerful graphics language e The ability to store and manipulate coordinate pairs straight and curved paths coordinate transforma tions pen shapes and complete pictures e A Flexible and powerful mechanisms for construct ing smooth curves and straight lines e The ability to draw straight and curved lines of any thickness and to fill a region given its boundary e Mechanisms for solving linear equations so that geometric information can be specified in a largely declarative manner e A powerful macro facility that allows the language to be extended syntactically and semantically e Operators for intersecting curves finding tangent lines finding points on a curve that match a given tangent direction and extracting subpaths In addition to these features MetaPost allows pictures to contain text dashed lines clipping paths and areas filled with gray or other colors There are also data types for colors and recipes for dashed lines In ad dition there are important facilities for generating and manipulating typeset text Readers familiar with other graphics languages such as Kernighan s Pic 5 and Wichura s PicTEX 9 will see that MetaPost is cons2. box with rounded corners Other box shapes could also be provided if there were a demand for them There should also be a macro package for drawing graphs No such package has been designed yet but there have been promising preliminary experiments with the automatic generation of axis labels for uni form and logarithmic spacing 5 Conclusion Building on METAFONT has made MetaPost a very powerful and flexible graphics language It is espe Reprint MAPS 9 92 2 Nov 1992 Bijlage S cially well suited to generating figures in technical doc uments which may involve mathematical constraints that are best expressed symbolically Such figures lack the aesthetic requirements that make font design so challenging This paper has introduced the MetaPost language via examples concentrating on interesting features that dis tinguish the language from other graphics languages and from METAFONT Readers who want to use the language should refer to 3 The MetaPost interpreter is currently available to academic institutions under non disclosure agreement References 1 Leslie Carr Of METAFONT and PostScript In TEX User s Group Eighth Annual Meeting Confer ence Proceedings TEX User s Group Providence Rhode Island 1988 John D Hobby A METAFONT like system with PostScript output Tugboat the TEX User s Group Newsletter 10 4 505 512 December 1989 J D Hobby A user s manual for MetaPost Computing Science Tech
3. but the names for them are system dependent Some systems may use rptmr or ps times roman instead of Times Roman A TEX font such as cmr10 is a little dangerous because it does not have a space character or certain ASCII sym bols In addition MetaPost does not use the ligatures and kerning information that comes with a TEX font The MetaPost language does not need elaborate type setting abilities because there is a preprocessor that extracts TEX commands runs them through TEX or LaT X and translates the output into a form that the interpreter understands There is even a separate pre processor that handles troff commands Any time you say btex typesetting commands et ex in a MetaPost input file the preprocessor translates the typesetting commands into a MetaPost picture ex pression that can be used in a label or dotlabel statement For instance a statement of the form label 1lrt btex sqrt x etex coordinates was used to placed the label z in Figure 6 Reprint MAPS 9 92 2 Nov 1992 92 Introduction to MetaPost Bijlage S VE Figuur 6 A figure with labels done in TEX y axis ae Ee eer 2 x axis Figuur 7 An example of how typeset labels can be rotated Figure 7 illustrates some of the more complicated things that can be done with labels Since the result of btex etex is a picture it can be operated on like a pic ture In particular it is possible to rotate the picture b
4. dy Figuur 15 The relationship between the picture given to circleit and the associated variables The picture is indicated by a gray rectangle b O Figuur 16 Circular and oval boxes generated using the boxes mp macros separately as bpath b or in general bpath box name One interesting use of the bounding rectangle is for gen erating well targeted arrows as shown in Figure 13 Given a path from the center of Box a to the center of Box b there are MetaPost operators that make it con venient to chop off the parts of the path before the first intersection with bpath a and after the last intersec tion with bpath b There is also a special command box join equation text that controls the relative position of consecutive boxes Dutch TEX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands Within the equation text a and b represent the box names given in consecutive calls to boxit and the equation text gives equations to control the relative sizes and positions of the boxes For example the MetaPost code for Figure 14 uses boxjoin a se b sw a ne b nw to causes boxes to line up horizontally It is instructive to compare this figure with the similar one in the pic manual 5 The boxes mp macros also provide for circular and oval boxes These are a lot like rectangular boxes ex cept for the shape of the bounding path Such boxes Reprint MAPS 9 92 2 Nov 1992 96 Introduc
5. the next copy to form a dash 12bp long Dutch TEX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands 3 3 Arrows Drawing arrows like the ones in Figure 10 is simply a matter of saying drawarrow path expression instead of draw path expression This draws the given path with an arrowhead at the end If you want the arrowhead at the beginning of the path there is an operator that reverses a path For double headed arrows there is a drawdblarrow statement The size of the arrowhead is guaranteed to be larger than the line width but it might need adjusting if the line width is very large This is done by assigning a new value to the internal variable ahlength that determ ines arrowhead length as shown in Figure 11 Increas ing ahlength from the default value of 4 PostScript points to 1 5 centimeters produces the large arrowhead in Figure 11 There is also an ahangle parameter that controls the angle at the tip of the arrowhead The default value of this angle is 45 degrees as shown in the figure The arrowhead is created by filling the triangular region that is outlined in white in Figure 11 and then draw ing the boundary with the current line width Readers familiar with METAFONT will recognize this as the filldraw statement 4 Macro Packages This section describes auxiliary macros not included in Plain MetaPost The macros described in Section 4 1 Reprint MAPS 9 92 2 Nov 1992 94 Introduction to Meta
6. way to do this is to use the 1abe1 statement to specify the label text and the point to be labeled If you are labeling some feature of a diagram you probably want to offset the label slightly to avoid overlapping This is illustrated in Figure 5 where statements of the form label top a expression label 1ft b expressions put the a label above the midpoint of the line it refers to and the b label is to the left of the midpoint of its line In addition to top and 1ft there are six other optional suffixes for other label positions There is also a dot label command that marks a point with a dot and positions text as the label command does For instance the command dotlabel bot 0 0 0 0 generates a dot marked 0 0 as in Figure 5 For labeling statements such as label and dot label that use a string expression for the label text the string Dutch TEX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands gets typeset in a default font as determined by the string variable defaultfont The initial value of default font is likely to be cmr10 but it can be changed to a different font name by giving an assign ment such as defaultfont Times Roman When you change default font the new font name should be something that TEX would understand since MetaPost gets height and width information by read ing the t fm file See 7 It should be possible to use built in PostScript fonts
7. ways of drawing arrows generate There is a predefined dash pattern called evenly that makes dashes 3 points long separated by gaps of the same size Another predefined dash pattern withdots produces dotted lines with dots 5 points apart As shown in the figure scaling the dash pattern produces dots further apart or longer dashes further apart Another way to change a dash pattern is to alter its phase by shifting it horizontally Shifting to the right makes the dashes move forward along the path and shifting to the left moves them backward Figure 9 illustrates this effect The dash pattern can be thought of as an infin itely repeating pattern strung out along a horizontal line where the portion of the line to the right of the y axis is laid out along the path to be dashed When you shift a dash pattern so that the y axis crosses the middle of a dash the first dash gets truncated Thus the line with dash pattern e4 starts with a dash of length 12bp followed by a 12bp gap and another 12bp dash etc whilee4 shifted 18bp 0 produces a 6bp dash a 12 bp gap then a 12bp dash etc This dash pattern could be specified more directly via the dashpattern function dashpattern on 6bp off 12bp on 6bp This means draw the first 6bp of the line then skip the next 12bp then draw another 6bp and repeat If the line to be dashed is more than 30bp long the last 6bp of the first copy of the dash pattern will merge with the first 6bp of
8. Bijlage S Introduction to MetaPost 89 Introduction to MetaPost John D Hobby AT amp T Bell Laboratories 600 Mountain Ave Murray Hill New Jersey 07974 hobby research att com Abstract MetaPost is a picture drawing language very much like METAFONT except with PostScript output The language provides access to all major features of Level 1 PostScript and it has facilities for integrating graphics with typeset text This paper gives a brief overview of the MetaPost language and how it can be used A few of the more interesting features are described in detail Keywords Metapost graphics languages META FONT PostScript 1 Introduction Although METAFONT was originally designed as a font making tool many people have recognized that it is also a powerful graphics language The problem is that METAFONT s output is in the form of bitmap images instead of graphics primitives A diagram can sometimes be created in METAFONT and typeset as a single huge character but this is cumbersome and makes it difficult to deal with textual labels A good examples of work along these lines appears in 4 and 8 Another approach is to modify the METAFONT inter preter so that it outputs PostScript Previous work along these lines presented in 1 and 10 has concentrated on producing PostScript fonts rather than graphics Unlike these earlier systems the MetaPost system involves the creation of a new language similar to METAFONT
9. Post Bijlage S ahlength lt gt __ ahangle 7 ahlength Figuur 11 A large arrowhead with key parameters labeled and paths used to draw it marked with white lines nW e SW e ene dy dx lt ee av ese Figuur 12 The relationship between the picture given to boxit and the associated variables The picture is indicated by a gray rectangle Figuur 13 A well targeted arrow generated by trimming the dashed sections from a curved path make it convenient to do things that pic is good at 5 Section 4 2 makes some brief remarks about other macro packages In order to use a macro package it is necessary to give a MetaPost command that names the macro file and asks the interpreter to read it 4 1 Macros for Boxes The box making macros are contained in a macro file called boxes mp This file can be accessed by giv ing the MetaPost command input boxes before any figures that use the box making macros The basic tool for making boxes is the command boxit box name picture expression This creates variables box name c box name n box name e that can then be used for position ing the picture before drawing it The actual drawing is done by a separate command drawboxed that takes a list of box names If the command is boxit bb picture the box name is bb and the contents of the box is the pic ture In this case bb c the position where the cent
10. er Reprint MAPS 9 92 2 Nov 1992 of the picture is to be placed and bb sw bb se bb ne and bb nw are the corners of a rectangular path that will surround the picture Variables bb dx and bb dy give the spacing between the picture and the surrounding rectangle and bb off is the amount by which the picture has to be shifted to achieve all this When the boxit macro is called with box name 8 it gives linear equations that force 6 sw b se b ne and b nw to be the corners of a rectangle aligned on the z and y axes with the box contents centered inside as indicated by the gray rectangle in Figure 12 The values of 6 dx b dy and b c are left unspecified so that the user can give equations for positioning the boxes If no such equations are given macros such as drawboxed can detect this and give default values The default values for dx and dy variables are controlled by the internal variables defaultdx and defaultdy If b represents a box name drawboxed b draws the rectangular boundary of box b and then the contents of the box This bounding rectangle can be accessed Dutch TEX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands Bijlage S Introduction to MetaPost 95 ndtable An dj41 nk dk Nii hashtab _ ndblock Figuur 14 An example of what can be done with the boxes mp macros
11. eter such as GhostScript The input file in the figure has a single beginfig endfig block There could be more such blocks in which case each would produce a sep arate output file Since this paper is not intended to be a user s manual no attempt will be made to show the exact syntax used to create subsequent examples Instead we concen trate on general concepts with the aim of showing what MetaPost can do The interested reader can refer to 3 for details Another thing MetaPost can do is draw curved lines If points Po P P4 are as in Figure 2a asking the interpreter to connect them in order produces the curve in Figure 2b Asking for a smooth closed curve through the same se quence of points produces Figure 3a Since MetaPost has data types and operators for objects like curved lines it is possible to store the curve in a path vari able p and use a statement like draw p scaled s Reprint MAPS 9 92 2 Nov 1992 to draw rescaled versions of p Figure 3b was generated by placing this statement in a loop that scans various values of s There is also a fill statement that fills the interior of a closed curve with a color or a shade of gray The filled regions in Figure 3c illustrate how overlapping fills overwrite each other The figure was generated by filling the outermost curve with light gray then filling the next smaller curve with white then the next smaller curve with dark gray etc The examples given
12. id erably more powerful Section 2 gives a general idea of what the language is like and what can be done with it More detailed discussions of interesting features follow in Section 3 This includes Section 3 1 on integrating text and graph ics Section 3 2 on dealing with dashed lines and Sec tion 3 3 on drawing arrows Finally Section 4 deals with macro packages and Section 5 presents some con cluding remarks 2 Overview of the Language MetaPost is a batch oriented graphics language that achieves great power and flexibility by giving up some the ease of use found in interactive graphics editors such as MacDraw A MetaPost user prepares an input file such as the one shown in Figure 1 Invoking the MetaPost interpreter produces an encapsulated Post Script output file that can be included in a T X doc Presented at EuroTEX 92 September 14 18 Prague Czechoslovakia Dutch TEX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands Reprint MAPS 9 92 2 Nov 1992 90 Introduction to MetaPost beginfig 1 draw endfig end 20 20 0 0 0 30 30 0 0 0 Bijlage S A Figuur 1 A MetaPost input file and the resulting output en et em a Figuur 2 A sequence of points and a curve formed by connecting them 2 3 1 4 0 a b c Figuur 3 A closed curve and some effects that can be achieved by rescaling it ument or viewed with a PostScript interpr
13. lt in PostScript fonts This makes MetaPost output much more portable but it generally does not work with TEX fonts unless you have them in PostScript Type format Many dvi to PostScript programs download bitmaps for only those characters actually used in the document Such programs can handle MetaPost output if they un derstand the nonstandard PostScript comments that the MetaPost interpeter uses to indicate which characters need to be downloaded Recent versions of Rokicki s dvips have this capability 3 2 Dashed Lines The MetaPost language provides many ways of chan ging the appearance of a line besides just changing its width This is done by specifying a dash pattern when drawing a straight or curved line Figure 8 shows a few examples of dash patterns and the lines they Dutch TEX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands Bijlage S Introduction to MetaPost 93 withdots scaled 2 withdots evenly scaled 4 evenly scaled 2 evenly Figuur 8 Dashed lines each labeled with the dash pattern used to create it e e4 shifted 18bp 0 e e4 shifted 12bp 0 e e4 shifted 6bp 0 e e4 Figuur 9 Dashed lines each labeled with the corresponding dash pattern where e4 refers to the dash pattern evenly scaled 4 5 ___ _ _ 6 drawdblarrow z5 z6 3 __ 4 drawarrow reverse z3 z4 gt 2 drawarrow z1 z2 Figuur 10 Three
14. nical Report no 162 AT amp T Bell Laboratories Murray Hill New Jer sey April 1992 Can be obtained by mail ing send 162 from research cstr to netlib research att com 4 Alan Jeffrey Labelled diagrams in METAFONT TUGboat Communications of the TEX User s Group 12 2 227 229 June 1991 5 Brian W Kernighan Pic a graphics language for typesetting In Unix Research System Papers Tenth Edition pages 53 77 AT amp T Bell Laborat ories 1990 6 D E Knuth METAFONT the Program Addison Wesley Reading Massachusetts 1986 Volume D of Computers and Typesetting 7 D E Knuth The TEXbook Addison Wesley Reading Massachusetts 1986 Volume A of Computers and Typesetting 8 Richard O Simpson Nontraditional uses of METAFONT In Malcom Clark editor TEX Ap plications Uses Methods pages 259 271 Ellis Horwood 1990 9 Michael J Wichura The PiCTEX Manual TEX User s Group Providence Rhode Island 1987 Shimon Yanai and Daniel M Berry Environment for translating METAFONT to PostScript TUG boat Communications of the TEX User s Group 11 4 525 541 November 1990 S 05 femi 10 Dutch TeX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands
15. so far suggest that MetaPost al lows drawing and filling it has data types for num bers coordinate pairs and curved paths it has oper ators for doing things like rescaling paths and it has programming language constructions such as loops It also inherits from METAFONT the ability to solve lin ear equations and deal with a broad class of coordinate transformations Figure 4 illustrates linear equations and coordinate transformations It was generated by introducing an unknown transformation T giving a pair of equations Dutch TX Users Group NTG P O Box 394 1740 AJ Schagen The Netherlands Bijlage S ete Introduction to MetaPost 9 er Figuur 4 An example of repeated transformations Figuur 5 A labeled diagram that declare it to be shape preserving and declaring that it maps Point into Point 2 and Point 3 into Point 4 The figure was created by generating a simple picture P and repeatedly drawing P and transforming it by T 3 Interesting Features Anyone familiar with METAFONT can see that Sec tion 2 did not begin to cover all the language features mentioned in the introduction While it is impractical to give a detailed treatment of the entire language we can concentrate on a few of the features that distinguish MetaPost from METAFONT and from other graphics languages 3 1 Text in Pictures MetaPost has a number of features for including labels and other text in the figures it generates The simplest
16. tion to MetaPost are set up by the circleit macro circleit box name picture expression The circleit macro defines pair variable just as boxit does except that there are no corner points box name ne box name sw etc A call to circleit a gives relationships among pointsa c a s a e a n a w and distances a dx and a dy Together with a c and a off these variables describe how the pic ture is centered in an oval as can be seen from the Figure 15 The drawboxed and bpath macros work for circleit boxes just as they do for boxit boxes By default the boundary path fora circleit box is a circle large enough to surround the box contents with a small safety margin controlled by the internal variable circmargin Figure 16 gives an example The oval boundary paths around Start and Stop in the figure are due to equations of the form box name dx box name dy that force those boxes to be noncircular 4 2 Other Packages Why aren t the boxes mp macros automatically pre loaded like the plain macros One reason is that they are too specialized to really be treated as part of the core language Another reason is that boxes mp was intended to be the first of several macro packages each one extending the language to cover another specialized application In fact there already is another macro package called rboxes mp This package builds on boxes mp by providing another box shape a rectangular
17. y giving btex y axis etex rotated 90 as the argument to a label statement Here is how TEX material gets translated into a form MetaPost understands The MetaPost processor skips over btex etex blocks and depends on a pre processor to translate them into low level MetaPost commands If the main file is fig mp the translated TEX material is placed in a file named fig mpx This is normally done silently without any user intervention but it could fail if one of the btex etex blocks contains an erroneous TEX command Then the erro neous TEX input is saved in the filempxerr tex and the error messages appear in mpxerr log TEX macro definitions or any other auxiliary TEX commands can be enclosed in a verbatimtex etex block The difference between btex and verbatimtex is that the former generates a picture expression while the latter only adds material for TEX to process For instance if you want TEX to typeset labels using macros defined in mymac tex your MetaPost input file would look something like this verbatimtex input mymac etex Reprint MAPS 9 92 2 Nov 1992 beginfig 1 label btex TEX material using mymac tex etex coordinates MetaPost has an internal variable called prologues that controls the handling of text in pictures Giv ing this internal variable a positive value causes causes output to be formatted as structured PostScript gen erated on the assumption that text comes from bui
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