tug.org - Troy Henderson
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1. bly be constructed using external programs such a MATLAB or Octave Maple Mathematica Gnuplot et al A typical data file say data d to be used with the graph package may have contents 0 0 0 0 0 2 0 447214 0 4 0 632456 0 6 0 774597 0 8 0 894427 1 0 1 0 This data represents the graph of f x yx for six equally spaced points in 0 1 To graph this data the size of the graph must first be decided Choosing a width of 144 bp and a height of 89 bp a minimally controlled plot as in Figure 11 of this data can be generated by 13 draw begingraph 144bp 89bp gdraw data d endgraph The graph package provides many commands used to customize generated graphs and these commands are fully documented in the manual 2 for the graph package 1A 0 8 0 6 0 4 0 2 0 7 0 02 04 06 08 1 Figure 11 f x yx using the graph package 6 Including METAPOST Figures in ATEX In order to include a METAPOST figure in IAT EX the graphicx package is sug gested Below is an example of including a METAPOST figure with name foo 1 in a ATEX document documentclass article usepackage graphicx usepackage if pdf ifpdf DeclareGraphicsRule mps fi begin document includegraphics foo 1 end document 14 The ifpdf package and ifpdf fi command is used to prompt PDFIATRX to convert the METAPOST graphic to PDF on the fly using Hans Hagen s mptopdf This conve2. 8in The annulus is constructed by filling p with the baby blue color bbblue and then unfilling q The unfill command above is equivalent to fill q withcolor background where background is a built in color which is white by default Often times the unfill command appears to be the natural method for con structing figures like Figure 5 However the fill and unfill commands in Fig 8 Figure 5 unfill example ure 5 can be replaced by fill p reverse q cycle withcolor bbblue Figure 6 Avoiding an unfill The path p reverse q cycle travels around p in a counter clockwise directions since this is the direction that p traverses followed by a line segment to connect to q It then traverses clockwise around q using the reverse operator and finally returns to the starting point along a line segment using cycle This path is il lustrated in Figure 6 One reason for using this method to construct the annulus as opposed to the unfill command is to ensure proper transparency when placing the figure in an external document with a non white background If the former method is used and the annulus is placed on a non white background say ma genta then the result is Figure 7 It may be desired to have the interior of q be Figure 7 Improper transparency using unfill magenta instead of white This could be accomplished by redefining background however the latter method described above is a much simpler solution 4 3 Arrow c
3. to IAIFX instead of plain T X for text processing verbatimtex h amp latex documentclass minimal begin document etex beginfig n draw commands endfig end Often times it desirable to typeset labels with a justification that is not centered For example one may wish to place an A centered horizontally about 0 0 but placed immediately on top of 0 0 METAPOST provides eight suffixes to accommodate such needs The suffixes 1ft rt bot and top align the label on the left right bottom and top respectively of the designated point A hybrid of these four justifications provide four additional ones namely 11ft ulft lrt and urt to align the label on the lower left upper left lower right and upper right respectively of the designated point For example 12 label top btex A etex 0 0 places the A directly above 0 0 Figure 10 demonstrates each of the suffixes and their corresponding placement of the labels top ulft_urt lfthert bot lift lrt Figure 10 Label Suffixes 5 Graphing Functions One of the most common types of figures for TEX users are those which are the graphs of functions of a single variable Hobby recognized this and constructed a package to accomplish this task It is invoked by input graph METAPOST has the ability to construct data i e ordered pairs for graphing sim ple functions However for more complicated functions the data should proba
4. work on METAPOST a powerful graphics language based on Knuth s METAFONT but 1 All graphics in this article except Figure 2 are created with METAPOST and the source code and any required external data files for each of these graphics are embedded as file attachments in the electronic PDF version of the article with PostScript output and facilities for including typeset text 3 Although sev eral packages e g P CTEX Xy pic and then native TEX picture environement to name a few are available for creating graphics within TRX based documents they all rely on TEX Since TEX was designed to typeset text it seems natural that an external utility should be used to generate graphics instead Furthermore in the event that the graphics require typeset text then the utility should use TEX for this requirement This premise is exactly the philosophy of METAPOST Since METAPOST is a programming language it accommodates data struc tures and flow control and compilation of the METAPOST source code yields EPS graphics These features provide an elegant method for generating graph ics Figure 1 illustrates how METAPOST can be used programatically The figure is generated by rotating one of the circles multiple times to obtain the desired circular chain The programming language constructs of METAPOST also deliver Figure 1 Rotated circles a graceful mechanism for creating animations without having to manually cre ate each fram
5. The PracTpX Journal 2006 No 4 Article revision 2006 11 03 A Beginner s Guide to METAPOST for Creating High Quality Graphics Troy Henderson Address Abstract Department of Mathematical Sciences United States Military Academy West Point NY 10996 USA troyO tlhiv org http www tlhiv org Individuals that use TeX or any of its derivatives to typeset their docu ments generally take extra measures to ensure paramount visual quality Such documents often contain mathematical expressions and graphics to accompany the text Since TeX was designed for the creation of beautiful books and especially for books that contain a lot of mathematics 4 it is clear that it is sufficient and in fact exceptional at dealing with mathematics and text TEX was not designed for creating graphics however certain add on packages can be used to create modest figures TEX however is capable of including graphics created with other utilities in a variety of formats Because of their scalability Encapsulated PostScript EPS graphics are the most common types used This paper introduces METAPOST and demon strates the fundamentals needed to generate high quality EPS graphics for inclusion into TRX based documents 1 Introduction To accompany TEX Knuth developed METAFONT as a method of creating entire families of fonts from a set of dimensional parameters and outline descriptions 1 Approximately ten years later John Hobby began
6. debugging METAPOST Previewer View MetaPost Log Preview Scaling Factor 1 v Get MP Get EPS Get PDF verbatimtex documentclass 12pt famsart usepackage mflogo begin document etex input boxes beginfig 1 draw fullcircle scaled 2 36 drawarrow 0 0 36 unitvector 1 1 label Irt btex r etex 18 unitvector 1 13 endfig verbatimtex end document etex end Preview Output Clear Data Figure 2 METAPOST Previewer 3 Data Types There are nine data types in METAPOST numeric pair path transform color string boolean picture and pen These data types allow users to store fragments of the graphics for later use We will briefly discuss each of these data types and elaborate on how they are used in a typical METAPOST program o numeric numbers o pair ordered pairs of numerics o path B zier curves and lines picture pictures transform transformations such as shifts rotations and slants color triplets in the unit cube with red green and blue RGB components o string strings to be labeled o boolean true or false values o pen stroke properties Virtually all programming languages provide a way of storing and retriev ing numerical values This is precisely the purpose of the numeric data type in METAPOST Since graphics drawn with METAPOST are simply two dimensional pictures it is clear that an ordered pair
7. e of the animation The primary advantage of EPS is that it can be scaled to any resolution without a loss in quality It can also be easily converted to raster formats e g Portable Network Graphics PNG and Joint Photographic Ex perts Group JPEG et al or other vector formats including Portable Document Format PDF and Scalable Vector Graphics SVG et al 2 METAPOST Compilation A typical METAPOST source file consists of one or more figures Compilation of the source file generates an EPS graphic for each figure These EPS graphics are not self contained in that fonts used in labels are not embedded into the graphic If foo mp is a typical METAPOST source file then its contents are of the fol lowing form beginfig 1 draw commands endfig beginfig 2 draw commands endfig beginfig n draw commands endfig end Executing mpost foo mp yields the following output This is MetaPost Version version foo mp 1 2 3 n n output files written foo 1 foo n Transcript written on foo log For users who just want to get started using METAPOST a METAPOST Pre viewer is located at http www tlhiv org MetaPostPreviewer This previewer illustrated in Figure 2 is simply a graphical interface to METAPOST itself It generates a single graphic with the option to save the output in both EPS and PDF filetypes Users may also choose to save the source code and can view the compilation log to assist in
8. is needed to identify each point in the picture The pair data type provides this functionality Each point in the plane consists of an x i e abscissa part and a y i e ordinate part METAPOST uses the standard syntax for defining points in the plane e g x y where both x and y are numeric data typed variables In order to store paths between points the path data type is used All paths in METAPOST are represented as cubic B zier curves Cubic B zeier curves are simply parametric splines of the form x t y t where both x t and y t are piecewise cubic polynomials of a common parameter t Since B zier curves are splines they pairwise interpolate the points Furthermore cubic B zier curves are diverse enough to provide a smooth path between all of the points for which it interpolates METAPOST provides several methods for affecting the B zier curve between a list of points For example piecewise linear paths i e linear splines can be drawn between a list of points since all linear polynomials are also cubic polynomials Furthermore if a specific direction for the path is desired at a given point this constraint can be forced on the B zier curve The picture data type is used to store an entire picture for later use For exam ple in order to create animations usually there are objects that remain the same throughout each frame of the animation So that these objects do not have to be manually drawn for each frame a co
9. ng direction at z2 of 45 In order to require different incoming and outgoing directions we would use draw zi right dir 0 z2 dir 0 up z3 where 0 and 6 are the incoming and outgoing directions respectively 4 2 The fill Command Another common command in METAPOST is the fill command This is used to fill closed paths or cycles In order to construct a cycle cycle may be appended to the path declaration For example path p p zi right z2 dir 45 up z3 cycle fill p withcolor red draw p Figure 4 fill example produces Figure 4 Notice that p is essentially the same curved path as in Figure 3 with the additional piece that connects z3 back to z1 with a line segment using cycle Just as it is necessary to fill closed paths it may also be necessary to unfill closed paths For example the annulus in Figure 5 can be constructed by color bbblue bbblue 3 5 4 5 1 path p q p fullcircle scaled 2 54 q fullcircle scaled 2 27 fill p withcolor bbblue unfill q draw p draw q The fullcircle path is a built in path that closely approximates a circle in META POST with diameter 1 bp traversed counter clockwise This path is not exactly a circle since it is parameterized by a B zier curve and not by trigonometric func tions however visually it is essentially indistinguishable from an exact circle Notice that p is a fullcircle of radius 54bp 3 4in and q is a fullcircle of radius 27 bp 3
10. nvenient method for redrawing them is to store them into a picture variable for later use When constructing pairs paths or pictures in METAPOST it is often conve nient to apply affine transformations to these objects As mentioned above Figure 1 can be constructed by rotating the same circle several times before drawing it METAPOST provides built in affine transformations as building blocks from which other transformations can be constructed These include shifts rotations horizontal and vertical scalings and slantings There are five built in colors in METAPOST black white red green and blue However custom colors can be defined using the color data type Colors in METAPOST are simply ordered triplets of the form r g b where r g and b are numerics between 0 and 1 These values r g and b identify what fraction of the color is red green and blue respectively For example the built in color red is simply a synonym for 1 0 0 and black is a synonym for 0 0 0 If a particular color is to be used several times throughout a figure it is natural to store this color into a variable of type color for multiple uses The most common application of string data types is reusing a particular string that is typeset or labeled The boolean data type acts in the same way as in other programming languages to be used in conditional statements for testing Finally the pen data type is used to affect the actual stroke paths The defa
11. ommands When drawing simple graphs and other illustrations the use of arrows is often essential There are two arrow commands in METAPOST for accommodating this need drawarrow and drawdblarrow Both of these commands require a path argument For example drawarrow 0 0 72 72 draws an arrow beginning at 0 0 and ending at 72 72 along the line segment connecting these points The path argument of both drawarrow and drawdblarrow need not be line seg mented paths they may be any METAPOST path The only difference between drawarrow and drawdblarrow is that drawarrow places an arrow head at the end of the path and drawdblarrow places an arrow head at the beginning and the end of the path As an example to draw the curved path in Figure 3 with an arrow head at the end of the path i e at z3 the following command can be used drawarrow zi right z2 dir 45 up z3 and is illustrated in Figure 8 10 z3 z Figure 8 Using drawarrow along a path 4 4 The label command One of the nicest features of METAPOST is that it relies on TEX or TEX to type set labels within figures Almost all figures in technical documents are accompa nied by labels which help clarify the situation for which the figure is assisting to illustrate Such labels may include anything from simple typesetting as in Figures 3 6 and 8 to typesetting function declarations and even axes labeling The label command requires two arguments a st
12. ring to typeset and the point for which label is placed For example the command label A 0 0 will place the letter A at the coordinate 0 0 and the box around this label is centered vertically and horizontally at this point Simple strings like A require no real typesetting to ensure that they appear properly in the figure However many typeset strings in technical figures require the assistance of TEX to properly display them For example Figure 9 is an example where typesetting is preferred That is the axes labels and the function declaration look less than perfect if TEX is not used For reasons such as this METAPOST provides a way to escape to TEX in order to assist in typesetting the labels Therefore instead of labeling the A as above label btex A etex 0 0 provides a much nicer technique for typesetting the label The btex etex block instructs METAPOST to process everything in between btex and etex using TEX Therefore the function declaration in Figure 9 is labeled using label btex f x x72 etex a b 11 ad gt T Figure 9 Labeling text where a b is the point for which the label is to be centered Since many METAPOST users prefer to typeset their labels using L TEX instead of plain TEX METAPOST provides a convenient method for accommodating this This is done in the preamble of the METAPOST source file The following code ensures that the btex etex block escapes
13. rsion is necessary since PDFIATEX performs no PostScript processing 7 Conclusion METAPOST is an elegant programming language and it produces beautiful graphics The graphics are vectorial and thus can be scaled to any resolution without degradation There are many advanced topics that are not discussed in this article e g loops flow control subpaths intersections etc and the METAPOST manuall 3 is an excellent resource for these advanced topics How ever the METAPOST manual may seem daunting for beginners There are many websites containing METAPOST examples and several of these are referenced at http www tug org metapost Finally we mention that Knuth uses nothing but METAPOST for his diagrams References 1 N H F Beebe METAFONT http www math utah edu beebe fonts metafont html 2006 2 J D Hobby Drawing graphs with MetaPost Technical Report 164 AT amp T Bell Laboratories Murray Hill New Jersey 1992 Also available at http www tug org docs metapost mpgraph pdf 3 J D Hobby A user s manual for MetaPost Technical Report 162 AT amp T Bell Laboratories Murray Hill New Jersey 1992 Also available at http www tug org docs metapost mpman pdf 4 D E Knuth The TeXbook volume A of Computers and Typesetting Addison Wesley Boston 1986 15
14. ult unit of measurement in METAPOST is 1 bp 1 72 in and the default thickness of all stroked paths is 0 5 bp An example for using the pen data type may include changing the thickness of several stroked paths This new pen can be stored and then referenced for drawing each of the paths 4 Common Commands The METAPOST manual 3 lists 26 build in commands along with 23 function like macros for which pictures can be drawn and manipulated using METAPOST We will not discuss each of these commands here however we will focus on several of the most common commands and provide examples of their usage 4 1 The draw command The most common command in METAPOST is the draw command This com mand is used to draw paths or pictures In order to draw a path from z1 0 0 to z2 54 18 to z3 72 72 we should first decide how we want the path to look For example if we want these points to simply be connected by line segments then we use draw z1 z2 z3 However if we want a smooth path between these points we use draw z1 z2 z3 In order to specify the direction of the path at the points we use the dir operator In Figure 3 we see that the smooth path is horizontal at z1 a 45 angle at z2 and vertical at z3 These constraints on the B zier curve are imposed by draw zifright z2 dir 45 up z3 423 i Figure 3 draw examples Notice that z2 dir 45 forces the outgoing direction at z2 to be 45 This implies an incomi
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