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1. directly above 0 0 Figure 10 demonstrates each of the suffixes and their corresponding placement of the labels top ulft_urt lftHHrt bot llft lrt Figure 10 Label suffixes 5 Graphing functions Among 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 simple functions However for more complicated functions the data should probably be constructed using external programs such as 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 11 0 0 0 0 0 2 0 447214 0 4 0 632456 0 6 0 774597 0 8 1 0 0 894427 D 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 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 5 0 6 0 4 0 2 D a 0 02 04 06 08 1 Figure 112. 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 METAPOST 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 functions however visually it is essentially indistinguishable from an exact circle Figure 5 unfill example Notice that p is a fullcircle of radius 54bp 3 4 in and q is a fullcircle of radius 27 bp 3 8 in The annulus is constructed by filling p with the baby blue color bbblue and then unfilling q The unfill command above is equivalent to E fill q withcolor background where background is a built in color which is white by default Often the unfill command appears to be the natural method for constructing figures like Figure 5 However the fill and unfill commands in Figure 5 can be replaced by ss 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
3. f x yx using the graph package 6 Including METAPOST figures in BIEX In order to include a METAPOST figure in BIFX the graphicx package is suggested Below is an example of including a METAPOST figure with name foo 1 mps in a BIEX document documentclass article usepackage graphicx begin document includegraphics foo 1 mps end document Having a mps file extension on the graphic allows the same graphic to be included in both BTEX and PDFETRX documents When using PDFBI X the EPS graphic with file extension mps 12 is converted to PDF on the fly using Hans Hagen s mptopdf This conversion is necessary since PDFETEX performs no PS 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 manual 3 is an excellent resource for these advanced topics However 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 E Beebe Metafont http www math utah edu beebe fonts metafont html1 2006 2 J D Hobby
4. just want to get started using METAPOST a METAPOST previewer is available at http www tlhiv org mppreview 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 EPS PDF and SVG formats Users may also choose to save the source code and can view the compilation log to assist in debugging 3 Data types 3 1 Standard data types There are ten data types in METAPOST numeric pair path transform rgbcolor cmykcolor 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 numeric numbers pair ordered pairs of numerics path B zier curves and lines picture pictures transform transformations such as shifts rotations and slants rgbcolor or color triplets with each component between 0 and 1 red green and blue cmykcolor quadruplets with each component between 0 and 1 cyan magenta yellow and black string strings of characters o boolean true or false values pen stroke properties Virtually all programming languages provide a way of storing and retrieving numerical values This is precisely the purpose of the numeric data type in METAPOST Since graphics drawn with METAPOS
5. D A Beginners Guide to METAPOST for Creating High Quality Graphics Troy Henderson Stephan Hennig April 5 2011 Abstract Individuals that use TEX or any of its derivatives to typeset their documents 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 mathemat ics 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 demonstrates the fundamentals needed to generate high quality EPS graphics for inclusion into TeX based documents 1 Introduction To accompany TX 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 work on METAPOST a powerful graphics language based on Knuth s METAFONT but with PostScript output and facilities for including typeset text 3 Although several packag
6. Drawing graphs with METAPOST Technical Report 164 AT amp T Bell Labo ratories 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 TXbook volume A of Computers and Typesetting Addison Wesley Boston 1986 13
7. T are simply two dimensional pictures it is clear that an ordered pair 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 zier 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 example in order to create animations usually there are objects that remain the same throughout each frame of the animation So tha
8. drawarrow zif right z2 dir 45 up z3 and is illustrated in Figure 8 4 4 The label command One of the nicest features of METAPOST is that it relies on TEX or BIEX to typeset labels within figures Almost all figures in technical documents are accompanied 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 z3 D z2 zi Figure 8 Using drawarrow along a path The label command requires two arguments a string 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 Figure 9 Labeling text 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 TX in order to assist in typesetting the labels Therefore instead of labeling the A as above label btex A etex 0 0 p
9. es e g PICTEX Xy pic and the native BIEX picture environment to name a few are available for creating graphics within TeX 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 structures and flow control and compilation of the METAPOST source code yields EPS graphics These features provide an elegant method for generating graphics 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 All graphics in this tutorial 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 Attachments are indicated by a paper clip icon Figure 1 Rotated circles The programming language constructs of METAPOST also deliver a graceful mechanism for creating animations without having to manually create each frame 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 conver
10. is illustrated 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 magenta then the result is Figure 7 Figure 7 Improper transparency using unfill It may be desired to have the interior of q be 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 commands 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 a 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 segmented 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 i
11. k For example if we want these points to simply be connected by line segments then we use M draw z1 z2 z3 However if we want a smooth path between these points we use g 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 E draw zif right z2 dir 45 up z3 Notice that z2 dir 45 forces the outgoing direction at z2 to be 45 This implies an incoming direction at z2 of 45 In order to require different incoming and outgoing directions we would use EE draw zif right dir 0 z2 dir 0 up z3 Figure 3 draw examples where 0 and 0 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 zifright z2 dir 45 up z3 cycle fill p withcolor red draw p 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 Figure 4 fill example Just as it is necessary to fill closed paths it may also be necessary to unfill closed paths For example the annulus in
12. le declaration pair al it is possible to store points in the array a with numeric values as index The console output of ali 0 1 a 2 0 5 a 3 10 20 show a 1 show al 23 show a j a j 1 gt gt 0 1 gt gt 0 1 gt gt 10 25 Notice the point stored at array index 1 can be referred to as a 1 as well as just a1 omitting the brackets The latter convenient and often practised notation works as long as the index is a plain numeric value If the index is a numeric variable or an expression however the brackets have to be present since e g aj would clearly refer to an unrelated variable of that name instead of index j of variable a Aside MetaPost as a macro language doesn t really provide true arrays However from a user s perspective the MetaPost way of indexing variables perfectly looks like an array 4 Common commands The METAPOST manual 3 lists 26 built 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 command is used to draw paths or pictures In order to draw a path from z1 0 0 to z2 54 18 to zZ3 72 72 we should first decide how we want the path to loo
13. or is to be used several times throughout a figure it is natural to store this color into a variable of type rgbcolor or cmykcolor The data type color is a convenient synonym for rgbcolor Additionally there are five built in RGB colors in METAPOST black white red green and blue So the expression 4 red blue refers to a dark violet EEE in the RGB color model and in the example above 1 6 0 could be replaced by red 6green The most common application of string data types is reusing a particular string that is typeset or labeled The boolean data type is the same as in other programming languages and is primarily used in conditional statements for testing Finally the pen data type is used to affect the actual stroke paths The default 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 The following code declares a variable of type numeric one of type pair and two string variables numeric idx pair v string s name Note variables of type numeric need not necessarily be declared A formerly undeclared variable is automatically assumed to be numeric at first use 3 2 Arrays Just like many other programming languages MetaPost provides a way to access variables by index After the following variab
14. rovides 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 ae label btex f x x72 etex a b where a b is the point for which the label is to be centered Since many METAPOST users prefer to typeset their labels using BIFX instead of plain TFX METAPOST provides a convenient method for accommodating this done in the preamble of 10 the METAPOST source file The following code ensures that the btex etex block escapes to BIEX instead of plain TeX for text processing verbatimtex h amp latex documentclass minimal begin document etex beginfig n draw commands endfig end Often times it is desirable to typeset labels with a justification that are not necessarily centered For example one may wish to place an A centered horizontally about 0 0 but placed above 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 label top btex A etex 0 0 places the A
15. t these objects do not have to be manually drawn for each frame a convenient 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 convenient 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 For creating colored graphics METAPOST provides two data types rgbcolor and cmykcolor These data types correspond to the two supported color models RGB and CMYK While using the 4 RGB color model fractions of the primary colors red EEE green Mmm and blue Mmm are additively mixed Similarly in the CMYK color model the primary colors cyan E magenta Mami yellow m and black WEE are subtractively mixed The former model is suitable for on screen viewing whereas the latter model is preferred in high quality print Both color types are ordered tuples cy C2 C3 and c1 C2 C3 4 with components c being numerics between 0 and 1 For example in the RGB color model a light orange tone can be referred to as 1 6 0 Mill whereas in the CMYK color model 0 6 1 0 EE corresponds to a clearly different orange tone If a particular col
16. ted to raster formats e g Portable Network Graphics PNG and Joint Photographic Experts 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 self contained i e the fonts used in labels are embedded into the graphic provided that prologues 3 is declared If foo mp is a typical METAPOST source file then its contents are likely of the following form prologues 3 outputtemplate j c mps beginfig 1 draw commands endfig beginfig 2 draw commands endfig beginfig n draw commands endfig end Executing mpost foo mp prologues 3 outputtemp ate j mps verbatimtex HR atex documentclass minimal begin document etex beginfigf 0 draw fullcircle scaled 2 36 drawarrow origin 36 dir 45 label Irt btex r etex 18 dir 45 endfig end O PNG MetaPost Previewer by Troy Henderson MetaPost version 1 110 o SvG Reset View Log Popup Figure Download yields the following output This is MetaPost Version version foo mp 1 2 n output files written foo 1 mps Transcript written on foo log Figure 2 METAPOST Previewer n foo n mps For users who
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