A short introduction to mEtapost
Contents
1. Introduction to METAPOST In the code above the end point of the line is named z140 Here we see both conditions listed before first the distance vector between z210 and z2 is given by the distance vector between z and zo i e the base line rotated by 90 degrees scaled by an arbitrary factor Second z19 is located somewhere on the line defined by the points zp and 21 In both cases I used a numerical value named whatever This may become an arbitrary number In fact the value may change from statement to statement since the variable whatever is encapsu lated per statement z2 z0 z10 z1 Figure 4 Triangle 2 As shown in fig 4 METAPOST finds the correct position for z19 as starting point of a perpendicular line to the base line with z2 as end point 7 Time variables A path in METAPOST may be imagined as the travel of a vehicle Paths are parameterized by a time vari able what might be a bit misleading since of course the drawing is static So a path has a start and end time and any point is correlated to a time in between and vice versa Here is some example where time variables are used Listing 5 Time variables and subpaths pickup pencircle scaled ibp path pl pO origin up 3cm 2cm pi 5mm 2cm 3cm 5mm draw pO dashed withdots draw pi dashed withdots t0 t1 pO intersectiontimes p1 draw subpath 0 t0 of pO subpath ti length p1 of p1 z10 z2 whatever z1i2. get a PostScript file with the name ex 001 mps and if we add a fig ure with number 2 the PostScript output would be written into ex 002 mps Since pdfTEX recognizes files with the extension mps as METAPOST output the file could be easily used in a BIEX document with includegraphics ex 001 mps and the doc ument may be processed both by pdfTRX and in the 1001 K H ppner original workflow by compiling to DVI and using dvips As in C all statements may span multiple lines and are finished by the character The example figure itself shows a straight line from the origin to the point 1cm 2cm Then the path is closed by a B zier curve via the point located at 1 3cm 3cm For drawing a round pen with diameter of one PostScript point is used META POST knows the same units as TEX like bp for PS points cm mm The result is shown in fig 1 3 Defining points by linear equations While there is nothing exciting about the first ex ample we will see what makes METAPOST special in a moment Assume you want to draw a simple rectangle Then you know it consists of four corners e g with the lower left one in the origin that we will describe by the following equations Listing 2 Rectangle path p z0 origin xO x3 xi x2 yi y0 y3 y2 xi x0O 3cm y3 yO 2cm pO z0 z1 z2 z3 cycle fill pO withcolor blue draw pO withpen pencircle scaled ibp You see all corners besid
3. A short introduction to METAPOST K Hoppner Haardtring 230a 64295 Darmstadt Germany klaus hoeppner gmx de 1 History When Knuth developed TEX he also created a set of new fonts Computer Modern For this he created his own font description language and the program METAFONT that converts a METAFONT source into a bitmap usually stored in a file with the exten sion pxl or more often pk The major feature of METAFONT is that paths may be described with a set of linear equations that determines how the sin gle points of the path are related and this equation set is solved by the METAFONT program Addi tionally Knuth extensively used parameters within these equations so different font series e g bold and medium could be produced from the same equations by changing some parameters John D Hobby created METAPOST as a system using nearly the same programming language but with PostScript output It was presented first in TUGboat 1 while the first public versions were re leased in the early 1990s Some new features were added to the Meta language e g the ability to in clude stuff typeset by TEX into a METAPOST draw ing something that wasn t needed in METAFONT for creating glyphs of a font but is very useful to put text labels into graphics Meanwhile METAPOST is maintained by the METAPOST team with Taco Hoekwater as chief de veloper Since then many improvements were made For the future they plan to releas
4. ST it is possi ble to run METAPOST in a mode that will produce standalone PostScript output that contains a real EPS with all fonts embedded that can be displayed in any PS interpreter or may be used in other appli cations besides TEX documents A switch named prologues defines whether METAPOST will embed fonts or not Just use the definition prologues 3 at the start of your METAPOST file to get a standalone EPS figure The default value of prologues is 0 which means that no fonts will be embedded The meaning of other values of prologues may be looked up in the META POST manual they are only relevant for special cases 9 Conclusion This article was intended to just give a short intro duction to METAPOST I left out several things e g how to use colors defining macros loops etc Since the article is originally based on a talk that was part of a comparison of tools it is focussed on what makes METAPOST unique among other draw ing tools solving linear equations and having direct access on intersection points and time variables of paths If you are interested in learning METAPOST please have a look into the METAPOST manual 2 or into the ATEX Graphics Companion 3 that de scribes METAPOST among many other tools References 1 John D Hobby A METAFONT like System with PostScript Output TUGboat 10 4 1989 2 John D Hobby METAPOST A User s Manual Introduction to METAPOST 2008 3 Mich
5. e MPlib a com ponent library that contains the METAPOST engine and can be reused in other applications 2 Basics As mentioned before METAPOST defines its own programming language It consists of the following elements e points e pens e paths e numbers e colors originally RGB only meanwhile CMYK is supported Points are normally named by the letter z rep resented by a pair x y TUGboat Volume 0 2060 No 0 Proceedings of the 2060 Annual Meeting Paths may contain geometrical elements e g fullcircle or may consist of points that are con nected by lines or B zier curves Colors are tuples of three in case of RGB or four in case of CMYK numbers For a short example let s have a look on the following example Listing 1 1 example filenametemplate beginfig 1 pickup pencircle scaled ibp draw origin 1icm 2cm 0 5cem icm cycle endfig end j h3c mps Figure 1 Example figure as defined in listing 1 It shows that each METAPOST figure is put be tween beginfig and endfig with a number identi fying the figure So a METAPOST source may con tain several figures Originally when processing the source e g ex mp with METAPOST mpost ex the figure numbers were used as file extension for the resulting PostScript files In later releases the command filenametemplate was introduced that uses a syntax like the printf command in C In the example above we would
6. el Goossens Frank Mittelbach Sebas tian Rahtz Denis Roegel and Herbert Voss PTEX Graphics Companion The 2nd Edition Addison Wesley Professional 2007 TUGboat Volume 0 2060 No 0 Proceedings of the 2060 Annual Meeting 1005
7. es zo aren t defined di rectly as x y pairs but described by their relations While describing a rectangle with linear equations seems like a bit of overkill this METAPOST feature becomes really powerful for the construction of com plex paths z3 z2 2cm z0 3cm zl Figure 2 Rectangle resulting from code in listing 2 1002 4 Transformations of paths METAPOST supports the following transformations of paths e Translations pO shifted x1 x2 e Rotation pO rotated alpha e Scaling in both directions or in x or y direction individually pO scaled factor pO xscaled xfactor pO yscaled yfactor e Slanting pO slanted alpha For example the following ellipsis is the output of the code draw fullcircle xscaled 3cm yscaled 2cm rotated 30 5 Intersection points Finding the intersection points of paths is another nice METAPOST feature Assume you have a triangle Theory says if you draw three lines each of them from one corner of the triangle to the mid point of the opposite side all these lines will intersect at the same point The following code shows how this can be demonstrated in a METAPOST drawing Listing 3 Triangle 1 pickup pencircle scaled ibp path pl z0 origin zi z0 3cm right z2 z0 2 7cm dir 40 pO z0 z1 z2 cycle pi 5 z0 z1 z2 p2 5 z1 z22 z0 p3 5 z2 z0 z1 draw pi withcolor blue draw p2 withcolor blue draw p3 withcolor blue draw
8. ned to the variables while is used in linear equations The action of placing a label at zo in the exam ple is rather straightforward The label command centers the label at the given point In many cases a suffix is appended to the label command to de fine how the label is placed in relation to the given point i e top bot bottom 1ft left rt right or ulft 11ft urt lrt e g ulft means upper left and 1rt means lower right The label com mand may be replaced by dotlabel that draws a 1004 dot at the given point in addition to the label For example the code dotlabel urt this is a label z0 draws a dot at zp and places the given text in upper right direction from Zo Only simple text may be used for labels that are included by METAPOST directly But for real type setting we may use one of the best typesetting pro grams we know TRX itself We may include nearly arbitrary TEX stuff into labels All TEX snippets that occur in the METAPOST source are extracted and typeset with TEX before the result is included into the figure by METAPOST All the TEX stuff has to be embedded into an environment btex etex e g label btex z_0 etex z0 will center the label zo at this point Normally the plain TEX compiler is used for typesetting the btex etex fragments But the name of the pro gram may be passed in command line when calling METAPOST so to use TEX we just use the com mand m
9. pi intersectionpoint p2 TUGboat Volume 0 2060 No 0 Proceedings of the 2060 Annual Meeting withpen pencircle scaled 3bp draw p0 This code is rather simple It consists of three parts First the three points zp 22 are defined and path po is defined as the triangle with these points as corners Second the paths p p3 are defined Each consists of a line from one corner to the mid point of the opposite side This may be easily expressed in METAPOST since e g the statement 5 z1 z2 is just the point on half the line from z1 to 22 Finally after drawing all the paths defined above we mark the intersection point of p and pg This is directly given by the command pi intersectionpoint p2 It may be a bit more complicated if two paths have more than one intersection point The result of this drawing is shown in fig 3 z2 z0 z1l Figure 3 Construction of a triangle 6 Whatever it is Coming back to the triangle in the latest example another interesting task is the following draw a line from one corner that is orthogonal to the opposite side Let s assume we want to draw the line from point z2 so the opposite side is just the base line of our triangle Now we know two things 1 The line is orthogonal to the base line connec tion of z0 and 21 2 The starting point is in z2 the end point shall be on the base line This may be directly expressed in METAPOST Listing 4 Triangle 2
10. post tex latex ex1 Let t have a look how we can typeset a label with ATEX using Euler math fonts to typeset a for mula Listing 6 Typesetting a label with BTEX filenametemplate verbatimtex Zj h3c mps documentclass article usepackage euler begin document etex beginfig 1 dotlabel urt btex sqrt frac 1 1 x7 2 etex origin endfig The example contains some IATRX code within a verbatimtex etex environment that is taken verbatim as IXTRX code before typesetting all the la bels Please note that it is used to define a preamble with article as document class and loading the euler package While the begin document is present the closing end document is inserted automati cally The result of this code when compiled by METAPOST with using ATEX as typesetter as ex plained above is shown in fig 6 Including labels causes some difficulties with fonts Normally METAPOST doesn t embed fonts TUGboat Volume 0 2060 No 0 Proceedings of the 2060 Annual Meeting l 1 x Figure 6 Using P TeX for typesetting a label but just adds a reference to the used fonts into the PostScript output This isn t a problem when METAPOST is included in a TEX document since TEX will resolve all of these font references But the figures won t be usable standalone since Post Script interpreters like GhostScript will complain about unknown fonts In recent versions of METAPO
11. z0 rotated 90 z10 whatever z0 z1 TUGboat Volume 0 2060 No 0 Proceedings of the 2060 Annual Meeting We have two paths po and p a B zier curve from lower left to upper right and a straight line 1003 K Hoppner from upper left to lower right drawn with dotted lines Now we are not only interested in the intersec tion point of these paths but we want to combine the subpath of po before the intersection point with the subpath of p after this point drawn with a solid line in fig 5 In this case we need the time values of both paths in the intersection point For this the state ment pO intersectiontimes p1 is used The re sult of this is a pair in fact a point with the time value of po in the intersection point as first part x part and the time value of p as second part y part As soon as these time values are known the desired path is constructed using subpath oe Figure 5 Using time variables and subpaths 8 Text and Labels METAPOST allows to place labels into a figure In the simplest form the text may be included directly without any typesetting done by TEX defaultfont ptmr sr defaultscale 1 2 label this is a label z0 It will just add the text commands to write the label text in 12pt Times Roman since a font scaling fac tor of one refers to 10pt into the PostScript code Please note that is used in the code above since new values are assig
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