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1. Miscellaneous METAPOST Macros Matej Ko k April 15 2011 Abstract Technical communication with people is critical and harder than communicating with the machines METAPOST is a high level declarative and macro programming language Due to its unusual domain drawing pictures bare code fragments often look like cryptic gibberish In this document we try to prove that it is possible to write comprehensible METAPOST codel Contents 1 Various constants 2 tanforward expr p t d 3 tanbackward expr p t d 4 perpright expr p t d 5 perpleft expr p t d 6 drawkarrow expr path text t 7 drawtwowaykarrow expr path text t 8 drawinfinite expr path text t 9 drawhatched closedpath text t Copyright and License misc mp 1 Dab Additional macros for use with METAPOST Copyright C 2007 Matej Kosik lt kosik fiit stuba sk gt 1Disclaimer I do not explain METAPOST language here You can refer for example to 1 3 10 11 13 2a 2b April 15 2011 misc nw 2 This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General P2. dhatches enddef April 15 2011 misc nw 15 References 1 John D Hobby A User s Manual for METAPOST April 1994 2 Donald E Knuth The Art of Computer Programming Fundamental Algorithms volume 1 Addison Wesley Publishing Co Reading Massachusetts 2 edition 1973 3 Urs Oswald METAPOST A Very Brief Tutorial October 2002
3. iers in the attempt to avoid name clashes produces the following figure misc mp 2b lt 11 14 gt path _pictureboundary picture _unclippedhatches path _boundingrectangle pair _lowerleft _lowerright _upperleft _upperright 2Which are unfortunately not excluded April 15 2011 misc nw 14 14 misc mp 2b 413 def drawhatched expr p _unclippedhatches nullpicture _boundingrectangle bbox p Reveal dimensions of the bounding rectangle of a given path _lowerleft llcorner _boundingrectangle _lowerright lrcorner _boundingrectangle _upperleft ulcorner _boundingrectangle _upperright urcorner _boundingrectangle save width height width xpart _lowerright xpart _lowerleft height ypart _upperleft ypart _lowerleft Find smallest square to which that rectangle fits if width lt height _lowerright _lowerleft height 0 _upperleft _lowerleft 0 height _upperright _lowerleft height height width height else _lowerright _lowerleft width 0 _upperleft _lowerleft 0 width _upperright _lowerleft width width height width fi _pictureboundary p drawhatchedcontinuation enddef def drawhatchedcontinuation text t Draw the hatches for i width step 15cm until width addto _unclippedhatches contour _lowerleft 0 i _upperright i 0 cycle withpen penc endfor clip _unclippedhatches to _pictureboundary draw _unclippe
4. ings in detail Let us first enlarge the arrow and depict its distinct points beginnegative middlenegative endpoint beginpoint middlepositive beginpositive The arrow begins in beginpoint and ends in endpoint These two points are are determined by the path which is given to this macro as a parameter Coordinates of all the other points are computed The length of the arrowhead is influenced by the karrowheadlength variable Its default value is 8 points misc mp 2b lt 4 Tap karrowheadlength 8pt April 15 2011 misc nw The following figure illustrates the karrowheadlength karrowheadlength 8pt beginnegative beginpoint endpoint beginpositive middlenegative karrowheadlength 2 endpoint beginpoint middlepositive The karrowheadangle determines the angle shown in the figure below beginnegative karrowheadangle endpoint beginpositive 6 April 15 2011 misc nw 7 Ta misc mp 2b lt 45 7bp karrowheadangle 45 Default head angle of the end point The karrowheadmiddleangle determines the angle shown in the figure below middlenegative karrowheadmiddleangle endpoint middlepositive 7b misc mp 2b lt 7a Tep karrowheadmiddleangle 25 Default head angle of the middle point Auxiliary variables used for passing values between the main macro and its continuation Te misc mp 2b lt 7b 7d gt path _mainpath _positivea
5. mputes the distinct points shown in the figure above The value of subp path is denoted in green Compute mainpath positivearrowpath and negativearrowpath 9 7d endpoint point length p of p subp p cutbefore fullcircle scaled 2 karrowheadlength shifted endpoint middlepositive point 5 length subp of subp rotatedaround endpoint 5 karrowheadmiddleangle beginpositive point 0 of subp rotatedaround endpoint 5 karrowheadangle middlenegative point 5 length subp of subp rotatedaround endpoint 5 karrowheadmiddleangle beginnegative point 0 of subp rotatedaround endpoint 5 karrowheadangle _mainpath p _positivearrowpath beginpositive middlepositive endpoint _negativearrowpath beginnegative middlenegative endpoint 10a 10b April 15 2011 misc nw 10 7 drawtwowaykarrow expr path text t This macro has a very similar effect as the drawkarrow except for that the arrowhead is drawn not only at the end of a given path but also at the beginning of that path For example this code drawtwowaykarrow 0 0 7 5mm 7 5mm 15mm 0 withcolor red produces a following two way arrow AN The implementation is lazy We actually draw two k arrows On the original path and on the reversed path The value passed from the main macro to the continuation the mainpath identifier is already taken misc mp 1 lt 2a path __mainpath The main macro
6. point t of p If we have a path p and we choose some time t then z are coordinates of a point along the curve p in time t The perpright macro computes coordinates of the point z1 Point z is at the end of an abscissa beginning in point zo which has length 1 and it is perpendicular to the path p 3b misc mp 2b lt 3a 4p def perpright expr p t 1 1 0 rotated angle direction t of p 90 shifted point t of p enddef April 15 2011 misc nw 4 5 perpleft expr p t d It is very similar to perpright except coordinates in the opposite direction are returned See the figure below zo point t of p rpleft p t icm misc mp 2b lt 3b 5D def perpleft expr p t 1 1 0 rotated angle direction t of p 90 shifted point t of p enddef April 15 2011 misc nw 5 6 drawkarrow expr path text t This macro draws an arrow similar to the arrows found in 2 It can be used in the same way as the original drawarrow macro which is part of the plain format Here are some example usages u icm drawkarrow 0 0 u u 2u 0 drawkarrow 0 0 0 2u withcolor red drawkarrow 0 0 u u 2u 0 drawkarrow 0 0 0 2u dashed withdots scaled 25 KA NE En NE That is as you can see the text after the drawkarrow has analogous meaning as the text after the original drawarrow macro It only draws arrowhead in a different way Implementation of this macro is fairly delicate so we will explain th
7. rrowpath _negativearrowpath 7d misc mp 2b lt 7c 8p def drawkarrow expr p begingroup save subp endpoint beginpoint beginpositive middlepositive beginnegative middlenegative path subp pair endpoint beginpoint beginpositive middlepositive beginnegative middlenegative Compute mainpath _positivearrowpath and negativearrowpath 9 endgroup _drawkarrowcontinuation enddef April 15 2011 misc nw 8 Continuation of the drawkarrow macro It will use the computed mainpath _positivearrowpath and negativearrowpath It will also use several times the text which follows the path expres sion that follows the drawkarrow macro invocation That is consider the following statement drawkarrow 0 0 0 2u dashed withdots scaled 25 When drawkarrow macro is expanded the drawkarrow 0 0 0 2u tokens are removed from the input stream Immediately before invocation of the _drawkarrowcontinuation the input stream looks as follows dashed withdots scaled 25 And this rest up to the nearest semicolon is consumed by the drawkarrowcontinuation macro and this text will be within this macro available under name t misc mp 2b lt 7d 10b gt def _drawkarrowcontinuation text t draw _mainpath t draw _positivearrowpath t draw _negativearrowpath t enddef April 15 2011 misc nw 9 beginnegative middlenegative endpoint beginpoint middlepositive beginpositive The code below co
8. th pathlength 2 middlepoint point middlepathlength of p _firsthalfpath subpath 0 middlepathlength of p _secondhalfpath subpath middlepathlength pathlength of p _middlenondrawncircle fullcircle scaled inflen shifted middlepoint z0 _firsthalfpath intersectionpoint _middlenondrawncircle April 15 2011 misc nw 12 zi _secondhalfpath intersectionpoint _middlenondrawncircle _middlepath z0 z1 middlepathlength length _middlepath z2 perpleft _middlepath middlepathlength 4 infwidth 2 z3 perpright _middlepath middlepathlength 3 4 infwidth 2 _middlepath z0 z2 middlepoint z3 z1 _drawinfinitecontinuation enddef def _drawinfinitecontinuation text t draw _firsthalfpath cutafter _middlenondrawncircle t draw _middlepath t draw _secondhalfpath cutbefore _middlenondrawncircle t enddef 13 April 15 2011 misc nw 13 9 drawhatched closedpath text t This macro enables you to hatch interior of a given closed path Example drawhatched 0 0 0 30 dir 45 30 60 dir 45 60 30 60 0 cycle produces the following image The text after the path expression influences the drawing of particular hatches Le drawhatched 0 0 0 30 dir 45 30 60 dir 45 60 30 60 0 cycle withcolor red withpen pencircle scaled 2pt Auxiliary variables used for passing values between the main macro and its continuation The underscore was prepended before their identif
9. ublic License for more details You should have received a copy of the GNU General Public License along with this program if not write to the Free Software Foundation Inc 51 Franklin Street Fifth Floor Boston MA 02110 1301 USA 1 Various constants misc mp 1 41 10ap color yellow cyan yellow red green cyan green blue 2 tanforward expr p t d The purpose of this macro is illustrated on figure below z tanforward p t 1cm N zo point t of p If we have a path p and we choose some time t then z are coordinates of a point along the curve p in time t The tanforward macro computes coordinates of the point z1 Point z1 is on a tangent constructed in point zo It is in 1cm distance from point Zo misc mp 2b 3ap def tanforward expr p t d d 0 rotated angle direction t of p shifted point t of p enddef April 15 2011 misc nw 3 3 tanbackward expr p t d The tanforward macro returns coordinates along the tangent in positive direction this tanbackward macro returns coordinates of a point in the opposite direction See the figure below zo point t of p w z tanbackward p t 1cm 3a misc mp 2b lt 2b 3bp def tanbackward expr p t d d 0 rotated 180 angle direction t of p shifted point t of p enddef 4 perpright expr p t d The purpose of this macro is illustrated on figure below z perpright p t 1cm e 4 2 lt o
10. which consumes the path expression followed by its continuation which swal lows the rest of the text up to the first semicolon misc mp 2b 48 11 gt def drawtwowaykarrow expr p __mainpath p drawtwowaykarrowcontinuation enddef def drawtwowaykarrowcontinuation text t drawkarrow __mainpath t drawkarrow reverse __mainpath t enddef April 15 2011 misc nw 11 8 drawinfinite expr path text t This macro can be used for drawing paths whose middle mid time contains a mark which tells the reader that it is infinite or it was not drawn in its entirety This macro can be used in a similar way as normal draw macro which is part of the plain format With expression such as drawinfinite 0 0 3cm 0 you can produce the following A Let us enlarge the mark in the middle of this kind of path and denote distinct points Z2 middlepoint 23 misc mp 2b lt 10b 13 gt inflen 2cm The length along the line curve of the sign infwidth 4cm The width perpendicularly to the line curve Auxiliary variables used for passing values between the main macro and its continuation path _mainpath _firstpath _secondpath def drawinfinite expr p save middlepoint middletime tangent pathlength _middlepath middlepathlength pair middlepoint path tangent _middlenondrawncircle _firsthalfpath _secondhalfpath _middlepath save z pair z pathlength length p middlepathleng
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