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1. By default the ticks are placed at 5cm distance but you can change this by setting tickstep toa different value tickstep 1cm ticklength 2mm drawticks fullsquare xscaled 4cm yscaled 3cm tickstep tickstep 2 ticklength ticklength 2 drawticks fullsquare xscaled 4cm yscaled 3cm The ticklength variable specifies the length of a tick Here we manipulated both the variables to get a more advanced system If visualizing a path would mean that we would have to key in al those draw commands you could hardly call it a comfortable tool Therefore we can say drawwholepath fullsquare scaled 3cm rotated 30 randomized 5mm The drawwholepath command shows everything except the axis A If even this is too much labour you may say 2 G visualizepaths This redefines the draw and fill command in such a way that they also show all the information visualizepaths draw fullsquare scaled 3cm rotated 30 randomized 2mm You may compare this feature to the showmakeup command available in CONTEXT that redefines the Tpx primitives that deal with boxes glues penalties and alike Preliminary Version November 11 2001 Of course you may want to take a look at the MeTAPosT manual for its built in more verbose tracing options One command that may prove to be useful is show that you can apply to any variable This command reports the current value if known to the
2. This goes to the background def inelayer MyLayer option test setupbackgrounds text leftmargin background MyLayer setlayer MyLayer x 5cm y 5cm rotate framed This goes to the background In this case the framed text will be placed in the background of the current page with the given offset to the topleft corner Instead of a fixed position you can inherit the current position using the position directive Say that we have a layer called YourLayer which we put in the background of the text area def inelayer YourLayer setupbackgrounds text text background YourLayer We can now move some framed text to this layer using set layer with the directive position set to yes here setlayer YourLayer position yes inframed Here here Here You can influence the placement by explicitly providing an offset hoffset and or voffset a position x and or y ora location directive location Normally you will use the offsets for the layer was a whole and the positions for individual contributions The next example demonstrates the use of a location directive here setlayer YourLayer position yes location c inframed Here nestlerel Many layers can be in use at the same time In the next example we put something in the page layer By default we turn on position tracking which visualizes the bounding box of the content and shows the reference p
3. We use ruledhbox to show the tight bounding box of the graphic The line correction takes care of proper spacing around non textual content like graphics This is only needed when the graphic is part of the text flow Ae Next we draw two circles of equal radius one centered at point A the other at point B startbuffer d def draw_circles path circleA circleB numeric radius distance distance xpart pointB xpart pointA radius 2 3 distance circleA fullcircle scaled 2 radius circleB circleA shifted pointB draw circleA draw circleB enddef stopbuffer As you can see we move down the stand_out macro so that only the additions are colored red startbuffer 2 start_everything draw_basics stand_out draw_circles stop_everything stopbuffer We now use processMPbuffer a b c d 2 to include the latest step The next step in the construction of the perpendicular bisector requires that we find and label the points of intersection of the two circles centered at points A and B The intersection points are calculated as follows Watch the reverse operation which makes sure that we get the second intersection point startbuf fer e def draw_intersection pair pointC pointD pointC circleA intersectionpoint circleB These spacing commands try to get the spacing around the content visually compatible and take the heigh
4. oT n 7 N redpart 0 625 d greenpart 0 S bluepart 0 ii a r We can also ask for the path itself pathpart the pen penpart and the dashpattern dashpart but these can only be assigned to variables of the corresponding type A path can be stroked or filled in which case it is a cyclic path It can have a non natural bounding box be a clip path consist of line segments or contain text All these characteristics can be tested label rt filled amp condition filled p 4cm 1 25cm label rt stroked amp condition stroked p 4cm 0 75cm label rt textual amp condition textual p 4cm 0 25cm label rt clipped amp condition clipped p 4cm 0 25cm label rt bounded amp condition bounded p 4cm 0 75cm label rt cycle amp condition cycle pathpart p 4cm 1 25cm filled false Pa Bie XN stroked true textual false a clipped false Na bounded false cycle true In this code snippet condition is a macro that takes care of translating a boolean value into a string like decimal does with a numeric value def condition primary b if b true else false fi enddef Clip paths and bounding boxes are kind of special in the sense that they can obscure components The following examples demonstrate this In case of a clip path or bounding box the pathpart operator returns this path In any case that asking for a value does not make sense
5. startuseMPgraphic text split t ulcorner q urcorner q intersectionpoint q b llcorner q lrcorner q intersectionpoint q l q cutbefore t 1 1 cutafter b r q cutbefore b r r cutafter t stopuseMPgraphic In order to test what we have reached so far we draw the original path the left and right part of the reduced path and both the top and bottom point startuseMPgraphic text draw drawarrow p withpen pencircle draw t withpen pencircle draw b withpen pencircle drawarrow 1 withpen pencircle drawarrow r withpen pencircle stopuseMPgraphic scaled 1pt scaled 2pt scaled 2pt scaled 1pt scaled 1pt withcolor red withcolor green withcolor blue Again we use includeMPgraphic to combine the components into a graphic startuseMPgraphic text includeMPgraphic text path includeMPgraphic text vars includeMPgraphic text move includeMPgraphic text split includeMPgraphic text draw stopuseMPgraphic Then we use useMPgraphic text to call up the picture The offset is not optimal Note the funny gap at the top We could try to fix this but there is a better way to optimize both paths We lower the top edge of q s bounding box by topskip then cut any part of the left and right pieces of q that lie above it Similarly we raise the bottom edge and cut off the pieces that fall below this line startuseMPgraphic text cutoff path tt bb t
6. butt Q ar 3 Q ia jon Vv E z z Gi eon 7 N origin 1 1 metapost macro linecap butt metapost variable linecap rounded metapost variable linecap squared metapost variable linejoin mitered metapost variable Preliminary Version November 11 2001 DS jm g It 2 my om Se a is e a 5 o a ee amp lt D o oO a O go label bot o gt fA Z 6 a D A Preliminary Version November 11 2001 linejoin rounded metapost variable linejoin beveled metapost variable label MetaFun origin metapost macro label top MetaFun origin metapost macro label bot MetaFun origin metapost macro label 1ft MetaFun origin metapost macro label rt MetaFun origin metapost macro label Ilft label 11ft MetaFun origin 8 metapost macro label lrt label lrt MetaFun origin 8 metapost macro label urt label urt MetaFun origin 8 metapost macro label ulft label ulft MetaFun origin 8 metapost macro btex text etex draw btex MetaTeX etex Meta leX metapost primitive Preliminary Version November 11 2001 E 1 E 2 E3 E 4 ES Literature There is undoubtly more literature about meTaPosT and the tools discribed in this document than is mentioned below More information on TgX METAFONT and meTtaPosT can be found at the internet
7. Preliminary Version November 11 2001 111 found_point line l true rrr found_point line r false n n t 1 indent n abs xpart 111 xpart llcorner q width n abs xpart rrr xpart 111 endfor stopuseMPgraphic startuseMPgraphic text save write parshape amp decimal n to data_file for i 1 upto n write decimal indent i amp bp amp decimal width i amp bp to data_file endfor stopuseMPgraphic We can call this macro using the part we used in the previous examples startuseMPgraphic text includeMPgraphic text macro path p p 0 1 1 0 1 0 cycle scaled 65pt provide_parshape p shape path 5 baselinedistance offset baselinedistance distance between lines strutheight height of a line strutdepth depth of a line strutheight height of first line stopuseMPgraphic After we called useMPgraphic text the resulting file looks as follows You can call up this file by its anonymous name MPdatafile since this macro gets the value of the graphic at hand parshape 8 20 52388bp 47 26309bp 16 02335bp 55 46606bp 5 80219bp 78 90923bp 1 01128bp 96 9222bp 2 63658bp 108 52017bp 8 43097bp 101 52347bp 19 3177bp 79 74997bp 19 3177bp 79 74997bp So reading in this file at the start of a paragraph will setup Tpx to follow this shape The final implementation is a bit more complicated since it takes care of pa
8. Preliminary Version November 11 2001 Content Conventions 1 Welcome to METAPOST TI Paths sarsar fan creeks enh ies ss 1 2 Transformations 13 Constructing paths 1 4 Drawing pictures 1 5 Variables 1 6 Conditions 0 0055 17 LOOPS oeregeseryacarengeispis 1 8 Macros ciorerrisneriipsiiinsi 1 9 PHS s2c esaecexede os bbaenwtnes 1 10 COlGOS sencirs cise scedelion Gacawne eaves 1 11 Dashes 0005 L12 Text wedded abit ay veds bees 1 13 Linear equations 114 Clipping 008 1 15 Cutting and pasting 2 Afew more details 2 1 Making graphics 2 2 Bounding boxes 2 3 Units on oe a bebe Gees Aes 24 Scaling and shifting 2 5 Curve construction 2 6 Inflection tension and curl 2 7 Transformations 2 8 Only this far 2 9 Directions 2 10 Analyzing pictures 2 11 Additional operators 3 Embedded graphics 3 1 Getting started 3 2 External graphics 3 3 Integrated graphics 3 4 Graphic buffers 3 5 Communicating color 3 6 Common definitions 3 7 One page graphics 3 8 Managing resources Preliminary Version November 11 2001 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 6 1 6 2
9. left 0 0 left 1 1 metapost macro 0 0 right 1 1 metapost macro up 0 0 f up 1 1 metapost macro 0 0 down 1 1 metapost macro Preliminary Version November 11 2001 path amp path U unitvector N fullcircle x NA unitcircle O fullsquare B unitsquare L Preliminary Version November 11 2001 0 0 75 25 amp 75 25 1 1 metapost primitive origin unitvector 1 1 metapost variable fullcircle metapost variable unitcircle metafun variable fullsquare metafun variable unitsquare metapost variable M fulldiamond lt gt unitdiamond Q halfcircle CN quartercircle A circle Tj Ircircle D urcircle D fulldiamond metafun variable unitdiamond metafun variable halfcircle metapost variable quartercircle metapost variable licircle metafun variable ircircle metafun variable urcircle metafun variable Preliminary Version November 11 2001 ulcircle D tcircle D bcircle d Icircle GA rcircle ae lltriangle A lrtriangle N Preliminary Version November 11 2001 ulcircle metafun variable tcircle metafun variable bcircle metafun variable lcircle metafun variable rcircle metafun variable lltriangle metafun variable lrtriangle m
10. starttext setupcolors state start startMPpage colorcircle 10cm red green blue stopMPpage stoptext Given that you have PDFTgX TEXEXEC and CONTEXT installed you can now say texexec pdf test When processing is finished there should be a file test pdf that contains a graphic that shows the color circles defined in a previous chapter Preliminary Version November 11 2001 B B 1 METAPOST syntax In the metaFont book as well as the MeTAPOST manual you can find the exact specification of the language Below you find the full metarost syntax to which we add the basic MetaFun extensions If this page looks too cryptic you can safely skip to the next chapter Syntax diagrams The following syntax diagrams are derived from the diagrams in the MetaPost manual The gt represents means and the symbol stands for or The diagrams describe the hard coded metarost syntax as well as most of the macros and variables defined in the plain metarost format that belong to the core of the system They also include some of the more fundamental MetaFun commands atom variable argument number or fraction internal variable expression begingroup statement list expression endgroup nullary op btex typesetting command etex pseudo function primary atom numeric expression numeric expression numeric expression numeric expression num
11. path intersectionpoint path fullcircle intersectionpoint fulldiamond N metapost macro ZN N DA Attributes withcolor color withcolor 5 0 0 Q metapost primitive Preliminary Version November 11 2001 withcolor cmyk dashed withdots dashed evenly withpen penrazor transform Preliminary Version November 11 2001 withcolor cmyk 0 5 5 0 metafun macro dashed withdots metapost primitive dashed evenly metapost primitive withpen pencircle scaled 2mm metapost macro withpen pensquare scaled 2mm metapost macro withpen penrazor scaled 2mm metapost macro withpen penspeck transform rN Md filldraw 7 x3 d drawfill drawdot withpen penspeck metapost macro draw fullcircle metapost macro fill fullcircle metapost macro filldraw fullcircle metapost macro drawfill fullcircle metapost macro drawdot origin metapost macro Preliminary Version November 11 2001 drawarrow 7 IN NZ unfilldraw undrawfill ww undrawdot Preliminary Version November 11 2001 drawarrow fullcircle metapost macro undraw fullcircle metapost macro unfill fullcircle metapost macro unfilldraw fullcircle metapost macro undrawfill fullcircle metapost macro undrawdot origin metapost macro 288 Q f or S
12. veryraggedcenter setupalign broad left veryraggedleft The broad increases the raggedness We defined three different graphics a b and c because we want some to be unique which saves some processing Of course we don t reuse the random graphics In the definition of processword we have to use noindent because otherwise TEx will put each graphic on a line of its own Watch the space at the end of the macro Graphics and macros Because X s typographic engine and metarost s graphic engine are separated interfacing be tween them is not as natural as you may expect In CONTEXT we have tried to integrate both as good as possible but using the interface is not always as convenient as it should be What method you follow depends on the problem at hand The official MeTAPOST way to embed Tpx code into graphics is to use btex etex As soon as CONTEXT writes the graphic data to the intermediate metarost file it looks for these commands When it has encountered an etex CONTEXT will make sure that the text that is to be typeset by TEx is not expanded This is what you may expect because when you would embed those commands in a stand along graphic they would also not be expanded if only because meTaPosT does not know Tpx With expansion we mean that TeX commands are replaced by their meaning which can be quite extensive When metarost sees an btex command it will consult a so called mpx file This file holds the METAPOST
13. MetaFun We show the transformations in relation to the origin and make the origin stand out a bit more by painting it a bit larger in white first draw origin withpen pencircle scaled 1 5mm withcolor white draw origin withpen pencircle scaled 1mm withcolor 625red The origin is in the lower left corner of the picture IMetaFun Because the transformation keywords are proper english we let the pictures speak for themselves currentpicture currentpicture shifted 0 1cm MetaFun currentpicture currentpicture rotated 180 4 Wi currentpicture currentpicture rotatedaround origin 30 e currentpicture currentpicture scaled 1 75 MetaFun currentpicture currentpicture scaled 1 4 Wi currentpicture currentpicture xscaled 3 50 MNI amp to F124 3 currentpicture currentpicture xscaled 1 nuesto Mi more details Preliminary Version November 11 2001 currentpicture INNTetaFunl currentpicture currentpicture MetarFun currentpicture Maekakun currentpicture gash currentpicture reflectedabout llcorner currentpicture urcorner currentpicture 45 gsti Only this far When you take a close look at the definitions of the Computer Modern Roman fonts defined in the metaront book you will notice a high level of abstraction Instead of hard coded points you will find points defined
14. do_it 2 btex margin etex do_it 3 btex text etex do_it 4 btex margin etex do_it 5 btex edge etex Since we want the graphic to match the dimensions of the text area of the current page we have to make sure that the bounding box is adapted accordingly By this action the labels will fall outside the bounding box When we directly embed a graphic this works ok but when we start scaling and reusing due to the object reuse mechanism the graphic will be clipped to the bounding box setbounds currentpicture to unitsquare xyscaled width height In the following sections we will demonstrate how you can put graphics behind these 25 areas as well as behind the left and right page Setting up backgrounds One way of protecting a document for unwanted usage is to put an annoying word in the back ground If you like this you may try the following The macro ysized is part of the macros that come with CONTgXT and scales a picture to a specific size Preliminary Version November 11 2001 Page startuniqueMPgraphic concept draw btex bf CONCEPT etex rotated 60 withcolor 8white currentpicture currentpicture ysized overlayheight 5cm stopuniqueMPgraphic def ineoverlay concept uniqueMPgraphic concept You can now put this graphic in the page background by saying setupbackgrounds page background concept You may consider the next alternative a bit
15. pic n btex RotFont 1 etex stopMPdrawing The main macro is a bit more complicated but by using a few scratch numerics we can keep it readable def rotatetokens 1 2 3 47 delta extra radius tokens vbox bgroup MPtoks emptytoks resetMPdrawing startMPdrawing picture pic numeric wid len rot numeric delta extra radius n r len 0 n 0 delta 1 extra 2 radius 3 stopMPdrawing handletokens 4 with processrotationtoken startMPdrawing r len n Pi for i 1 upton wid abs xpart Ircorner pic i xpart llcorner pic i rot extra delta len i 5wid len m 180 2delta draw pic i rotatedaround origin 270 shifted r radius ypart 5 ulcorner picli llcorner pic i rotatedaround origin rot endfor stopMPdrawing MPdrawingdonetrue getMPdrawing resetMPdrawing egroup We can use this macro as follows startcombination 3 1 rotatetokens 0 0 0 Does it work ok A rotatetokens 20 0 0 Does it work ok B Preliminary Version November 11 2001 Typesetting in rotatetokens 20 30 0 Does it work ok C stopcombination work P at Wor f Pia Worg Prd 7 4 o o x A AA 5 9 A B C The previous macro is not really an example of generalization but we used it for demonstrating how to build graphics in a stepwise way If you put the steps in bu
16. Often we want to take a slice starting at a specific point This is provided by cutafter and its companion cutbefore Watch out this time we use a non cyclic path zO z21 22 23 zO z1 z2 z3 cutafter z2 Preliminary Version November 11 2001 zO z1 z2 23 cutbefore z1 Here is a somewhat silly way of accomplishing the same thing but it is a nice introduction to METAPOST S point operation In order to use this command effectively you need to know how many points make up the path z0 z1 z2 z3 cutbefore point 2 of z0 z1 z2 z3 As with subpath you can use fractions to specify the time on the path although the resulting point is not necessarily positioned linearly along the curve z0 z1 z2 z3 cutbefore point 2 5 of z0 z1 z2 z3 If you really want to know the details of where fraction points are positioned you should read the mMetaFONT book and study the source of METAFONT and mMETAPOST Where you will find the complicated formulas that are used to calculate smooth curves Preliminary Version November 11 2001 zO z1 cycle Like any closed path this path has points where the tangent is horizontal or vertical Early in this chapter we mentioned that a pair or point can specify a direction or vector Although any angle is possible we often use one of four predefined directions right 1 0 up 0 1 left 1 0 down 0 1 We can us
17. Thist list is still incomplete and needs to be checked against the formal syntax diagrams There are also a couple of MetaFun macros added that need to find their way to here D1 Paths pair 1 05 metapost concept pair pair 0 0 75 0 1 25 1 1 metapost macro 0 0 75 0 1 25 1 1 metapost macro pair pair 0 0 75 0 1 25 1 1 metapost macro Preliminary Version November 11 2001 pair pair N pair softjoin pair 2 controls pair J controls pair and pair L tension numeric s N 0 0 75 0 1 25 131 metapost macro 0 0 75 0 softjoin 1 25 1 1 metapost macro 0 0 controls 75 0 1 1 metapost primitive 0 0 controls 75 0 and 1 25 1 1 metapost primitive 0 0 75 0 tension 2 5 1 25 1 1 metapost primitive Preliminary Version November 11 2001 tension numeric and numeric 0 0 75 0 tension 2 5 and 1 5 1 25 1 1 metapost primitive N N tension atleast numeric 0 0 75 0 tension atleast 1 1 25 1 1 metapost primitive cycle 0 0 1 0 1 1 cycle metapost primitive curl numeric 0 0 curl 1 75 0 1 25 4 1 metapost primitive dir numeric 0 0 dir 30 1 1 metapost primitive Preliminary Version November 11 2001
18. definesymbol step 3 processMPbuffer a b c d e f g 3 definesymbol step 4 processMPbuffer a b c d e f g 4 definesymbol step 5 processMPbuffer a b c d e f g 5 A field stack is a sequence of overlayed graphics We will arrange to manually cycle with clicks of the mouse through the sequence of graphs depicting the construction of the midpoint of segment A B So in fact we are dealing with a manual simulation The definition of such a stack is as follows definefieldstack midpoint construction step 1 step 2 step 3 step 4 step 5 frame on offset 3pt framecolor darkyellow rulethickness 1pt The first argument is to be a unique identifier the second argument takes a list of symbols while the third argument accepts settings More on this command can be found in the CONTEXT manuals The stack is shown as figure 13 6 Its caption provides a button which enables the reader to cycle though the stack We call this a stack because the graphics are positioned on top of each other Only one of them is visible at any time placefigure here fig steps Bisecting a line segment with compass and straightedge Just click goto here JS Walk_Field midpoint construction to walk through the construction This stack is only visible in a PDF viewer that supports widgets fieldstack midpoint construction At the start of this section we mentioned three methods When we use the first method of putting
19. externalfigure somecow pdf width 4cm setlayer BackLayer x 8cm y 18cm location c externalfigure somecow pdf width 5cm These examples again demonstrate how we can influence the placement by assigning an anchor point to position Preliminary Version November 11 2001 5 4 hoffset an additional horizontal displacement voffset an additional vertical displacement You can position data anywhere in the layer When positioning is turned on the current position will get a placeholder You can change the dimensions of that placeholder when position is set to overlay zero dimensions are used x the horizontal displacement y the vertical displacement width the non natural width height the non natural height location lrtbc1t 1b rt rb The location directive determines what point of the data is used as reference point You can keep track of this point and the placement when you enable test mode This is how the rectangles in the previous examples where drawn option test show positioning information When you are enhancing the final version of a document you can explicitly specify on what page the data will go Use this option with care page the page where the data will go Because layers can migrate to other pages they may disappear due to the background not being recalculated In case of doubt you can force repetitive background calculation by
20. hexpression list incr numeric variable decr numeric variable dashpattern on off list interpath numeric expression path expression path expression buildcycle path expression list thelabel label suffix expression pair expression thefreelabel expression pair expression pair expression anglebetween pathexpression pathexpression expression pointarrow pathexpression numeric or pair primary numeric expression numeric expression leftarrow pathexpression numeric or pair primary numeric expression centerarrow pathexpression numeric or pair primary numeric expression rightarrow pathexpression numeric or pair primary numeric expression paired numeric or pair Preliminary Version November 11 2001 path expression list path expression path expression list path expression on off list on off list on off clause on off clause on off clause on numeric tertiary off numeric tertiary boolean expression expression color expression expression numeric atom atom numeric expression expression numeric primary primary numeric tertiary tertiary numeric variable variable internal variable pair expression expression pair primary
21. stopuseMPgraphic We can manipulate the heigth and depth of the line to give different and maybe better results startuseMPgraphic text vars baselineskip 8pt Preliminary Version November 11 2001 strutheight 4pt strutdepth 2pt offset 4pt topskip Spt stopuseMPgraphic This kind of graphic trickery in itself is not enough to get TEx into typesetting within the bounds of a closed curve Since METAPOST can write information to a file and TEx can read such a file a natural way to handle this is to let meTaPosT write a parshape specification startuseMPgraphic text macro def provide_parshape expr p offset baselineskip strutheight strutdepth topskip includeMPgraphic text move includeMPgraphic text split includeMPgraphic text cutoff includeMPgraphic text draw includeMPgraphic text calc includeMPgraphic text loop includeMPgraphic text save enddef stopuseMPgraphic We have to adapt the for loop to register the information about the lines After the loop we write those values to a file using another loop startuseMPgraphic text loop path line pair 111 rrr numeric vvsize n n 0 if strutheight strutdepth lt baselineskip vvsize vsize else vvsize vsize div baselineskip baselineskip fi for i topskip step baselineskip until vvsize line ulcorner q urcorner q shifted 0 i
22. For them I owe much inspiration to both my parents My mother Jannie constantly demonstrates me that computer graphics will never improve nature She also converted one of my first METAPOST graphics into a patchwork that will remind me forever that handcraft is more vivid than computer artwork My father Hein has spent a great deal of his life teaching math and I m sure he would have loved metarost I inherited his love for books I therefore dedicate this document to them Colofon This manual is typeset with CONTEXT and metarost No special tricks are used and everything you see in here is available for CONTEXT users The text is typeset in Palatino and Courier We used PDFT X as TeX processing engine Since this document is meant to be printed in color some examples will look sub optimal when printed in black and white Copyright Hans Hagen PRAGMA Advanced Document Engineering Hasselt NL copyright November 11 2001 Info internet www pragma ade com support ntg context ntg nl email pragma wxs nl Introduction This document is about meTAPosT and TEX The former is a graphic programming language the latter a typographic programming language However in this document we will not focus on real programming but more on how we can interface between those two languages We will do so by using CONTEXT a macro package written in TeX where support for MeTAPoOST is integrated in the core The TX macros are integrated in CONTEXT
23. Since the page background is applied last the previous layers can considered to be the fore ground to the page background layer And indeed it is available as an overlay under the name foreground as we already saw in the example Foregrounds are available in most cases but for the moment not when we are dealing with the text area Since anchoring the graphics is imple mented rather independent of the position of the graphics themselves this is no real problem we can put them all on the page layer if needed in separate overlays How is such a graphic defined In fact these graphics are a special case of the already present mechanism of including metarost graphics The circles are defined as follows startMPpositiongraphic mypos circle initialize_box MPpos MPvar self path p p llxy lrxy urxy ulxy cycle pickup pencircle scaled ipt fill p withcolor 800white draw p withcolor 625yellow anchor_box MPanchor MPvar self stopMPpositiongraphic Drawing the lines is handled in a similar fashion startMPpositiongraphic mypos line path pa pb pab numeric na nb initialize_box MPpos MPvar from na nxy pa llxy lrxy urxy ulxy cycle initialize_box MPpos MPvar to nb nxy pb llxy lrxy urxy ulxy cycle if na nb pab center pa center pb pab pab cutbefore pab intersectionpoint pa pab pab cutafter pab intersectionpoint pb pickup pencircle scaled
24. The MetaFun register macro takes the following arguments register tag width height x offset y offset The width and height are available in the macros MPlayerwidth and MPlayerheight and are equivalent to MPw tag and MPh tag setMPlayer test somepos 1 location c Does it work al right setMPlayer test somepos 2 framed width MPlayerwidth height MPlayerheight background color backgroundcolor white It Works setMPlayer test somepos 3 externalfigure cow mps width 2cm Combining the graphic and the text is handled by the macro getMPlayer getMPlayer test useMPgraphic oeps Does it work al right It Works Preliminary Version November 11 2001 Positional graphics J9 The macro getMPlayer is built on top of framed The settings passed as optional second argument are the same as those to framed getMPlayer test frame on offset 5pt useMPgraphic oeps As you see you need a bit twisted mind to handle graphics this way but at least the functionality is there to create complex graphics in a declarative way Some examples In due time there will a few more examples here For that the interface has to be more frozen than it currently is positional graphics Preliminary Version November 11 2001 6 1 Page backgrounds Especially in
25. addto currentpicture doublepath pat The fill command on the other hand is defined as addto currentpicture contour pat Preliminary Version November 11 2001 Re Both macros are actually a bit more complicated but this is mainly due to the fact that they also have to deal with attributes like the pen and color they draw with You can use doublepath and contour directly but we will use draw and 111 whenever possible Given a picture pic the following code is valid addto currentpicture also pic You can add pictures to existing picture variables where currentpicture is the picture that is flushed to the output file Watch the subtle difference between adding a doublepath contour or picture Variables At this point you may have noted that mMetaPost is a programming language Contrary to some of today s languages Metarost is a simple and clean language Actually it is a macro language Although metarost and 7x are a couple the languages differ in many aspects If you are using both you will sometimes wish that features present in one would be available in the other When using both languages in the end you will understand why the conceptual differences make sense Being written in PASCAL it will be no surprise that MeTAPosT has some PASCAL like features although some may also recognize features from ALGOL68 in it First there is the concept of variables and assignments There are several data types so
26. al len n n 1 for i 1 upton abs xpart lIrcorner pic i xpart llcorner picli len i wid 2 i 1 pl wid pos POST Preliminary Version November 11 2001 at arctime pos of RotPath ap point at of RotPath ad direction at of RotPath draw pic i shifted wid 2 0 rotated angle ad shifted ap endfor stopMPdrawing MPdrawingdonetrue getMPdrawing resetMPdrawing egroup So how does this compare to earlier results The original full text as typeset by Tpx looks like We now follow some arbitrary path In the examples the text is typeset along the path with followtokens We now follow some arbitrary path We now follow some arbitrary path Since we did not set a path a dummy path is used We can provide a path by re defining the graphic followtokens startuseMPgraphic followtokens grap path RotPath RotPath fullcircle stopuseMPgraphic oF gO ay amp 9 s 3 2 J y Ay Citar s taS startuseMPgraphic followtokens path RotPath RotPath reverse fullcircle stopuseMPgraphic startuseMPgraphic followtokens path RotPath RotPath 3cm 1cm 0 1cm 3cm 1cm stopuseMPgraphic Preliminary Version November 11 2001 9 5 startuseMPgraphic followtokens path RotPath RotPath 3cm 0 3cm
27. fill z1 z2 z3 amp z3 z4 z1 amp cycle withcolor MPvar color stopuniqueMPgraphic As you can see we pass two arguments to the graphic definition The first argument is the name the second argument is a comma separated list of variables This list serves two purposes First this list is used to create a unique profile for the graphic This means that when we change the value of a variable a new graphic is generated that reflects the change A second purpose of the list is to convert TeX data structures into METAPOST ones especially dimensions and colors The graphic itself is not that spectacular We use amp because we don t want smooth connections def ineblank EnglishRule medium def EnglishRule startlinecorrection EnglishRule setlocalhsize noindent reuseMPgraphic EnglishRule stoplinecorrection When setting the variables we used localhsize This variable is set by setlocalhsize We need to use noindent a rather familiar Tsx primitive that we use here to start a non indented paragraph being the graphic The line correction is needed to get the spacing around the rule graphic right We pass a blank skip identifier that is mapped to a convenient medium skip Preliminary Version November 11 2001 Shapes symbals andi buttons 1 2 Why is this called an English line startnarrower EnglishRule Is it because they cannot draw
28. metafun macro fullcircle lrmoved 1 25 metafun macro fullcircle urmoved 1 25 metafun macro fullcircle ulmoved 1 25 metafun macro fullcircle slanted 5 metapost primitive Preliminary Version November 11 2001 path rotated numeric fullsquare rotated 45 metapost primitive path rotatedaround pairnnumeric fullsquare rotatedaround 25 5 45 metapost macro 7 path reflectedabout pair pair fullcircle reflectedabout 25 1 25 1 metapost macro reverse fullcircle shifted 5 0 metapost primitive counterclockwise path counterclockwise fullcircle shifted 5 0 metapost macro C N Sa S Preliminary Version November 11 2001 280 tensepath path N NAZ subpath numeric numeric of path ie 5 or Fy F Z N No a Q O 5 oO H gs o a y N No c ot Q Q 5 gP H ge 5 N NF c o z 5 io H Ze gt g Z N No tensepath fullcircle metapost macro subpath 1 5 of fullcircle metapost primitive llcorner fullcircle metapost primitive lrcorner fullcircle metapost primitive urcorner fullcircle metapost primitive ulcorner fullcircle metapost primitive Preliminary Version November 11 2001 center path Z N Naf boundingbox path Z N NO innerboundingbox path N VA Fa N outerboundingbox path x Le path picture xsized numer
29. width 3 textwidth background demo circle startcombination 3 3 framed Loffset none TeX tt offset none framed Loffset overlay TeX tt offset overlay framed Loffset 0pt TeX tt offset Opt framed Loffset 1pt TeX tt offset 1pt framed Loffset 2pt TeX tt offset 2pt framed Loffset 4pt TeX tt offset 4pt framed Loffset 3pt TeX tt offset 3pt framed frameoffset 3pt TeX tt frameoffset 3pt framed backgroundoffset 3pt TeX tt backgroundoffset 3pt stopcombination RR p eR eR offset none offset overlay offset 0pt offset 1pt offset 2pt offset 4pt offset 3pt frameoffset 3pt backgroundoffset 3pt Figure 4 1 The three offsets As the first row in figure 4 1 demonstrates instead of a value one can pass a keyword The overlay keyword implies that there is no offset at all and that the lines cover the content With none the frame is drawn tight around the content When the offset is set to Opt or more the text is automatically set to at least the height of a line You can turn this feature of by saying strut off More details can be found in the CONTsXT manual In figure 4 2 we have set offset to 3pt frameoffset to 6pt and backgroundoffset to 9pt Both the frame and background offset are sort of imaginary since they don t contribute to the size of the box layout Pre
30. 2001 Embedded Braphics 3 8 Another advantage is that when using CONTEXT you don t have to bother about specials font inclusion and all those nasty things that can spoil a good day An example of such a graphic is the file mfun 888 that resides on the computer of the author output pdftex setupcolors state start setupMPpage offset 1pt background color backgroundcolor gray definecolor gray s 625 definecolor red r 625 definecolor yellow r 625 g 625 startuseMPgraphic test fill fullsquare rotated 45 scaled 4cm withcolor MPcolor yellow stopuseMPgraphic starttext startMPpage includeMPgraphic test fill fullcircle scaled 3cm withcolor MPcolor red stopMPpage stoptext Given that the CONTEXT english interface format is present on your system you can process this file with TEXEXEC for instance using PDFTexX The once directive saves some runtime texexec once pdf mfun 888 You can define many graphics in one file The TEXEXEC manual describes how to selectively process pages If you use PDFTsX you can include individual pages from PDF files placefigure A silly figure demonstrating that stand alone graphics can be made externalfigure mfun 888 page 1 In this case the page 1 specification is not really needed You can scale and manipulate the figure in any way supported by the macro package that you use Managing resource
31. 36pt superellipsed superness elseif alternative 2 36pt squeezed squeezeness elseif alternative 3 36pt randomized randomness else 36pt fi pickup pencircle scaled 3pt fill Page withcolor MPcolor yellow fill p withcolor MPcolor white draw p withcolor MPcolor red randomseed seed p Field Text Text enlarged if alternative 1 48pt superellipsed superness elseif alternative 2 48pt squeezed squeezeness elseif alternative 3 36pt randomized randomness else 48pt fi transformed t def right_menu_button expr nn rr pp xx yy ww hh dd if pp gt 0 and rr gt 0 q rightsuperbutton p xx yy RightEdgeWidth hh fill q withcolor MPcolor white draw q withcolor if rr 2 MPcolor gray else MPcolorfred fi fi 3 enddef MPmenubuttons right StopPage stopuseMPgraphic When we choose the alternatives 21 and 22 we get this result page 5 page 1 page 2 page 3 page 4 page 5 Defining styles Preliminary Version November 11 2001 12 Functions METAPOST provides a wide range of functions like sind and floor We will discuss most of them here and define a few more We will use some of the Calculator Demo graphics to make this chapter more readable Preliminary Version November 11 2001 Preliminary Version November 11 2001 13 13 1 A few applications For those who n
32. 50cm 1cm In a similar fashion we can define linear shaded This time we only pass two points and two colors def test_shade expr a b pickup pencircle scaled 1mm Preliminary Version November 11 2001 8 2 color ca ca MPcolorfa color cb cb MPcolor b color cc cc MPcolor c sh define_linear_shade a b ca cb fill fullsquare scaled 2cm withshade sh draw a withcolor cc draw b withcolor cc enddef Although one can control shading to a large extend in practice only a few cases really make sense test_shade origin origin shifted 1cm 0 test_shade origin shifted 1cm 0 origin shifted 1cm 0 test_shade origin shifted 1cm 1cm origin shifted 1cm icm Clipping In this chapter we will use the graphic representation although simplified of a Dutch cow to demonstrate clipping Figure 8 1 A cow Since this cow is defined as a mETAPOST graphic we use the suffix mps instead of eps or a number although CONTEXT will recognize each as being mMetarost output The placement of the cow is defined as placefigure A cow externalfigure cow mps width 4cm Clipping is combined with a matrix as in figure 8 2 The content to be clipped is divided in nx by ny rectangles For instance nx 5 and ny 8 will produce a 40 cell grid with 5 columns of 8 rows Preliminary Version November 11 2001 iR 11 3 1 F
33. 6 3 6 4 6 5 7 1 7 2 7 3 7 4 7 9 8 1 8 2 8 3 8 4 9 1 9 2 Enhancing the layout Overlays 00 200 Overlay variables Stacking overlays Foregrounds 4 Typesetting graphics Graphics and macros Positional graphics The concept 0 06 Anchors and layers More layers 44 Complex text in graphics Some examples Page backgrounds The basic layout Setting up backgrounds Multiple overlays Crossing borders Advanced features Shapes symbols and buttons Interfacing to TEX Random graphics Graphic variables Shape libraries Symbol collections Special effects 0 Shading 004 Clipping vie bsge0ds veede whe s Patterns sreriercreieissreeisa 101 a a Typesetting in METAPOST The process 00 Environments 05 103 103 105 105 106 107 109 117 117 118 121 126 128 129 129 133 136 137 144 145 145 146 149 149 151 153 153 157 161 161 163 163 163 93 Eabels Sxcend t ds hed Woivectededa oieeedeans 164 9 4 TEX TERE rererere pessa kuat 164 9 5 Talking to T X 174 10 Debug
34. Here the suppresses expansion of btex bfd 1 etex The process is iterated by handletokens for each character of the text MetaPost is Fun Before we typeset the text now available in pieces in pic in a circle we will first demonstrate what they look like You may like to take a look at the file mpgraph mp to see what is passed to METAPOST startMPdrawing pair len len origin for i 1 upton draw picli shifted len draw boundingbox picli shifted len withpen pencircle scaled 25pt withcolor red len len xpart lrcorner pic i xpart llcorner picli 0 endfor stopMPdrawing We can call up this drawing with getMPdrawing but first we inform the compiler that our METAPOST drawing is completed MPdrawingdonetrue getMPdrawing This results in MetaPost is Compare this text with the text as typeset by Tpx MetaPost is Fun Preliminary Version November 11 2001 Bypesetting in and you will see that the text produced by metarost is not properly kerned When putting characters after each other TeX uses the information available in the font to optimize the spacing between characters while Metarost looks at characters as separate entities But since we have stored the optimal spacing in len we can let metarost do a better job Let s first calculate the correction needed startMPdrawing for i 1 upt
35. Variables saved and declared in a group are local to that group Once the group is exited the variables cease to exist Grouping is not bound to macros and may be used anywhere in your code vardef randomscaledpath expr p s begingroup save r numeric r r round 1 uniformdeviate 4 p xscaled s r yscaled s r endgroup enddef In this particular case we could have omitted the grouping since vardef macros are always grouped automatically Therefore we could have defined the macro as Preliminary Version November 11 2001 Welcome tO METAB 1 9 vardef randomscaledpath expr p s save r numeric r r round 1 uniformdeviate 4 p xscaled s r yscaled s r enddef The command save r declares that the variable r is local to the macro Thus any changes to the new numeric variable r are local and will not interfere with a variable r defined outside the macro This is important to understand as variables outside the macro are global and accessible to the code within the body of the macro Macro definitions may be nested but since most meTaPosT code is relatively simple it is seldom needed Nesting is discouraged as it makes your code less readable Besides def and vardef metarost also provides the classifiers primarydef secondarydef and tertiarydef You can use these classifiers to define macros like those provided by MeTaPost itself p
36. and the MeTAPosT macros are bundled in MetaFun When Donald Knuth wrote his typographical programming language Tpx he was in need for fonts especially mathematical fonts So as a side track he started writing METAFONT a graphical language When you read between the lines in the METAFONT book and the source code the name John Hobby is mentioned alongside complicated formulas It will be no surprise then that since he was tightly involved in the development of MeTAFONT after a few years his mMetarost showed up While its ancestor METAFONT was originally targeted at designing fonts MeTAPOST is more oriented to drawing graphics as used in scientific publications Since METAFONT produced bitmap output some of its operators make use of this fact METAPOsT on the other hand produces POST SCRIPT code which means that it has some features not present in METAFONT and vise versa With MetaFun I will demonstrate that metaPosT can also be used or misused for less technical drawing purposes We will see that metarost can fill in some gaps in TX especially its lack of graphic capabilities We will demonstrate that graphics can make a document more attractive even if it is processed in a batch processing system like Tex Most of all we will see that embedding METAPOST definitions in the TeX source enables a smooth communication between both programs The best starting point for using metarostT is the manual written by its author John Hobby You can fi
37. my deepest interests in ar tificial intelligence and es thetic theory I felt com pelled to make some com ments to clarify certain impor tant issues raised by The Con test 4 Figure 9 2 A continuous text typeset in a non standard shape spread over four areas and right alligned rotatedaround origin 90 xscaled overlaywidth yscaled overlayheight drawoptions withcolor 625red stopuseMPgraphic followtokens This is just a dummy text kerned by T kern 1667em lower 5ex hbox E kern 125emX and typeset in a circle using setMFPfont M setMFPfont E setMFPfont T setMFPfont A setMFPfont P setMFPfont O setMFPfont S setMFPfont T quad stopbuffer Preliminary Version November 11 2001 test 3 test 4 Figure 9 3 A continuous text typeset in a non standard shape spread over four areas tracing on def ineoverlay edge getbuffer circle The text and graphics come together in a framed text startbuffer quote framed offset 6pt background edge frame off getshapetext stopbuffer placefigure One more time Hofstadter s quotation getbuffer quote Preliminary Version November 11 2001 x Donald Knuth has spent the past several years working on VX Q a system allowing him to control many gt si aspects of the design of his forthc
38. sind sqrt stroked textpart textual top ulcorner uniformdeviate unitvector unknown urcorner xpart xxpart xypart ypart yxpart yypart type boolean color numeric pair path pen picture string transform primary binop gt and dotprod div infont mod Preliminary Version November 11 2001 secondary binop gt or intersectionpoint intersectiontimes tertiary binop 2 amp lt lt Oo gt gt cutafter cutbefore of operator arctime direction directiontime directionpoint penoffset point postcontrol precontrol subpath substring variable tag suffix suffix empty suffix subscript suffix tag suffix parameter subscript number numeric expression internal variable ahangle ahlength bboxmargin charcode day defaultpen defaultscale labeloffset linecap linejoin miterlimit month pausing prologues showstopping time tracingoutput tracingcapsules tracingchoices tracingcommands tracingequations tracinglostchars tracingmacros tracingonline tracingrestores tracingspecs tracingstats tracingtitles truecorners warningcheck year symbolic token defined by newinternal pseudo function min expression list max
39. 1 c k lt 0 without losing information Nevertheless the previous blue bar is presented all right This is due to the fact that in MetaFun the CMYK colors are handled as they should even when metarost does not support this color model If you use this feature independent of CONTEXT you need to enable it by setting cmykcolors to true You have to convert the resulting graphic to PDF by using for instance the mptopdf suite see chapter A In CONTEXT you can influence this conversion by changing parameters related to color handling setupcolors cmyk yes mpcmyk no Unless you know what you are doing you don t have to change the default settings both yes In the CONTEXT reference manual you can also read how color reduction can be handled Special care should be paid to gray scales Combining equal quantities of the three color inks will not lead to a gray scale but to a muddy brown shade fill fullsquare xyscaled 10cm 2cm withcolor 5white fill fullsquare xyscaled 6cm 1 5cm withcolor cmyk 5 5 5 0 fill fullsquare xyscaled 2cm 1cm withcolor cmyk 0 0 0 5 In figure 3 4 to 3 6 you can see some more colors defined in the CMYK color space When you display the screen version of this document you will notice that the way colors are displayed can differ per viewer This is typical for CMYK colors and has to do with the fact that some assumptions are made with respect to the print medium c 1 y 3 k 3 c 9 y 15 c 2
40. 1cm zi 0 0 z2 2u 4u z3 4u 0 def sample expr p c draw p withpen pencircle scaled 2 5mm withcolor white draw p withpen pencircle scaled 2 0mm withcolor c enddef We can draw three curved paths sample zi curl 0 z2 curl 0 z3 625red sample z1 curl 2 z2 curl 2 z3 625yellow sample zi curl 1 z2 curl 1 z3 625white These third gray curve is the default situation so here we could have left the curl specifier out of the expression Preliminary Version November 11 2001 The curly specs have a lower bound of zero and no upper bound When we use MeTarosT maximum value of infinity instead of 2 we get These curves were defined as sample z1 curl O z2 curl O z3 625red sample z1 curl infinity z2 curl infinity z3 625yellow sample z1 curl 1 22 curl 1 z3 625white It may sound strange but internally Metapost can handle larger values than infinity sample z1 curl infinity z2 curl infinity z3 625red sample zi curl 4infinity z2 curl 4infinity z3 625yellow sample z1 curl 8infinity z2 curl 8infinity z3 625white Although this is quite certainly undefined behaviour interesting effects can be achieved When you turn off metarost s first stage overflow catcher you can go upto 8 times infinity which being some 32K is still far from what e
41. 8white draw p withcolor 625red stopuniqueMPgraphic Preliminary Version November 11 2001 Embedded graphics The last class of embedded graphics are the runtime graphics When a company logo is defined in a separate file mylogos mp you can run this file by saying startMPrun input mylogos stopMPrun The source for the logo is stored in a file named mylogos mp beginfig 21 draw fullsquare withcolor 625red draw fullsquare rotated 45 withcolor 625red picture cp cp currentpicture def copy addto currentpicture also cp enddef copy scaled 9 withcolor 625white copy scaled 7 withcolor 625yellow copy scaled 6 withcolor 625white copy scaled 4 withcolor 625red copy scaled 3 withcolor 625white fill fullcircle scaled 2 withcolor 625yellow currentpicture currentpicture scaled 50 endfig end In this example the result is available in the file mprun 21 This file can be included in the normal way using externalfile mprun 21 width 5cm Figure 3 1 The logo is defined in the file mylogos mp as figure 21 and processed by means of the mprun method p taphics Preliminary Version November 11 2001 3 4 Graphic buffers In addition to the macros defined in the previous section you can use CONT XT s buffers to handle graphics This can be handy when making documentation so it makes sense to spend a few words on
42. E a eer Thus I came to the conclusion that the designer ofa new system must not only be the implementer and first large scale user the designer should also write the first user and first large scale user the designer should also write the first user manual The separation of any of these four c Sep me tnd Ifthad Be peri cf any lee crores ed avert EX Hee I1 had not participated fully in all these activities literally hundreds of imps has not participated fully in all these activities literally hundreds of improvements would never have oer te ve Stn het ad no mave Baugh hon pe yw npr But a system cannot e ae eerste Once tha nia Sig scope ae ly robust he rel tet begin a3 people with many the initial design is complete and fairly robust the real test begins as people with many different viewpoints undertake their own experiments viewpoints undertake their own experiments Douglas R Hostadter Douglas R Hostadter Donald Knuth has spent the past several years working on a system allowing him to control Donald Knuth has spent the past several years working on forthcoming books from the P pect tied a eae coped eee shapes of the letters Seldom has an author had anything remotely like this power to control the ea ices METAEON families known or ji je a In his article The Concept of a Meta Font Knuth sets forth for the first time the underlying Ia hoart The Concept of a Meta Font Knuth sets forth for the first time the
43. NC useMPgraphic fuzzycount n 68 NC NR a unique random one each time startuseMPgraphic fuzzycount begingroup save height span drift d cp height 3 5 baselinedistance span 1 3 height drift 1 10 height pickup pencircle scaled 1 12 height draw if i mod 5 0 else def d uniformdeviate drift enddef for i 1 upto MPvar n d 4 5span d d 0 5span height d d d d height d fi shifted span i d drift endfor picture cp cp currentpicture for readability setbounds currentpicture to llcorner cp shifted 0 ypart llcorner cp lrcorner cp shifted 0 ypart lrcorner cp urcorner cp ulcorner cp cycle endgroup stopuseMPgraphic The core of the macro is the for loop Within this loop we draw groups of four plus one lines The draw path s look a bit complicated but this has to do with the fact that a mod returns 0 4 while we like to deal with 1 5 The height adapts itself to the height of the line The bounding box correction at the end ensures that the baseline is consistent and that the random vertical offsets fall below the baseline Because we want to be sure that n has a value we preset it by saying setupMPvariables fuzzycount n 10 Preliminary Version November 11 2001 In the table it makes sense to adapt the drawi
44. Version November 11 2001 Welcome tO METAP 1 14 Clipping For applications that do something with a drawing for instance Tpx embedding a graphic in a text flow it is important to know the dimensions of the graphic The maximum dimensions of a graphic are specified by its bounding box A bounding box is defined by its lower left and upper right corners If you open the POSTSCRIPT file produced by metarost you may find lines like ApBoundingBox 46 46 46 46 or when supported hpHiResBoundingBox 45 35432 45 35432 45 35432 45 35432 The first two numbers define the lower left corner and the last two numbers the upper right corner From these values you can calculate the width and height of the graphic A graphic may extend beyond its bounding box It depends on the application that uses the graphic if that part of the graphic is shown In metarost you can ask for the all four points of the bounding box of a path or picture as well as the center llcorner p lower left corner lrcorner p lower right corner urcorner p upper right corner ulcorner p upper left corner center p the center point You can construct the bounding box of path p out of the four points mentioned llcorner p lrcorner p urcorner p ulcorner p cycle You can set the bounding box of a picture which can be handy if you want to build a picture in steps and show the intermediate results
45. a def start_everything enddef def stop_everything enddef stopbuffer We are going to draw a few dots and to force consistency we first define a macro draw_dot The current step will be highlighted in red using stand_out startbuffer b numeric u w u 5cm w 1pt pickup pencircle scaled w def draw_dot expr p draw p withpen pencircle scaled 3w enddef def stand_out drawoptions withcolor 625red enddef stopbuffer First we construct the macro that will plot two points A and B and connect them with a line segment startbuffer c def draw_basics pair pointA pointB path lineAB pointA origin pointB pointA shifted 5u 0 lineAB pointA pointB draw lineAB draw_dot pointA label 1lft btex A etex pointA draw_dot pointB label rt btex B etex pointB enddef stopbuffer The code in this buffer executes the preceding macros The _ everything commands are still undefined but later we can use these hooks for special purposes startbuffer 1 start_everything stand_out draw_basics stop_everything stopbuffer This graphic can now be embedded by the CONTEXT command processMPbuffer This com mand like the ordinary buffer inclusion commands accepts a list of buffers startlinecorrection blank ruledhbox processMPbuffer a b c 1 stoplinecorrection applications Preliminary Version November 11 2001
46. a clipping path for instance has no color a zero null value is returned draw fullcircle withpen pencircle scaled 3mm clip currentpicture to fullcircle setbounds currentpicture to fullcircle n 1 length 1 stroked false clipped true bounded false draw fullcircle withpen pencircle scaled 3mm setbounds currentpicture to fullcircle clip currentpicture to fullcircle n 1 length 1 stroked false clipped false bounded true Aew more details Preliminary Version November 11 2001 clip currentpicture to fullcircle draw fullcircle withpen pencircle scaled 3mm setbounds currentpicture to fullcircle 5 1 length 0 stroked false clipped true bounded false 2 length 1 stroked true clipped false bounded false 5 clip currentpicture to fullcircle setbounds currentpicture to fullcircle draw fullcircle withpen pencircle scaled 3mm 1 length 1 stroked false clipped false bounded true 2 length 1 stroked true clipped false bounded false 5 5 setbounds currentpicture to fullcircle clip currentpicture to fullcircle draw fullcircle withpen pencircle scaled 3mm 5 1 length 1 stroked false clipped true bounded false 2 length 1 stroked true clipped false bounded false 5 setbounds currentpicture to fullcircle draw fullcircle withpen pencircle
47. a closed path can be filled The closed alternative looks as follows We will see many examples of filled closed path later on Welcomestow lt Tarot Preliminary Version November 11 2001 zZ0 z1 22 23 z0 cycle Here the final will try to make a smooth connection but because we already are at the starting point this is not possible However the cycle command can automatically connects to the first point Watch the difference between the previous and the next path zO z1 z22 z3 cycle It is also possible to combine two paths into one that don t have common head and tails First we define an open path zO z1 z2 z0 z3 z1 cycle Preliminary Version November 11 2001 Welcome fo verae With buildcycle we can combine two path into one buildcycle z0 z1 z2 z0 z3 z1 cycle We would refer readers to the METAFONT book and the Metarost manual for an explanation of the intricacies of the buildcycle command It is an extremely complicated command and there is just not enough room here to do it justice We suffice with saying that the paths should cross at least once before the buildcycle command can craft a combined path from two given paths We encourage readers to experiment with this command In order to demonstrate another technique of joining paths we first draw a few strange paths The last of these three graphics demonstrat
48. a page graphic is StartPage all kind of commands StopPage Between the StartPage and StopPage command you have access to a wide range of variables page PaperHeight PaperWidth PrintPaperHeight PrintPaperWidth PageOffset PageDepth margins TopsSpace BackSpace text MakeupHeight MakeupWidth vertical TopHeight TopDistance HeaderHeight HeaderDistance TextHeight FooterDistance FooterHeight BottomDistance BottomHeight horizontal LeftEdgeWidth LeftEdgeDistance LeftMarginWidth LeftMarginDistance TextWidth RightMarginDistance RightMarginWidth RightEdgeDistance RightEdgeWidth Since using these variables to construct paths is not that handy the areas are available as predefined paths which we will demonstrate here In figure 6 2 you see two pages odd and even with a background spanning the outer margin and the text area You can access an area in two ways The area itself is available as Area StartPage fill Area Text Text withcolor 85white StopPage If you use an area this way you will notice that it is not positioned at the right place An Area is just a rectangle If you want a positioned area you should use the Field array StartPage fill Field Text Text withcolor 85white StopPage Preliminary Version November 11 2001 Page Edward R Tufte We thrive in information thick worlds because of our marvelous and everyday capacity to select e
49. all the graphics in an external metarost file the following framework suits We assume that the file is called step mp and that it is kept by the user along with his document source We start with the definitions of the graphic steps These are the same as the ones shown previously def draw_basics enddef def draw_circles enddef def draw_intersection enddef def draw_bisector enddef def draw_midpoint enddef def stand_out enddef Preliminary Version November 11 2001 A few As eB Figure 13 6 Bisecting a line segment with compass and straightedge Just click here to walk through the construction This stack is only visible in a PDF viewer that supports widgets We can safe some code by letting the _everything take care of the beginfig and endfig macros def start_everything expr n beginfig n enddef def stop_everything endfig enddef The five graphics now become start_everything 1 stand_out draw_basics stop_everything start_everything 2 draw_basics stand_out draw_circles stop_everything start_everything 3 draw_basics draw_circles stand_out draw_intersection stop_everything start_everything 4 draw_basics draw_circles draw_intersection stand_out draw_bisector stop_everything start_everything 5 draw_basics draw_circles draw_intersectio
50. also program in a language like MeTAFONT where the pt is the base unit This means that a circle scaled to 100 in METAPOST is not the same as a circle scaled to 100 in MeTAFONT Consider the next definition pickup pencircle scaled 0 fill unitsquare xscaled 400pt yscaled 5cm withcolor 625red fill unitsquare xscaled 400bp yscaled 5cm withcolor 625yellow drawoptions withcolor white label rt 400 pt origin shifted 0 25cm label rt 400 bp origin shifted 0 25cm When processed the difference between a pt and bp shows rather well Watch how we use rt to move the label to the right you can compare this with Tsx s macro rlap You might want to experiment with 1ft top bot ulft urt 11ft and 1rt The difference between both bars is exactly 1 5pt as calculated by TEX 400 bp 400 pt Where xx is anchored in tradition and therefore more or less uses the pt as the default unit META Post much like POSTSCRIPT has its roots in the computer sciences There to simplify calculations an inch is divided in 72 big points and 72pt is sacrificed Preliminary Version November 11 2001 2 4 When you consider that POSTSCRIPT is a high end graphic programming language you may wonder why this sacrifice was made Although the difference between 1bp and 1pt is miniscule this difference is the source of much unknown confusion When TEx users talk about a 10pt fo
51. can be sure that in due time extensions will show up You can skip this chapter if you are no CONTEXT user The concept After Tex has read a paragraph of text it will try to break this paragraph into lines When this is done the result is flushed and after that Tex will check if a page should be split off As a result we can hardly predict how a document will come out Therefore when we want graphics to adapt themselves to this text we have to deal with this asynchronous feature of Tex in a rather advanced way Before we present one way of dealing with this complexity we will elaborate on the nature of such graphics When Tpx entered the world of typesetting desktop printers were not that common let alone color desktop printers But times have changed and nowadays we want color and graphics if possible integrated in the text To accomplish this several options are open 1 Use a backend that acts on the typeset text this is the traditional way using specials to embed directives in the DVI output file 2 Use the power of a second language and pass snippets of code to the backend which takes care of proper handling of those snippets impressive results are booked by passing POSTSCRIPT to the DVI file 3 Extend Tex in such a way that Tpx itself takes care of these issues this is the way PDFTEX works The first method is rather limited although for business graphics acceptable results are booked The second method is very powerful but
52. can start working placing the label vardef anglebetween expr endofa endofb common length str save curve where path curve numeric where where turningnumber common endofa endofb cycle curve unitvector endofa common endofa common rotated where 90 unitvector endofb common scaled length shifted common draw thefreelabel str point 5 of curve common withcolor black curve enddef The macro thefreelabel is part of MetaFun and is explained in detail in section 13 2 This macro tries to place the label as good as possible without user interference pair a a pair b b drawarrow anglebetween a b origin 1cm btex alpha etex withcolor 625red 2cm 1cm drawarrow origin a 3cm 1cm drawarrow origin b Instead of a picture we may also pass a string but using Tex by means of btex etex often leads to better results fe Because in most cases we want the length to be consistent between figures and because passing two paths is more convenient than passing three points the final definition looks slightly different numeric anglelength anglelength 20pt vardef anglebetween expr a b str path path string save endofa endofb common curve where pair endofa endofb common path curve numeric where endofa point length a of a endofb point length b of b if round point O of a round point O of b common point O0 of a else common
53. coding The advantage of using symbols is that you can redefine them depending on the situation So definesymbol yes em Yes creates a symbol that lets symbol yes expand into Yes Since nearly anything can be a symbol we can also say definesymbol yes mathematics star or even the already defined symbol x by saying definesymbol yes symbol star It may be clear that we can use a graphic as well def metabuttonsymbol 1 uniqueMPgraphic meta button type 1 definesymbol menu left metabuttonsymbol 101 definesymbol menu right metabuttonsymbol 102 definesymbol menu list metabuttonsymbol 103 definesymbol menu index metabuttonsymbol 104 definesymbol menu person metabuttonsymbol 105 definesymbol menu stop metabuttonsymbol 106 definesymbol menu info metabuttonsymbol 107 definesymbol menu down metabuttonsymbol 108 def inesymbol menu up metabuttonsymbol 109 definesymbol menu print metabuttonsymbol 110 Since we have collected some nice buttons in a meTaPosT file already we can use a rather simple definition startuniqueMPgraphic meta button type size linecolor fillcolor if unknown context_butt input mp butt fi some_button MPvar type MPvar size MPvar linecolor MPvar fillcolor stopuniqueMPgraphic This leaves a few settings setupMPvariables meta button type 1 size 2 bodyfontsize fillcolor gray linecolo
54. defaultfont at 20pt We can store the current meaning of a primitive or macro ina new macro We do so with infont let normalinfont infont Preliminary Version November 11 2001 Ante 211 We can only know the size if we know the name of the font so we have to redefine infont to pick up this name def infont primary name hide lastfontsize fontsize name normalinfont name enddef Because we are replacing an operator and since METAPOST expects one we have to use def instead of vardef which is actually a kind of variable For the same reason we have to pick up a primary If we would use a expr name we would end up in an unwanted look ahead The hide macro hides the assignment and makes this macro behave like a vardef with respect to hiding expressions We may not put a semi colon after the because it would stop Metarost from reading on and thereby invoke an error message We can now define at This macro picks up an expression which can me more than just a number and return a scale transform that normalized the given size to the design size def at expr size scaled size lastfontsize enddef Because this macro is defined global and therefore can be used apart from infont we predefine the size numeric lastfontsize lastfontsize fontsize defaultfont When defined this way at a comfortable 20 points the string MetaFun comes out as follows Meta
55. e e e a fifth iteration Preliminary Version November 11 2001 sixths iteration 2 6 The next example demonstrates how the resolution depends on the length and nature of the segment drawmidpoints fullsquare xscaled 200pt yscaled 40pt randomized 10pt 5 Inflection tension and curl The metarost manual describes the meaning of as choose an inflection free path between these points unless the endpoint directions make this impossible When you start searching for nice examples to demonstrate the difference between and you will be surprised that honouring the request for less inflection is more often impossible than you would expect We will demonstrate this to a few graphics In the four figures on the next pages you will see that is not really suited for taming wild curves If you really want to make sure that a curve stays within certain bounds you have to specify it as such using control or intermediate points In the figures the gray curves draw the random path using on top of yellow curves using As you can see only in a few occasions the yellow inflection free curves show up The tension specifier can be used to influence the curvature To quote the meTaPosT manual once more The tension parameter can be less than one but it must be at least 3 4 The following paths are the same z 22
56. else a pat intersection_point lin fi 5 b pat intersection_point lin shifted 0 strutdepth Preliminary Version November 11 2001 if intersection_found if sig if xpart b gt xpart a a b shifted 0 strutdepth fi else if xpart b lt xpart a a b shifted 0 strutdepth fi fi fi a enddef stopuseMPgraphic Instead of using meTaPosT s intersectionpoint macro we use one that comes with CONTEXT That way we don t get an error message when no point is found and can use a boolean flag to take further action Since we use a vardef all calculations are hidden and the a at the end is returned so that we can use this macro in an assignment The sig variable is used to distinguish between the beginning and end of a line the left and right subpath startuseMPgraphic text step path line pair 111 rrr for i topskip step baselineskip until vsize line ulcorner q urcorner q shifted 0 i 111 found_point line l true rrr found_point line r false stopuseMPgraphic Here we divide the available space in lines The first line starts strutheight from the top We can now finish our graphic by visualizing the lines Both the height and depth of the lines are shown startuseMPgraphic text line fill 1ll rrr rrr shifted 0 strutheight 111 shifted 0 strutheight cycle withcolor 5white fill 1ll rrr
57. enddef draw unitslant xscaled 5cm yscaled icm withpen pencircle scaled 5mm withcolor 625red An even better alternative is path unitslant unitslant origin origin shifted 1 1 draw unitslant xscaled 5cm yscaled icm withpen pencircle scaled 5mm withcolor 625yellow 25 Curve construction Chapter 3 of the MeTAaFONT book explains the mathematics behind the construction of curves Both METAFONT and metarosT implement B zier curves The fact that these curves are called after Pierre B zier obscures the fact that the math behind them originates with Sergei Bernshtein The points on the curve are determined by the following formula z t 1 z1 3 1 t 7tz2 3 1 723 zy Here the parameter t runs from 0 1 As you can see we are dealing with four points In practice this means that when we construct a curve from multiple points we act on two points and the two control points in between So the segment that goes from z to z4 is calculated using these two points and the points that METAFONT METAPOST calls post control point and pre control point Z1 Z2 Z7 Z4 Z6 Z5 A tew more details Preliminary Version November 11 2001 The previous curve is constructed from the three points z1 z4 and z7 The curve is drawn in METAPOST by z1 z4 z7 and is made up out of two segments The first segment is determined by the following points
58. hardly portable since it depends on the DVI to POSTSCRIPT postprocessor But what about the third method There has been some reluctance to divert from traditional Tex and DVI but since PDFTgX came around and the lack of a postprocessing stage forced new primitives into the core the third option mentioned before more and more became reality Much of what I will discuss here can be realized in DVI using a dedicated postprocessor to extract the information needed Although we think that the PDFT X way is the natural way to go CONTEXT also supports the same mechanism in DVI As said a decent portion of TgxX s_attention_is focussed on breaking paragraphs into lines and Fee s determining the optimal point to split off the page Tryitg tolocate the optimal points to break lines is a dynamic process The space between words is flexible nd we don t know in advance when a d or piece of a word maybe it s best to talk of typographic instead will end up on th page It might even cross the page boundary In the previous paragraph word and fglobs are encircled and connected by an arrow This graphic can only be drawn when the positions and dimensions are known which is after the paragraph is typeset and the best breakpoints are chosen Because the text must be laid on top o the graphic the graphic must precede the first word in the typeset stream or it must be positione on a separate layer In the latter case it can be calculated
59. in terms of being the same as this point or touching that point In this section we will spend some time on this touchy aspect This rectangle is a scaled instance of the predefined MetaFun path fullsquare which is centered around the origin currentpicture currentpicture currentpicture currentpicture currentpicture currentpicture pickup pencircle scaled 2mm path p p fullsquare scaled 2cm draw p withcolor 625white Preliminary Version November 11 2001 yscaled 5 yscaled 1 slanted 5 zscaled 75 25 On this path halfway between two of its corners we define a point q pair q q 5 llcorner p lrcorner p We draw this point in red using draw q withcolor 625red As you can see this point is drawn on top of the path L There are four of those midpoints and when we connect them we get Q Because path p is centered around the origin we can simply rotate point q a few times draw q q rotated 90 q rotated 180 q rotated 270 cycle withcolor 625red There are situations where you don t want the red path to be drawn inside another path or more general where you want points to touch instead of being overlayed Q We can achieve this by defining point q to be located on top of the midpoint pair q q top 5 llcorner p lrcorner p The predefined macro top moves the point over
60. j n 1 dodrawmidpoints j i g d n 1 fi enddef vardef drawmidpoints expr p n save a b c d pair a b c d for x 0 upto length p 1 a point x of p b postcontrol x of p d point x 1 of p c precontrol x 1 of p dodrawmidpoints a b c d n endfor enddef We demonstrate these macros on two paths first we show how the depth of the recursion improves the resolution for i 1 upto 7 drawmidpoints fullcircle xscaled 100pt i 5pt yscaled 40pt i 5pt i endfor Preliminary Version November 11 2001 A few niare details Preliminary Version November 11 2001 e e points first order curve second order curve third order curve left side curves right side curves Preliminary Version November 11 2001 points first order points e second order points left side points right side points Preliminary Version November 11 2001 e e e e a e first iteration second iteration e ee e e AS e e e e e t e e eo e a e e e e m e e o third iteration fourth iteration Cees e aN e e e e H R H J N 8
61. local to this macro When processed this code produces the following graphic This graphic shows that we need a bit more control over the exact position of the arrow It would be nice if we could start the arrow at the point or end there or center the arrow around the point Therefore the real implementation is a bit more advanced vardef pointarrow expr pat loc len off save l r s t path 1 r numeric s pair t t if pair loc loc else point loc along pat fi s len 2 off if s lt 0 s 0 elseif s gt len s len fi r pat cutbefore t r r cutafter point arctime s of r of r s len 2 off if s lt 0 s 0 elseif s gt len s len fi l reverse pat cutafter t 1 reverse l cutafter point arctime s of 1 of 1 1 r enddef This code fragment also demonstrates how we can treat the loc argument as pair coordinates or fraction of the path We calculate the piece of path before and after the given point separately and paste them afterwards as 1 r By adding braces we can manipulate the path in expressions without the danger of handling r alone We can now implement left center and right arrows by providing this macro the right param eters The offset the fourth parameter is responsible for a backward displacement This may seem strange but negative values would be even more confusing def rightarrow expr p t l pointarrow p t 1 1 enddef def left
62. natural dimensions unless of course we adapt the bounding box manually When you limit your graphic to a simple shape say a rectangle shifting it to some place can get obscured by this fact Therefore the following series of shapes appear to be the same draw unitsquare xscaled 6cm yscaled 1 5cm withpen pencircle scaled 2mm withcolor 625red draw unitsquare shifted 5 5 xscaled 6cm yscaled 1 5cm withpen pencircle scaled 2mm withcolor 625red draw unitsquare shifted 5 5 xscaled 6cm yscaled 1 5cm withpen pencircle scaled 2mm withcolor 625red Preliminary Version November 11 2001 Afew draw unitsquare xscaled 6cm yscaled 1 5cm shifted 1cm 1cm withpen pencircle scaled 2mm withcolor 625red draw unitsquare xscaled 6cm yscaled 1 5cm shifted 1 5cm 1cm withpen pencircle scaled 2mm withcolor 625red However when we combine such graphics into one we will see in what respect the scaling and shifting actually takes place draw unitsquare xscaled 6cm yscaled 2cm withpen pencircle scaled 3 0mm withcolor 625yellow draw unitsquare shifted 5 5 xscaled 6cm yscaled 2cm withpen pencircle scaled 3 0mm withcolor 625red draw unitsquare xscaled 6cm yscaled 2cm shifted 1cm 1cm withpen pencircle scaled 3 0mm withcolor 625white draw unitsquare xscaled 6cm yscaled 2cm shifted 1 5cm 1cm withpen pencircle scaled 1 5mm withcolor white draw unitsquare sh
63. odd Figure 6 3 A background with split areas This can easily be solved by enlarging the areas a bit The next example demonstrates this on the text area which is shown in figure 6 4 startuseMPgraphic page StartPage pickup pencircle scaled 2pt fill Page withcolor 625white fill Field Text Text enlarged 5cm withcolor 850white draw Field Text Text enlarged 5cm withcolor 625red StopPage stopuseMPgraphic The enlarged macro can be used like shifted and accepts either a numeric or a pair How do we define a background as in figure 6 2 Because Field provides us the positioned areas we can use the corners of those startuseMPgraphic page StartPage path Main if OnRightPage Main lrcorner Field QuterMargin Text llcorner Field Text Text ulcorner Field Text Text urcorner Field OuterMargin Text cycle else Main llcorner Field OQuterMargin Text Preliminary Version November 11 2001 Edward R Tufte Edward R Tufte We thrive in information thick worlds because of our marvelous and everyday capacity to select We thrive in information thick worlds because of our marvelous and everyday capacity to select edit single out structure highlight group pair merge harmonize synthesize condense reduce boil down E ai a cay list abstract sean look into discriminate e itemize review dip into flip through 5 skim refine CEES gai a goats Donald E Knuth D S
64. or convert the graphic to PDF and view the result in a suitable PDF viewer like ACROBAT Of course you can embed such a file in a CONTEXT document using a command like externalfigure yourfile 7 We will go in more detail about embedding graphics in chapter 3 If you have installed CONTEXT somewhere on your system there resides a file mp tool mp If you make a stand alone graphic it s best to put the following line at the top of your file Preliminary Version November 11 2001 Aew more details 22 input mp tool By loading this file the resulting graphic will provide a high resolution bounding box which enables more accurate placement The file also sets the prologues 1 so that viewers like GHOSTVIEW can refresh the file when it is changed In the next chapter we will explain in detail how to embed the metarost code in your TEX file but first we will introduce some more METAPOST commands From now on we will omit the encapsulating beginfig and endfig macros If you want to process these examples yourself you should add those commands pickup pencircle scaled 5cm draw unitsquare xscaled 8cm yscaled 1cm withcolor 625white draw origin withcolor 625yellow pickup pencircle scaled ipt draw bbox currentpicture withcolor 625red In this example we see a mixture of so called primitives as well as macros A primitive is something hard coded a built in com
65. packages in balloons and typeset as a paragraph We will demonstrate that Tpx can typeset graphics using the following statement As you may know X s ambassador is a lion while METAFONT is represented by a lioness It is still unclear if they have a relationship but if so and if a baby is born may it enjoy MetaFun The low level CONTEXT macro processwords provides a mechanism to treat the individual words of its argument The macro is called as follows processwords As you may know TEX s ambassador is a lion while METAFONT is represented by a lioness It is still unclear if they have a relationship but if so and if a baby is born may it enjoy METAFUN In order to perform a task you should also define a macro processword which takes one argument The previous quote was typeset with the following definition in place def processword 1 1 A slightly more complicated definition is the following def processword 1 noindent framed 1 space We now get Preliminary Version November 11 2001 _ Enhancing the layout As you may know TgxX s Jambassador lis a jlion while METAFONT is represented by a lioness It jis still unclear if they have a jrelationship ibut if so and if la ba
66. point z of the curve the postcontrol point z2 of z the precontrol point z3 of z4 point z4 of the curve Fe Ge be On the next pages we will see how the whole curve is constructed from these quadruples of points The process comes down to connecting the mid points of the straight lines connecting the points mentioned We do this three times which is why these curves have are classified as third order approximations The first series of graphics demonstrates the process of determining the mid points The third order midpoint is positioned on the final curve The second series focuses on the results new sets of four points that will be used in a next stage The last series only shows the third order midpoints As you can see after some six iterations we have already reached a rather good fit of the final curve The exact number of interactions depends on the resolution needed You will notice that the construction speed density differs per segment Just in case you are interested how such graphical simulations can be organized we show the simplified code We loop over all segments of the curve where for each segment the left and right side sub curves are handled recursive upto the requested depth here n vardef dodrawmidpoints expr a b c d n save e f g h i j pair e f g h i j e 5 a b f 5 b c g 5 c d h 5 e f i 5 f g j 5 h i draw j if n gt 1 dodrawmidpoints a e h
67. random alternative made me think of those organic building with non equal windows we have a few of those in The Netherlands so I decided to label this style as pre organic If you use CONTEXT you can load this style with usemodule pre organic At the end of this file there is a small test file so when you process the file s pre 19 tex with TEXEXEC and the options mode demo and pdf you will get a demo document We use one of the standard screen paper sizes and map it onto the same size so that we get a nicely cropped page Other screen sizes are S4 and S5 setuppapersize S6 S6 Like in this MetaFun manual we use the Palatino as main bodyfont This font is quite readable on even low resolution screens although I admit that this style is developed using an 1400 x 1050 pixel LCD screen so the author may be a little biased setupbodyfont pp1 The layout specification sets up a text area and a right edge area where the menus will go see chapter 6 for a more in depth discussion on the layout areas Watch how we use a rather large edge distance By setting the header and footer dimensions to zero we automatically get rid of page body ornaments like the page number This style is the 19 presentation style Those numbered styles are internally mapped onto more meaningful names like in this case pre organic Preliminary Version November 11 2001 setuplayout
68. representation of the text typeset by Tex Before METAPOST processes a graphic definition file it first calls another program that filters the btex commands from the file and generates a TEX file from them Next this file is processed by T X and after that converted to a mpx file In CONTEXT we let TeXEXEC take care of this whole process Because the btex etex commands are filtered from the raw METAPOST source code they cannot be part of macro definitions and loop constructs When used that way only one instance would be found while in practice multiple instances may occur This drawback is overcome by MetaFun s textext command This commands still uses btex etex but writes those commands to a separate file each time it is used After the first METAPOST run this file is merged with the original file and metarost is called again So at the cost of an additional run we can use text typeset by Tex in a more versatile way Because METAPOST runs are much faster than TX runs the price to pay in terms if run time is acceptable Opposite to btex etex the Tex code in textext command is expanded but as long as CONTpXT is used this is seldom a problem because most commands are kind of protected If we define a graphic with text to be typeset by Tpx there is a good change that this text is not frozen but passes as argument A rather Tpx like solution for passing arbitrary content to such a graphic is the following Preliminary Vers
69. rrr shifted 0 strutdepth 111 shifted 0 strutdepth cycle withcolor 7white draw 111 withpen pencircle scaled 2pt draw rrr withpen pencircle scaled 2pt draw l1ll rrr withpen pencircle scaled 5pt stopuseMPgraphic startuseMPgraphic text done endfor stopuseMPgraphic The result is still a bit disappointing startuseMPgraphic text includeMPgraphic text path includeMPgraphic text vars includeMPgraphic text move includeMPgraphic text split ypesettingyn Meteo Preliminary Version November 11 2001 includeMPgraphic text cutoff includeMPgraphic text draw includeMPgraphic text calc includeMPgraphic text step includeMPgraphic text line includeMPgraphic text done stopuseMPgraphic In order to catch the overflow at the bottom we need to change the for loop a bit so that the number of lines does not exceed the available space The test that surrounds the assignment of vvsize makes sure that we get better results when we on purpose take a smaller height startuseMPgraphic text step path line pair 111 rrr numeric vvsize if strutheight strutdepth lt baselineskip vvsize vsize else vvsize vsize div baselineskip baselineskip fi for i topskip step baselineskip until vvsize line ulcorner q urcorner q shifted 0 i 111 found_point line l true rrr found_point line r false
70. scaled bounding box However when we show the natural bounding box you will notice that a more complicated bit of calculations is needed The right clip path is calculated using the following expressions Watch how we use rt and top to correct for the linewidth numeric d 1x ly ux uy d line 2 lx 3d d 3 ly d ux rt x5 d 3 uy top y6 path r r 1x ly ux ly ux uy 1x uy cycle The clipping path is applied by saying Preliminary Version November 11 2001 afew clip currentpicture to r The result is quite acceptable But if you watch closely to how this graphic extends into to left margin of this document you will see that the bounding box is not yet right setbounds currentpicture to r We use the same path r to correct the bounding box There are a few subtle points involved like setting the 1inejoin variable If we had not set it to mitered we would have got round corners We don t set the linecap since a flat cap would not extend far enough into the touching curve and would have left a small hole The next example shows what happens if we set these variables to the wrong values In fact we misuse the fact that both curves overlay each other The complete logo definition is a bit more extensive since we also want to add a background Because we need to clip the blue foreground graphic we must te
71. shared by all btex etex pictures METAPOST provides verbatimtex DefineSomeCommands etex However in CONTEXT one has a better mechanism available The advantage of using that method is that otherwise all graphics let metaPosT or TEXEXEC invoke TEX even if no TeX pictures are constructed The best way to pass environments is the following As an example we switch to the 15 basic POSTSCRIPT fonts startMPenvironment setupbodyfont pos stopMPenvironment Preliminary Version November 11 2001 F Bypesetting in Meraeost 9 3 9 4 This means that in code like the following a Times Roman will be used startMPcode draw btex Meta is a female lion etex xysized the textwidth the textheight stopMPcode We have included the graphic on the next page in a slightly different look You may consider coloring the dots to be an exercise in clipping An environment can be reset with resetMPenvironment or by passing reset as key to startMPenvironment startMPenvironment reset setupbodyfont pos stopMPenvironment Labels In MEeTAPOST you can use the label macro to position text at certain points label x origin The font and scale are determined by two variables defaultfont and defaultscale the former expecting the name of a font in the form of a string the latter expecting a numeric to be used in the scaling of the font Should you choose not
72. that handy especially if you start wondering why you need to supply a slanted path Therefore metaPosT provides a more convenient mechanism to define a pattern picture p p dashpattern on 3mm off 3mm draw 0 0 10cm 0 dashed p withpen pencircle scaled 1mm Preliminary Version November 11 2001 1 12 Most dashpatterns can be defined in terms of on and off This simple on off dashpattern is predefined as picture evenly Because this is a picture you can and often need to scale it draw 0 0 10cm 0 dashed evenly scaled 1mm withpen pencircle scaled imm Opposite to a defaultpen there are no default color and default dash pattern The macro drawoptions provides you a way to set the default attributes drawoptions withcolor red Text Since METAFONT is meant for designing fonts it will be no surprise that the only means for including text are those that permit you to add labels to positions for the sole purpose of documentation Because MeTAPOST is derived from METAFONT it provides labels too but in order to let users add more sophisticated text like a math formula to a graphic it also provides an interface to TEx Because we will spent a whole chapter on text in meTaPosT we will limit ourselves to just some basics pair a a 3cm 3cm label top top a label bot bot a label 1ft lft a label rt rt a These four labels sh
73. the distance similar to the current pen width Preliminary Version November 11 2001 Because we are dealing with two drawing operations and since the path inside is drawn through the center of points we need to repeat this move in order to draw the red path really inside the other one pair q q top top 5 llcorner p lrcorner p Operations like top and its relatives bot 1ft and rt can be applied sequentally We already showed that q was defined as a series of rotations draw q q rotated 90 q rotated 180 q rotated 270 cycle withcolor 625red As an intermezzo we will show an alternative definition of q Because each point is rotated 90 degrees more we can define a macro that expands into the point and rotates of afterwards Because each consecutive point on the path is rotated an additional 90 degrees we use the META Post macro hide to isolate the assignment The hide command executes the hidden command and afterwards continues as if it were never there You must confuse this with grouping since the hidden commands are visible to its surroundings def qq q hide q q rotated 90 enddef draw qq qq qq qq cycle withcolor 625red The macro top uses the characteristics of the current pen to determine the displacement However for the more complicated pen shapes we need a different trick to get an inside path Let s start by defining a elliptical path picku
74. the range 0 1 and represent percentages Black is represented by definecolor black 1 r 0 g 0 b 0 definecolor black 2 c 0 m 0 y 0 k 1 definecolor black 3 s 0 Predefined colors are passed to Metapost graphics via the MPcolor First we define some colors definecolor darkyellow y 625 a CMYK color definecolor darkred r 625 a RGB color definecolor darkgray s 625 a gray scale These are the colors we used in this document The next example uses two of them startuseMPgraphic color demo pickup pencircle scaled 1mm path p p fullcircle xscaled 10cm yscaled 1cm fill p withcolor MPcolor darkgray draw p withcolor MPcolor darkred stopuseMPgraphic useMPgraphic color demo The previous example uses a pure RGB red shade combined with a gray fill oo Since meTAPOST does not support the CMYK color space and native gray scales although gray colors are reduced to the more efficient POSTSCRIPT setgray operators in the output the macro MPcolor takes care of the translation from CMYK to RGB as well as gray to RGB However there is a fundamental difference between a yellow as defined in CONTEXT using CMYK and an RGB yellow in METAPOST Eimibeel ect graphics Preliminary Version November 11 2001 def inecolor cmyyellow Ly 1 def inecolor rgbyellow r 1 g 1 definecolor cmydarkyellow y 625 definecolor rgbdarkyellow r 62
75. to a three sided one which itself converges to a two sided one In the two sided alternative it s not that hard to prove that the angle is indeed 90 degrees do_draw_problem 40 1 0 1 0 do_draw_problem 41 0 8 1 0 do_draw_problem 42 0 6 1 0 do_draw_problem 43 0 4 1 0 do_draw_problem 44 0 2 1 0 do_draw_problem 45 0 0 1 0 do_draw_problem 30 0 0 1 0 do_draw_problem 31 0 0 0 8 do_draw_problem 32 0 0 0 6 do_draw_problem 33 0 0 0 4 do_draw_problem 34 0 0 0 2 do_draw_problem 35 0 0 0 0 We already showed a picture with coordinates This picture was generated using some alternative coordinates def do_draw_problem expr n i j draw_problem 4000 n 400pt 400pt 400pt 600pt il 400pt 600pt 550pt 600pt jl 400pt 400pt 550pt 400pt enddef Preliminary Version November 11 2001 Welcome to ME 0 0 0 4 0 0 0 2 0 0 0 0 Figure 1 2 The solution Preliminary Version November 11 2001 show_labels true do_draw_problem 50 0 6 1 0 As soon as you can see a clear pattern in some code it s time to consider using loops In the previous code we used semi indexes like 12 in z12 In this case 12 does reflect something related to square 1 and 2 but in reality the 12 is just twelve This does not harm our expressions A different approach is to use a two dimensional a
76. to set these yourself they default to cmr10 and 1 0 respectively However you can change the defaults as follows defaultfont defaultscale tir 1 2 These settings select Adobe Times at about 12pt You can also set these variables to CONTEXT related values For CONTgXT graphics they are set to defaultfont defaultscale truefontname Regular the bodyfontsize 10 This means that they will adapt themselves to the current body font in this document texnansi uplr8a and the current size of the bodyfont here 10 0pt 10 TEX text In the next example we will use a special mechanism for building graphics step by step The advantage of this method is that we can do intermediate calculations in TeX Our objective is to write a macro that draws text along a circular path While doing so we want to achieve the following e the text should be properly kerned i e the spacing between characters should be optimal e the position on the circle should vary and e the radius of the circle should vary Typebettinngain vet POST Preliminary Version November 11 2001 This implementation is not the most straightforward one but by doing it step by step at least we see what is involved Later we will see a better method If you run these examples yourself you must make sure that the Tpx environment of your document matches the one used by metarost Here we u
77. underlying it BE ee ona E E alee my De ea well However despite my some points in it that 1 feel might be e ee eo mene some points in it that I feel might be ees ely by eva seniors ae ab thy ae pots tat ouch Gaston despot ents Aho by any ar th pontiac ye ieres HE SE a Sy SG in artificial intelligence and esthetic theory I felt compelled to make some comments to clarify certain important issues raised by The Concept of a Meta I certain important issues raised by The Concept of a Meta Font even odd Figure 6 4 A background with enlarged text area lrcorner Field Text Text urcorner Field Text Text ulcorner Field OuterMargin Text cycle fi 3 Main Main enlarged 6pt pickup pencircle scaled 2pt fill Page withcolor 625white fill Main withcolor 850white draw Main withcolor 625red StopPage stopuseMPgraphic In this definition we calculate a different path for odd and even pages When done we enlarge the path a bit If you want to use different offsets in all directions you can use moved corner points startuseMPgraphic page StartPage def somewhere Cuniformdeviate 1cm uniformdeviate 1cm enddef path Main Main Field Text Text lrmoved somewhere Field Text Text llmoved somewhere Field Text Text ulmoved somewhere Field Text Text urmoved somewhere cycle pickup pencircle scaled 2pt Preliminary Version November 11 2001 fill Page wi
78. vardef generic variable delimited part undelimited part binary def parameter symbolic token parameter delimited part empty delimited part parameter type parameter tokens parameter type expr suffix text Preliminary Version November 11 2001 parameter tokens parameter parameter tokens parameter parameter Symbolic token undelimited part empty parameter type parameter precedence level parameter expr parameter of parameter precedence level primary secondary tertiary binary def primarydef secondarydef tertiarydef pseudo procedure drawoptions option list label label suffix expression pair expression dotlabel label suffix expression pair expression labels label suffix point number list dotlabels label suffix point number list freelabel expression pair expression pair expression freedotlabel expression pair expression pair expression point number list suffix point number list suffix label suffix empty 1ft rt top bot ulft urt 11ft 1rt Preliminary Version November 11 2001 command clip picture variable to path expression interim internal variable right ha
79. we use a Times Roman instead of a Palatino we get quite different results We thrive in information thick worlds because of our marvelous and everyday capacity to select edit single out structure highlight group pair merge harmonize synthesize focus organize condense reduce boil down choose categorize classify list abstract scan look into idealize isolate discriminate distinguish pigeonhole pick over sort integrate blend inspect filten lump skip smooth chunk approximate cluster aggregate outline summarize itemize review dip through browse glance into leaf through skim refine enumerate glean synopsize winnow the wheat from the chaff and separate the sheep from the goats This font has far less kerning Even more interesting is the Lucida Bright Handwriting font which is defined in such a way that no kerning is needed at all thrive in information thick worlds because of our marvelous and everyday capacity to select edit single out structure highlight group pair merge harmonize synthesize focus organize condense reduce boil down choose categorize classify list
80. 0verlayHeight ypart center p drawoptions withpen pencircle scaled ipt withcolor 625red b a randomized 0 2 fill b withcolor 85white draw b c center p c b intersectionpoint c shifted 0 0 c shifted 0 o0 p p shifted c center p b boundingbox p randomized 0 8 fill b withcolor 85white draw b draw p withcolor black setbounds currentpicture to a stopuseMPgraphic Preliminary Version November 11 2001 Enhancing the lay There is not so much basic instruction as of now as there was in the old days showing the differences between good and bad typographic design Yet another definition uses super ellipsed shapes instead of random ones We need a high degree of superness 95 in order to make sure that the curves don t touch the texts startuseMPgraphic FunnyFrame picture p numeric o path a b pair c p textext rt MPstring FunnyFrame o BodyFontSize a unitsquare xyscaled OverlayWidth OverlayHeight p p shifted 20 0verlayHeight ypart center p drawoptions withpen pencircle scaled 1pt withcolor 625red b a superellipsed 95 fill b withcolor 85white draw b b boundingbox p superellipsed 95 fill b withcolor 85white draw b draw p withcolor black setbounds currentpicture to a stopuseMPgraphic Many people are just fascinated by their PC s tricks and th
81. 1cm stopuseMPgraphic startuseMPgraphic followtokens path RotPath RotPath 3cm 0 1cm icm 3cm 0 stopuseMPgraphic startuseMPgraphic followtokens path RotPath RotPath 3cm 0 1cm 1cm Ocm 2cm 3cm 0 stopuseMPgraphic When turned on tracing will produce bouding boxes as well as draw the path Tracing can be turned on by saying startMPinclusions boolean TraceRot TraceRot true stopMPinclusions Talking to T X Sometimes others may say oftentimes we are in need for some fancy typesetting If we want to typeset a paragraph of text ina non standard shape like a circle we have to fall back on parshape ae ey POST Preliminary Version November 11 2001 Unfortunately Tex is not that strong in providing the specifications of more complicated shapes unless you are willing to do some complicated arithmetic Tx Given that MeTaPosT knows how to deal with shapes the question is Can Metarost be of help In the process of finding out how to deal with this we first define a simple path Because we are going to replace pieces of code we will compose the graphic from components First we create the path startuseMPgraphic text path path p p 0 1 1 0 1 0 cycle scaled 65pt stopuseMPgraphic This shape is not that beautiful but it has a few characteristics that will help us to identify border
82. 3 1 Three ways of marking angles Figure 13 1 shows the first three alternative methods implemented here Instead of using unitvectors we now calculate the points using the arctime and arclength primitives In stead of complicated expressions we use the MetaFun operators along and on The following expressions are equivalent pointa point anglelength ona middle point 5 along curve A few lpplications _ Preliminary Version November 11 2001 13 4 pointa point arctime anglelength of a of a middle arctime 5 arclength curve of curve of curve The third method can be implemented in different more math intensive ways but the current implementation suits rather well and is understood by the author Color circles In chapter 3 we showed a few color circles Drawing such a graphic can be done in several ways and here we will show a few methods First we will demonstrate how you can apply cutafter and curbefore next we will show how the metarost macro buildpath can be used and finally we will present a clean solution using subpath We will assume that the circle is called with the macro colorcircle 4cm red green blue We need to calculate seven paths The first implementation does all the handywork itself and thereby is rather long complicated and unreadable It does not really use the strenghth of META POST yet vardef colorcircle expr size red g
83. 5 g 625 Figure 3 2 demonstrates what happens when we multiply colors by a factor Since we are not dealing with real CMYK colors multiplication gives different results for CMYK colors passed as MPcolor yellow 1 1 0 5 5 0 MPcolor rgbyellow MPcolor rgbdarkyellow 5 MPcolor rgbyellow MPcolor cmyyellow MPcolor cmydarkyellow 5 MPcolor cmyyellow Figure 3 2 All kinds of yellow So 625red is the same as r 5 but 625yellow is not the same as y 5 but matches r 5 g 5 Figure 3 3 shows the pure and half reds 1 0 0 625 0 0 MPcolor red MPcolor darkred 625 MPcolor red Figure 3 3 Some kinds of red In order to prevent problems we advise you to stick to RGB color specifications when possible That way you prevent not only conversion problems but the also often obscure ways printing and viewing devices handle CMYK However reality demands that sometimes CMYK colors are used so how can we deal with that In the MetaFun macro collection there is a macro cmyk that takes four arguments representing the cyan magenta yellow and black component fill fullsquare xyscaled 10cm 1cm withcolor cmyk 1 0 3 3 Preliminary Version November 11 2001 If you take a close look at the numbers you will notice that the cyan component results in a 100 ink contribution You will also notice that 30 black ink is added This means that we cannot safely convert this color to RGB r
84. 5 y 8 c 45 y 1 Figure 3 4 CMYK support disabled conversion to RGB c 1 y 3 k 3 c 9 y 15 c 25 y 8 c 45 y 1 Figure 3 5 CMYK support enabled no support in METAPOST c 1 y 3 k 3 c 9 y 15 c 25 y 8 c 45 y 1 Figure 3 6 CMYK support enabled no conversion to RGB support in METAPOST Preliminary Version November 11 2001 3 6 ae Common definitions When using many graphics there is a chance that they share common definitions Such shared components can be defined by startMPinclusions color mycolor mycolor 625red stopMPinclusions All metarost graphics defined in the document end up in the files mpgraph mp and mprun mp When processed they produce sometimes many graphic files When using TEXEXEC to process documents these two files are processed automatically after a run so that in a next run the right graphics are available When you are using the web2c distribution CONTEXT can call MeTAPOsT at runtime and thereby use the right graphics instantaneously In order to use this feature you have to enable write18 in the file texmf cnf Also in the file cont sys tex that holds local preferences or in the document source you should say runMPgraphicstrue This enables runtime generation of graphics using the low level TeX command write18 First make sure that your local brand of Tex supports this feature A simple test is making a Tx file with the followin
85. 5red stopMPgraphic Since we reuse the graphic the dimensions are sort of fixed and because the graphic is calculated once scaling it will result in incompatible line widths Embedded graphies Preliminary Version November 11 2001 Cc C These graphics were placed with hbox bgroup loadcurrentMPgraphic width 5cm height 1cm placeMPgraphic quad loadcurrentMPgraphic width 8cm height 1cm placeMPgraphic egroup Imagine what happens when we add some buttons to an interactive document without taking care of this side effect All the frames would look different Consider the following example startuniqueMPgraphic right or wrong pickup pencircle scaled 075 fill unitsquare withcolor 8white draw unitsquare withcolor 625red currentpicture currentpicture xscaled overlaywidth yscaled overlayheight stopuniqueMPgraphic Let s define this graphic as a background to some buttons def ineoverlay button uniqueMPgraphic right or wrong setupbuttons background button frame off hbox button previous previouspage quad button next nextpage quad button index index quad button table of contents content The buttons will look like Compare these with Here the graphic was defined as startuniqueMPgraphic wrong or right pickup pencircle scaled 3pt path p p unitsquare xscaled overlaywidth yscaled overlayheight fill p withcolor
86. 90 degrees are often identified by a rectangular symbol We will now extend the previously defined macro in such a way that more types can be drawn numeric anglelength anglelength 20pt numeric anglemethod anglemethod 1 vardef anglebetween expr a b str path path string save pointa pointb common middle offset pair pointa pointb common middle offset save curve path curve save where numeric where if round point O of a round point O of b Preliminary Version November 11 2001 A few applications common point O0 of a else common a intersectionpoint b fi pointa point anglelength on a pointb point anglelength on b where turningnumber common pointa pointb cycle middle common pointa rotatedaround pointa where 90 intersectionpoint common pointb rotatedaround pointb where 90 if anglemethod 1 curve pointa unitvector middle pointa pointb middle point 5 along curve elseif anglemethod 2 middle common rotatedaround 5 pointa pointb 180 curve pointa middle pointb elseif anglemethod 3 curve pointa middle pointb elseif anglemethod 4 curve pointa controls middle pointb middle point 5 along curve fi draw thefreelabel str middle common withcolor black curve enddef oy ny KA Of fs Nae IN Os method 1 method 2 method 3 Figure 1
87. C you should say texexec mptex yourfile mp This is the preferred way when a graphic contains Tpx directives btex cum suis or when the METAPOST file is generated by CONTEXT We will use lots of color Don t worry if your red is not our red or your yellow does not match ours We ve made color definitions to match the overall design of this document but you should feel free to use any color of choice in the upcoming examples By default CONTgXT has turned its color mechanism off If you want your graphics to have color you should say setupcolors state start Preliminary Version November 11 2001 Preliminary Version November 11 2001 1 1 Welcome to METAPOST In this chapter we will introduce the most important MeTAPOST concepts as well as demonstrate some drawing primitives and operators This chapter does not replace the METAFONT book or METAPOST manual both of which provide a lot of explanations examples and dirty tricks As its title says the METaFONT book by Donald E Knuth is about fonts Nevertheless buying a copy is worth the money because as a METAPOST user you can benefit from the excellent chapters about curves algebraic expressions and linear equations The following sections are incomplete in many aspects More details on how to define your own macros can be found in both the Mete FONT book and metarost manual but you will probably only appre
88. For this purpose we scale down the graphic to a comformatble 40 of course by using an additional buffer We also visualize the bounding box startbuffer h def stop_everything setbounds currentpicture to bb draw bb withpen pencircle scaled 5pt withcolor 625yellow currentpicture currentpicture scaled 4 enddef stopbuffer The graphic itself is defined as follows Watch how we use the default buffer to keep the definitions readable startbuffer startcombination 5 1 processMPbuffer a b c h d e f g 1 step 1 processMPbuffer a b c h d e f g 2 step 2 processMPbuffer a b c h d e f g 3 step 3 processMPbuffer a b c h d e f g 4 step 4 processMPbuffer a b c h d e f g 5 step 5 stopcombination stopbuffer placefigure here fig 1 till 5 The five graphics each with the same bounding box getbuffer As the original purpose of these graphics was not to show them side by side but to present them as field stack in a document to be viewed at the computer screen For this purpose we have to define the graphics as symbols Atfew applications Preliminary Version November 11 2001 step 1 step 2 step 3 step 4 step 5 Figure 13 5 The five graphics each with the same bounding box definesymbol step 1 processMPbuffer a b c d e f g 1 definesymbol step 2 processMPbuffer a b c d e f g 2
89. Fun Additional operators In this section we will introduce a few MetaFun operators like enlarged squeezed randomized xyscaled sized and superellipsed We can hardly cover them all since MetaFun is evolving A fe more details Preliminary Version November 11 2001 zd Embedded graphics In addition to the beginfig endfig method there are other ways to define and include a META post graphic Each method has its advantages and disadvantages In the previous chapter we were still assuming that the graphic was defined in its own file In this chapter we will introduce the interface between CONTEXT and metarost and demonstrate how the definitions of the graphics can be embedded in the document source Getting started From now on we will assume that you have CONTEXT running on your platform Since PDF has full graphics support we also assume that you use PDFTgX or know how to go from DVI to PDF Since this document is not meant as a CONTEXT tutorial we will limit this introduction to the basics needed to run the examples A simple document looks like starttext Some text stoptext You can process this document with the PERL based command line interface to CONTEXT If the source code is embedded in the file mytext tex you can say texexec pdf mytext As an alternative to pdf you can explicitly set the output driver in your document setupoutput pdftex startt
90. MyGraphic startreusableMPgraphic name overlaywidth overlayheight path p p unitsquare xscaled overlaywidth yscaled overlayheight fill p withcolor 625yellow draw p withcolor 625red stopreusableMPgraphic reuseMPgraphic name overlaywidth overlayheight After this we can say defineoverlay my graphic MyGraphic button background my graphic frame off Go Home firstpage Say that we have a 30pt by 20pt button then the identifier will be name 30pt 20pt Different dimensions will lead to other identifiers so this sort of makes the graphics unique We can bypass the ugly looking def by using a third class of embedded graphics the unique graphics startuniqueMPgraphic name path p p unitsquare xscaled overlaywidth yscaled overlayheight fill p withcolor 625yellow draw p withcolor 625red stopuniqueMPgraphic Now we can say defineoverlay my graphic uniqueMPgraphic name button background my graphic frame off Go Home firstpage You may wonder why unique graphics are needed when a single graphic might be used multiple times by scaling it to fit the situation Since a unique graphic is calculated for each distinctive case we can be sure that the current circumstances are taken into account Also scaling would result in incomparable graphics Consider the following definition startMPgraphic draw unitsquare xscaled 5cm yscaled icm withpen pencircle scaled 2mm withcolor 62
91. November 11 2001 Preliminary Version November 11 2001 To do decimal ddecimal dddecimal conditional real unfill support define some variables as internal breaks compatibility attributes to text along a path attributes to text shapes more positional things e g funny buttun style a few styles better equation explanation more auxiliary macros documenting metafun macros summary of commands check on completeness in covering commands text overlayed over mp hyperlinks and so expr a b c versus expr a b expr c shading etc in ps driver straight copy to file the logic behind grouping and global assignments 0 QQ and no in vardefs clearxy mpgraph or mp graph miterlimit dir angle counterclockwise turningnumber hide labeloffset interim labeloffset 0 joinup vardef newpath suffix path enddef OH Preliminary Version November 11 2001 Preliminary Version November 11 2001
92. Package the graphic components in buffers and paste those together as graphics that can be processed at run time The first method is the most independent one which has its advantages if we want to use the graphics in other applications too The second method works well in graphics where parts of the definitions change between invocations of the graphic This method follows the template startuseMPgraphic whatever stopuseMPgraphic startuseMPgraphic result includeMPgraphic whatever stopuseMPgraphic useMPgraphic result The disadvantage of this method is that it cannot be combined with btex etex since it is nearly impossible to determine when how and to what extent the content of a graphic should be expanded before writing it to the temporary metarost file Therefore we will demonstrate how buffers can be used This third method closely parallels the first way of defining graphics A nice side effect is that we can easily typeset these buffers verbatim which we did to typeset this document We are going to do a classic compass and straightedge construction the bisection of a line segment joining two arbitrary points We will construct 5 graphics where each one displays one step of the construction We will embed each graphic in a start stop command Later we will see the advantage of this strategy Preliminary Version November 11 2001 Atfew applications startbuffer
93. a intersectionpoint b fi 3 A few applications Preliminary Version November 11 2001 where turningnumber common endofa endofb cycle curve unitvector endofa common endofa common rotated where 90 unitvector endofb common scaled anglelength shifted common draw thefreelabel str point 5 of curve common withcolor black curve enddef This macro has a few more if s than its predecessor First we test if the label is a string and if so we calculate the picture ourselves otherwise we leave this to the user path a b c d e f a origin 2cm 1cm b origin 1cm 2cm c origin 2cm 2cm d origin 2cm 1cm e origin 1cm 2cm f origin 1cm 2cm for i a b c d e f drawarrow i endfor anglelength 1 0cm drawoptions withcolor 625red drawarrow anglebetween a b btex alpha etex drawarrow anglebetween c d btex gamma etex drawarrow anglebetween e f btex epsilon etex anglelength 1 5cm drawoptions withcolor 625yellow drawdblarrow anglebetween b c btex beta etex drawarrow reverse anglebetween d e btex delta etex drawarrow anglebetween a f btex zeta etex Because anglebetween returns a path you can apply transformations to it like reversing Close reading of the previous code learns that the macro handles both directions pi 7 NA Multiples of
94. a straight one This could be true after a few strong beers but then how do Germans draw a line EnglishRule stopnarrower As expected the rule adapts itself to the current width of the text The height of the rule in the middle matches the height of a character with no ascenders and descenders Why is this called an English line Is it because they cannot draw a straight one This could be true after a few strong beers but then how do Germans draw a line Random graphics Given enough time and paper we can probably give you some HHT HAL LT LHT AHT LT LH LHT AHT IMT LHT LHA LAT LHT LI IHT IH DA De LHT LT LHT LHT LHT LUHY LMT At IT JHI IHI L LHT L Lhit IHT LHT LHAT LHT LI IHT Lh LT LIY IAT LT LHT LA LHT AHAT AHAT LHC LHT IHAT IHT DAT LHE IHT LH LHT LA Let IHT LAT LH LI AHI AHT LHA LMT IHT IHT LHT AHT IHT LA LHT LHA LHT LHT LHT LAT LHT LHT LHA LHT LHT IHT LHT LT IH LHT LHT LHT LHT 4HY LHT LAT IT LHT AHI MAT LHT LHT LHI AHT LHT LHT LT IHT LT LHT LIH LHAT SHAG AAG LHE PHAT LING IHT JYT IHT LIN LMT LIHT LHT LMT IHY AA JHT AE LAr LHE LHT LHI LHT LAA LHA AHY JHA LNG IHT LHA IHHT IHT JHA LHA JHT LMG LAG ANAT IHT HE ANT LAY At LHT LHT AHAT et LHT UMG LT DER LHT LM JHT IHT LHT LHT LHT LHT IHT LHA LHA JHT LAH IAY AH AAT LHA II LHT IA LHA HAT IHA LIM PHT LHT Lt LH reasons why metarost is fun To mention a few you can enhance the layout with graphic ornaments you can tune your graphics at runtime and simple high quality graphics can be very effec
95. abstract look into idealize isolate discriminate distinguish pigeonhole pick over sort integrate blend inspect filten lump skip hunk average approximate cluster aggregate outline summarize itemiz i into flip through browse glance into leaf through skim refine synopsize winnow the wheat from the chaff andi separate the sheep You can ask for the number of components with length A component can be a stroked or filled path or a text resulting from an infont operation If the last path is a clip path or when the whole picture has an forced boundingbox the picture is treated as a whole We will demonstrate this later You may wonder if this within loop construct has any real application and as you can expect it has In section 13 4 a macro is defined that draws a color circle If you want the inverted alternative you can pass the inverted color specification but wouldn t it be more convenient if there was an operator that did this for you automatically Unfortunately there isn t one so we have to define one ourselve a macro Preliminary Version November 11 2001 These circles were dra
96. ackground component by using a different anchor point setuplayer BackLayer position yes setlayer BackLayer x 1icm y 19cm location b1 externalfigure somecow pdf width 5cm setlayer BackLayer x 12cm y 20cm location br externalfigure somecow pdf width 5cm setlayer BackLayer x 8cm y 17cm location t1 externalfigure somecow pdf width 3cm setlayer BackLayer x 9cm y 18cm location tr externalfigure somecow pdf width 4cm Preliminary Version November 11 2001 Positional graphics One of the reasons for developing the layer mechanism was that we needed to slightly change the position of figures in the final stage of typesetting The previous pages demonstrate how one can position anything anywhere on the page but in the case of figures the position may depend on where the text ends up on the page Normally when you manipulate a document this way you are in the final stage of typesetting You may qualify this as desk top publishing without actually using a desktop Figure 5 1 setlayer BackLayer position yes location c voffset 5cm width 50pt height 50pt startMPcode externalfigure somecow pdf xscaled 100bp yscaled 100bp rotated 25 l stopMPcode The previous example also demonstrated the use of meTaPosT for rotating the picture The MPfi
97. ainer The StartPage StopPage pair takes care of proper placement of the whole graphic startuseMPgraphic page includeMPgraphic rightsuperbutton StartPage path p q pickup pencircle scaled 3pt p Field Text Text enlarged 36pt superellipsed 90 fill Page withcolor MPcolor yellow fill p withcolor MPcolor white draw p withcolor MPcolor red p Field Text Text enlarged 48pt superellipsed 90 def right_menu_button expr nn rr pp xx yy ww hh dd if pp gt 0 and rr gt 0 q rightsuperbutton p xx yy RightEdgeWidth hh Preliminary Version November 11 2001 Defining styles _ Douglas R Hofstadter E Knuth Hermann Zapf N N 5 oN 5 lt c YU oN Co as N G as A Simple Style Demo Figure 11 1 The auxiliary lines used to calculate the button shapes Preliminary Version November 11 2001 fill q withcolor MPcolor white draw q withcolor if rr 2 MPcolor gray else MPcolorfred fi fi 3 enddef MPmenubuttons right StopPage stopuseMPgraphic The TeX macro MPmenubuttons expands into a list of in this case four calls to the MeTAPOST macro right_menu_button This list is generated by CONTEXT when it generates the menu Because the page background is applied last this list is available at that moment expr nn rr pp xx yy ww hh dd This rather lon
98. air WA path enlarged numeric path enlarged pair path llenlarged numeric QO path lrenlarged numeric Q Preliminary Version November 11 2001 fullcircle shifted 2 25 metapost primitive fullcircle enlarged 25 metafun macro fullcircle enlarged 1 25 metafun macro fullcircle llenlarged 25 metafun macro fullcircle lrenlarged 25 metafun macro PEE Reference ie El path urenlarged numeric D AS path ulenlarged numeric O path llenlarged pair path lrenlarged pair y path urenlarged pair fullcircle urenlarged 25 metafun macro fullcircle ulenlarged 25 metafun macro fullcircle llenlarged 1 25 metafun macro fullcircle lrenlarged 1 25 metafun macro fullcircle urenlarged 1 25 metafun macro Preliminary Version November 11 2001 path ulenlarged pair 6 path llmoved numeric path Irmoved numeric le path urmoved numeric Q path ulmoved numeric O Preliminary Version November 11 2001 fullcircle ulenlarged 1 25 metafun macro fullcircle llmoved 25 metafun macro fullcircle lrmoved 25 metafun macro fullcircle urmoved 25 metafun macro fullcircle ulmoved 25 metafun macro path Ilmoved pair path lrmoved pair path urmoved pair path ulmoved pair A path slanted numeric fullcircle llmoved 1 25
99. are scaled 2cm fill p shifted 3cm 0 pickup pencircle scaled 5cm fill p shifted 6cm 0 fill p shifted 9cm 0 withpen pencircle scaled 5cm Units Like TeX METAPOST supports multiple units of length In Tgx these units are hard coded and handled by the parser where the internal unit of length is the scaled point sp something on the nanometer range Because MeTAPOST is focused on POSTSCRIPT output its internal unit is the big point bp All other units are derived from this unit and available as numeric instead of hard coded Preliminary Version November 11 2001 Afew mm cm 2 83464 pt 0 99626 dd 1 06601 bp 1 28 34645 pc 11 95517 cc 12 79213 in 72 Careful reading reveals that only the bp and in are fixed while the rest of the dimensions are scalar multiples of bp Since we are dealing with graphics the most commonly used dimensions are pt bp mm cm and in Pie V W pt bp 25 4mm 2 54cem lin mda dh dh dh d The text in the center of the leftmost graphic is typeset by meTaPosT as a label fill fullsquare scaled 72 27pt withcolor 625yellow fill fullcircle scaled 72 27pt withcolor white label 72 27pt center currentpicture In metarost the following lines are identical draw fullcircle scaled 100 draw fullcircle scaled 100bp You might be tempted to omit the unit but this can be confusing particularly if you
100. arrow expr p t l pointarrow p t 1 1l enddef def centerarrow expr p t l pointarrow p t l 0 enddef We can now apply this macro as follows Preliminary Version November 11 2001 Welcome to MET Watch how we can pass a point point 5 of p as well asa fraction 4 The following graphic demonstrates a few more alternatives The arrows are drawn using the previously defined macros Watch the positive and negative offsets in call to pointarrow drawarrow leftarrow p point 1 of p 2cm withcolor red drawarrow centerarrow p point 2 of p 2cm withcolor blue 3 drawarrow rightarrow p point 3 of p 2cm withcolor green 3 drawarrow pointarrow p 60 4cm 5cm withcolor yellow drawarrow pointarrow p 75 3cm 5cm withcolor cyan drawarrow centerarrow p 90 3cm withcolor magenta Preliminary Version November 11 2001 24 A few more details In this chapter we will see how to define a metarost graphic and how to include it in a document Since the exact dimensions of graphics play an important role in the placement of a graphic we will explore the way a bounding box is constructed We will also pay attention to the usage of units and the side effects of scaling and shifting since they can contradict our expectations in unexpected ways Furthermore we will explore a few obscure areas Making graphics We will use Metapo
101. aw tracing command tracingall loggingall tracingnone if test if boolean expression balanced tokens alternatives fi alternatives empty else balanced tokens elseif boolean expression balanced tokens alternatives loop loop header loop text endfor loop header for symbolic token progression for symbolic token for list for symbolic token within picture expression forsuffixes symbolic token suffix list forever progression numeric expression upto numeric expression numeric expression downto numeric expression numeric expression step numeric expression until numeric expression for list expression for list expression Preliminary Version November 11 2001 suffix list suffix suffix list suffix B 2 List of things Maybe I ll add an extended version of the commands and variables here Preliminary Version November 11 2001 This document This document is produced in CONTgXT and can serve as an example of how to integrate METAPOST graphics into 1px In this appendix we will discuss some details of producing this document We did not use any special tricks so most of the examples you have seen were coded just as shown We use buffers to ensure that the code used to produce the accompanying g
102. aw 1 shifted loc withcolor 625yellow draw loc withcolor 625red s enddef The macro xyscaled is part of MetaFun and scales in two directions at once The METAPOST primitive intersectiontimes returns a pair of time values of the point where two paths intersect The first part of the pair concerns the first path We are now a small step from the exact placement If we change the last line of the macro into s shifted 1 we get the displacement we want Although the final look and feel is also determined by the text itself the average result is quite acceptable Because we also want to pass pictures and add a bit of offset too the final implementation is slightly more complicated The picture is handled with an additional condition and the offset with the MetaFun macro enlarged numeric freelabeloffset freelabeloffset 3pt vardef thefreelabel expr str loc ori save S p q l picture s path p q pair l interim labeloffset freelabeloffset s if string str thelabel str loc else str shifted center str shifted loc fi setbounds s to boundingbox s enlarged freelabeloffset p fullcircle scaled 2 length loc ori shifted ori q freesquare xyscaled urcorner s llcorner s l point xpart p intersectiontimes ori loc of q Acta applications Preliminary Version November 11 2001 13 3 setbounds s to boundingbox s enlarg
103. ber 11 2001 defineoverlay left page useMPgraphic left page defineoverlay right page useMPgraphic right page setupbackgrounds leftpage background left page setupbackgrounds rightpage background right page Now we only have to split the previously defined graphic into two parts In order to force consistency we isolate the code that fills and draws The left page code looks like startreusableMPgraphic left page StartPage path Main Main llcorner Field OuterMargin Text lrcorner Field Text Text urcorner Field Text Text ulcorner Field QuterMargin Text cycle includeMPgraphic draw page StopPage stopreusableMPgraphic The right page text looks similar startreusableMPgraphic right page StartPage path Main Main lrcorner Field OuterMargin Text llcorner Field Text Text ulcorner Field Text Text urcorner Field QuterMargin Text cycle includeMPgraphic draw page StopPage stopreusableMPgraphic Watch how we used a reusable graphic first and a simple usable one next Actually the next graphic is not a stand alone graphic startuseMPgraphic draw page Main Main enlarged 6pt pickup pencircle scaled 2pt fill Page withcolor 625white fill Main withcolor 850white draw Main withcolor 625red stopuseMPgraphic We have seen some predefined paths and locations Apart from the Page path they take two arguments that sp
104. ber not followed by numberi syntax Preliminary Version November 11 2001 scalar multiplication op gt number or fractioni not followed by add op number transformer rotated numeric primary scaled numeric primary shifted pair primary slanted numeric primary transformed transform primary xscaled numeric primary yscaled numeric primary zscaled pair primary xyscaled numeric primary reflectedabout pair expression pair expressioni rotatedaround pair expression numeric expression enlarged numeric or pair primary randomized numeric or pair primary sqeezed numeric or pair primary superellipsed numeric primary xsized numeric primary ysized numeric primary xysized pair primary randomshifted numeric or pair primary numeric or pair primary numeric primary pair primary nullary op false normaldeviate nullpicture pencircle true whatever unary op type abs angle arclength ASCII bbox bluepart bot bounded boundingbox ceiling center char clipped cosd cycle dashpart decimal dir filled floor fontpart fontsize greenpart hex innerboundingbox inverse known length 1ft llcorner lrcorner makepath makepen mexp mlog not oct odd outerboundingbox pathpart penpart redpart reverse round rt
105. better but still it renders the text unreadable Like xysized the macro enlarged is not part of standard metarost but comes with CONTEXT startuniqueMPgraphic copyright picture p p btex COPYRIGHT etex rotated 90 setbounds p to boundingbox p enlarged ipt draw p withcolor 8white currentpicture currentpicture xysized overlaywidth overlayheight stopuniqueMPgraphic def ineoverlay copyright uniqueMPgraphic copyright Again we put this graphic in the background By using a unique graphic we make sure that it s rendered only once and reused when possible setupbackgrounds text rightmargin background copyright In both cases we slightly scale down the graphic We do so because otherwise a small portion of the text if clipped off This is unrelated to TeX or MeTAPOST but a characteristic of the font Compare the following Palatino Computer Modern and Times o s the Palatino is the body font of this text definefont fP Palatino at 5cm definefont fC ComputerModern at 5cm definefont fT Times Roman at 5cm showboxes hbox hbox fP o hbox fC o hbox fT o The dashed line is the baseline Watch how the bounding boxes differ and sometimes cross the shape So in order not to loose part of a glyph when clipping you need to add a bit space Figure 6 1 shows the two backgrounds in action age backgrounds Prelim
106. by is born may it enjoy MetaFun If we can use framed we can also use backgrounds def processword 1 noindent framed frame off background lions 1 We can add a supperellipsed frame using the following definition startuniqueMPgraphic lions a path p p fullsquare xyscaled overlaywidth overlayheight superellipsed 85 pickup pencircle scaled ipt fill p withcolor 850white draw p withcolor 625yellow stopuniqueMPgraphic def ineoverlay lions uniqueMPgraphicf lions a a Gen ave startuseMPgraphic lions b path p p fullsquare xyscaled overlaywidth overlayheight randomized 5pt pickup pencircle scaled ipt fill p withcolor 850white draw p withcolor 625yellow stopuseMPgraphic def ineoverlay lions uniqueMPgraphicf lions b startuniqueMPgraphic lions c path p p fullsquare xyscaled overlaywidth overlayheight squeezed 2pt pickup pencircle scaled ipt fill p withcolor 850white draw p withcolor 625yellow stopuniqueMPgraphic def ineoverlay lions uniqueMPgraphicflions c Ehhan ing the layout Preliminary Version November 11 2001 4 6 Jag yod Fa bul K Fioness These paragraphs were typeset with the following settings setupalign broad right veryraggedright setupalign broad middle
107. c 1 n 1 1 5LineHeight n 0 p origin shifted 1 0 origin shifted PaperWidth 1 0 Preliminary Version November 11 2001 Enhancingithe lay Figure 4 4 Penalty lines for i PaperHeight 1 step l until 1 ni nt i1 drawoptions withcolor 85white fill p shifted 0 i StrutHeight reverse p shifted 0 i StrutDepth cycle drawoptions withpen pencircle scaled 25pt withcolor 5white draw p shifted 0 i draw p shifted 0 itExHeight draw textext origin How are those penalty lines called in english I may not steal candies amp decimal n shifted 1 i endfor StopPage stopMPpage This code demonstrates the use of LineHeight ExHeight StrutHeight and StrutDepth We set the interline spacing to 1 5 so that we get a bit more loose layout The variables mentioned are set each time a graphic is processed and thereby match the current font settings Preliminary Version November 11 2001 3d Positional graphics In this chapter we will explore stepwise some of the more advanced but also conceptually more difficult graphic capabilities of CONTXT It took quite some experiments to find the right way to support these kind of graphics and you
108. cases startuseMPgraphic text draw drawarrow p withpen pencircle scaled ipt withcolor red stopuseMPgraphic Now we use CONTsXT s includeMPgraphic command to build our graphic from the previously defined components startuseMPgraphic text includeMPgraphic text path includeMPgraphic text draw stopuseMPgraphic When called with useMPgraphic text we get For the moment we start the path at x 0 y gt 0 but later using more complicated macros we will see that we can use arbitrary paths We are going to split the path in two and will use the point that make up the bounding box as calcutated by metarosrt The next graphic shows one of these points the lower left corner available as point llcorner p startuseMPgraphic text draw draw p withpen pencircle scaled 3pt withcolor red draw boundingbox p withpen pencircle scaled ipt draw llcorner p withpen pencircle scaled 5pt stopuseMPgraphic Preliminary Version November 11 2001 _liypesetting jn The five points that MeTAPosT can report for each path or picture are llcorner lower left corner lrcorner lower right corner urcorner upper right corner ulcorner upper left corner center intersection of the diagonals If we want to typeset text inside this circle we need to know where a line starts and ends Given that lines are horizontal and straight we therefore need to calculate the intersectio
109. ce between the point given and the content of the label When we set the offset to zero we get the following output This kind of positioning works well as long as we know where we want the label to be placed However when we place labels automatically for instance in a macro we have to apply a few clever tricks There are fore sure many ways to accomplish this goal but here we will follow the mathless method The previous graphic visualizes the bounding box of the labels This bounding box is rather tight and therefore the placement of labels will always be suboptimal Compare the alignment of the left and rightmost labels The btex etex method is better since then we can add struts like btex strut right etex to force labels with uniform depths and heights The next graphic demonstrates that this looks better indeed Spending some time on such details pays back in better graphics lower left Now what happens when we want to place labels in other positions In the worst case given that we place the labels manually we end up in vague arguments in favour for one or the other placement Preliminary Version November 11 2001 Me Although any automatic mechanism will be sub optimal we can give it a try to write a macro that deals with arbitrary locations This macro will accept three arguments and returns a pictur
110. ch carefully If instead of an offset we pass a path metarost is able to calculate the right dimensions and offsets This is needed since we need these later on startuseMPgraphic test 4 numeric w h o def shape 0 0 w 0 0 amp w 0 0 75w o 5h w 20 h 0 amp w 20 h 0 0 h o0 cycle enddef w h 6cm o 6pt path p p shape w h 6cm o Opt path q q shape build_parshape p q 6pt 6pt baselinedistance strutheight strutdepth strutheight draw q withpen pencircle scaled ipt stopuseMPgraphic Since we also want these graphics as backgrounds we define them as overlays If you don t want to show the graphic you may omit this step defineoverlay test 1 useMPgraphic test 1 defineoverlay test 2 useMPgraphic test 2 defineoverlay test 3 useMPgraphic test 3 defineoverlay test 4 useMPgraphic test 4 As text we use a quote from Douglas R Hofstadter s book Metamagical Themas Questing for the Essence of Mind and Pattern Watch how we pass a list of shapes startshapetext test 1 test 2 test 3 test 4 input douglas Douglas R Hofstadter stopshapetext Finally we combine text and shapes Since we also want a background we use framed The macros parwidth and parheight are automatically set to the current shape dimensions The normal result is shown in figure 9 2 startbuffer setupframed offset overlay align normal frame o
111. ciate the nasty details if you have written a few simple ones yourself This chapter will give you a start Many of the concepts introduced here will be discussed in more detail in later chapters So you may consider this chapter to be an appetizer for the following chapters If you want to get started quickly you can safely skip this chapter now Paths Paths are the building blocks of metarost graphics In its simplest form a path is a single point e10 15cm Such a point is identified by two numbers which represent the horizontal and vertical position often referred to as x and y or x y Because there are two numbers involved in MeTAPosT this point is called a pair Its related datatype is therefore pair The following statements assigns the point we showed previously to a pair variable pair somepoint somepoint 1cm 1 5cm A pair can be used to identify a point in the two dimensional coordinate space but it can also be used to denote a vector being a direction or displacement For instance 0 1 means go up Looking through math glasses you may consider them vectors and if you know how to deal with them MeTtarost may be your friend since it knows how to manipulate them You can connect points and the result is called a path A path is a straight or bent line and is not necessarily a smooth curve An example of a simple rectangular path is In the next examples we use the debugging features discussed in cha
112. color 625yellow Another case when top and friends cannot be applied in a general way is the following Consider the three paths path p q r Preliminary Version November 11 2001 p fullcircle scaled 3cm q p shifted 7cm Ocm r center p center q We draw these paths with draw p withpen pencircle scaled 10pt withcolor 625red draw q withpen pencircle scaled 10pt withcolor 625yellow draw r withpen pencircle scaled 20pt withcolor 625white The line is drawn from center to center and since the line has a non zero width and a round line cap it extends beyond this point If we want to line to stop at the circular paths we can cut off the pieces that extend beyond those paths pair pr qr pr p intersectionpoint r qr q intersectionpoint r r r cutbefore pr cutafter qr This time we get Due to the thicker line width used when drawing the straight line part of that line is still visible inside the circles So we need to clip off a bit more r r cutbefore point 5pt on r r r cutafter point 5pt on r The point on operation is a MetaFun macro that takes a dimension This problem was posted at the CONTEXT mailing list by Marc van Dongen Preliminary Version November 11 2001 29 In order to save you some typing MetaFun provides a macro cutends that does the same job r r cuten
113. color to gray we use the following formula This kind of conversion also takes place in black and white televisions G 30r 59g 11b Preliminary Version November 11 2001 E _ Preliminary Version November 11 2001 4 1 Enhancing the layout One of the most powerful and flexible commands of CONTgXT is framed We can use the back ground features of this command to invoke and position graphics that adapt themselves to the current situation Once understood overlays will become a natural part of the CONTEXT users toolkit Overlays Many CONTEXT commands support overlays The term overlay is a bit confusing since such an overlay in most cases will lay under the text However because there can be many layers on top of each other the term suits its purpose When we want to put a MeTAPosT graphic under some text we go through a three step process First we define the graphic itself startuniqueMPgraphic demo circle path p p fullcircle xscaled overlaywidth yscaled overlayheight fill p withcolor 85white draw p withpen pencircle scaled 2pt withcolor 625red stopuniqueMPgraphic This graphic will adapt itself to the width and height of the overlay Both overlaywidth and overlayheight are macros that return a dimension followed by a space The next step is to register this graphic as an overlay defineoverlay demo circle uniqueMPgraphic demo circle We can now use this
114. commonly used scratch variable we don t save its value Watch how we use u as the loop step In spite of what you eyes tell you this graphic only has two explicit color directives both being 50 black In the next example we will use some real colors Figure 13 3 The simultaneous contrast effect In figure 13 3 the small squares in the center of each colored pair of big squares have the same shade but the way we perceive them is influenced by their surroundings Both set of squares are defined using usable graphics The top squares are defined as startuseMPgraphic second includeMPgraphic first fill fullsquare scaled size withcolor topshade fill fullsquare scaled delta withcolor centershade stopuseMPgraphic and the bottom squares are coded as startuseMPgraphic third includeMPgraphic first fill fullsquare scaled size withcolor bottomshade fill fullsquare scaled delta withcolor centershade stopuseMPgraphic Because both graphics share code we have defined that code as a separate graphic that we include The only point of interest in this definition is the fact that we let MeTAaPosT interpolate between the two colors 5 startuseMPgraphic first numeric size delta size 2 5cm delta size 3 color mainshade topshade bottomshade centershade mainshade MPcolor funcolor topshade 9mainshade bottomshade 5mainshade Preliminary Version N
115. construct very advanced boolean expressions If you have a bit of programming experience you will appreciate the extensive support of condi tionals in METAPOST Loops Yet another programming concept present in METAPOST is the loop statement the familiar for loop of all programming languages GE APOST Preliminary Version November 11 2001 for i 0 step 2 until 20 draw 0 i endfor As explained convincingly in Niklaus Wirth s book on algorithms and datastructures the for loop is the natural companion to an array Given an array of length n you can construct a path out of the points that make up the array draw for i 0 step 1 until n 1 p i endfor pln If the step increment is not explicitly stated it has an assumed value of 1 We can shorten the previous loop construct as follows draw for i 0 upto n 1 p i endfor p n After seeing if in action the following for loop will be no surprise draw origin for i 0 step 10 until 100 down i 0 endfor This gives the zig zag curve ab abababalabatateal You can use a loop to iterate over a list of objects A simple 3 step iteration is for i p q r fill i withcolor 8white draw i withcolor red endfor Using for in this manner can sometimes save a bit of typing The list can contain any expression and they may be of different types In the previous example the i is an independe
116. cro Preliminary Version November 11 2001 A few i 13 6 13 7 startuseMPgraphic first numeric height width radius gap gap Im height 2 5cm width height 2 radius height 2 5 color mainshade leftshade rightshade centershade mainshade MPcolor funcolor leftshade 9mainshade rightshade 5mainshade centershade 5 leftshade rightshade fill unitsquare xyscaled width height withcolor leftshade fill unitsquare xyscaled width height withcolor rightshade draw fullcircle scaled radius shifted 0 height 2 withpen pencircle scaled radius 2 withcolor centershade stopuseMPgraphic The graphics of the second row extend those of the first by drawing a white line through the middle In this example setting the linecap is not really needed because rounded top and bottoms in white are invisible and the part that extends beyond the points does not count in calculating the bounding box startuseMPgraphic second includeMPgraphic first interim linecap butt pickup pencircle scaled gap draw 0 0 0O height withcolor white stopuseMPgraphic The third row graphics again extend the first graphic First we copy the picture constructed so far Wath the double assignment Next we clip the pictures in half and shift the right half down over the width of the circle startuseMPgraphic third includeMPgraphic first p
117. d and uses the frame commands that are built in CONTEXT Instead of letting Tex draw the frame we use METAPOST which we also use for handling the title The graphic is defined as follows startuseMPgraphic FunnyFrame picture p numeric w h o p textext rt MPstring FunnyFrame w OverlayWidth h OverlayHeight o BodyFontSize p p shifted 20 h ypart center p draw p drawoptions withpen pencircle scaled 1pt withcolor 625red draw 20 h 0 h 0 0 w 0 w h xpart urcorner p h draw boundingbox p withcolor 625red setbounds currentpicture to unitsquare xyscaled w h stopuseMPgraphic The macros that use this graphic combine some techniques of defining macros using predefined CONTEXT classes and passing information to graphics def ineoverlay FunnyFrame useMPgraphic FunnyFrame def ineframedtext FunnyText frame off background FunnyFrame def StartFrame startFunnyText def StopFrame stopFunnyText def FrameTitle 1 setMPtext FunnyFrame hbox spread 1tem hss strut 1 hss setMPtext FunnyFrame There is a little bit of low level Tex code involved like an horizontal box hbox that stretches one em space beyond its natural size spread 1em with a centered text to times hss We could also have taken care of the offset in the graphic itself Bhhan ing the Lavout_ Preliminary Version November 11 2001 In t
118. d path fullcircle This path is constructed using 8 points As you can see these points are not distributed equally along the path In the following graphic the second and third point of the curve are colored red and point 2 5 is colored yellow Point 0 is marked in black This point is positioned halfway point 2 and 3 Preliminary Version November 11 2001 Welcome Wero It is clear that unless you know exactly how the path is constructed other methods should be available A specific point on a path is accessed by point of but the next example demonstrates two more alternatives path p p fullcircle scaled 3cm xscaled 2 pickup pencircle scaled 5mm draw p withcolor 625white draw point 3 of p withcolor 625red draw point 6 along p withcolor 625yellow draw point 3cm on P So in addition to on to specify a point by number in metaPosT terminology called time we have along to specify a point as fraction of the path and on to specify the position in a dimension The on and along operators are macros and can be defined as primarydef len on pat arctime len of pat of pat enddef primarydef pct along pat arctime pct arclength pat of pat of pat enddef These macros introduce two new primitives arctime and arclength While arctime returns a number denoting the time of the point on the path arclength returns a dimension When mathematicians draw parametric cur
119. d rotatedaround is not a primitive but a macro defined in terms of shifts and rotations Another transformation macro is mirroring or in METAPOST terminology reflectedabout Preliminary Version November 11 2001 The reflection axis is specified by a pair of points For example in the graphic above we used the following command to reflect the square about a line through the given points p reflectedabout 2 4cm 5 2 4cm 3cm The line about which the path is mirrored Mirroring does not have to be parallel to an axis p reflectedabout 2 4cm 5 2 6cm 3cm The rectangle now becomes The table also mentioned zscaled A zscaled specification takes a vector as argument p zscaled 2 5 The result looks like a combination of scaling and rotation and conforms to the formula in the previous table Transformations can be defined in terms of a transform matrix Such a matrix is stored in a transform variable For example transform t t identity scaled 2cm shifted 4cm icm We use the associated keyword transformed to apply this matrix to a path or picture Preliminary Version November 11 2001 Le p transformed t In this example we ve taken the identity matrix as starting point but you can use any predefined transformation The identity matrix is defined in such a way that it scales by a factor of one in both dir
120. dd Figure 6 2 A background with combined areas The location of an area is available in Location so the previous definition is the same as StartPage fill Area Text Text shifted Location Text Text withcolor 85white StopPage The following definition fills and draws the margin and text areas startuseMPgraphic page StartPage pickup pencircle scaled 2pt fill Page withcolor 625white fill Field OuterMargin Text withcolor 850white fill Field Text Text withcolor 850white draw Field OuterMargin Text withcolor 625red draw Field Text Text withcolor 625red StopPage stopuseMPgraphic This background is assigned to the page layer by saying def ineoverlay page useMPgraphic page setupbackgrounds page background page As you can see in figure 6 3 the text is typeset rather tightly between the left and right margins Preliminary Version November 11 2001 rhus 1 came to the conclusion that the designer ofa new system must not only be the implemented and first large scale user the designer should also write the first user manual The separation of any of these four components would have hurt TX significantly If I had be successful if it is too strongly inf design is complet coll obit rea GA Segoe se people wih art eriments tain important issues raised by The Concept of a Meta Font ertain important issues raised by The Concept ofa Meta Font even
121. dimensions of the resulting graphic Putting something in such a ruled box is often a quick way to test spacing Figure 8 4 A quarter circle applied to a cows head Although a clip path definition can contain any METAPOST command even graphics it must contain at least one clipping path The first one encountered in the resulting graphic is used In the example we used a path that is built out of three subpaths 0 h w h down left 0 0 cycle We start in the top left corner and draw a straight line Next we draw a curve to the origin Directives like down and right force the curve in a certain direction With cycle we close the path Because we use this path as a clipping path we use clip instead of draw or fill Clipping as such is not limited to graphics Take for instance the text buffer startbuffer sample framed align middle width 4cm background screen frame off A METAPOST clip is not the same as a video clip although we can use METAPOST to produce a video clip stopbuffer We can call up such a buffer as if it were an external figure Figure 8 5 shows the result This time we use a different clip path startMPclip text clip clip currentpicture to fullcircle shifted 5 5 xscaled width yscaled height stopMPclip To load a buffer we have to specify its name and type as in placefigure here fig clipped text 1 A clipped buffer text clip nx 1 ny 1 mp text clip
122. directly after the paragraph is typeset bu in the former case a second pass is needed Because such graphics are not bound to one paragraph the multi pass option suits better because it gives us more control the more we know about he Preliminary Version November 11 2001 E Positional graphies 32 final state the better we can act upon it Think of graphics on the first page that depend on the content of the last page or as in this paragraph backgrounds that depend on the typeset text It may be clear now that we need some positional information in order to provide features like the one shown here The fact that we will act upon in a second pass simplifies the task although it forces us to store the positional information in some place between runs This may look uncomfortable at first sight but it also enables us to store some additional information Now why is that needed A position has no dimensions it s just a place somewhere on the page In order to do tricks like shown here we also need to know the height and depth of lines at a specific point as well as the width of the box es we re dealing with In the encircled examples the dimensions of the box following the positional node are stored along with the position In the background example we store the current height and depth of the strut an imaginary character with maximum height and depth and no widt
123. ds More information about how to define tables can be found in the CONTEXT documentation and Up To Date documents vertical Table 7 2 A hashed table This table is defined as bTABLE frame off meta hash linecolor darkyellow offset 3ex bTR bTD background meta hash right right eTD bTD background meta hash left left eTD bTD background meta hash horizontal horizontal eTD bTD background meta hash vertical vertical eTD eTR eTABLE The graphics themselves are defined in a metaPost module In this particular example the macro some_hash is defined in the file mp back mp This macro takes six arguments some_hash width height linewidth linecolor angle gap Preliminary Version November 11 2001 5 symbols and buttons Because we don t want to define a specific overlay for each color and linewidth we will use variables in the definition of the unique graphic startuniqueMPgraphic meta hash linewidth linecolor angle gap if unknown context_back input mp back fi some_hash overlaywidth overlayheight MPvar linewidth MPvar linecolor MPvarfangle MPvar gap stopuniqueMPgraphic These variables are preset using setupMPvariables setupMPvariables meta hash gap 25 bodyfonts
124. ds 5pt This time we draw the path in a different order draw r withpen pencircle scaled 20pt withcolor 625white draw p withpen pencircle scaled 10pt withcolor 625red draw q withpen pencircle scaled 10pt withcolor 625yellow That way we hide the still remaining overlapping part of the line Directions Quite often you have to tell mMeTAPosT in what direction a line should be drawn A direction is specified as a vector There are four predefined vectors up down left right These are defined as follows pair up down left right up down 0 1 right left 1 0 We can use these predefined pairs as specification and in calculations dotlabel top up up 1cm dotlabel bot down down icm dotlabel 1lft left left 1cm dotlabel rt right right 1cm drawoptions withpen pencircle scaled 25mm withcolor 625 red drawarrow origin up 1cm drawarrow origin down icm drawarrow origin left icm drawarrow origin right 1cm Preliminary Version November 11 2001 up left right down This graphic can also be defined in a more efficient but probably more cryptic way The next definition demonstrates a few nice tricks Instead of looping over the four directions we loop over their names Inside the loop we convert these names or strings into a pair by scanning the string using scantokens The freedotlabel macr
125. e thefreelabel some string or picture a position the origin Our testcase is just a simple for loop that places a series of labels The freedotlabel macro is derived from thefreelabel pickup pencircle scaled 1mm path p p fullcircle scaled 3cm draw p withcolor 625yellow for i 0 step 5 until 7 5 freedotlabel text point i of p center p endfor As a first step we will simply place the labels without any correction We also visualize the bounding box vardef thefreelabel expr str loc ori save s picture s s thelabel str loc draw boundingbox s withpen pencircle scaled 5pt s enddef To make our lives more easy we also define a macro that draws the dot as well as a macro that draws the label vardef freedotlabel expr str loc ori drawdot loc draw thefreelabel str loc ori enddef vardef freelabel expr str loc ori draw thefreelabel str loc ori enddef Now we get Afet applications Preliminary Version November 11 2001 The original label macros permit us to align the label at positions 4 corners and 4 points halfway the sides It happens that circles are also composed of 8 points Because in most cases the label is to be positioned in the direction of the center of a curve and the point at hand it makes sense to take circles as the starting points for positioning the labels To help us in positioning we d
126. e endfor Preliminary Version November 11 2001 currentpicture currentpicture xsized size popcurrentpicture enddef Here we first fill the primary circles next we fill the secondary ones which also cover the center which is why finally we fill the center with white The circle uses the following colors colorcircle 4cm 2 5 8 8 2 5 5 8 2 The next graphic demonstrates how the subpaths look that build the shapes o We did not mention what the push and pop commands are responsible for Scaling the current picture is well defined as long as we deal with one graphic However if the current picture already has some content this content is also scaled The push and pop commands let us add content to the current picture as well as manipulating the picture as a whole without any side effects The final result is put on top of the already drawn content Preliminary Version November 11 2001 13 5 Fool yourself When doing a literature search on the human perception of black white edges I ran into several articles with graphics that I remember having seen before in books on psychology physiology and or ergonomics One of the articles was by Edward H Adelson of MIT and we will use a few of his example graphics in our exploration to what extend metarost can be of help in those disciplines Since such graphic normally occur in t
127. e overlay is typeset Because they are located in the background they don t cover the hpos G 4 text while the lines do The previous paragraph was typeset by saying As said the circles are on the background layer but the lines are not They are positioned on top of the text This is a direct result of the definition of the page background defineoverlay foregraphics positionoverlay foregraphics defineoverlay backgraphics positionoverlay backgraphics setupbackgrounds page background backgraphics foreground foregraphics Preliminary Version November 11 2001 E Positional graphics In this definition the predefined overlay foreground inserts the page data itself so the foreground graphics end up on top This example also demonstrates that you should be well aware of the way CONTEXT builds a page There are six main layers in some cases with sublayers The body text goes into the main text layer which unless forced otherwise lays on top 1 paper background 3 page backgrounds 5 logo areas 2 area backgrounds 4 text areas 6 main text The paper background is used for special sometimes internal purposes There are three page backgrounds left right and both The text areas logo areas and backgrounds are a 5 x 5 matrices leftedge leftmargin text rightmargin rightedge x top header text footer and bottom The main text is what you are reading now
128. e between the characters can be increased while extra rotates the whole string around the origin The radius variable can be used to increase the distance to the origin Without these variables the assignment would have been rot i pos i 5wid li len n 180 Placing the pictures is now rather easy startMPdrawing for i 1 upton draw picli shifted radius 0 rotatedaround origin rot i endfor stopMPdrawing The pictures are now positioned on half a circle properly kerned This was defined as follows The path variable tcycle is predefined to the top half of a fullcircle startMPdrawing def moved expr i shifted radius 0 rotatedaround origin rot i enddef pickup pencircle scaled 5pt for i 1 upton draw picli moved i draw boundingbox pic i moved i withcolor red draw origin center pic i moved i withcolor green endfor draw tcircle scaled 2r withcolor blue stopMPdrawing We will now package all of this into a nice efficient macro using of course the predefined scratch registers MPtoks and MPbox First we define the token processor Note again the expansion inhibition switch POST Preliminary Version November 11 2001 def processrotationtoken 17 appendtoks 1 to MPtoks setbox MPbox hbox RotFont the MPtoks startMPdrawing n n 1 len n the wd MPbox stopMPdrawing startMPdrawing
129. e it still is a numbered section header CONTsXT will write the header to the table of contents definehead Topic chapter setuphead Topic number no We will use a bold font in the table of contents We also force a complete list setuplist Topic criterium all style bold before after The TitlePage macro looks horrible because we want to keep the interface simple a list of small sentences separated by def TitlePage 1 startstandardmakeup switchtobodyfont big def vfill bfb let par bfd setupinterlinespace gray vskip 5cm 1 vskip 5cm is really needed stopstandardmakeup An presentation that uses this style may look like the one below You can choose among three alternatives useenvironment pre organic setupoutput pdftex setupMPvariables page alternative 1 starttext TitlePage A Few Nice Quotes A Simple Style Demo Hans Hagen August 2000 Topic Douglas R Hofstadter input douglas page Topic Donald E Knuth input knuth page Topic Edward R Tufte input tufte page Topic Hermann Zapf input zapf page stoptext We will not implement the two other alternative shapes squeezed and randomized Definingstyles Preliminary Version November 11 2001 page 1 page 2 page 3 page 4 page 5 page 1 page 2 page 3 page 4 page 5 We combine all alternatives into one page graphic The alternative is chose
130. e next assignments are therefore legal framed background color backgroundcolor red framed background screen backgroundscreen 8 framed background circle framed background color cow backgroundcolor red framed background color cow grid backgroundcolor red In the last three cases of course you have to define circle cow and grid as overlay These items are packed in a comma separated list which is to be surrounded by Preliminary Version November 11 2001 Enhancing the layout_ 4 4 Foregrounds The overlay system is actually a system of layers Sometimes we are confronted with a situation in which we want the text behind another layer This can be achieved by explicitly placing the foreground layer as in figure 4 3 pg ge frame on top layer frame on bottom layer Figure 4 3 Foreground material moved backwards The graphic layer is defined as follows startuniqueMPgraphic backfore draw fullcircle xscaled overlaywidth yscaled overlayheight withpen pencircle scaled 2pt withcolor 625yellow stopuniqueMPgraphic def ineoverlay backfore uniqueMPgraphic backfore The two framed texts have a slightly different definition The leftmost graphic is defined as framed background backfore backgroundoffset 4pt fone two three unknown The rightmost graphic is specified as framed background foregr
131. e the tension in the previous example by tension i and 2i we get the following graphic Preliminary Version November 11 2001 If we swap both values tension 2i and i we get We mentioned control points We will now draw a few extreme tensions and show the control points as MeTaPost calculates them sample zi tension 0 75 z2 z3 625red sample z1 tension 2 00 z2 z3 625yellow sample z z2 23 625white First we will show the symmetrical tensions The asymetrical tensions are less prominent We use the following values sample zi tension 75 and 10 Z2 23 625red sample zi tension 10 and 75 Z2 23 625yellow sample zl z2 23 625white Preliminary Version November 11 2001 You may try yourself what happens when we use meTAaPosT maximum value of infinity instead of 10 A third magic directive is curl The curl is attached to a point between like curl 2 Anything between curly braces is a direction specifier so instead of a curl you may specify a vector like 2 3 a pair of numbers as in 2 3 or a direction like dir 30 Because vectors and angles are straightforward we will focus a bit on curl zO Z z2 zO curl 1 z1 curl 1 z2 So a curl of 1 is the default When set to 1 the begin and or end points are approached Given the following definitions u
132. e these predefined directions in combination with directionpoint and cutafter The following command locates the first point on the path that has a tangent that points vertically upward and then feeds this point to the cutafter command z0 z1 cycle cutafter directionpoint up of z0 z1 cycle You are not limited to predefined direction vectors You can provide a pair denoting a direction In the next example we use the following cyclic path z0O z1 cycle Using is not mandatory but make the expression look less complicated Welcome fo Methe T Preliminary Version November 11 2001 1 4 z0 z1 cycle cutafter directionpoint 1 1 of z0 z1 cycle We will apply these commands in the next chapters but first we will finish our introduction in METAPOST We have seen how a path is constructed and what can be done with it Now it is time to demonstrate how such a path is turned into a graphic Drawing pictures Once a path is defined either directly or as a variable you can turn it into a picture You can draw a path like we did in the previous examples or you can fill it but only if it is closed Drawing is done by applying the draw command to a path as in draw Ocm icm 2cm 2cm 4cm Ocm cycle The rightmost graphic was made with fi11 fill Ocm 1icm 2cm 2cm 4cm 0cm cycle If you try to duplicate this drawing you will notice that you wi
133. eMPgraphic This graphic is typeset with useMPgraphic text Before we are going to use them we define some variables that specify the text We use a baseline distance of 8 points The part of the line above the baseline is 7 2 points while the maximum depth is 2 8 points These ratios are the ones we use in CONTEXT Because we don t want the text to touch the circle so we also define an offset too startuseMPgraphic text vars baselineskip 8pt strutheight 7 2 10 baselineskip strutdepth 2 8 10 baselineskip offset baselineskip 2 topskip strutheight stopuseMPgraphic We more of less achieve the offset by scaling the path In doing so we use the width and height which we call hsize and vsize thereby conforming to Tex naming scheme First we calculate both dimensions from the bounding box of the path Next we down scale the path to compensate for the offset When done we recalculate the dimensions startuseMPgraphic text move pair t b path q 1 r hsize xpart lrcorner p xpart llcorner vsize ypart urcorner p ypart lrcorner q p xscaled hsize 2offset hsize yscaled vsize 2offset vsize hsize xpart lrcorner q xpart llcorner vsize ypart urcorner q ypart lrcorner stopuseMPgraphic We adapt the text split code to use the reduced path instead of the original Preliminary Version November 11 2001
134. ecify their position on the layout grid path Area an area similar to a CONTEXT one pair Location the position of this area Preliminary Version November 11 2001 path Field 10 path Page the area positioned at theright place the page itself Some less used and more obscure variables are the following numeric Hstep numeric Vstep numeric Hsize numeric Vsize the horizontal distance to the previous area the horizontal distance to the previous area the width of an area the height of an area The array variables are accessed by using constants horizontal LeftEdge LeftEdgeSeparator LeftMargin LeftMarginSeparator Text RightMarginSeparator RightMargin RightEdgeSeparator RightEdge vertical Top TopSeparator Header HeaderSeparator Text FooterSeparator Footer BottomSeparator Bottom In addition to these there are Margin InnerMargin and OuterMargin which adapt themselves to the current odd or even page The same is true for Edge InnerEdge and OuterEdge although these will seldom be used since interactive documents are always single sided We started this chapter with spending a lot of code to simulate the page areas It will be clear now that in practice this is much easier using the mechanism described here In figure 6 6 we see all used areas Areas that are not used are not drawn which saves some testing This background was defined as s
135. ections and shifts over the zero vector Transform variables can save quite some typing and may help you to force consistency when many similar transformations are to be done Instead of changing the scaling shifting and other transformations you can then stick to just changing the one transform variable Constructing paths In most cases a path will have more points than the few shown here Take for instance a so called super ellipse i 5 ag 6 These graphics provide a lot of information In this picture the crosshair in the center is the origin and the dashed rectangle is the bounding box of the super ellipse The bounding box specifies the position of the graphic in relation to the origin as well as its width and height In the graphic on the right you can see the points that make up the closed path as well as the control points Each point has a number with the first point numbered zero Because the path is closed the first and last point coincide We ve used the commands and as path connecting directives In the next series of examples we will demonstrate a few more However before doing that we define a few points using the predefined z variables zO 0 5cm 1 5cm z1 2 5cm 2 5cm z2 6 5cm 0 5cm z3 2 5cm 1 5cm Here z1 is a short way of saying x1 x2 When a z variable is called the corresponding x and y variables are available too Later we will discuss Metarost capability to deal with expressio
136. ed freelabeloffset s shifted 1 enddef Watch how we temporarily enlarge the boundingbox of the typeset label text We will now test this macro on a slightly rotated circle using labels typeset by Tex The reverse is there purely for cosmetic reasons to suit the label texts funny macros defining Can t we i We can and on go on pickup pencircle scaled 1mm path p p reverse fullcircle rotated 25 scaled 3cm draw p withcolor 625yellow pair cp cp center p freedotlabel btex strut We can etex point 0 of p cp freedotlabel btex strut go on etex point 1 of p cp freedotlabel btex strut and on etex point 2 of p cp freedotlabel btex strut in etex point 3 of p cp freedotlabel btex strut defining etex point 4 of p cp freedotlabel btex strut funny etex point 5 of p cp freedotlabel btex strut macros etex point 6 of p cp freedotlabel btex strut Can t we etex point 7 of p cp Unfortunately we can run into problems due to rounding errors Therefore we use a less readable but more safe expression for calculating the intersection point Instead of using point loc as endpoint we use loc shifted over a very small distance into the direction loc from ori In the assignment to 1 we replace loc by 1 eps arclength ori loc unitvector loc ori Marking angles A convenient METAPOST macro is unitvector When we draw a line segment from the origin to the point retur
137. ed to unzip this zipped archive in the root of the texmf or texmf local tree After that you need to generate a format file by saying texexec make TEXExec Unfortunately Tex lacks a real command line interface This means that when we want to process a file under a different regime we need to adapt the document source For this reason we wrote the PERL script TEXEXEC This script is meant to make using Tpx a bit more user friendly and it will be no surprise that meTaPosT is supported as well Unless you have enabled runtime generation of graphics after each run you have to process the files mpgraph mp and mprun mp However when you use TgXEXEC the files will be processed automatically You can disable this feature with the switch nomprun This can be handy when debugging files since by default CON TXT will run Metarost in batch mode texexec nomprun myfile When you run TeXEXEC this way you must not forget to process the two files mentioned especially if their content has changed It is possible to run TeX and metarost in so called batch mode If you pass TsXEXEC the switch batch both programs will not send messages to the screen texexec batch myfile Stand alone graphics that have btex etex directives embedded can be processed by TEXEXEC by saying texexec mptex myfile mp To what extend this feature works well depends on the Xx implementation you use You can set up some METAPOST specific variables in the in
138. eed to be inspired we will demonstrate how metarost can be used to enhance your document with simple graphics In these examples we will try to be not too clever simply because we lack the experience to be that clever The real tricks can be found in the files that come with METAPOST Simple drawings In the words of John Hobby the creator of Metarost meTAPOST is particularly well suited for generating figures for technical documents where some aspects of a picture may be controlled by mathematical or geometrical constraints that are best expressed symbolically In other words METAPOST is not meant to take the place of a freehand drawing tool or even an interactive graphics editor An example of such a picture is the following one which is dedicated to David Arnold who asked me once how to draw a spring So imagine that we want to draw a schematic view of a system of four springs A rather natural way to define such a system is zi z3 2cm 0 z2 0 2cm 2cm 0 z4 0 2cm pickup pencircle scaled 1 5pt drawoptions withcolor 625red draw spring z1 z2 75cm 2 10 draw z1 1 5 z1 draw spring z2 z3 75cm 2 9 draw z2 1 1 22 draw spring z3 z4 75cm 2 8 draw z3 1 5 z3 draw spring z4 z1 75cm 2 7 draw z4 1 1 z4 Here the macro spring takes 5 arguments two points the width of the winding the length of the connecting pieces and the number of elements half w
139. efine a special square path freesquare This path is constructed out of 8 points that match the positions that are used to align labels path freesquare freesquare 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 cycle scaled 5 We now show this free path together with a circle using the following definitions drawpath fullcircle scaled 3cm drawpoints fullcircle scaled 3cm drawpointlabels fullcircle scaled 3cm currentpicture currentpicture shifted 5cm 0 drawpath freesquare scaled 3cm drawpoints freesquare scaled 3cm drawpointlabels freesquare scaled 3cm We use two drawing macros that are part of the suite of visual debugging macros 7 6 5 2 e e e 3 e 1 e e 8 e 0 e 4 4e 0e 8 J e J J 5 J 7 1 2 3 6 As you can see point 1 is the corner point that suits best for alignment when a label is put at point 1 of the circle We will now rewrite thefreelabel in such a way that the appropriate point of the associated freesquare is found vardef thefreelabel expr str loc ori save S p q 1 picture s path p q pair 1 s thelabel str loc p fullcircle scaled 2 length loc ori shifted ori Preliminary Version November 11 2001 A few applications q freesquare xyscaled urcorner s llcorner s 1 point xpart p intersectiontimes ori loc of q draw q shifted loc withpen pencircle scaled 5pt dr
140. erellipsed 95 fill b withcolor OverlayColor draw b withcolor OverlayLineColor b boundingbox p superellipsed 95 fill b withcolor OverlayColor draw b withcolor OverlayLineColor draw p withcolor black setbounds currentpicture to a stopuseMPgraphic Many people are just fascinated by their PC s tricks and think that a widely praised program called up on the screen will make everything automatic from now on We used the following command to pass the settings setupframedtexts FunnyText backgroundcolor lightgray framecolor darkred rulethickness 2pt offset bodyfontsize before blank big medium after blank big width textwidth In a real implementation we should also take care of some additional spacing before the text which is why we have added more space before than after the framed text We demonstrated that when defining graphics that are part of the layout you need to have access to information known to the typesetting engine Take figure 4 4 The line height needs to match the font and the two thin horizontal should match the x height We also need to position the baseline being the lowest one of a pair of lines in such a way that it suits the proportions of the line as specified by the strut A strut is an imaginary large character with no width setupbodyfont lbr hw startMPenvironment setupbodyfont lbr hw stopMPenvironment startMPpage StartPage path p numeri
141. eric expression of operator expression of primary of operator expression along primary of operator expression on primary unary op primary str suffix z suffix numeric atom expression expression scalar multiplication op primary secondary primary secondary primary binop primary secondary transformer tertiary secondary tertiary secondary binop secondary Preliminary Version November 11 2001 subexpression tertiary path expression path join path knot expression subexpression expression tertiary binop tertiary path subexpression direction specifier path subexpression path join cycle path knot tertiary path join Eee direction specifier basic path join direction specifier direction specifier empty curl numeric expression pair expression numeric expression numeric expression basic path join F a tension tension controls tension tension numeric primary tension atleast numeric primary tension numeric primary and numeric primary controls gt controls pair primary controls pair primaryiandhpair primary argument symbolic token number or fraction number number num
142. ersion November 11 2001 91 9 2 Typesetting in METAPOST You can add text to Metarost graphics and you can choose whether or not to have it typeset by TEX Let s take a closer look at how this in itself a rather tricky feature is implemented The process You can let METAPOST process text that is typeset by TX Such text is first embedded in the METAPOST file in the following way btex Some text to be typeset by TEX etex This returns a picture but only after metapost has made sure that Tex has converted it into something useful This process of conversion is slightly system dependent and even a bit obscure First MeTAPOST calls a program that filters the btex etex commands next it calls Tex by passing the output routine in order to make sure that each piece of text ends up on its own page and afterwards it again calls a program that converts the DVI pages into MeTAPOST pictures In CONTEXT when using WEB2C you can generate the graphics at run time This takes more time than processing the graphics afterwards but has the advantage that Tex knows immediately what graphic it is dealing with When enabled CONTEXT will call either mMeTAPOsT or when the graphic contains btex etex commands call TEXEXEC which in turn makes sure that the right auxiliary programs are executed TEXEXEC CONTEXT TEXEXEC METAPOST Figure 9 1 How Tpx and metarost work together Environments In case you want to pass code that is
143. ertical displacement the baseline distance the height and depth of the line and the height of the first line topskip in Tex terminology The height and depth of a line are often called strut height and depth with a strut being an invisible character with maximum dimensions startuseMPgraphic test 1 path p p fullcircle scaled 6cm build_parshape p 6pt 0 0 baselinedistance strutheight strutdepth strutheight draw p withpen pencircle scaled ipt stopuseMPgraphic The second shape is a diamond This is a rather useless shape unless the text suits the small lines at the top and bottom startuseMPgraphic test 2 path p p fullsquare rotated 45 scaled 5cm build_parshape p 6pt 0 0 baselinedistance strutheight strutdepth strutheight draw p withpen pencircle scaled ipt stopuseMPgraphic The third and fourth shape demonstrate that providing a suitable offset is not always trivial POST Preliminary Version November 11 2001 startuseMPgraphic test 3 numeric w h w h 6cm path p p 5w h 0 h 0 0 w 0 amp w 0 75w 5h w h amp w h cycle build_parshape p 6pt 0 0 baselinedistance strutheight strutdepth strutheight draw p withpen pencircle scaled ipt stopuseMPgraphic Contrary to the first third shapes here we use a different path for the calculations and the drawing Wat
144. es But a system cannot be successful the initial design is Sra anys sat ees viewpoints undertake their own Douglas R Hostadter Donald Knuth has spent the past several years working on a system allowing forthcoming books from the Edward R Tufte We thrive in information sie yc Reser E O a edit single out structure highlight group pair merge harmonize synthesize condense reduce boil down See aeai a cay list abstract sean look into gt flip through y skim refine Saioari ee E ian es anne eae goats Donald E Knuth Thus I came to the conclusion that the designer ofa new system must not only be the implementer and first large scale user the designer should also write the first user manual tne crores Weis Bt ann 11 had Once E as pele wt may diferent lertake their own experiments Douglas R Hostadter Donald Knuth has spent the past several years working on a system allowing his books from contrast his Werarowr system for ae wailable In his article The Concept of a Meta Font Knuth sets forth for the first time the underlying philosophy of wetaroor as well as some of its products Not only is the concept exiting and clearly charmingly written as well However despite my article there are some points in it that I feel might be important issues raised by The Concept of a Meta Font certain important issues raised by Tha Concepeofe a Meta Font even o
145. es the use of soft join z0 z1 z2 z3 zO z1 22 z3 Watch how soft join removes a point in the process of smoothing a connection The smoothness is accomplished by adapting the control points of the neighbouring points in the appropriate way z0 z1 softjoin z2 z3 Preliminary Version November 11 2001 Once a path is known you can cut off a slice of it We will demonstrate a few alternative ways of doing so but first we show one more time the path that we take as starting point zO z1 z2 z3 cycle This path is made up out of five points where the cycle duplicates the first point and connects the loose ends The first point has number zero We can use these points in the subpath command which takes two arguments specifying the range of points to cut of the path specified after the keyword of subpath 2 4 of z0 z1 z2 z3 cycle The new sub path is a new path with its own points that start numbering at zero The next graphic shows both the original and the subpath from point 1 upto 3 zO z1 z2 z3 cycle subpath 1 3 In spite of what you may think a point is not fixed This is why in Metarost a point along a path is officially called a time The next example demonstrates that we can specify any time on the path Preliminary Version November 11 2001 _Weleometo veranos z0 z1 22 23 cycle subpath 2 45 3 85
146. etafun variable urtriangle N ultriangle A flex pair pair pair 2 urtriangle metafun variable ultriangle metafun variable flex 0 0 1 1 1 0 metapost macro superellipse pair pair pair pairnumeric superellipse 1 5 5 1 0 5 5 0 75 Q path smoothed numeric pair path cornered numeric pair N metapost macro unitsquare scaled 1 5 smoothed 2 metafun macro lltriangle scaled 1 5 cornered 1 metafun macro Preliminary Version November 11 2001 D2 path superellipsed numeric __unitsquare scaled 1 5 superellipsed 75 path randomized numeric pair __unitsquare scaled 1 5 randomized 2 2 path squeezed numeric pair___unitsquare scaled 1 5 squeezed 2 1 L Transformations path scaled numeric Preliminary Version November 11 2001 unitsquare scaled 1 5 superellipsed 75 metafun macro unitsquare scaled 1 5 randomized 2 2 metafun macro unitsquare scaled 1 5 squeezed 2 1 metafun macro fullcircle scaled 25 metapost primitive path xscaled numeric path xyscaled numeric aN A path xyscaled pair fullcircle xscaled 25 metapost primitive fullcircle yscaled 25 metapost primitive fullcircle zscaled 2 25 metapost primitive fullcircle xyscaled 25 metapost primitive fullcircle xyscaled 2 25 metapost primitive Preliminary Version November 11 2001 path shifted p
147. etex etex zi1 z12 z13 z14 z21 Z22 Z23 zZ24 z31 Z32 Z33 z34 z41 z42 z43 z44 z0 z1 z2 z3 z4 Now we can end the condition that enables us to hide the labels and the macro Watch how we also end the figure fi Tf APOST 3 Preliminary Version November 11 2001 endfig enddef The definition of mark_rt_angle is copied from the mMetarPost manual and shows how compact a definition can be angle_radius 10pt def mark_rt_angle expr a b c draw 1 0 1 1 0 1 zscaled angle_radius unitvector a b shifted b enddef We are going to draw a lot of pictures so we define an extra macro This time we hard code some values The fractions i and j are responsible for the visual iteration process def do_draw_problem expr n i j draw_problem 4000 n 400pt 400pt 300pt 600pt i 300pt 600pt 550pt 800pt j 400pt 400pt 550pt 500pt enddef The beginfig and endfig macros package the code into a graphic capsule which is output to the resulting file We will spend some more words on that later Of course we could have used some loop here but defining an auxiliary macros probably takes more time than simply calling the drawing macro directly The results are shown on a separate page It does not need that much imagination to see the four sided problem converges
148. ext Some text and or graphics stoptext Yet another alternative is interface english output pdftex starttext Some text and or graphics stoptext Here the interface directive tells TEXEXEC that it should force the english user interface We will use color and since traditionally Tex is rather unaware of color this feature is turned off by default so if you want to see color you should type setupcolors state start starttext Some color blue text and or color green graphics stoptext Preliminary Version November 11 2001 Embedded graphies 3 2 As an alternative you can run TEXEXEC like texexec pdf color mytext In later chapters we will occasionally see some more CONTEXT commands show up If you want to know more about what CONTEXT can do for you we recommend the beginners manual and the reference manual as well as the manual that comes with TEXEXEC External graphics Since TeX has no graphic capabilities built in a graphic is referred to as an external figure A METAPOST graphic often has a number as suffix so embedding such a graphic is done by externalfigure graphic 123 width 4cm An alternative method is to separate the definition from the inclusion An example of a definition is useexternalfigure pentastar star 803 height 4cm useexternalfigure octostar star 804 pentastar Here the second definition inherits the characteristics
149. externalfigure sample type buffer width 4cm Preliminary Version November 11 2001 Spec METAPOST clip is 1 the same as a video clip although we can use METAPOST to aduce a video cl Figure 8 5 A clipped buffer text The next few lines demonstrate that we can combine techniques like backgrounds and clipping startuseMPgraphic clip outline draw fullcircle xscaled overlaywidth yscaled overlayheight withpen pencircle scaled 4mm withcolor 625red stopuseMPgraphic defineoverlay clip outline useMPgraphic clip outline placefigure here fig clipped text 2 A clipped buffer text framed background clip outline offset overlay frame off clip nx 1 ny 1 mp text clip externalfigure sample type buffer width 4cm We could have avoided the framed here by using the clip outline overlay as a background of the sample In that case the resulting linewidth would have been 2 5 mm instead of 5 mm since the clipping path goes through the center of the line METAPOST clip 1s the same as a video clip although we can use METAPOST to sduce a video cli Figure 8 6 A clipped buffer text In most cases the clip path will be a rather simple path and defining such a path every time you need it can be annoying Figure 8 7 shows a collection of predefined clipping paths These are available after loading the metarost clipping library u
150. ff Preliminary Version November 11 2001 186 width parwidth height parheight startcombination 2 2 framed background test 1 getshapetext test 1 framed background test 2 getshapetext test 2 framed background test 3 getshapetext test 3 framed background test 4 getshapetext test 4 stopcombination stopbuffer By using a buffer we keep placefigure readable placefigure here fig shapes A continuous text typeset in a non standard shape spread over four areas and right alligned getbuffer The traced alternative is shown in figure 9 3 This one is defined as placefigure here fig traced shapes A continuous text typeset in a non standard shape spread over four areas tracing on startMPinclusions boolean trace_parshape trace_parshape true stopMPinclusions getbuffer This mechanism is still somewhat experimental and will be optimized and extended with name spaces and more We can combine all those tricks although the input is somewhat fuzzy First we define a quote typeset in a circular paragraph shape startuseMPgraphic center build_parshape fullcircle scaled 8cm 0 0 0 baselinedistance strutheight strutdepth strutheight stopuseMPgraphic startshapetext center input douglas stopshapetext def ineoverlay center useMPgraphic center We will surround this tex
151. ffers This time we use the special command processMPbuffer since getbuffer will typeset the code fragment which is not what we want startlinecorrection blank processMPbuf fer red graphic stoplinecorrection The line correction macros take care of proper spacing around the graphic The blank directive tells CONTEXT to add more space before and after the graphic startlinecorrection blank processMPbuf fer yellow graphic stoplinecorrection Preliminary Version November 11 2001 Efnbeddeti graphics Dak Which mechanism you use multiple buffers or re usable graphics depends on your preferences Buffers are slower but don t take memory while re usable graphics are stored in memory which means that they are accessed faster Communicating color Now that color has moved to the desktop even simple documents have become more colorful so we need a way to consistently apply color to text as well as graphics In CONTEXT colors are called by name The next definitions demonstrate that we can define a color using different color models RGB or CMYK Depending on the configuration CONTEXT will convert one color system to the other RGB to CMYK or vice versa The full repertoire of color components that can be set is as follows definecolor color one r 1 g 2 b 3 definecolor color two c 4 m 5 y 6 k 7 definecolor color three s 8 The numbers are limited to
152. ffers you can even combine steps and replace them at will This is how we made the previous step by step examples We put each sub graphic in a buffer and then called the ones we wanted We now present a more general approach to typesetting along a given path This method is not only more robust and general it is also a more compact definition especially if we omit the tracing and testing code We use a familiar auxiliary definition The setstrut and strut commands ensure that the lines have the proper depth and height def processfollowingtoken 1 appendtoks 1 to MPtoks setbox MPbox hbox RotFont setstrut strut the MPtoks startMPdrawing n n 1 len n the wd MPbox stopMPdrawing startMPdrawing pic n btex RotFont setstrut strut 1 etex stopMPdrawing The definition of followtokens is as follows Keep in mind that RotFont is defined in the META Post environment You may notice that we have added a directive to include the Metarost graphic called followtokens Storing the path in a graphic container instead of using startMPdrawing is less sensitive for interference with other drawing processes def followtokens 17 vbox bgroup MPtoks emptytoks resetMPdrawing startMPdrawing includeMPgraphic followtokens picture pic numeric len n n 0 stopMPdrawing handletokens 1 with processfollowingtoken startMPdrawing numeric al pl at wid pos pair ap ad al arclength RotPath pl
153. from the first one These graphics can be summoned like placefigure A five point star drawn by METAPOST externalfigure pentastar Here the stars are defined as stand alone graphics in a file called star mp Such a file can look like def star expr size n pos for a 0 step 360 n until round 360 1 1 n draw origin size 2 0 rotatedaround origin a shifted pos endfor enddef beginfig 803 pickup pencircle scaled 2mm star 2cm 5 origin endfig beginfig 804 pickup pencircle scaled 1mm star icm 8 origin pickup pencircle scaled 2mm star 2cm 7 3cm 0 endfig end This star macro will produce graphics like embedded praphigs Preliminary Version November 11 2001 3 3 X X KK K Integrated graphics An integrated graphic is defined in the document source or in a style definition file The most primitive way of doing this is beginning with the definition of the graphic startMPgraphic fill fullcircle scaled 200pt withcolor 625white stopMPgraphic Next the graphic can be loaded using loadcurrentMPgraphic foptional setups Finally the graphic is placed in the document with placeMPgraphic The optional setups are passed on to the figure inclusion macro which in CONTEXT is the command externalfigure Since every definition replaces the previous one this method forces you to embed the defini tions in the running text I
154. g stopbuffer 3 Asiei applications Preliminary Version November 11 2001 The following code draws the intersection of line C D and line segment A B which can be shown to be the midpoint of segment A B startbuf fer g def draw_midpoint pair pointM pointM lineCD intersectionpoint lineAB draw_dot pointM label 11ft btex M etex pointM enddef stopbuffer startbuffer 5 start_everything draw_basics draw_circles draw_intersection draw_bisector stand_out draw_midpoint stop_everything stopbuffer As long as we place the graphics as individual insertions in our document everything is fine However if we wish to place them all at once or as we shall see later place them on top of one another in a fieldstack it makes sense to give them all the same bounding box We can do this by completing the start_everything and stop_everything commands startbuf fer a def start_everything Preliminary Version November 11 2001 A few path bb draw_basics draw_circles draw_intersection draw_bisector draw_midpoint bb boundingbox currentpicture currentpicture nullpicture enddef def stop_everything setbounds currentpicture to bb enddef stopbuffer In figure 13 5 we demonstrate the effect of this redefinition
155. g line immediate write1l8 echo It works If this fails you should consult the manual that comes with your system locate an expert or ask around on the CONTgXT mailing list Of course you can also decide to let TEXEXEC take care of processing the graphics afterwards This has the advantage of being faster but has the disadvantage that you need additional px runs If you generate the graphics at run time you should consider to turn on graphic slot recycling which means that you often end up with fewer intermediate files recycleMPslotstrue There are a few more low level switches and features but these go beyond the purpose of this manual Some of these features like the option to add tokens to everyMPgraphic are for experts only and fooling around with them can interfere with existing features One page graphics Although all of what is demonstrated in this document is done in CONTEXT some of the features discussed here can also be done in plain Tpx In the MetaFun distribution there is a file called plainfun tex which loads the appropriate CONTEXT modules Many low level macros are rather generic and can be used in plain Tex without problems However the big advantage of using CONTEXT is that graphics can be part of the text flow and that you can put them on layers If you don t want this and only want to make stand alone graphics you may still consider using CONTEXT for that purpose Preliminary Version November 11
156. g list of arguments represents the following variables number referred page current page x coordinate y coordinate width height and depth The last six variables originate in the positioning mechanism Because the variables are only available after a second Tpx pass we only draw a button shape when the test for the page numbers succeeds startuseMPgraphic rightsuperbutton vardef rightsuperbutton expr pat xpos ypos wid hei save p ptop pbot t b edge shift width height path p ptop pbot pair t b numeric edge shift width height edge xpos wid shift ypos hei p rightpath pat ptop infinity shift edge shift pbot infinity shift hei edge shift hei t p intersectionpoint ptop b p intersectionpoint pbot p subpath 0 xpart p intersectiontimes ptop of p p subpath xpart p intersectiontimes pbot length p of p p t point 1 of ptop amp point 1 of ptop point 1 of pbot amp point 1 of pbot b cycle enddef stopuseMPgraphic The calculation of the button itself comes down to a combining segments of the main shape and auxiliary lines The rightpath macro returns the right half of the path provided This half is shown as non dashed line Preliminary Version November 11 2001 Topics are identified with Topic which is an instance of chapter headings The number is made invisible Sinc
157. ght of the main text area Because they are stored in TEx dimension registers we have to prefix them by the pickup pencircle scaled 2pt numeric wl h xf yO u u 5cm numeric width width the textwidth numeric height height the textheight We now specify the lower left corners using instead of the which means that Metarost will calculate w 3 and h 3 for us wli 2u w 2 3u w 4 3u w 5 2u h 1 iu h 2 1u h 4 1u h 5 1u w 1 w 2 w 3 w 4 w 5 4u width h 1 h 2 h 3 h 4 h 5 4u height x 1 1u yi 1u x 2 x 1 w 1 5u y 2 y 1 h 1 5u x 3 x 2 w 2 5u y 3 y 2 h 2 5u x 4 x 3 w 3 5u y 4 y 3 h 3 5u x 5 x 4 w 4 5u y 5 y 4 h 4 5u Because we are going to repeat ourselves we draw the areas using a macro Depending on its importance we color it red or yellow def do_it expr xx yy cc draw unitsquare xyscaled wlxx hlyy shifted x xx ylyy withcolor if cc 625red else 625yellow fi enddef fill unitsquare xyscaled width height withcolor 85white do_it 1 1 false do_it 5 1 false do_it 2 1 false do_it 3 1 false do_it 4 1 false do_it 1 2 false do_it 5 2 false do_it 2 2 true do_it 3 2 true do_it 4 2 true do_it 1 3 false do_it 5 3 false do_it 2 3 true do_it 3 3 true do_it 4 3 tr
158. ging 5 191 11 Defining styles 197 11 1 Adaptive buttons 197 12 Functions 005 205 13 A few applications 207 13 1 Simple drawings 207 13 2 Free labels 210 13 3 Marking angles 215 13 4 Color circles 0 0 221 13 5 Fool yourself 227 13 6 P zzl s vesist einsa toraa tA 230 13 7 Flow charts 230 13 8 Chemistry 6 231 13 9 Growing graphics 231 13 10 Simple Logos 239 13 11 Animations 243 14 MetaFun macros 245 15 Example graphics 247 A Programs 6 e eee 249 A l METAPOST cee eee eee 249 AQ TEX stecbed audi ped ad tiredis 249 AS Coni Xi shock oiend Soe aeec bes 249 A4 TRXExec 1 ee eee eee 250 A5 MPtoPDF 250 A 6 Testcase 0 0 e eee 251 B METAPOST syntax ee eee 253 B 1 Syntax diagrams 253 B 2 Listofthings 262 C This document 263 D Reference 0000005 265 DAL Paths s25sc ec dsiacts cade Saag tas 265 D 2 Transformations 273 D3 POMS ced ode ek aieee dead oud cent 282 D4 Attributes 00 284 DD Text s eg64 beck tenis bi vy hds NA 289 E Literature 00 291 E 1 METAFONT and METAPOST 291 E2 TEX svacesveset veae S
159. gth of the vector b a Because the unscaled spring has length n 2h scaling by the expression xpart b a ypart b a n 2h gives the spring the same length as the vector b a Because we have drawn our spring in the vertical position we first rotate it 90 degrees clockwise to a horizontal position and then rotate it through an angle equal to the angle in which the vector b a is pointing After that we shift it to the first point The main complications are that we also want to draw connecting lines at the beginning and end as well as support springs that connect arbitrary points Since no check is done on the parameters you should be careful in using this macro When we want to improve the readability we have to use intermediate variables Since the macro is expected to return a path we must make sure that the content matches this expectation A few applications Preliminary Version November 11 2001 vardef spring expr a b w h n pair vec path pat numeric len numeric ang vec b a pat for i 1 upto n 1 if odd i fi w 2 i endfor 0 n pat 0 0 0 h pat shifted 0 h 0 n h 0 n 2h len xpart vec ypart vec n 2h ang 90 tangle vec pat yscaled len rotatedaround origin ang shifted a enddef If you use vardef then the last statement is the return value Here when p spring z1 z2 75cm 2 10 is be
160. gure macro encapsulates the code ina shortcut You can achieve special effects by using the layers behind floating bodies and alike but always keep in mind that the readability of the text should not be violated too much setlayer BackLayer Figure 5 2 position yes voffset 1 5cm width 3cm height 2cm MPfigure somecow pdf scaled 5 slanted 5 We have already seen a lot of parameters that can be used to control the content of a layer There are a few more General housekeeping takes place with state start enable the layer stop disable the layer position no use absolute positions yes use relative positions overlay idem but ignore the size direction normal put new data on top reverse put new data below old data Sometimes all data needs to be offset in a similar way You can use both offset parameters for that Preliminary Version November 11 2001 Instead of using relative positions you can also use absolute ones Of course you need to know how your coordinates relate to the rest of the layout definition setuplayer BackLayer position no setlayer BackLayer x 8cm y 18cm location b1 externalfigure somecow pdf width 5cm setlayer BackLayer x 8cm y 18cm location br externalfigure somecow pdf width 5cm setlayer BackLayer x 8cm y 18cm location t1 externalfigure somecow pdf width 3cm setlayer BackLayer x 8cm y 18cm location tr
161. h along with the current text width In order to process the graphics we tag each point with a name so that we can attach actions to those points In fact they become trigger points As we will demonstrate we also need to store the current page number This brings the data stored with a point to lt identifier gt lt pagenumber gt lt x gt lt y gt lt width gt lt height gt lt depth gt The page number is needed in order to let the graphics engine determine boundary conditions Backgrounds like shown here can span multiple pages In order to calculate the right backgrounds some additional information must be available like the top and bottom of the current text area In fact these are just normal points that can be saved while processing the split off page So apart from positioning anchors in the text we need anchors on crucial points of the layout This means that this kind of support cannot be fully integrated into the Tpx kernel unless we also add extensive support for layout definitions and that is probably not what we want As soon as something x y shows up a logical question is where 0 0 is located Although this is a valid question the answer is less important than you may expect Even if we know that 0 0 is officially located in the bottom left corner of the page the simple fact that in CONTEXT we are dealing with a mixed page concept like paper size and print paper size or left and right pages forces u
162. h depend on the width of the graphic Instead of calculating the blue shape such that it will be a filled outline we will draw the logo shape using line segments This is why we need the line parameter numeric width width 3cm numeric height height width 2 numeric line line height 4 We want sharp corners which can be achieved by setting linejoin to mitered linejoin mitered pickup pencircle scaled line The colors are rather primary blue and yellow At the time of writing this manual Dutch trains are still painted yellow so we will use that shade as background color color nsblue nsblue 0 0 1 color nsyellow nsyellow 1 1 0 Preliminary Version November 11 2001 A few We will now describe the main curves Although these expressions are not that advanced they demonstrate that we can express relationships instead of using assignments zi 0 height 2 z2 width 2 height 4 y1 z3 width 2theight 4 y4 z4 width 0 path p p z1 z2 z3 z4 Although it is accepted to consider z to be a variable it is in fact a vardef macro that expands into a pair x y This means that the previous definitions internally become x1 y1 0 height 2 x2 y2 width 2 height 4 y1 x3 y3 width 2theight 4 y4 x4 y4 width 0 These 8 relations can be solved by metarosr since all dependencies are know
163. h a graphic to a layer we can pass variables We can also set specific variables in other ways as we will see later setMPpositiongraphic G 1 mypos circle setMPpositiongraphic G 1 mypos line to G 2 In the second definition we let the variable to point to another position When needed we can ask for the value of to by MPvar to For reasons of convenience the current position is assigned automatically to from and self This means that in the line we saw in the graphic initialize_box MPpos MPvar self MPvar self will return the current position which fed to MPpos will return the list of positional numbers We already warned the reader this is not an easy chapter More layers Overlays are one of the nicer features of CONTEXT and even more nice things can be build on top of them Overlays are defined first and then assigned to framed boxes using the background variable You can stack overlays which is why they are called as such You can use the special overlay called foreground to move the topmost often text layer down in the stack background overlay a text graphic hyperlink or widget position overlay a series of macros triggered by positions background layer a box that can hold boxes with offsets The last kind of layer can be used in other situations as well but in most cases it will be hooked into a background overlay Preliminary Version November 11 2001 Positional graphics
164. he graphic in a figure and figures are grouped already We will use the predefined z variable or actually a macro that returns a variable This variable has two components an x and y coordinate So we don t save z but the related variables x and y save x y a b c d e f g h We draw four squares and instead of hard coding their corner points we use METAPOST s equation solver Watch the use of which means that we just state dependencies So where in languages like PERL the equal sign is used in assignments in METAPOST it is used to express an relationship APOST Preliminary Version November 11 2001 In a first version we will just name a lot of simple relations as we can read them from a sketch drawn on paper z11 242 p 221 z12 q z31 z22 r 241 z32 8 a x12 x11 b y12 yi c x22 x21 d y22 y21 e x32 x31 f y32 y31 g x42 x41 h y42 y41 zii x11 y11 z12 x12 y12 z13 x12 b y12 a z14 x11 b ylita z21 x21 y21 z22 x22 y22 Z23 x22 d y22 c z24 x21 d y2itc z31 x31 y31 z32 x32 y32 z33 x32 f y32te 234 x31 f y31te z41 x41 y41 z42 x42 y42 Z43 x42 h y42 g z44 x41 h y4itg The line that involve the pairs a upto h can be written in a more compact way a b z12 z11 c d z22 z21 e f z32
165. he previous graphic we calculated the big rectangle taking the small one into account This was needed because we don t use a background fill The next definition does so there we can use a more straightforward approach by just drawing and filling the small rectangle on top of the big one startuseMPgraphic FunnyFrame picture p numeric o path a b pair c p textext rt MPstring FunnyFrame a unitsquare xyscaled OverlayWidth OverlayHeight o BodyFontSize p p shifted 2o 0verlayHeight ypart center p drawoptions withpen pencircle scaled ipt withcolor 625red b a randomized 0 2 fill b withcolor 85white draw b b boundingbox p randomized 0 8 fill b withcolor 85white draw b draw p withcolor black setbounds currentpicture to a stopuseMPgraphic There is not so much basic instruction as of now as there was in the old days showing the differences between good and bad typographic design Because we use a random graphic we cannot on forehand guarantee that the left and right edges of the small shape touch the horizontal lines in a nice way The next alternative displaces the small shape plus text so that its center lays on the line On the average this looks better startuseMPgraphic FunnyFrame picture p numeric o path a b pair c p textext rt MPstring FunnyFrame a unitsquare xyscaled OverlayWidth OverlayHeight o BodyFontSize p p shifted 2o
166. height 3 4 the bodyfontsize currentfontscale span 1 3 height drift 1 10 height hsize the hsize vstep the lineheight xmax hsize div 5span pickup pencircle scaled 1 12 height def d uniformdeviate drift enddef for i 1 upto MPvar n xpos i 1 mod 5 xmax span ypos i 1 div 5 xmax vstep draw _ Shapes symbols and buttons Preliminary Version November 11 2001 Ta 7 4 if i mod 5 0 d 4 5span d d 0 5span height d else d d d height d fi shifted xpos ypos d drift endfor picture cp cp currentpicture if ypart ulcorner cp ypart llcorner cp lt vstep setbounds currentpicture to 1lcorner cp shifted 0 ypart llcorner cp lrcorner cp shifted 0 ypart lrcorner cp urcorner cp ulcorner cp cycle fi endgroup stopuseMPgraphic Graphic variables In the previous sections we have seen that we can pass information to the graphic by means of variables How exactly does this mechanism work To do an explanation of the mechanism to pass variables Shape libraries Unfortunately it takes some effort to define graphics attach them to an overlay and invoke the background However the good news is that since in many cases we want a consistent layout we only have to do it once The next table has some hashed backgroun
167. ic Preliminary Version November 11 2001 center fullcircle metapost macro boundingbox fullcircle metafun macro innerboundingbox fullcircle metafun macro outerboundingbox fullcircle metafun macro currentpicture xsized 5cm metafun macro path picture ysized numeric currentpicture ysized 2cm metafun macro path picture xysized numeric currentpicture xysized 3cm 2cm metafun macro z Wo OOo center fullcircle metapost primitive top center fullcircle metapost macro bot center fullcircle metapost macro Preliminary Version November 11 2001 3 E l N wi i 10 5 EAL E 5 x 7 NE 5 A E y ge 3 5 z z oO mt ss se 5 oe ge o D gt Q ge a oO G O 5 a 2 5 J oO H A Q r ge o D x NA Preliminary Version November 11 2001 lft center fullcircle metapost macro rt center fullcircle metapost macro point 2 of fullcircle metapost primitive point 5 on fullcircle metafun macro point icm along fullcircle metafun macro precontrol 2 of fullcircle metapost primitive postcontrol numeric of path postcontrol 2 of fullcircle metapost primitive ax reed directionpoint pair of path directionpoint 2 3 of fullcircle metapost primitive x NA numeric pair pair 5 00 0 1 1 metapost concept
168. ical method but the next one took only a few minutes of trial and error To save some memory we redefine the colors graphic When we call this macro as colorcircle 4cm red green blue we get applications Preliminary Version November 11 2001 vardef colorcircle expr size red green blue save r g b rr gg bb cc mm yy save radius path r g b rr bb gg cc mm yy numeric radius radius 5cm pickup pencircle scaled radius 25 r g b fullcircle scaled radius shifted 0 radius 4 r r rotatedaround origin 15 g g rotatedaround origin 135 b b rotatedaround origin 255 r r rotatedaround center r 90 g g rotatedaround center g 90 gg buildcycle buildcycle reverse r b g cc buildcycle buildcycle b reverse g r rr gg rotatedaround origin 120 bb gg rotatedaround origin 240 yy cc rotatedaround origin 120 mm cc rotatedaround origin 240 fill fullcircle scaled radius withcolor white fill rr withcolor red fill cc withcolor white red fill gg withcolor green fill mm withcolor white green fill bb withcolor blue fill yy withcolor white blue for i rr gg bb cc mm yy draw i withcolor 5white endfor currentpicture currentpicture xsized size enddef Since we don t want to duplicate a graphic this time we show the dark alternatives col
169. ically like the files that implement page layout support and flow charts I will also add some information on how to generate documented sources Preliminary Version November 11 2001 Preliminary Version November 11 2001 15 Example graphics In this chapter we will show some of the graphics that we made the last few years using METAPOST They give an impression of what kind of non mathematical drawings can be made Preliminary Version November 11 2001 is i Preliminary Version November 11 2001 A l A 2 A 3 Programs After a graphics is defined in the metarost language you have to compile it into a POSTSCRIPT graphic using metarpost the program An additional next step is conversion into PDF In this chapter we will discuss the programs involved in this process METAPOST Of course we use METAPOST This program can be found in most x distributions and the binary is called mpost It uses a few auxiliary programs to prepare files that are passed on to Tex and if you can locate the metaPosT binary you may assume that its companion programs are around somewhere too When you use the macros that come with CONTEXT you may wish to package them in a memory dump file that can be loaded fast You can do that by the following command mpost ini metafun You have to move the resulting mem file to the location where Metarost e
170. icture p q p q currentpicture clip p to unitsquare xscaled width yscaled height clip q to unitsquare xscaled width yscaled height currentpicture p addto currentpicture also q shifted 0 radius 2 stopuseMPgraphic Puzzles Maybe Flow charts Instead of starting anew every time you can use predefined macros like those in the flow chart module Let s see how we can influence the MeTAPOST code Maybe not here Preliminary Version November 11 2001 13 8 13 9 Chemistry METAPOST can do it s work unseen as in the chemistry module that comes with CONTXT There METAPOST is used as one of the graphical plug ins It demonstrates that we can put METAPOST to work without seeing any code Growing graphics Although metarost is not really suited an a simulation engine it is possible to build graphics that are built and displayed incrementally with a sequence of mouse clicks The following example is the result of an email discussion David Arnold and the author had while MetaFun evolved Instead of defining the graphics in a separate metapost file we will incorporate them in the document source in which they are used We can use several methods 1 Define macros and figures in a separate file and include the graphics as external graphics 2 Define everything in the document source as usable graphics and include the graphics using useMPgraphic 3
171. ifted 5 5 xscaled 6cm yscaled 2cm withpen pencircle scaled 1mm withcolor black draw origin withpen pencircle scaled imm d Preliminary Version November 11 2001 As you can see the transformations are applied in series Sometimes this is not what we want in which case we can use parentheses to force the desired behaviour The lesson learned is that scaling and shifting is not always the same as shifting and scaling draw origin origin shifted 4cm 0cm shifted 4cm 0cm withpen pencircle scaled icm withcolor 625white draw origin origin shifted 4cm 0cm shifted 4cm 0cm withpen pencircle scaled 8mm withcolor 625yellow draw origin origin shifted 4cm 0cm shifted 4cm 0cm withpen pencircle scaled 6mm withcolor 625red draw origin origin shifted 4cm 0cm shifted 4cm 0cm withpen pencircle scaled 4mm withcolor white Ce Especially when a path results from a call to a macro using parentheses around a path may help as in the following example def unitslant origin origin shifted 1 1 enddef draw unitslant xscaled 5cm yscaled 1cm withpen pencircle scaled 1cm withcolor 625red draw unitslant xscaled 5cm yscaled 1cm withpen pencircle scaled 5mm withcolor 625yellow The next definition of unitslant is therefore better Preliminary Version November 11 2001 def unitslant origin origin shifted 1 1
172. igure 8 2 A clipped cow Here we have divided the cow in six cells so that we can clip its head and tail This kind of clipping enables you to zoom in or focus on a specific part of a graphic setupclipping nx 3 ny 2 startcombination clip x 1 y 1 externalfigure cow mps width 4cm 1 1 clip x 3 y 1 externalfigure cow mps width 4cm 3 1 stopcombination Alternatively we can specify a width height hoffset and voffset as demonstrated in figure 8 3 n Figure 8 3 Another clipped cow placefigure here fig clipped cow 2 Another clipped cow clip width 2cm height 2cm hoffset 0cm voffset 0cm externalfigure cow mps width 4cm Because METAPOST supports clipping it will be no surprise that both techniques can be combined In the next example we will zoom in on the head of the cow We also use this opportunity to demonstrate how you can package a clip in a figure definition startMPclipfhead clip w width h height clip currentpicture to O h w h down left 0 0 cycle stopMPclip placefigure here fig circular clipped cowhead A quarter circle applied to a cows head ruledhbox clip nx 2 ny 2 x 1 y 1 mp head clip externalfigure cow mps width 4cm Special effects _ Preliminary Version November 11 2001 A more advanced clip is demonstrated in figure 8 4 We added ruledhbox to demonstrate the
173. ill define the command that generates topic entries The alternative right lets the topic list inherit its characteristics from the menu startinteractionmenu right placelist Topic alternative right vfill but CloseDocument close stopinteractionmenu We have now arrived at the more interesting part of the style definition the graphic that goes in the page background Because this graphic will change we define a useable Metapost graphic Page backgrounds are recalculated each page opposite to the other backgrounds that are calculated when a new background is defined or when repetitive calculation is turned on setupbackgrounds page background page def ineoverlay page useMPgraphic page setupMPvariables page alternative 3 We will implement three alternative backgrounds First we demonstrate the relatively simple super ellipsed one The main complication is that we want the button shapes to follow the right edge of the curve that surrounds the text We don t know in advance how many lines of text there will be in a button and we also don t know at what height it will end up Therefore we need to calculate each button shape independently and for that purpose we need to know its position see chapter 5 In figure 11 1 you can see what auxiliary lines we need in order to be calculate the button shapes We separate the calculation of the button shape from the rest by embedding it in its own usable graphic cont
174. in primitive and is defined as the point on the pen furthest to the right of the given direction Deep down in metarost pens are actually simple paths and therefore metarost has a notion of a point on the penpath In the METAFONT book and mMetarosTt manual you can find in depth discussions on pens We re still not there Like in a previous example we need to shift over twice the pen width To get good results we should determine the width of the pen at that particular point which is not trivial The more general solution which permits us to specify the amount of shifting is as follows E re details Preliminary Version November 11 2001 vardef penpoint expr pnt of p save n d numeric n d n d if pair pnt pnt else pnt 1 fi point n of p shifted Cpenoffset direction n of p of currentpen scaled d enddef When the point specification is extended with a distance in which case we have a pair expression the point and distance are derived from this specification First we demonstrate the simple case draw penpoint 0 of p for i 1 upto length p 1 penpoint i of p endfor cycle withcolor 625red In the next graphic we draw both an inner and and outer path draw penpoint 0 2 of p for i 1 upto length p 1 penpoint i 2 of p endfor cycle withcolor 625red draw penpoint 0 2 of p for i 1 upto length p 1 penpoint i 2 of p endfor cycle with
175. inary Version November 11 2001 Edward R Tufte and everyila tapacity to selec synthesize foc not only be the implementer manual ould have hurt TEX dreds of improve ntly FL had id never have int viewpoints undertake Douglas R Hostadter Preliminary Version November 11 2001 Preliminary Version November 11 2001 concept copyright Figure 6 1 Two examples of annoying backgrounds If you really want to add such texts to a document in CONTEXT we don t have to use the page back ground but can use one of the layout areas instead like text text or text leftmargin setupframedtexts FunnyText backgroundcolor lightgray framecolor darkred rulethickness 2pt offset bodyfontsize bef ore blank big medium after blank big width textwidth There is one drawback when your left and rightmargin have different dimensions the text will be scaled differently on odd and even pages Normally this is no problem for a draft As an alternative you can use the setuptexts command and wraps the graphic in a box with the right dimensions using code like startuniqueMPgraphic copyright picture p p btex COPYRIGHT etex rotated 90 setbounds p to boundingbox p enlarged ipt draw p withcolor 8white xyscale_currentpicture the leftmarginwidth the textheight stopuniqueMPgraphic setup
176. indexing the variable name as in n 3 5 Multi dimensional arrays are also supported Since you need a bit of imagination to find an application for 5 dimensional arrays we restrict ourselves to a two dimensional example numeric n n 2 3 10 A nice feature is that the bounds of such an array an array need not be set beforehand This also means that each cell that you access is reported as unknown unless you have assigned it a value Conditions The existence of boolean variables indicates the presence of conditionals Indeed the general form of meTaPosT s if then else conditional follows if n 10 draw p else draw q fi Watch the colons after the if and else clause They may not be omitted The semi colons on the other hand are optional and depend on the context You may say things like draw if n 10 p else q fi Here we can omit a few semi colons draw if n 10 p else q fi withcolor red Adding semi colons after p and q will definitely result in an error message since the semi colon ends the draw operation and withcolor red becomes an isolated piece of nonsense There is no case statement available but for most purposes the following extension is adequate draw p withcolor if n lt 10 red elseif n 10 green else blue fi There is a wide repertoire of boolean tests available if picture p if known n if odd i if cycle q Of course you can use and or not and to
177. indings The definition of spring is less complicated than readable Preliminary Version November 11 2001 A few def spring expr a b w h n C 0 0 0 h for i 1 upto n 1 if odd i fi w 2 i h endfor O nth 0 n 2h yscaled xpart b a ypart b a n 2h rotatedaround origin 90 angle b a shifted a enddef First we build a path starting in the origin going left or right depending on the counter being an odd number pat 0 0 for i 1 upto n 1 if odd i pat pat w 2 i else pat pat 4 w 2 i fi 4 endfor pat pat 0 n Once you are accustomed to the way meTtarost interprets specialists may say expand the source code you will start using if and for statements in assignments The previous code can be converted in a one liner using the pattern pat for i 1 upto n 1 x y endfor 0 n The loop splits out a series of x y but the last point is added outside the loop Otherwise pat would have ended with a dangling Of course we need to replace x y by something meaningful so we get pat for i 1 upto n 1 if odd i fi w 2 i endfor 0 n We scale this path to the length needed The expression b a calculates a vector starting at a and ending at b In metarost the expression a b is identical to Va b Thus the expression xpart b a ypart b a calculates the len
178. ing code Here we assume that you have a file called tufte tex on your system which is the case if you have CONTEXT installed However you can just as easily use any file having a paragraph of two of text starttext setupinteraction state start setupbackgrounds state repeat def ineoverlay nextpage overlaybutton nextpage setupbackgrounds text text background nextpage dorecurse 20 input tufte par stoptext Note that you can move forward from page to page in the resulting PDF file by clicking on each page with the mouse Now compile this file without setting the background state to repeat and note the difference as you click pages with the mouse Setting the state was not needed when we used the page background setupbackgrounds page background nextpage The dorecurse macro is handy for testing since it saves us typing One can nest this macro as in Preliminary Version November 11 2001 6 4 dorecurse 20 dorecurse 10 Hello World par The current step is available in recurselevel and the depth nesting level in recursedepth Crossing borders In many cases the previously mentioned background areas will suffice but in the case of more complicated backgrounds you may wish to use mMeTAPosT to draw graphics that combine or span these areas At runtime CONTEXT saves information on the layout that can be picked up by metarost The framework for
179. ing parsed the macro is expanded the variables are kept invisible for the assignment and the path at the end is considered to be the return value Ina def the whole body of the macro is pasted in the text while in a vardef only the last line is visible We will demonstrate this with a simple example def one n n n ntl enddef def two n n 1 n n enddef Now when we say pair a b numeric n n 10 a one b two we definitely get an error message This is because when macro two is expanded METAPOST sees something b n n t 1 By changing the second definition in vardef two n n 1 n n enddef the increment is expanded out of sight for b and the pair n n is returned We can draw a slightly better looking spring by drawing twice with a different pen The following commands use the spring macro implemented by the vardef path p p 0 0 spring 5cm 0 2 5cm 0 5cm 0 10 3cm 0 draw p withpen pencircle scaled 2pt draw p withpen pencircle scaled ipt withcolor 8white This time we get WWWV Since the spring macro returns a path you can do whatever is possible with a path like drawing an arrow ww Preliminary Version November 11 2001 Afew 13 2 Or even watch how we use the neutral unit u to specify the dimensions U S hed v Ld This was keyed in as drawarrow 0 0 spring 5c
180. ink that a widely praised program called up on the screen will make every thing automatic from now on There are quite some hard coded values in these graphics like the linewidths offsets and colors Some of these can be fetched from the framed environment either by using X macros or dimensions or by using their MetaFun counterparts In the following table we summarize both the available metarost variables and their Tex counterparts They may be used intermixed METAPOST variable x command meaning Overlay Width overlaywidth current width Overlay Height overlayheight current height OverlayDepth overlayheight current depth often zero OverlayColor MPcolor overlaycolor background color OverlayLineWidth overlaylinewidth width of the frame OverlayLineColor MPcolor color of the frame BaseLineSkip the baselineskip main line distance LineHeight the baselineskip idem BodyFontSize the bodyfontsize font size of the running text StrutHeight strutheight space above the baseline StrutDepth strutdepth space below the baseline _Efihancing the layout Preliminary Version November 11 2001 startuseMPgraphic FunnyFrame picture p numeric o path a b pair c p textext rt MPstring FunnyFrame o BodyFontSize a unitsquare xyscaled OverlayWidth OverlayHeight p p shifted 2o 0verlayHeight ypart center p pickup pencircle scaled OverlayLineWidth b a sup
181. interactive documents adding backgrounds to the page and text areas not only enhances readability but also makes it more convenient to identify header footers and navigational areas In this chapter we will demonstrate that with mMETAPOST we can go beyond the Tpx based features present in CONTEXT The basic layout In the CONTEXT manual you can find many details on the composition of the page When Tx typesets text crossing the page boundary triggers Tex s output routine This routine is responsible for pasting the body text that goes onto a page into the correct area A simple representation of such a page is The red areas are the header and footer while the yellow areas contains the text flow We can turn headers on and off and or hide them For this reason the header text and footer areas together make up the height of the text A close look at the left picture will reveal that the two arrows point to the center of the lines This is achieved by the top and 1ft directives If we would not have clipped the picture the arrow would have stuck half a line width outside the gray area that represents the page When constructing such pictures one should really pay attention to such details since it pays off in the overall look and feel of the document The vertical arrow represents the top space while the horizontal arrow denotes the distance to the back of the cover back space By changing their values you can shift the main body text
182. interest artificial intelligence and esthetic theory 1 felt compelled to make some comments to clarify ertain important issues raised by The Concept of a Meta Font inary Version November 11 2001 even odd Figure 6 6 A quick way to draw all used areas Preliminary Version November 11 2001 7 1 Shapes symbols and buttons One can use meTAPOST to define symbols and enhance buttons Here we introduce some of the gadgets that come with CONTEXT as well as explain how to integrate such gadgets yourself Interfacing to TREX In the early days of MeTAPOsST support in CONTEXT Tobias Burnus asked me if it was possible to define English rules What exactly does an english rule look like Here is one As you can see such a rule has to adapt itself to the current text width normally hsize in TX or on request localhsize in CONTpXT We need to set the height to a reasonable size related to the font size and we also need to take care of proper spacing Of course we want to run METAPOST as less times as possible so we need to use unique graphics Let s start with the graphic setupMPvariables EnglishRule height 1ex width localhsize color darkgray startuniqueMPgraphic EnglishRule height width color numeric height height MPvarfheight xl 0 x3 MPvar width x2 x4 5x3 yi y3 0 y2 y4 height 2
183. ion November 11 2001 Enhancing the layout def RotatedText 1 2 startuseMPgraphic RotatedText draw btex 2 etex rotated 1 stopuseMPgraphic useMPgraphic RotatedText This macro takes two arguments the identifies an argument RotatedText 15 Some Rotated Text The text is rotated over 15 degrees counter clockwise x me gorated i So In CONTXT we seldom pass settings like the angle of rotation in this way The next alternative is therefore better def RotatedText 1 2 setupMPvariables RotatedText rotation 90 1 startuseMPgraphic RotatedText draw btex 2 etex rotated MPvarf rotation stopuseMPgraphic useMPgraphic RotatedText We now need to pass the angle as a key value pair RotatedText rotation 15 Some Rotated Text The rotated text becomes Som Rota teq leg In this case the graphic is rather simple but when a large graphic is used it makes sense to keep its definition outside the macro In order to do so we need a way to pass the argument to the graphic def RotatedText 1 2 setupMPvariables RotatedText 1 setMPtext RotatedText 2 useMPgraphic RotatedText setupMPvariables RotatedText rotation 90 startuseMPgraphic RotatedText draw MPbetex RotatedText rotated MPvar rotation stopuseMPgraphic You may wonder why we don t use the variable mechanism here The main reason is that the text mechan
184. ipt draw pab withcolor 625yellow anchor_box MPanchor MPvar from fi stopMPpositiongraphic The command startMPpositiongraphic defines a graphic in this example we have called it mypos circle l Positional graphics Preliminary Version November 11 2001 a The Metarost macro initialize_box returns the characteristics of the box as identified by MPpos After this call the corners are available in llxy lrxy urxy and ulxy The center is defined by cxy and the path stored in pxy When we are finished drawing the graphic we can anchor the result with anchor_box This macro automatically handles positioning on specific layers The position macro MPpos returns the current characteristics of a position The previously defined G positions return position page x y width height depth G1 123 182 7137pt 370 73187pt 31 93997pt 6 915pt 2 81999pt G2 123 110 05482pt 357 5999pt 21 16998pt 4 735pt 2 81999pt G3 123 228 98412pt 357 5999pt 27 57999pt 6 915pt 0 15999pt G4 123 368 29483pt 344 46793pt 16 29994pt 4 735pt 0 15999pt The numbers represent the pagenumber p the current position x y and the dimensions of the box w h d if known These values are fed directly into metapost graphics but the individual components can be asked for by MPp MPx MPy MPw MPh and MPd In the previous definition of the graphic we saw another macro MPvar When we invoke a graphic or attac
185. ircles but the shade definition is frozen and the same one is used for all 5 circles This means that the center of the shading stays at the first circle circular_shade fullcircle scaled icm 0 MPcolor a MPcolor b picture s s currentpicture currentpicture nullpicture for i 0 step 2cm until 8cm addto currentpicture also s shifted i 0 endfor Unlike Tex metaPost does not keep its specials attached to the current path and flushes them before the graphic data Since we use these specials to register shading information it is rather hard to tightly connect a specific shade with a certain fill especially if an already performed fill is not accessible which is the case when we copy a picture This may seem a disadvantage but fortunately it also has its positive side In the next example we don t copy but reuse an already defined shade By storing the reference to this shade and referring to it by using withshade we can use a shade that operates on multiple shapes sh define_circular_shade origin origin 0O 8cm MPcolor a MPcolor b for i 0 step 2cm until 8cm fill fullcircle scaled 1cm shifted i 0 withshade sh endfor 0 O lt The low level macro define_circular_shade is fed with two pairs points two radius and two colors The shade is distributed between the colors according to the radius Shading can hardly be called an easy issue The macros that we provide here are in fact simplifica
186. ism offers a few more features one of which is that is passes the text straight on without the danger of unwanted expansion out Preliminary Version November 11 2001 RotatedText rotation 165 Some Rotated Text That this method works equally well is demonstrated below Par Paejo X duro S There are three ways to access a text defined with setMPtext Imagine that we have the following definitions setMPtext 1 Now is this TeX or not setMPtext 2 See what happens here setMPtext 3 Text streams become pictures The MPbetex macro returns a btex etex construct The MPstring returns the text as a META post string between quotes The raw text can be fetched with MPtext startMPcode picture p p MPbetex 1 picture q q textext MPstring 2 J picture r r thelabel MPtext 3 origin for i p boundingbox p draw i withcolor 625red endfor for i q boundingbox q draw i withcolor 625yellow endfor for i r boundingbox r draw i withcolor 625white endfor currentpicture currentpicture scaled 2 draw origin withpen pencircle scaled 2 0mm withcolor white draw origin withpen pencircle scaled 1 5mm withcolor black stopMPcode The first two lines return text typeset by Tx while the last line leaves this to METAPOST Pee walma hane rph If you watch closely you will notice that the first red alternative is
187. itialization file texexec ini By default these variables are set up as follows set MpExecutable to mpost set MpToTeXExecutable to mpto set DviToMpExecutable to dvitomp Also when using the WEB2C implementation you can set the following variables in the file texmf cnf MPXCOMMAND texexec mptex TEX texexec once batch nomp MPtoPDF The small suite of TeX macros in the file mptopdf provides a quick way to convert MeTAPOST files to PDF using a slightly stripped down plain Tpx PDFIgxX and a few CONTEXT modules Although Preliminary Version November 11 2001 A 6 CONTEXT can handle metarost files directly this conversion is seldom needed However it can be handy to convert the file to be able to preview it Before we can apply this conversion we have to generate a format which in WEB2C looks like pdftex ini mptopdf Since this conversion only works with PDFTpX or its Tpx alternative the session is aborted when another Tpx is used When finished the resulting fmt file should be moved to the right location When TXEXEC is properly set up you can also use this PERL script to handle the generation of the format and move texexec make alone tex pdftex format mptopdf The conversion itself is accomplished by pdftex amp mptopdf relax filename number The relax is needed since we don t want to process the file directly Instead we pick up the filename using everypar Because this file is still the firs
188. ituation where METAPOST has to be more clever The whatever variable is defined as a sort of anonymous variable and it is left to MeTaPost to make sure that it s solved somehow We will never really use it The macro mark_rt_angle draws the angle symbol and later we will see how it is defined First we draw the labels Unfortunately we cannot package btex etex into a macro because it is processed in a rather special way Therefore we have to put a lot of code here if show_labels We use a bigger pen for drawing the dots pickup pencircle scaled 5pt The macro dotlabel draws a dot and places the typeset label dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel dotlabel urt rt bot 1lft btex ulft btex ulft btex 1lft btex lrt btex 11lft btex urt btex ulft btex urt btex ulft btex urt btex urt btex lrt btex urt btex 1lft btex lrt btex btex lft btex top btex btex btex Z_ 11 Z_ 12 Z_ 13 Z_ 14 Z_ 21 Z_ 22 Z_ 23 Z_ 24 Z_ 31 Z_ 32 Z_ 33 Z_ 34 Z_ 41 Z_ 42 Z_ 43 Z_ 44 Z_ 0 Z_ 1 Z_ 2 Z_ 3 Z_ 4 etex etex etex etex etex etex etex etex etex etex etex etex etex etex etex etex etex etex etex
189. ize angle 45 linewidth overlaylinewidth linecolor overlaylinecolor The last step in this process is to define the different alternatives as overlays def metahashoverlay 1 uniqueMPgraphic meta hash angle 1 def ineoverlay meta hash right metahashoverlay 45 def ineoverlay meta hash left metahashoverlay 45 def ineoverlay meta hash horizontal metahashoverlay 180 defineoverlay meta hash vertical metahashoverlay 90 As we can see in the definition of the table we can pass settings to the bTABLE command Actually we can pass such settings to each command that supports backgrounds or more precisely framed Table 7 3 is for instance defined as bTABLE frame off meta hash linewidth 4pt align middle offset 2ex bTR bTD background meta hash left meta hash right meta hash linecolor darkyellow left par amp par right eTD bTD background meta hash horizontal meta hash vertical meta hash linecolor darkred horizontal par amp par vertical eTD eTR eTABLE The long names are somewhat cumbersome but in that way we can prevent name clashes Also since the Metarost interface is english the variables are also english Table 7 3 A double hashed table Shapes symbols nd buttons Preliminary Version November 11 2001 19 Symbol collections In CONTEXT a symbol can de defined without much
190. lcorner and urcorner or if you like ulcorner and 1rcorner and the MetaFun command boundingbox does so The four corners that make up the bounding box are either the natural ones or the ones forced by setbounds You can force metarost to report the natural ones by setting truecorners to 1 The next example demonstrates this feature pickup pencircle scaled 2mm path p q draw fullcircle scaled 4cm slanted 5 withcolor 625white setbounds currentpicture to boundingbox currentpicture enlarged 5mm interim truecorners 0 p boundingbox currentpicture interim truecorners 1 q boundingbox currentpicture pickup pencircle scaled 1mm draw p withcolor 625red draw q withcolor 625yellow We use interim because truecorners is an internal MeETAPOST variable Since METAPOST can handle fonts it can even generate font metric files it is no surprise that we can also ask for the natural size of a font For this we use fontsize However you should beware of the fact that the size reported is in base points Since this is MeTAPOST s native unit this is no problem in calculations but to may look confusing when you show this size on your terminal and get less that 10 reported for a cmr10 font show fontsize cmri0 In order to demonstrate that fontsize is useful we extend the infont command In the process we show a few macro definition tricks What we want is a Tx like specification of a font size draw MetaFun infont
191. le too startMPdrawing for i 1 upton picli pic i shifted 0 ypart 5 ulcorner pic i llcorner pic i endfor stopMPdrawing So now we have Ceti Ovna c When we typeset on a half circle we should map the actual length onto a partial circle We denote the radius with an r and shift the pictures to the left startMPdrawing numeric r r len n Pi for i 1 upton picli picli shifted r 0 endfor stopMPdrawing You can now use the following code to test the current state of the pictures Of course this code should not end up in the final definitions startMPdrawing draw origin withpen pencircle scaled Spt withcolor red for i 1 upton draw picli draw boundingbox pic i withpen pencircle scaled 25pt withcolor red endfor stopMPdrawing _ Later we will write a compact efficient macro to take care of rotation However for the moment so as not to overwhelm you with complicated code we will rotate each individual picture with the following code fragment startMPdrawing numeric delta extra radius rot delta extra radius 0 for i 1 upton rot i extratdelta pos i 5wid i len n 180 2delta Preliminary Version November 11 2001 Typesetting in Mer BP per endfor stopMPdrawing Here we introduce a few variables that we can use later to tune the result a bit With delta the spac
192. liminary Version November 11 2001 4 2 4 3 ruledhbox framed offset 3pt frameoffset 6pt backgroundoffset 9pt background screen backgroundscreen 85 Welcome in the hall of frame Welcome in the hall of frame Figure 4 2 The three offsets Overlay variables The communication between TeX and embedded metarost graphics takes place by means of some macros overlay status macro meaning overlaywidth the width of the graphic as calculated from the actual width and back ground offset overlayheight the height of the graphic as calculated from the actual height depth and background offset overlaydepth the depth of the graphic if available overlaycolor the background color if given overlaylinecolor the color of the frame overlaylinewidth the width of the frame The dimensions of the overlay are determined by dimensions of the background which normally is the natural size of a framed When a background offset is specified itis added to overlayheight and overlaywidth Colors can be converted by MPcolor and in addition to the macros mentioned you can use all macros that expand into a dimension or dimen registers prefixed by the T X primitive the this and other primitives are explained in The TEXbook by Donald Knuth Stacking overlays A background can be a gray scale screen a color color a previously defined overlay identifier or any combination of these Th
193. ll become a sequence of glyphs MP this string will become a sequence of glyphs TEX The second line is typeset by Tpx and is properly kerned As we may expect from TEX the TeX command becomes the Tpx logo Instead of passing strings to infont you can also pass characters using char for example char 73 When you use infont you normally expect the font to be ASCII conforming If this is not the case you must make sure that the encoding of the font that you use matches your expectations In this respect the TEx based method is more safe because when set up properly TEx normally knows what it is dealing with 1 13 Linear equations In the previous sections we used the assignment operator to assign a value to a variable Although for most of the graphics that we will present in later chapters an assignment is appro priate specifying a graphic in terms of expressions is not only more flexible but also more in the spirit of the designers of METAFONT and METAPOST The METAFONT book and meTAPOsT manual provide lots of examples some of which involve math that we don t consider to belong to everyones repertoire But even for non mathematicians using expressions can be a rewarding challenge The next introduction to linear equations is based on my first experiences with metapost and involves a mathematical problem someone chalenged me with It did not take me much time to see that a sort of graphical proof was far more easy than some pr
194. ll get black lines instead of red and a black fill instead of a gray one When drawing or filling a path you can give it a color use all kinds of pens and achieve special effects like dashes or arrows Preliminary Version November 11 2001 These two graphics were defined and drawn using the following commands Later we will explain how you can set the line width or penshape in terms of MeTAPOST path p p Ocm icm 2cm 2cm 4cm 0Ocm 2cm 1cm cycle drawarrow p withcolor 625red draw p shifted 7cm 0 dashed withdots withcolor 625yellow Once we have drawn one or more paths we can store them in a picture variable The straightfor ward way to store a picture is to copy it from the current picture picture pic pic currentpicture The following command effectively clears the picture memory and allows us to start anew currentpicture nullpicture We can shift rotate and slant the picture stored in pic as we did with paths We can say draw pic rotated 45 withcolor red A picture can hold multiple paths You may compare a picture to grouping as provided by drawing applications draw Ocm O0cm 1icm icm draw icm Ocm Ocm icm picture pic pic currentpicture draw pic shifted 3cm 0cm draw pic shifted 6cm 0Ocm pic currentpicture draw pic shifted Ocm 2cm We first draw two paths and store the resulting cross in a picture variable Then we draw this
195. m drawarrow origin a drawarrow origin b drawarrow anglebetween a b scaled 1cm withcolor 625red where anglebetween is defined as def anglebetween expr a b unitvector a a rotated 90 unitvector b enddef Both unitvectors return just a point on the line positioned 1 unit later scaled to 1cm from the origin We connect these points by a curve that starts in the direction on the first point If we omit the a rotated 90 direction specifier we get f These definitions of anglebetween are far from perfect If we don t start in the origin we get the curve in the wrong place and when we swap both points we get the wrong curve The solution for the displacement is given in the metarost manual and looks like this we package the macro a bit different Aew applications Preliminary Version November 11 2001 def anglebetween expr endofa endofb common length unitvector endofa common endofa common rotated 90 unitvector endofb common scaled length shifted common enddef As you can see we compensate for the origin of both vectors This macro is called with a few more parameters We need to pass the length since we want to add the shift to the macro and the shift takes place after the scaling pair a b c a 2cm 1cm b 8cm icm c 1cm 5cm drawarrow c a drawarrow c b drawarrow anglebetween a b c 1icm withcol
196. m 0 2 5cm 0 5cm 0 10 3cm 0 withpen pencircle scaled 2pt withcolor 625red and numeric u u 1mm pickup pencircle scaled u 2 drawoptions withcolor 625red draw 0 0 spring 5u 0 25u 0 5u 0 10 30u 0 drawoptions dashed evenly withcolor 5white draw 0 0 spring 5u 0 35u 0 25 35 5u 0 10 40u 0 Free labels The metarost label macro enables you to position text at certain points This macro is kind of special since it also enables you to influence the positioning For that purpose it uses a special kind of syntax which we will not discuss here in detail pickup pencircle scaled 1mm path p p fullcircle scaled 3cm draw p withcolor 625yellow dotlabel rt right point O of p dotlabel urt upper right point 1 of p dotlabel top top point 2 of p dotlabel ulft upper left point 3 of p dotlabel 1lft left point 4 of p dotlabel llft lower left point 5 of p dotlabel bot bottom point 6 of p dotlabel 1Irt lower right point 7 of p The label command just typesets a text while dotlabel also draws a dot at the position of the label The thelabel command returns a picture top upper left upper right left right lower left lower right bottom A few applications Preliminary Version November 11 2001 There is a numeric constant labeloffset that can be set to influence the distan
197. mand while a macro is a collection of such primitives packaged in a way that they can be recalled easily Where scaled is a primitive and draw a macro unitsquare is a path variable an abbreviation for unitsquare 0 0 1 0 1 1 0 1 cycle The double dash is also a macro used to connect two points with a straight line segment However cycle is a primitive which connects the last point of the unitsquare to the first on unitsquare s path Path variables must first be declared as in path unitsquare A large collection of such macros is available when you launch metarost Consult the METAPOST manual for details In the first line of our example we set the drawing pen to 5cm You can also specify such a dimension in other units like points pt When no unit is provided metarost will use a big point bp the POSTSCRIPT approximation of a point The second line does just as it says it draws a rectangle of certain dimensions in a certain color In the third line we draw a colored dot at the origin of the coordinate system in which we are drawing Finally we set up a smaller pen and draw the bounding box of the current picture using the variable currentpicture Normally all drawn shapes end up in this picture variable Bounding boxes If you take a close look at the last picture in the previous section you will notice that the bounding box is larger than the picture This is one of the nasty side effects
198. me of which we already have seen numeric real number in the range 4096 4096 boolean a variable that takes one of two states true or false pair point or vector in 2 dimensional space path a piecewise collection of curves and line segments picture collection of stroked or filled paths string sequence of characters like metapost There are too additional types transform and pen but we will not discuss these in depth transform transformation vector with six elements pen pen specification You can achieve interesting effects by using pens with certain shapes For the moment you may consider a pen to be a path itself that is applied to the path that is drawn The numeric data type is used so often that it is the default type of any non declared variable This means that n 10 is the same as numeric n n 10 When writing collections of macros it makes sense to use the second method because you can never be sure if n isn t already declared as a picture variable and assigning a numeric to a picture variable is not permitted Preliminary Version November 11 2001 Welcome to METREDE 1 6 1 7 Because we often deal with collections of objects such as a series of points all variables can be organized in arrays For instance numeric n n 3 10 n 5 13 An array is a collection of variables of the same type that are assigned and accessed by
199. mporarily store it when we fill the background numeric width height line delta width 5cm height width 2 line height 4 delta line applications Preliminary Version November 11 2001 13 11 linejoin mitered pickup pencircle scaled line color nsblue nsblue 0 0 1 color nsyellow nsyellow 1 1 0 zi 0 height 2 z2 width 2 height 4 y1 z3 width 2 height 4 y4 z4 width O0 z5 x4 height 2 y1 z6 x4 2y1 z7 1 5 z5 z6 path p p z1 z2 z3 z4 path q q z3 z4 z5 z7 numeric d 1x ly ux uy d line 2 lx 3d d 3 ly d ux rt x5 d 3 uy top y6 path r r 1x ly ux ly ux uy 1x uy cycle lx lx delta ly ly delta ux uxtdelta uy uytdelta path s s 1x ly ux 1ly ux uy 1x uy cycle draw p withcolor nsblue draw q withcolor nsblue addto currentpicture also currentpicture rotatedaround 5 z2 z3 180 shifted height 4 height 2 picture savedpicture savedpicture currentpicture clip currentpicture to r setbounds currentpicture to r savedpicture currentpicture currentpicture nullpicture fill s withcolor nsyellow addto currentpicture also savedpicture For practical use it makes sense to package this definition in a macro to which we pass the dimensions Animations Although metarost is
200. n xi 0 yl height 2 x2 width 2 height 4 y2 yl k x3 width 2 height 4 y3 y4 x4 width y4 0 Since we express the variables x and y in terms of relations we cannot reuse them since that would mean that inconsistent relations occur So the following lines will lead to an error message zi 10 20 zi 30 50 For similar reasons we may not assign a value using to such a z variable Within a METAPOST figure z variables are automatically saved which means that they can be reused for each figure So far we have defined the following segment of the logo 2 3 The next expressions are used to define the second segment The third expression determines z7 to be positioned on the line z5 z6 where we extend this line by 50 z5 x4theight 2 y1 z6 x4 2y1 z7 1 5 z5 z6 path q q z23 z4 z5 z7 A fey applications Preliminary Version November 11 2001 If we combine these two segments we get 3 a e e e 2 0 1 e e 20 31 However when we draw them using the right linewidth and color you will notice that we re not yet done The second curve is similar to the first one but rotated over 180 degrees addto currentpicture also currentpicture rotatedaround 5 z2 z3 180 shifted height 4 height 2 In order to get the sharp edges we need to clip off part of the curves and at first sight we may consider using a
201. n draw_bisector stand_out draw_midpoint stop_everything The definitions of the symbols now refer to an external figure A few appligations Preliminary Version November 11 2001 13 10 definesymbol step 1 externalfigure step 1 definesymbol step 2 externalfigure step 2 definesymbol step 3 externalfigure step 3 definesymbol step 4 externalfigure step 4 definesymbol step 5 externalfigure step 5 Which method is used depends on the way the graphics are used In this example we wanted to change the definition of _ everything so here the third method was quite useful Simple Logos Many company logos earn their beauty from their simplicity One of the logos that most dutch people have imprinted in their mind is that of the Dutch Railway Company NS An interesting feature of this logo is that although it is widely known drawing it on a piece of paper from mind is a task that many people fail This logo makes a good candidate for demonstrating a few fine points of drawing graphics like using linear equations setting line drawing characteristics clipping and manipulating bounding boxes The implementation below is quite certainly not according to the official specifications but it can nevertheless serve as an example of defining such logos As always we need to determine the dimensions first Here both the height and line widt
202. n Unless you take special precautions variables are global by nature and persistent outside macros picture finalpicture finalpicture nullpicture Just as numeric allocates an integer variable the picture primitive allocates a picture data struc ture We explicitly have to set this picture to nothing using the built in primitive nullpicture Later on we will add the drawn paths as accumulated in currentpicture to this finalpicture in the following manner addto finalpicture also currentpicture shifted n 3cm 0 Since we want to add a few more and don t want them to overlap we shift them Therefore we have to erase the current picture as well as increment the shift counter currentpicture nullpicture n nti The drawfill macro is one of the MetaFun macros Another handy macro is boundingbox When used instead of bbox you don t have to set the margin to zero Figure 2 2 The influence of pens on fill There is a subtle point in filling a shape In figure 2 2 you see the influence of the pen on a fill operation An indirect specification has no influence and results in a filled rectangle with sharp corners The third rectangle is drawn with a direct pen specification which results in a larger shape with rounds corners However the bounding box is the same in all three cases The graphic is defined as follows This time we don t use a complicated macro drawoptions withcolor 625white path p p unitsqu
203. n by setting the alternative variable as we demonstrated in the example startuseMPgraphic page includeMPgraphic rightsuperbutton StartPage numeric alternative seed superness squeezeness randomness path p q transform t This is one of those cases where a transform variable is useful We need to store the random seed value because we want the larger path that is used in the calculations to have the same shape alternative MPvarfalternative seed uniformdeviate 100 if alternative gt 10 superness 85 realfolio 1 lastpage 25 squeezeness 12pt realfolio 1 lastpage 10pt else superness 90 squeezeness 12pt fi s randomness squeezeness alternative alternative mod 10 If you read closely you will notice that when we add 10 to the alternative we get a page dependant graphic So in fact we have five alternatives We use CON XT macros to fetch the real page number and the number of the last page In further calculations we use the lower alternative numbers which is why we apply a mod The rest of the code is not so much different from the previous definition The hard coded point sizes match the page dimensions 600pt by 450pt quite well t identity if alternative 3 shifted 9pt 9pt fi Preliminary Version November 11 2001 randomseed seed p Field Text Text enlarged if alternative 1
204. n points of the lines and the path As a first step we calculate the top and bottom of the path and after that we split off the left and right path startuseMPgraphic text split pair t b path 1 r t ulcorner p urcorner p intersectionpoint p b llcorner p lrcorner p intersectionpoint p l p cutbefore t 1 1 cutafter b r p cutbefore b r r cutafter t stopuseMPgraphic The intersectionpoint macro returns the point where two paths cross If the paths don t cross an error is reported when the paths cross more times just one point is returned The cutafter and cutbefore commands do as their names say and return a path In the text split code fragment t and b are the top points of the main path while 1 and r become the left and right half of path p We now draw the original path using a thick pen and both halves with a thinner pen on top of the original The arrows show the direction startuseMPgraphic text draw draw p withpen pencircle scaled 3pt withcolor red drawarrow 1 withpen pencircle scaled 1pt withcolor green drawarrow r withpen pencircle scaled 1pt withcolor blue stopuseMPgraphic We use includeMPgraphic to assemble the components Typesettingin POST Preliminary Version November 11 2001 startuseMPgraphic text includeMPgraphic text path includeMPgraphic text split includeMPgraphic text draw stopus
205. n the following graphic the endpoints of a non closed curve have only one control point iD This time we used the path 1 5cm 1 5cm 2cm 0cm 1cm 1icm When you connect points by a smooth curve metapost will calculate the control points itself unless you specify one or more of them Preliminary Version November 11 2001 Weleoine to 1 2 This path is specified as 1cm icm 1 5cm 1 5cm controls 3cm 2cm 2cm 0cm In this path the second and third point share a control point Watch how the curve is pulled in that direction Itis possible to pull a bit less by choosing a different control point icm icm 1 5cm 1 5cm controls 2 75cm 1 25cm 2cm 0cm Now we get H We can also specify a different control point for each connecting segment This path is defined as 1cm icm controls 5cm 2cm and 2 5cm 2cm 2cm 5cm Transformations We can store a path in a path variable Before we can use such a variable we have to allocate its memory slot with path path p p 1cm icm 1 5cm 2cm 2cm 0Ocm Although we can manipulate any path in the same way using a variable saves us the effort to key in a path more than once Fosi Preliminary Version November 11 2001 In this graphic the path stored in p is drawn twice once in its displaced form The displacement is defined a
206. n this document we also generate graphic while we finish a page so there is a good change that when we have constructed a graphic which will be called the next page the wrong graphic is placed Therefore you may as well forget these commands since there are more convenient ways of defining and using graphics which have the added advantage that you can predefine multiple graphics thereby separating the definitions from the usage The first alternative is a usable graphic Such a graphic is calculated anew each time it is used An example of a usable graphic is startuseMPgraphic name fill fullcircle scaled 200pt withcolor 625yellow stopuseMPgraphic When you put this definition in the preamble of your document you can place this graphic anywhere in the file saying useMPgraphic name As said this graphic is calculated each time it is placed which can be time consuming Apart from the time aspect this also means that the graphic itself is incorporated many times Therefore for graphics that don t change CONTEXT provides reusable graphics startreusableMPgraphic name fill fullcircle scaled 200pt withcolor 625yellow stopreusableMPgraphic This definition is accompanied by Preliminary Version November 11 2001 Embedded Braphics reuseMPgraphic name Imagine that we use a graphic as a background for a button We can create a unique and reusable graphic by saying def
207. nce when you write advanced macros Later we will discuss in detail how you can use either METAPOST or TEX to typeset text section 1 12 and chapter 9 so here we limit our exploration to a quick introduction The most direct way of processing text in METAPOST is using the infont operator this string will become a sequence of glyphs MP The same string typeset by Tpx showed up as this string will become a sequence of glyphs TEX The following metarost features are not covered by the metaPost manual but most of them are discussed in the appendix of the graph package written by John Hobby It is possible to disassemble a picture by means of a special for loop using the within specifier The following code walks over a picture and draws the components with their bounding boxes for i within currentpicture draw boundingbox i withcolor 625yellow endfor We can use the disassemble loop feature to look into the previously shown example text this string will become a sequence of glyphs MP this string will become a sequence of glyphs TX The second line is typeset by Tpx The resulting DVI code is converted into a series of pictures which METAPOST pastes into one picture You may also notice that in the set of pictures that originate in TEX the space is replaced by a shift this is because TeX knows no space An interesting aspect of this loop over a picture feature is that it can provide your insight in how TEx is com
208. nd side let symbolic token symbolic token newinternal symbolic token list pickup expression randomseed numeric expression save symbolic token list setbounds picture variable to path expression shipout picture expression special string expression addto command drawing command font metric command show command tracing command mpxbreak verbatimtex typesetting command etex show command show expression list showvariable symbolic token list showtoken symbolic token list showdependencies symbolic token list symbolic token symbolic token symbolic token list expression list expression expression list expression addto command addto picture variable also picture expression option list addto picture variable contour path expression option list addto picture variable doublepath path expression option list option list empty drawing option option list drawing option witcolor color expression withpen pen expression dashed picture expression Preliminary Version November 11 2001 drawing command draw picture expression option list fill type path expression option list fill type gt fill draw filldraw drawfill unfill undraw unfilldraw drawarrow drawdblarrow cutdr
209. nd this manual at every main Tpx repository Also a copy of the MeTAFONT book from Donald Knuth is worth every penny if only because it will give you the feeling that many years of graphical fun lays ahead In this MetaFun manual we will demonstrate how you can embed graphics in a TEX document but we will also introduce most of the features of meTAPOsT For this reason you will see a lot of METAPOST code For sure there are better methods to solve problems but Ihave tried to demonstrate different methods and techniques as much as possible I started using Metarost long after I started using TFX and I never regret it Although I like Tex very much I must admit that sometimes using MeTAPOST is even more fun Therefore before we start exploring both in depth I want to thank their creators Donald Knuth and John Hobby for providing me these fabulous tools Of course I also need to thank Han Th Thanh for giving the Tex community PDFTgX as well as providing me the hooks I considered neccessary for implementing some of the features presented here I also want to thank David Arnold and Ton Otten for their fast proofreading for providing me useful input and for testing the examples Without Davids patience and help this document would be far from perfect English and less complete Without Tons help many small typo s would have gone unnoticed Hans Hagen November 11 2001 Preliminary Version November 11 2001
210. ned by this macro the segment has a length of 1 base point This macro has a wide range of applications but some basic knowlegde of vector algebra is handy The following lines of metaPost code demonstrate the basics behind unitvectors pair uv pickup pencircle scaled imm autoarrows true draw fullcircle scaled 2cm withcolor 625red for i 10 35 40 20 85 15 draw origin i dashed evenly withcolor 625white drawarrow origin unitvector i scaled 1cm withcolor 625yellow Preliminary Version November 11 2001 LA few endfor draw origin withcolor 625red The circle has a radius of 1cm and the three line segments are drawn from the origin in the direction of the points that are passed as arguments Because the vector has length of 1 we scale it to the radius to let it touch the circle By setting autoarrows we make sure that the arrowheads are scaled proportionally to the linewidth of 1 mm An application of this macro is drawing the angle between two lines In the mMetapost manual you can find two macros for drawing angles mark_angle and mark_rt_angle You may want to take a look at their definitions before we start developing our own alternatives i The previous graphic demonstrates what we want to accomplish a circular curve indicating the angle between two straight lines The lines and curve are drawn with the code pair a b a 2cm 1cm b 8cm 1ic
211. ng to the lineheight but a more general solution is to adapt the height to the fontsize height 3 4 the bodyfontsize currentfontscale In the table we called the graphic directly but how about making it available as a conversion macro In CONTEXT this is not that hard def fuzzycount 1 tx useMPgraphic fuzzycount n 1 def ineconversion fuzzy fuzzycount Because such a counter should not be that large we use tx to switch to a smaller font This also demonstrates how the graphic adapt itself to the font size We can now use this conversion for instance is an itemize To save space we use three columns and no white space between the lines The 2 broad directive makes sure that we have enough room for the number I one tl four fil seven ll two m five Iti eight Il three WMI six Will nine startitemize fuzzy pack 2 broad columns three item one item two item three item four item five item six item seven item eight item nine stopitemize A careful reader will have noticed that the previous definition of the fuzzy counter drawing is not suited to generate the graphics we started with useMPgraphic fuzzycount n 1001 This time we want to limit the width to the current hsize We only need to add a few lines of code Watch how we don t recalculate the bounding box when more lines are used startuseMPgraphic fuzzycount begingroup save height vstep hsize span drift d cp
212. ng two pencils and holding them together in one hand If you position them in a 45 degrees angle and draw a circle you will get something like Preliminary Version November 11 2001 If you take a calligraphic pen with a thin edge of 5cm you will get You can define such a pen yourself path p p fullcircle xscaled 2cm yscaled 3cm pen doublepen doublepen makepen 0 0 3cm 3cm pickup doublepen draw p Here we define a new pen using the pen command Then we define a path and make a pen out of it using the makepen macro The path should be a relatively simple one otherwise METAPOST will complain You can use makepen with the previously introduced withpen draw p withpen makepen 0 0 3cm 3cm and pickup pickup makepen 0 0 3cm 3cm draw p You can use makepen and makepath to convert paths into pens and vice versa Pens are very important when defining fonts which is why MeETAFONT was created Since META post has a slightly different audience it lacks some features in this area but offers a few others instead Nevertheless one can try to design a font using meTAPosT Of course pens are among the designers best kept secrets But even then not every O is a nice looking one E Preliminary Version November 11 2001 1 10 1 11 Colors So far we have seen some colors in graphics It must be said that mMeTAPosT col
213. not that well suited for free hand drawings you can use it to make stylistics animations Preliminary Version November 11 2001 A few applications Preliminary Version November 11 2001 14 MetaFun macros CONTEXT comes with a series of MeTAPOST modules In this chapter we will summarize the most important TeX and metarost macros More information can be found in the documentation of the modules Unless you want to write low level CONTEXT code yourself there is no real reason to look into the modules that deal with mMetarost support supp mps tex low level inclusion macros and housekeeping supp mpe tex experimental extensions like specials supp pdf tex METAPOST to PDF conversion meta ini tex high level inclusion macros and interfacing meta tex subsystems and handy macros The last category will certainly grow Some of these modules are preloaded others can be loaded using the command useMPlibrary like useMPlibrary clp txt for loading the predefined clipping paths and text tricks The Metarost code is organized in files named mp mp The core file is mp tool mp and this file can comfortably be used in stand alone graphics The collection of metarost code files will grow in due time but as long as you use the MetaFun format you don t have to keep track of the organization of files Most files relate to subsystems and are loaded automat
214. ns which are expressed usin an instead of In this case the expression related to z0 is expanded into z0 x0 y0 0 5cm 1 5cm But let s for this moment forget about their expressive nature and simply see them as points which we will now connect by straight line segments Welcome toiMerarast Preliminary Version November 11 2001 z0 z1 z2 z3 cycle z0 z1 22 23 cycle Z2 Z3 cycle r 5 i z0 z1 z2 z3 cycle f I 3 o 4 e i i l f L 2m If you compare this graphic with the one using the result is the same but there is a clear difference in control points As a result combining with or makes a big difference Here we get a non smooth connection between the curves and the straight line Preliminary Version November 11 2001 Welcome tomerarest zO z1 z2 z3 cycle As you can see in the next graphic when we use we get a smooth connection between the straight line and the rest of the curve z0 z1 z2 z3 cycle So far we have joined the four points as one path Alternatively we can constrict subpaths and connect them using the ampersand symbol amp zO z1 z22 amp z2 z3 z0 amp cycle So far we have created closed path Closing is done by cycle The following path may look closed but is in fact open zO z1 z22 23 z0 Only
215. nt a desktop publisher hears 10bp In a similar vein when we define a papersize having a width of 600pt and a height of 450pt which is papersize S6 in CONTEXT a POSTSCRIPT or PDF viewer will report slightly smaller values as page dimensions This is because those programs claim the pt to be a bp This confusion can lead to interesting discussions with desktop publishers when they have to use TEX They often think that their demand of a baseline distance of 13 4 is met when we set it to 13 4pt while actually they were thinking of 13 4bp which of course in other programs is specified using a pt suffix Therefore when embedding graphics in CONTEXT we strongly recommend that you use pt as the base unit instead The main reason why we spend so many words on this issue is that when neglected large graphics may look inaccurate Actually when taken care of it is one of the many reasons why Tex documents always look so accurate Given that the eye is sensitive to distortions of far less than 1pt you can be puzzled by the fact that many drawing programs only provide a bounding box in rounded units Thereby they round to the next position to prevent unwanted cropping For some reason this low resolution has made it into the high end POSTSCRIPT standard In CONTEXT we try to deal with these issues as well as possible Scaling and shifting When we draw a shape metarost will adapt the bounding box accordingly This means that a graphic has its
216. nt variable local to the for loop If you want to change the loop variable itself you need to use forsuffixes In the next loop the paths p q and r are all shifted forsuffixes i p q r i i shifted 3cm 2cm endfor Sometimes you may want to loop forever until a specific condition occurs For this METAPOST provides a special looping mechanism numeric done i j n n 0 forever i round uniformdeviate 10 j round uniformdeviate 2 if unknown done i j drawdot ixcm j cm n n 1 done i J j n fi exitif n 10 endfor Preliminary Version November 11 2001 1 8 Here we remain in the loop until we have 10 points placed We use an array to keep track of placed points The metarost macro uniformdeviate n returns a random number between 0 and n and the round command is used to move the result toward the nearest integer The unknown primitive allows us to test if the array element already exists otherwise we exit the conditional This saves a bit of computational time as each point is drawn and indexed only once The loop terminator exitif and its companion exitunless can be used in for forsuffixes and forever Macros In the previous section we introduced upto Actually this is not part of the built in syntax but a sort of shortcut defined by def upto step 1 until enddef You just saw a macro definition where upto i
217. o is part of MetaFun and takes three arguments a label string or alternatively a picture a point location and the center of gravity The label is positioned in the direction opposite to this center of gravity pair destination for whereto up down left right destination scantokens whereto 1cm freedotlabel whereto destination origin drawarrow origin destination withpen pencircle scaled 25mm withcolor 625 red endfor So in this code fragment we use the string as string and by means of scantokens as a point or vector up left right down The previous definition is a stepping stone to the next one This time we don t use points but the dir command This command converts an angle into a unitvector pair destination for whereto 0 step 30 until 330 destination dir whereto 1 5cm freedotlabel decimal whereto destination origin drawarrow origin destination withpen pencircle scaled 25mm withcolor 625 red endfor In metarost the angles go counter clockwise which is not that illogical if you look at it from the point of view of vector algebra A felv More details Preliminary Version November 11 2001 2 10 120 Y g 150 30 180 0 210 330 240 300 Analyzing pictures Unless you really want to know all details you can safely skip this section The metarost features discussed here are mainly of importa
218. oe wet ses 291 E3 CONTpXT 291 E4 TOOIS sscnc Sa eads ways dbs wom eee 291 E 5 Distributions 291 Index Seve Wis Sl bce eee a ae hs 293 Preliminary Version November 11 2001 Conventions When reading this manual you may be tempted to test the examples shown This can be done in several ways You can make a file and process that file by Metarost Such a file looks like input mp tool 4 some initializations and auxiliary macros input mp spec 4 macros that support special features beginfig 1 fill fullcircle scaled 5cm withcolor red a graphic endfig end Don t forget the semi colons that end the statements If the file is saved as yourfile mp then the file is processed by mpost yourfile The results are available in yourfile 1 and can be viewed with GHOSTSCRIPT You don t need to close the file so reprocessing is very convenient Alternatively you can use CONTEXT In that case a simple file looks like starttext startuseMPgraphic dummy fill fullcircle scaled 5cm withcolor red stopuseMPgraphic useMPgraphic dummy stoptext If the file is saved as yourfile tex then you can produce a DVI file with texexec yourfile A PDF file viewable in ACROBAT or GHOSTVIEW is produced with texexec pdf yourfile Depending on how your system is set up CONTEXT will run metarost during the Tex run or afterwards If you want to process a MeTarost file separately using TEXEXE
219. oes not hide the fact that metarost lacks a real unfill operation Since we don t consider this unfill a suitable operator you may wonder how we achieved the above result Preliminary Version November 11 2001 fill 0 0 0 h w h w 0 ww 0 w hh ww hh ww 0 cycle This feature depends on the POSTSCRIPT way of filling closed paths which comes down to filling either the left or the right hand side of a curve The following alternative works too fill 0 0 0 h w h w hh ww hh ww 0 w hh w 0 cycle The next alternative will fail This has to do with the change in direction at point 0 0 halfway through the path Sometimes changing direction can give curious but desirable effects but here it brings no good fill 0 0 0 h vat w h a w 0 0 0 ww 0 ww hh T w hh ww 0 cycle This path fails because of the way POSTSCRIPT implements its fill operator More details on how POSTSCRIPT interpreters handle fills can be found in the reference manuals Some of the operations we have seen are hard coded into metarost and are called primitives Others are defined as macros that is a sequence of METAaPOST commands Since they are used often you may expect draw and fil1 to be primitives but they are not They are macros defined in terms of primitives Given a path pat you can consider a draw to be defined in terms of
220. of METAPOST s bbox macro This macro draws a box but with a certain offset The next example shows how we can manipulate A few more details Preliminary Version November 11 2001 this offset Remember that in order to process the next examples you should embed the code in beginfig and endfig macros Also in stand alone graphics don t forget to say input mp tool first pickup pencircle scaled 5cm draw unitsquare xscaled 8cm yscaled 1cm withcolor 625white path bb bboxmargin Opt bb bbox currentpicture draw bb withpen pencircle scaled ipt withcolor 625red In the third line we define a path variable We assign the current bounding box to this variable but first we set the offset to zero The last line demonstrates how to draw such a path Instead of setting the pen as we did in the first line we pass the dimensions directly Where draw draws a path the fill macro fills one In order to be filled a path should be closed which is accomplished by the cycle primitive as we saw in constructing the unitsquare path pickup pencircle scaled 5cm fill unitsquare xscaled 8cm yscaled 1cm withcolor 625white path bb bboxmargin Opt bb bbox currentpicture draw bb withpen pencircle scaled ipt withcolor 625red This example demonstrates that when we fill the path the resulting graphic is smaller Where draw follows the center of a path fill stays inside the pa
221. of which contains the drawfill macro which provides the outer bounding box We will demonstrate its use in another more complicated example picture finalpicture finalpicture nullpicture numeric n n 0 bboxmargin Opt pickup pencircle scaled 5cm def shape unitsquare scaled 2cm withcolor 625white draw bbox currentpicture withpen pencircle scaled 5mm withcolor 625red addto finalpicture also currentpicture shifted n 3cm 0 currentpicture nullpicture n ntl enddef fill shape draw shape filldraw shape drawfill shape currentpicture finalpicture Here we introduce a macro definition shape In metarost the start of a macro definition is indicated with the keyword def Thereafter you can insert other variables and commands even other macro definitions The keyword enddef signals the end of the macro definition The result is shown in figure 2 1 watch the bounding boxes Close reading of the macro will reveal that the fill draw filldraw and drawfill macros are applied to the first unitsquare path in the macro Figure 2 1 A fill draw filldraw and drawfill applied to the same square Preliminary Version November 11 2001 23 In this macro bbox calls a macro that returns the enlarged bounding box of a path By setting bboxmargin we can influence how much the bounding box is enlarged Since this is an existing variable we don t have to allocate it like we do with numeric
222. oint def inelayer BackLayer position yes setupbackgrounds page background BackLayer Next we define an overlay that we can put behind for instance framed texts We use METAPOST to draw Shape defineoverlay Shape BackLayer uniqueMPgraphic Shape startuniqueMPgraphic Shape path p p fullcircle xyscaled OverlayWidth OverlayHeight fill p withcolor MPcolor lightgray draw p withpen pencircle scaled 1pt withcolor MPcolor darkred stopuniqueMPgraphic We can now put this background shape behind the running text for instance with some inframed background Shape text with a frame some Shaped text with a frame Positional graphics Preliminary Version November 11 2001 some text with a frame some text with a frame The Shaped macro was defines as some inframed background Shape text with a frame some Shaped text with a frame Watch how the graphics are moved to the background while the frame of the first text stays oni top since it remains part of the text flow ra N 7 some text with a frame some text with a frame In the previous instance of the example we have reversed the stacking Reversal can be done with the direction directive some inframed background Shape text with a frame some Shaped text with a frame You can influence the placement of a b
223. olor In POSTSCRIPT level 2 the way this color changes can be circular linear or according to a user defined function Circular and linear shades look like this there I m Circul Whov this is Lii As you can see the shade lays behind the text as background overlay These overlays are unique METAPOST graphics so they will adapt themselves to the dimensions of the foreground defineoverlay circular shade uniqueMPgraphic CircularShade defineoverlay linear shade uniqueMPgraphic LinearShade The two framed texts are defined as framed background circular shade frame off bf white Hi there I m Circular and framed background linear shade frame off bf white Whow this is Linear We still have to define the graphics Here we use a macro that takes four arguments a path a number identifying the center of shading and the colors to start and end with Preliminary Version November 11 2001 Spetial effects startuniqueMPgraphic CircularShade path p gt p unitsquare xscaled overlaywidth yscaled overlayheight circular_shade p 0 MPcolor a MPcolor b stopuniqueMPgraphic startuniqueMPgraphic LinearShade path p gt p unitsquare xscaled overlaywidth yscaled overlayheight linear_shade p 0 MPcolor a MPcolor b stopuniqueMPgraphic The METAPOST macros circular_shade and linear_shade add information to the METAPOST out
224. oming S65 Ce books from the typesetting and layout down gt L to the very shapes of the letters Seldom has B world By contrast his METAFONT system for de signing families of typefaces has not become _ as well known or available In his article The Concept of a Meta Font Knuth sets forth for the Figure 9 4 One more time Hofstadter s quotation Here also I will rewrite things a bit so that we can avoid startMPdrawing outside the macro and thereby avoid problems I can also add the maps cdrom cover as example Preliminary Version November 11 2001 Preliminary Version November 11 2001 10 Debugging Those familiar with CONT XT will know that it has quite some visual debugging features build in So what may you expect of the METAPOST macros that come with CONTEXT In this chapter we will introduce a few commands that show some insight in what metapost is doing to your paths Since the outcome of MeTarost code is in many respects more predictable than that of TEx code we don t need that advanced visual debugging features Nevertheless we provide a few that are all based on visualizing paths This visualization is achieved by using dedicated drawing commands path p p fullcircle scaled 4cm drawpath p drawpoints p drawpointlabels p Since control points play an important role in defining the shape visualizing them ma
225. on wid i abs xpart lrcorner picli xpart llcorner pic i posl i len i wid i endfor stopMPdrawing This compares well to the text as typeset by TEx MetaPost is Fun We can now use the values in pos to position the pictures according to what Tpx considered to be the best relative position startMPdrawing for i 1 upton draw picli shifted pos i 0 draw boundingbox pic i shifted pos i 0 withpen pencircle scaled 25pt withcolor red endfor stopMPdrawing That this correction is adequate is demonstrated in the next graphic If you look closely you will see that for instance the o is moved to the left under the capital P MetaPost is When we want to position the pictures along a circle we need to apply some rotations especially because we want to go clockwise Since we don t want to use complicated math or more advanced METAPOST code yet we will do it in steps startMPdrawing for i 1 upto n picli picli rotatedaround origin 270 endfor stopMPdrawing 2 uonane We will now center the pictures around the baseline Centering comes down to shifting over half the height of the picture This can be expressed by ypart 5 ulcorner pic i llcorner pic i Preliminary Version November 11 2001 but different ways of calculating the distance are possib
226. on the page In a double sided layout scheme the back space is automatically mirrored on even pages Since we want to teach a bit of MeTaPosT now and then we will also show how these graphics were drawn An advanced meTAPOST user may wonder why we hard code the dimensions and Preliminary Version November 11 2001 avoid metarost s powerful mechanisms for defining relations Our experience has taught us that in pictures like this providing a general solution seldom pays large dividents or savings in time startuseMPgraphic layout 1 pickup pencircle scaled 1mm fill unitsquare xyscaled 7cm 8cm withcolor 85white fill unitsquare xyscaled 5cm 5cm shifted 1cm 1 5cm withcolor 625yellow fill unitsquare xyscaled 5cm 1cm shifted 1cm 5cm withcolor 625red fill unitsquare xyscaled 5cm 1icm shifted 1cm 6 5cm withcolor 625red draw unitsquare xyscaled 5cm 7cm shifted 1cm 5cm withcolor 25white drawarrow 2cm 8cm top 2cm 7 5cm drawarrow Ocm 7cm lft 1cm 7cm clip currentpicture to unitsquare xyscaled 7cm 8cm stopuseMPgraphic As you can see the left graphic is defined as a series of rectangles The xyscaled macro is part of the CONTEXT files and saves some typing and space It is defined as a primary requiring both left and right operands primarydef p xyscaled q p xscaled xpart q yscaled ypart q enddef Zooming in on the top left corner only
227. oof with a lot of sin this and cos that and long forgotten formulas I was expected to prove that the angle between the lines connecting the mid points of four squares drawn upon the four sides of a box is ninety degrees see figure 1 1 Because we have seen most of the MeTaPOST commands and features we will package the solution in a macro Also because this macro has an educational purpose we will add some labels to the points that we use However generating these labels is optional and controlled by a boolean boolean show_labels show_labels false The macro accepts four pair of coordinates that determine the central four sided shape All of them are expressions Preliminary Version November 11 2001 Tpost Za Z44 Figure 1 1 The problem def draw_problem expr n p q r s beginfig n We did not yet discuss the beginfig macro In a metarost file you can put many graphics Each graphic is surrounded by beginfig and endfig The number here the variable n will become the prefix of the output file Because we want to call this macro more than once we have to save the locally used values Instead of declaring local variables one can hide their use for the outside world In most cases variables behave global If we don t save them the next call will lead to errors due to conflicting equations We can omit the grouping commands because we wrap t
228. or 625red That the results are indeed correct is demonstrated by the output of following example However when we swap the points we get This means that instead of rotating over 90 degrees we have to rotate over 90 or 270 degrees That way the arrow will also point in the other direction There are undoubtly more ways to determine the direction but the following method also demonstrates the use of turningnumber which reports the direction of a path For this purpose we compose a dummy cyclic path vardef anglebetween expr endofa endofb common length save tn tn turningnumber common endofa endofb cycle show tn unitvector endofa common endofa common rotated tn 90 unitvector endofb common scaled length shifted common enddef Because we use an intermediate variable just to keep things readable we have to use vardef to hide the assignment for the outside world We demonstrate this macro using the following code pair a b c a 2cm 1cm b 3cm cm c 1cm 5cm drawarrow c a drawarrow c b drawarrow anglebetween a b c 0 75cm withcolor 625red drawarrow anglebetween b a c 1 50cm withcolor 625red Watch how both arrows point in the direction of the line that is determined by the second point Preliminary Version November 11 2001 A few ty We now have the framework of an angle drawing macro ready and
229. or model is not that advanced although playing with colors in the Metarost way can be fun In later chapters we will discuss some extensions that provide shading Colors are defined as vectors with three components a red green and blue one Like pens colors have their with command withcolor 4 5 6 You can define color variables like color darkred darkred 625 0 0 You can now use this color as withcolor darkred Given that red is already defined we also could have said withcolor 625red Because for MeTAPOsT colors are just vectors you can do things similar to points A color halfway red and green is therefore accomplished with withcolor 5 red green Since only the RGB color space is supported this is about all we can tell about colors for this moment Later we will discuss some nasty details Dashes A dash pattern is a simple picture that is build out of straight lines Any slightly more complicated picture will be reduced to straight lines and a real complicated one is rejected and in this respect METAPOST considers a circle to be a complicated path The next example demonstrates how to get a dashed line First we built picture p that we apply to a path Here we use a straight path but dashing can be aplied to any path picture p p nullpicture addto p doublepath 0 0 3mm 3mm shifted 6mm 6mm draw 0 0 10cm 0 dashed p withpen pencircle scaled 1mm This way of defining a pattern is not
230. orcircle 4cm 5red 5green 5blue This kind of unsafe path calculations are very sensitive to breaking Changing the radius 4 into something else demonstrates this but we will not challenge this macro that much Therefore the 50 color circle shows up as This command is part of MetaFun and can be used to determine nice color combinations by also looking at their complementary colors Preliminary Version November 11 2001 A fw colorcircle 4cm 7red 5green 3blue The next circle that we draw shows the three main colors used in this document This circle is not that beautiful colorcircle 4cm 625red 625yellow 625white This definition can be cleaned up a bit by using transform but the fuzzy buildcycle s remain vardef colorcircle expr size red green blue save r g b rr gg bb cc mm yy save radius path r g b rr bb gg cc mm yy numeric radius radius 5cm pickup pencircle scaled radius 25 transform t t identity rotatedaround origin 120 r fullcircle scaled radius shifted 0 radius 4 rotatedaround origin 15 g r transformed t b g transformed t r r rotatedaround center r 90 g g rotatedaround center g 90 gg buildcycle buildcycle reverse r b g cc buildcycle buildcycle b reverse g r rr gg transformed t bb rr transformed t yy cc transformed
231. ound backfore backgroundoffset 4pt fone two three unknown The current values of the frame color and frame width are passed to the overlay It often makes more sense as well as is more consistent to use colors defined at the document level startuniqueMPgraphic super ellipse path p p unitsquare xscaled overlaywidth yscaled overlayheight superellipsed 85 pickup pencircle scaled overlaylinewidth fill p withcolor MPcolor overlaycolor draw p withcolor MPcolor overlaylinecolor stopuniqueMPgraphic defineoverlay super ellipse uniqueMPgraphic super ellipse This background demonstrated that a super ellipse is rather well suited as frame Enitaneing the layout Preliminary Version November 11 2001 4 5 framed background super ellipse frame off width 3cm align middle framecolor darkyellow rulethickness 2pt backgroundcolor darkgray white This is a Super Ellipsed sentence Such a super ellipse looks quite nice and is a good candidate for backgrounds for which the superness should be at least 85 Typesetting graphics I have run into people who consider it kind of strange when you want to use TeX for non mathematical typesetting If you agree with them you may skip this section with your eyes closed One of the CONT XT presentation styles number 15 tagged as balls stepwise builds screens full of sentences quotes or concepts
232. ovember 11 2001 centershade 5 topshade bottomshade stopuseMPgraphic The color funcolor is provided by CONTEXT and since we want to use this graphic with differ ent colors this kind of mapping is quite convenient The bunch of graphics is packaged in a combination with empty captions Note how we set the color before we include the graphic startcombination 5 2 definecolor funcolor red useMPgraphic second definecolor funcolor green useMPgraphic second definecolor funcolor blue useMPgraphic second definecolor funcolor yellow useMPgraphic second definecolor funcolor white useMPgraphic second definecolor funcolor red useMPgraphic third definecolor funcolor green useMPgraphic third definecolor funcolor blue useMPgraphic third definecolor funcolor yellow useMPgraphic third definecolor funcolor white useMPgraphic third stopcombination We use a similar arrangement for the following graphic where we have replaced the definitions of first second and third by new definitions Figure 13 4 Koffka s examples of manipulating contrast by changing the spatial configura tion The definition of the first row of figure 13 4 is used in the second and third and therefore is the most complicated We use quite some scratch variables to reach a high level of abstraction The xyscaled operator is a MetaFun ma
233. overlay in any command that provides the framed functionality Since this graphic is defined as unique CONTEXT will try to reuse already calculated and embedded graphics when possible framed background demo circle This text is overlayed The background can be set to color screen an overlay identifier like demo circle oracomma separated list of those his text is overlayed The framed command automatically draws a ruled box which can be quite useful when debug ging a graphic However in this case we want to turn the frame off framed background demo circle frame off This text is overlayed his text is overlayed Preliminary Version November 11 2001 EBEnhanging the layon it In this case it would have made sense to either set the offset to a larger value or to set backgroundoffset In the latter case the ellipse is positioned outside the frame The difference between the three offsets offset frameoffset and backgroundoffset is demonstrated in figure 4 1 While the offset is added to the natural or specified dimensions of the content of the box the other two are applied to the frame and background and don t add to the dimensions In the first row we only set the offset while in the second row the text offset is set to 3pt When not specified the offset has a comfortable default value of 25ex some 25 of the height of an x setupframed
234. ow up at the position specified after the dot If we don t specify a position we will get a centered label top lft rt bot The command dotlabel also typesets a point as dot and has the same arguments but swapped which makes using these commands kind of trial and error pair a a 3cm 3cm dotlabel top top a dotlabel bot bot a dotlabel 1ft lft a dotlabel rt rt a top lftert bot The command thelabel returns a picture with the label so that you can say pair a a 3cm 3cm pickup pencircle scaled imm drawdot a withcolor 625yellow draw thelabel rt the right way a withcolor 625red You can of course rotate slant and manipulate such a label picture like any other picture ethe right way POST Preliminary Version November 11 2001 The font can be specified in the string defaultfont and the scale in defaultscale Labels are defined using the low level operator infont The next statement returns a picture draw this string will become a sequence of glyphs MP infont defaultfont scaled defaultscale The infont operator is not that clever and does not apply kerning Also typesetting math or accented characters is not supported The way out of this problem is using btex etex draw btex this string will become a sequence of glyphs TeX etex The difference between those two methods is shown below this string wi
235. p pencircle xscaled 3mm yscaled 5mm rotated 30 path p p fullcircle xscaled 6cm yscaled 3cm draw p withcolor 625white We draw this path using a non standard pen In the MetaFONT manual you will find methods to draw shapes with similar pens where the pen is also turning as it does in real calligraphy Here we stick to a more simple one Preliminary Version November 11 2001 A few more details We construct the inner path from the points that make up the curve Watch how we use a for loop to compose the new path When used this way no semi colon may be used to end the loop since it would isolate the color directive draw point 0 of p for i 1 upto length p point i of p endfor withcolor 625red The points are still located on the original path We can move the points to the inside by shifting them over the penwidth in the direction perpen dicular to the point which is a good approximation Because we use this transformation more than once we wrap it into a macro This also keeps the code readable vardef inside expr pnt of p point pnt of p shifted penoffset direction pnt of p of currentpen enddef draw inside 0 of p for i 1 upto length p inside i of p endfor withcolor 625red Whenever you define a pen MeTAPOST stores its characteristics in some private variables which are used in the top and alike directives The penoffset is a built
236. pen pencircle scaled 2 5 withcolor black drawlineoptions withpen pencircle scaled 1 withcolor 5white drawlabeloptions Two more options are draworiginoptions and drawboundoptions which are used when visu alizing the bounding box and origin swappointlabels true path p p fullcircle xscaled 4cm yscaled 3cm drawarrowpath p drawcontrollines p drawpoints p drawcontrolpoints p drawpointlabels p drawboundingbox p draworigin In this example we have set swappointlabel1s to change the place of the labels You can set the variable originlength to tune the appearance of the origin Preliminary Version November 11 2001 Here we used the options path p p fullcircle xscaled 6cm yscaled 3cm rotated 15 drawarrowpath pi drawcontrollines p withcolor drawpoints p withcolor drawcontrolpoints p withcolor drawpointlabels p withcolor drawboundingbox p draworigin withcolor 625red 625yellow 625yellow 625yellow 625red Sometimes it makes sense to draw a simple coordinate system and for that purpose we have three more macros They draw axis and tickmarks drawticks unitsquare xscaled 4cm yscaled 3cm shifted 1cm 1cm The system drawn is based on the bounding box specification of the path passed to the macro You can also draw one axis using drawxticks or drawyticks Here we show the previous command Preliminary Version November 11 2001
237. picture two times so that we now have three copies of the cross We store the accumulated drawing again so that after duplication we finally get six crosses NL NL NL ZN 7 ZN NL NL Z 7 ZN ZN You can often follow several routes to reach the same solution Consider for instance the following graphic fill 0 0 ww 0 ww hh w hh w h 0 h cycle fill ww 0 w 0 w hh cycle POST Preliminary Version November 11 2001 The points that are used to construct the paths are defined using the constants w h ww and hh These are defined as follows w 4cm h 2cm ww 1cm hh 1 5cm In this case we draw two shapes that leave part of the rectangle uncovered If you have a background this technique allows the background to show through the graphic A not uncommon practice when making complicated graphics is to use unfill operations Since METAPOST provides one let us see what happens if we apply this command fill 0 0 w 0 w h 0 h cycle unfill ww 0 w hh ww hh cycle This does not always give the desired effect because METAPOST s unfil1 is not really an unfill but a fill with color background Since this color is white by default we get what we just showed So if we set background to black using background black we get Of course you can set the variable background to a different color but this d
238. posing a paragraph thrive ini information thick worlds because of marvelous andi everyday capacity to select edit single out structure highlight group pair merge harmonize synthesize focus organize condense reduce boil down choose categorize catalog classify list abstract scan look into idealize isolate discriminate distinguish pigeonhole pick over sort integrate blend inspect filter lump skip smooth average cluster aggregate outline summarize itemize review into flip through browse glance into leaf through skim refine enumerate synopsize winnow the wheat from the chaff and separate the sheep from the Preliminary Version November 11 2001 You may also notice that rules produced by Tx are converted to straight line segments Because the line extends 50 of its linewidth beyond a point there is a slight overshoot This picture was defined in a few lines draw btex framed width fit align middle input tufte relax etex for i within currentpicture draw boundingbox i withpen pencircle scaled 2pt withcolor 625yellow endfor If
239. positioned with the baseline on the origin X This picture demonstrates that we can also position textext s and label s on the baseline For this purpose the repertoire of positioning directives top 1ft etc is extended with a origin directive Matve hinE E NORTEL picture q q textext origin MPstring 2 3 picture r r thelabel origin MPtext 3 origin We will now apply this knowledge of text inclusion in graphics to a more advanced example The next definitions are the asnwer to a question on the CONTEXT mailinglist with regards to framed texts with titles Preliminary Version November 11 2001 Enhancing the Coming back to the use of typefaces in electronic publishing many of the new typographers receive their knowledge and information about the rules of typography from books from computer magazines or the instruction manuals which they get with the purchase of a PC or software In this example the title is positioned on top of the frame Title and text are entered as FrameTitle Zapf 1 StartFrame Coming back to the use of typefaces in electronic publishing many of the new typographers receive their knowledge and information about the rules of typography from books from computer magazines or the instruction manuals which they get with the purchase of a PC or software StopFrame The implementation is not that complicate
240. primary path expression expression path subexpression subexpression pen expression expression picture expression expression picture variable variable string expression expression suffix parameter parameter transform primary primary program statement list end statement list empty statement list statement statement empty equation assignment declaration macro definition compound pseudo procedure command Preliminary Version November 11 2001 compound begingroup statement list endgroup beginfig numeric expression statement list endfig equation expression right hand side assignment variable right hand side internal variable right hand side right and side expression equation assignment declaration type declaration list declaration list generic variable declaration list generic variable generic variable Symbolic token generic suffix generic suffix empty generic suffix tag generic suffix macro de nition macro heading replacement text enddef macro heading def Symbolic token delimited part undelimited part vardef generic variable delimited part undelimited part
241. pter 10 to visualize the points paths and bounding boxes Preliminary Version November 11 2001 TAP This path is constructed out of four points A path can be open or closed The previous path is an example of a closed path An open path looks like this When we close this path and in a moment we will see how to do this the path looks like HH The open path is defined as E Preliminary Version November 11 2001 1cm icm 1 5cm 1 5cm 2cm 0cm The double period connector tells metapost that we want to connect the lines by a smooth curve If you want to connect points with straight line segments you should use Closing the path is done by connecting the first and last point using the cycle command 1cm icm 1 5cm 1 5cm 2cm 0cm cycle Feel free to use or at any point in your path 1cm icm 1 5cm 1 5cm 2cm 0cm cycle This path when drawn looks like this H As you can see in some of the previous examples MmETAPOST is capable of drawing a smooth curve through the three points that make up the path We will now examine how this is done 16 The six small points are the so called control points These points pull their parent point in a certain direction The further away such a point is the stronger the pull Each point has at most two control points As you can see i
242. put file which is interpreted by the converter built in CONTEXT Shading comes down to inter polation between two or more points or user supplied ranges A poor mans way of doing this is to build the graphics piecewise with slightly changing colors But instead of manually stepping through the color values we can use the more efficient and generalized POSTSCRIPT level 2 and PDF level 1 3 shading feature circular 0 circular 1 circular 2 circular 3 circular 4 linear 0 linear 1 linear 2 linear 3 Because shading support is not built in MeTAPOST it has to be implemented using so called specials directives that end up in the output file Unfortunately these are not coupled to the specific path which means that we have to do a significant amount of internal bookkeeping Also in PDF we have to make sure that the graphics and their resources being the shading functions are packaged together Because of this implementation shading may behave somewhat unexpected at times A rather normal case is the next one where we place 5 shaded circles in a row path p p fullcircle scaled icm for i 0 step 2cm until 8cm circular_shade p shifted i 0 0 MPcolor a MPcolor b endfor Preliminary Version November 11 2001 At first sight in the next situation we would expect something similar because we simply copy the same circle 5 times However due to the way we have implemented shading in CONTEXT we do indeed copy the c
243. r darkred These symbols are collected in table 7 4 and are called up with the CONTEXT commands like symbol menu left If needed we can collect these button symbols in a so called symbol set which permits us to instantly switch between sets with similar symbols Preliminary Version November 11 2001 shapes symbolsana buttans lt E E AKO Mao left right list index person stop info down up print Table 7 4 A collection of button symbols Preliminary Version November 11 2001 8 1 Special effects Sometimes we want to go beyond metapost s native features An example of such an extension is shading Although features like this should be used with care sometimes the documents look and feel can profit from it If you don t want the whole graphic but only a part of it clipping comes into play In addition to the standard clipping features we can use MeTAPOST to provide a decent clipping path In this chapter we will uncover the details Shading In this section we introduce different kind of shadings Since mMetaPost does not support this feature directly we have to fall back on a few tricks For the moment shading is only supported in PDF In the following examples we will use the next three colors def inecolor a darkyellow definecolor b s 8 definecolor c darkred A shade is a fill with a stepwise change in c
244. raphic is identical to the typeset code in the document Here is an example startbuffer dummy draw fullcircle xscaled 3cm yscaled 2cm rotatedaround origin 30 withcolor 625red stopbuffer Instead of using getbuf fer we used the following command startlinecorrection blank processMPbuf fer dummy stoplinecorrection The line correction commands take care of proper spacing around the graphic If you want to process more buffers at once you can pass their names as a comma separated list Alternatively we could have said startuseMPgraphic dummy draw fullcircle xscaled 3cm yscaled 2cm rotatedaround origin 30 withcolor 625red stopuseMPgraphic When including this graphic we again take care of spacing startlinecorrection blank useMPgraphic dummy stoplinecorrection Here a few layout thingies follow Preliminary Version November 11 2001 ethis documents Preliminary Version November 11 2001 D Reference In this chapter we will demonstrate most of the drawing related primitives and macros as present in plain metapost and MetaFun extensions If a path is shown and or a transformation is applied we show the original in red and the transformed path or point in yellow The small dark gray crosshair is the origin and the black rectangle the bounding box In some drawings in light gray we show the points that makeup the path
245. rate glean synopsize winnow the wheat from the chaff and separate the sheep from th tus I came to the conclusion that the designer of a new system must not only be the implemente ind first large scale user the designer should also write the first user manual The separation of any of these four components would have hurt TEX significantly IEI had lot participated fully in all these activities literally hundreds of improvements would never havi zen made because I would never have thought of them or perceived why they were important But a system cannot be successful if it is too strongly influenced by a single person Onc 1 initial design is complete and fairly robust the real test begins as people with many different Jewpoints undertake their own experiments ouglas R Hostadter jald Knuth has spent the past several years working on a system allowing him to control many ispects of the design of his forthcoming books from the typesetting and layout down to the ver shapes of the letters Seldom has an author had anything remotely like this power to control th inal appearance of his or her work Knuth s 7X typesetting system has become well known af wailable in many countries around the world By contrast his wetaronr system for designi families of typefaces has not become as well known or available In his article The Concept of a Meta Font Knuth sets forth for the first time the underlying jhilosophy of weraronr as well a
246. reen blue save r g b rr gg bb cc mm yy save b_r b_g g_r g_b save radius path r g b rr bb gg cc mm yy pair b_r b_g g_r g_b numeric radius radius 3cm pickup pencircle scaled radius 20 r g b fullcircle scaled radius shifted 0 radius 4 r r rotatedaround origin 15 drawarrow r withcolor red g g rotatedaround origin 135 drawarrow g withcolor green b b rotatedaround origin 255 drawarrow b withcolor blue b_r b intersectionpoint r draw b_r b_g b intersectionpoint g draw b_g g_r reverse g intersectionpoint r draw g_r g_b reverse g intersectionpoint b draw g_b bb b cutafter b_r bb bb cutbefore b_g 4 drawarrow bb gg g cutbefore b_g gg gg cutafter gr 4 drawarrow gg rr r cutbefore gr amp r cutafter b_r drawarrow rr cc b cutbefore b_r cc cc cutafter g_b drawarrow br yy g cutbefore g_r yy yy cutafter gb drawarrow rg mm r cutbefore gr amp r cutafter b_r drawarrow gb Preliminary Version November 11 2001 A few bb gg rr reverse bb cycle gt gg bb rotatedaround origin 120 rr bb rotatedaround origin 240 cc mm cc reverse yy cycle yy cc rotatedaround origin 120 mm cc rotatedaround origin 240 fill fullcircle scaled radius withcolor white fill rr wi
247. rent pen specifications EWelcsme to METAPOST Preliminary Version November 11 2001 If you forget about the colors the metarost code to achieve this is as follows p fullcircle scaled icm draw p scaled 3 withpen pencircle scaled 1mm P P draw p scaled 2 withpen pencircle P draw p scaled 4 withpen pencircle xscaled 2mm yscaled 4mm rotated 30 If this were the only way of specifying a pen we would be faced with a considerable amount of typing particularly in situations where we use pens similar to the fourth specification above For that reason METAPOST supports the concept of a current pen The best way to set this pen is to use the pickup macro pickup pencircle xscaled 2mm yscaled 4mm rotated 30 This macro also stores some characteristics of the pen in variables so that they can be used in the more complicated calculations that are involved in situations like drawing font like graphics If we substitute pencircle by pensquare we get a different kind of shapes In the non rotated pens the top bottom left and right parts of the curve are thinner You should look at pens in the way an artist does He follows a shape and in doing so he or she twists the pen and thereby the nib and puts more or less pressure on it The chance that you have an appropriate pen laying at your desk is not so large but you can simulate the following meTaPost s pen by taki
248. rimarydef x mod y enddef secondarydef p intersectionpoint q enddef tertiarydef p softjoin q enddef A primary macro acts like the binary operators or scaled and shifted Secondary macros are like and logical or and take less precedence The tertiary operators like lt or the path and string concatenation operator amp have tertiary macros as companions More details can be found in the MeTAFONT book When it comes to taking precedence MeTAPOST tries to be as natural as possible in the sense that you need to provide as few s as possible When in doubt or when surprised by unexpected results use parentheses Pens When drawing three attributes can be applied to it a dashpattern a pen and or a color You may consider an arrowhead an attribute but actually it is just an additional drawing appended to the path The predefined pencircle attribute looks like withpen pencircle where pencircle is a special kind of path stored in a pen variable Like any path you can transform it You can scale it equally in all directions withpen pencircle scaled imm You can also provide unequal scales creating an elliptically shaped and rotated pen withpen pencircle xscaled 2mm yscaled 4mm rotated 30 In the following graphic the circle in the center is drawn without any option which means that the default pen is used being a pencircle with a radius of half a base point The other three circles are drawn with diffe
249. rm t path p p t identity shifted a b rotated c scaled d fullcircle transformed t The previous lines of code are equivalent to path p p fullcircle shifted a b rotated c scaled d You always need a starting point in this case the identity matrix identity 0 0 1 0 0 1 By the way in POSTSCRIPT the zero vector is 1 0 0 1 0 0 So unless you want to extract the components using xpart xypart xxpart ypart yxpart and or yypart you may as well forget about the internal representation You can invert a transformation using the inverse macro which is defined as follows using an equation vardef inverse primary T transform T_ T_ transformed T identity T_ enddef Using transform matrices makes sense when similar transformations need to be applied on many paths pictures pens or other transforms However in most cases you will use the predefined commands scaled shifted rotated and alike We will now demonstrate the most common transformations in a text example draw btex bfd MetaFun etex draw boundingbox currentpicture withcolor 625yellow Before a meTAPOST run the btex etex s are filtered from the file and passed on to Tx After that the DVI file is converted to a list of pictures which is consulted by metarost We can manipulate these pictures like any graphic as well as draw it with draw Preliminary Version November 11 2001 A few
250. rray In doing so we can access the variables more easily using loops If we omit the labels and angle macro the previously defined macro can be reduced a lot def draw_problem expr n p q r s number and 4 positions beginfig n save X y z 1 1 3 3 p z 2 1 q z 3 1 r z 4 1 s for i 1 upto 4 z i 1 z i 2 z i 3 z i 4 x i 1 y i 1 z if i 1 4 else i 1 fi 2 x i 2 y i 2 x i 2 y i 2 y i 1 y i 2 x i 2 x i 1 x i 1 y i 2 y i 1 y i 1 x i 2 x i 1 z i 0 5 z i 1 z i 3 endfor z 0 whatever z 1 z 3 whatever z 2 z 4 pickup pencircle scaled 5pt for i 1 upto 4 draw z i 1 z i 2 z i 3 z i 4 cycle draw z i 1 z i 3 draw z i 2 z i 4 if i lt 3 endfor draw z i z it 2 dashed evenly fi draw 1 0 1 1 0 1 zscaled shifted endfig enddef unitvector z 1 z 0 10pt z 0 I think that we could argue quite some time about the readability of this code If you start from a sketch and the series of equations does a good job there is hardly any need for such improvements to the code On the other hand there are situations where the simplified reduced case can be extended more easilly for instance to handle 10 points instead of 4 It all depends on how you want to spend your free hours Preliminary
251. rtake their own experiments Douglas R Hostadter Donald Knuth has spent the past several years working on a system allowing him to control many Donald Knuth has spent the past several years working on a system allowing him to control many books from the aspects of the design of his forthcoming books from the typesetting and layout down to the very Pee eee eee ee eee final appearance of his or her work Knuth s TX typesetting system has become well known and available in many countries around the world Lie his metarowr system for designing ea ey ogee eee Tals ariela The Concept ofa Molao Knuth set forth or the first Erme the netving of wetarcar as well as some ofits products Not only is the concept exiting and clearly i However E in artificial int esthetic theory 1 make some comments to clarify certain important issues raised by The Concept of a Meta Font E in Coosa aate coo rey ism even odd Figure 6 5 A random text area The previous graphics are defined as usable ones which means that they will be recalculated each page This is rather inefficient when the shapes don t change But using a reusable graphic instead would result in only one graphic for both pages Since the layout for the left and right page differs another method is needed Instead of putting the same graphic on the page layer we put two different ones on the left and right page layer Preliminary Version Novem
252. s p shifted 4cm 2cm In a similar fashion you can rotate a path You can even combine shifts and rotations First we rotate the path 15 degrees counter clockwise about the origin p rotated 15 xe YA This rotation becomes more visible when we also shift the path to the right by saying rotated 15 shifted 4cm 0cm lt O Q Note that rotated 15 is equivalent to p rotatedaround origin 15 Preliminary Version November 11 2001 It may make more sense to rotate the shape around its center This can easily be achieved with the rotatedaround command Again we move the path to the right afterwards p rotatedaround center p 15 shifted 4cm 0cm Yet another transformation is slanting Just like characters can be upright or slanted a graphic can be p slanted 1 5 shifted 4cm 0cm The slant operation s main application is in tilting fonts The x coodinates are increased by a percentage of their y coordinate so here every x becomes x 1 5y The y coordinate is left untouched The following table summarizes the most important primitive transformations that METAPOST supports METAPOST code mathematical equivalent x y shifted a b x a y b x y scaled s sx SY x y xscaled s sx y x y yscaled s x sy x y zscaled u v xu yv xv yu x y slanted s x sy y x y rotated r x cos r y sin r x sin r y cos r The previously mentione
253. s A graphic consists of curves either or not filled with a given color A graphic can also include text which means that fonts are used Finally a graphic can have special effects like a shaded fill Einbsdldeet graphics Preliminary Version November 11 2001 Figure 3 7 A silly figure demonstrating that stand alone graphics can be made Colors fonts and special effects go under the name resources since they may demand special care or support from the viewing or printing device When fonts are used a meTaPosT file is not self contained This means that the postprocessing program has to deal with the fonts In CONTEXT the special driver and PDFTsX support is considered as such takes care of this Special effects like shading are supported by dedicated Metarost modules These are included in the CONTEXT distribution and will be discussed later in chapter 8 Since METAPOST supports color an embedded graphic can be rather colorful However when color support is disabled or set up to convert colors to gray scales CONTEXT will convert the colors in the graphic to gray scales You may wonder what the advantage is of weighted gray conversion Figure 3 8 shows the difference between natural colors weighted gray scaled and straightforward non weighted gray O56 full color weighted gray linear gray Figure 3 8 The advantage of weighted gray over linear gray When we convert
254. s each marked by an identifier X 1 X 2 and X 3 Each of these anchors can be associated with a series of graphic operations Here we defined setMPpositiongraphic X 1 mypos arrow to X 2 setMPpositiongraphic X 2 mypos arrow to X 3 These examples clearly demonstrate that we are not in complete control over to what extend graphics will cover text and vise versa A solution to this problem is using so called position overlays We can define such an overlay as follows startpositionoverlay backgraphics setMPpositiongraphic G 1 mypos circle setMPpositiongraphic G 2 mypos circle setMPpositiongraphic G 3 mypos circle setMPpositiongraphic G 4 mypos circle stoppositionoverlay startpositionoverlay foregraphics setMPpositiongraphic G 1 mypos line to G 2 setMPpositiongraphic G 2 mypos line to G 3 setMPpositiongraphic G 3 mypos line to G 4 stoppositionoverlay First we have defined an is overlay can be attached to some overlay layer like in our circles e are drawn as soon as the page overlay is typeset case the age Wedefine ts fext while the lines do The Because they are located in the background they don t cove previous paragraph was typeset by saying First we have defined an hpos G 1 overlay This overlay can be attached to some overlay layer like in our case the hpos G 2 page We define four small hpos G 3 circles These are drawn as soon as the pag
255. s some ofits products Not only is the concept exiting and clearly ll executed but in my opinion the article is charmingly written as well However despite my ferall enthusiasm for Knuth s idea and article there are some points in it that I feel might b laken wrongly by many readers and since they are points that touch close to my deepest interests artificial intelligence and esthetic theory I felt compelled to make some comments to clarify stain important issues raised by The Concept of a Meta Font Je thrive in information thick worlds because of our marvelous and everyday capacity to select it single out structure highlight group pair merge harmonize synthesize focus organize Fondense reduce boil down choose categorize catalog classify list abstract scan look into idealize isolate discriminate distinguish screen pigeonhole pick over sort integrate blend spect filter lump skip smooth chunk average approximate cluster aggregate outline sum arize itemize review dip into flip through browse glance into leaf through skim refine numerate glean synopsize the wheat from the chaff and separate the sheep from th oats Donald E Knuth thus I came to the conclusion that the designer of a new system must not only be the implemente pin first large scale user the designer should also write the first user manual The separation of any of these four components would have h
256. s the name of the macro The counterpart of upto is downto Whenever you use upto it is replaced by step 1 until This replacement is called expansion There are several types of macros A primary macro is used to define your own operators For example primarydef p doublescaled s p xscaled s 2 yscaled s 2 enddef Once defined the doublescaled macro is implemented as in the following example draw somepath doublescaled 2cm withcolor red When this command is executed the macro is expanded Thus the actual content of this command becomes draw somepath xscaled icm yscaled 4cm withcolor red If we had added a semi colon after s 2 we could not have set the color because the semicolon ends the statement The draw expects a path so the macro can best return one A macro can take one or more arguments as in def drawrandomscaledpath expr p s draw p xscaled s 2 yscaled s 2 enddef Welcome tolNerae0sia Preliminary Version November 11 2001 When using this macro it is expected that you will pass it two parameters the first being a path the second a numeric scale factor drawrandomscaledpath fullsquare 3cm Sometimes we want to return a value from a macro In that case we must make sure that any calculations don t interfere with the expectations Consider vardef randomscaledpath expr p s numeric r r round 1 uniformdeviate 4 p x
257. s to think in relative positions instead of absolute ones Therefore graphics even those that involve multiple positions are anchored to a position on the layer on which they are located The MPanchor macro takes care of this Users who simply want to use these features may wonder why we go into so much detail The main reason is that in the end many users will want to go beyond the simple cases and when dealing with these issues you must be aware and when defining graphics sometimes needs to take care too not only of height depth and width but also of the crossing of a page boundary and the height and depth of lines Given that unique identifiers are used for anchor points in CONTEXT you can have access to all the information needed aon C nee en r Ss w Sigs Anchors and layers a a S 7 In a previous section we saw that some were Grcled and connected by an As with most things in CONTEXT marking these words is separated from declaring what tode with those words This paragraph is keyed in as Positional graphics Preliminary Version November 11 2001 In a previous section we saw that some hpos X 1 words were hpos X 2 circled and connected by an hpos X 3 arrow As with most things in CONTEXT marking these words is separated from declaring what to do with those words This paragraph is keyed in as We see three so called position anchor
258. scaled s r yscaled s r enddef Because we want to use the same value of r twice we have to use an intermediate variable By using a vardef we hide everything but the last statement It is important to distinguish def macros from those defined with vardef In the latter case vardef macros are not a simple expansion and replacement Rather vardef macros return the value of their last statement In the case of the randomscaledpath macro a path is returned This macro is used in the following manner path mypath mypath randomscaledpath unitsquare 4cm Note that we send randomscaledpath a path unitsquare and a scaling factor 4cm The macro returns a scaled path which is then stored in the path variable mypath The following argument types are accepted expr something that can be assigned to a variable text arbitrary MeETAPOST code ending with a suffix a variable bound to another variable An expression is passed by value This means that in the body of the macro a copy is used and the original is left untouched On the other hand any change to a variable passed as suffix is also applied to the original Local variables must be handled in a special manner since they may conflict with variables used elsewhere Thisis because all variables are global by default The way out of this problem is using grouping in combination with saving variables The use of grouping is not restricted to macros and may be used anywhere in your code
259. scaled 3mm clip currentpicture to fullcircle 5 1 length 0 stroked false clipped false bounded true 2 length 1 stroked true clipped false bounded false 5 The description lines were generated by the following loop n 0 for i within currentpicture n n 1 label n amp decimal ne amp length amp decimal length ig amp stroked amp condition stroked i amp amp clipped amp condition clippedi amp amp bounded amp condition bounded i 0 n 5cm endfor If we have a textual picture we can also ask for the text and font Take the following picture picture p p MetaFun infont defaultfont scaled 2 rotated 30 slanted 5 p p shifted 0 ypart center p currentpicture p Here we can ask for Preliminary Version November 11 2001 Aew label rt textpart amp textpart p 4cm 0 25cm label rt fontpart amp fontpart p 4cm 0 25cm and get ust textpart MetaFun met fontpart texnansi uplr8a If we re dealing with a path the transformations have ended up in the path specification If we have a text picture we can explicitly ask for the transform components label rt xpart amp decimal xpart p 4cm 1 25cm label rt ypart amp decimal ypart p 4cm 0 75cm label rt xxpart amp decimal xxpart p 4cm 0 25cm label rt xypar
260. seMPlibrary clp We already saw how the circular clipping path was defined The diamond is defined in a similar way using the predefined path diamond startMPclip diamond clip currentpicture to unitdiamond Special eigas Preliminary Version November 11 2001 xscaled width yscaled height stopMPclip The definition of the negated ellipse negellipse uses the primary peepholed This primary is defined in one of the METAPOsT modules that come with CONT XT startMPclip negellipse clip currentpicture to unitcircle peepholed unitsquare xscaled width yscaled height stopMPclip The definition of peepholed is rather dirty and using peepholed is restricted to well defined situations like here It s called a primary because it acts as an operator at the same level as and scaled urellipse ulellipse llellipse lrellipse ellipse negellipse tellipse bellipse lellipse rellipse urtriangle ultriangle lltriangle Irtriangle diamond negdiamond Figure 8 7 A collection of predefined clipping paths 8 3 Patterns Like shades patterns can be implemented using specials Before I discuss this I first have to sort out how this can be implemented in a comfortable way 8 4 Fonts This section will demonstrate how we can manipulate fonts in MeTAPOST Don t expect too much from this section HE Preliminary Version November 11 2001 b Preliminary V
261. sed startMPenvironment setupbodyfont mt ppl pcr 10pt usetypescriptonce serif times name texnansi usetypescriptonce sans helvetica name texnansi usetypescriptonce palatino texnansi setupbodyfont palatino 10pt definefont RotFont RegularBold stopMPenvironment We let the bodyfont match the font used in this document and define RotFont to be the regular typeface the one you are reading right now but bold Since METAPOST is unaware of kerning we have to use Tpx to keep track of the positions We will split the text into tokens often characters and store the result in an array of pictures pic We will also store the accumulated width in an array len The number of characters is stored in n Ina few paragraphs we will see why the other arrays are needed While defining the graphic we need Tpx to do some calculations Therefore we will use startMPdrawing to stepwise construct the definition The basic pattern we will follow is resetMPdrawing startMPdrawing metapost code stopMPdrawing tex code startMPdrawing metapost code stopMPdrawing MPdrawingdonetrue getMPdrawing In the process we will use a few variables We will store the individual characters of the text in the variable pic it s width in wid and the length of the string so far in len Later we will use the pos array to store the position where a character ends up The variable n holds the number of tokens resetMPdrawing star
262. setupbackgrounds state repeat Complex text in graphics If you like to embed metarost snippets in CONTEXT you may want to combine text and graphics and let Metarost provide the position and the dimensions of the text to be typeset outside the METAPOST run For most applications using the MetaFun textext macro works well enough but when the typeset text needs to communicate with the typesetting engine for instance because it contains hyperlinks or references you can use the following method define a layer define a reusable graphic put your text into the layer combine the graphic with the text You must be aware of the fact that when the layer is flushed its content is gone You can take advantage of this by using the same graphic with multiple texts 3 Soon this feature will be hooked into the named pages handler This will be default behaviour when computers become faster Positional graphics Preliminary Version November 11 2001 def inelayer test You don t need to pass the width and height explicitly but when you do as such you have access to them later startuseMPgraphic oeps path p p fullcircle scaled 6cm fill p withcolor 8white draw p withpen pencircle scaled 1mm withcolor 625red register somepos 1 0cm 0cm center currentpicture register somepos 2 3cm icm 1cm 1cm register somepos 3 2cm 0cm 2cm 2cm stopuseMPgraphic
263. sites of the local Tpx user groups There are definitely references missing here but so far I only read wrote saw these METAFONT and METAPOST Knuth D E 1986 The METAFONT book Reading MA Addison Wesley Hobby J D 1997 A User s Manual for metarost Murray Hill NJ AT amp T Bell Laboratories TEX Knuth D E 1986 The TgXbook Reading MA Addison Wesley CONTEXT Otten A F amp Hagen J 1998 ConTgXt an Excursion Hasselt Pragma ADE Hagen J 1999 ConTEXt the Manual Hasselt Pragma ADE Hagen J 1999 ConTEXt up to date 3 Flowcharts Hasselt Pragma ADE Hagen J 1997 Puzzling Graphics in MetaPost Petten NTG Maps Tools H n Th Th nh amp Rahtz S P Q amp Hagen J 1998 The pdfTgX manual Brno Hasselt Oxford Hagen J 1999 TpXexec explained Hasselt Pragma ADE Hagen J 2000 Making Stand Alone MetaPost graphics Amsterdam NTG Maps Distributions Rahtz S P Q amp Goosens M 1999 The TpX Live Guide 4th edition The Whole World TUG s Hagen J 1999 How to Install ConTgxt Hasselt Pragma ADE Dol W amp Frambach E 1999 4T X for Windows Amsterdam NTG Preliminary Version November 11 2001 Preliminary Version November 11 2001 Index Concepts The main index will be prepared when the document is finished Commands The command index will be prepared when the document is finished Preliminary Version
264. st in a rather straightforward way and as much as possible we will try to avoid complicated math We will do a bit of drawing clipping and moving around Occasionally we will see some more complicated manipulations When defined as stand alone graphic a metarost file looks like this J Let s draw a circle beginfig 7 draw fullcircle scaled 3cm withpen pencircle scaled 1cm endfig end The main structuring components in such a file are the beginfig and endfig macros Like in one big story the file has many sub sentences where each sub sentence ends with a semi colon Although the end command at the end of the file concludes the story putting a period there is a finishing touch Actually after the end command you can put whatever text you wish your comments your grocery list whatever Comments in MeTAPOST prefixed by a percent sign as in Let s draw a circle are ignored by the interpreter but useful reminders for the programmer If the file is saved as yourfile mp then the file is processed by metarost by issuing the following command mpost yourfile after which you will have a graphic called yourfile 7 which contains a series of POSTSCRIPT commands Because meTtapost does all the work this file is efficient and compact The number of distinct POSTSCRIPT operators used is limited which has the advantage that we can postprocess this file rather easily We can view this file in a POSTSCRIPT viewer like GHOSTVIEW
265. t amp decimal xypart p 4cm 0 25cm label rt yxpart amp decimal yxpart p 4cm 0 75cm label rt yypart amp decimal yypart p 4cm 1 25cm xpart 0 ypart 25 7136 ps xxpart 2 23206 Met xypart 0 13397 yxpart 1 yypart 1 73206 We will now define the inverted macro using these primitives Because we have to return a picture we cannot use draw and fill but need to use the low level operators Because a picture can consist of more than one path we need a temporary picture pp vardef inverted expr p save pp picture pp pp nullpicture for i within p addto pp if stroked i or filled i if filled i contour else doublepath fi pathpart i dashed dashpart i withpen penpart i else also i fi withcolor white redpart i greenpart i bluepart i endfor PP enddef We probably need to handle a few more border cases but for general purposes this macro works as expected A few more details Preliminary Version November 11 2001 From the previous examples it may be clear that each picture has some associated data stored with it From the bounded boolean test we can deduce that the bounding box is part of this data Internally metarost keeps track of two bounding boxes the natural one and the forced one The forced one is actually a component of the picture which applies to all previously added graphics You can calculate the bounding box from the 1
266. t ulcorner q urcorner q shifted 0 topskip bb llcorner q lrcorner q shifted 0 strutdepth Preliminary Version November 11 2001 1 1 cutbefore 1 intersectionpoint tt 1 1 cutafter 1 intersectionpoint bb r r cutbefore r intersectionpoint bb r r cutafter r intersectionpoint tt stopuseMPgraphic Because we use includeMPgraphic to construct the graphic we can redefine text draw to show the result of this effort startuseMPgraphic text draw drawarrow p withpen pencircle scaled 1pt withcolor red drawarrow 1 withpen pencircle scaled 1pt withcolor green drawarrow r withpen pencircle scaled 1pt withcolor blue stopuseMPgraphic The text graphic now becomes startuseMPgraphic text includeMPgraphic text path includeMPgraphic text vars includeMPgraphic text move includeMPgraphic text split includeMPgraphic text cutoff includeMPgraphic text draw stopuseMPgraphic Or as graphic We are now ready for an attempt to calculate the shape of the text For each line we have to calculate the left and right intersection points and since a line has a height and depth we have to determine which part touches first startuseMPgraphic text calc vardef found_point expr lin pat sig pair a b a pat intersection_point lin shifted 0 strutheight if intersection_found a a shifted 0 strutheight
267. t mm yy transformed t fill fullcircle scaled radius withcolor white E E A fe applications Preliminary Version November 11 2001 fill rr withcolor red fill cc withcolor white red fill gg withcolor green fill mm withcolor white green fill bb withcolor blue fill yy withcolor white blue for i rr gg bb cc mm yy draw i withcolor 5white endfor currentpicture currentpicture xsized size enddef This rather nice circle is defined as colorcircle 4cm 4 6 8 8 4 6 6 8 4 The final implementation which is part of MetaFun is slightly more efficient vardef colorcircle expr size red green blue save r g b c m y W save radius path r g b c m y Ww numeric radius radius 5cm pickup pencircle scaled radius 25 transform t t identity rotatedaround origin 120 fullcircle rotated 90 scaled radius shifted 0 radius 4 rotatedaround origin 135 ri b r transformed t g b transformed t c buildcycle subpath 1 7 of g subpath 1 7 of b c transformed t m y transformed t w buildcycle subpath 3 5 of r subpath 3 5 of g subpath 3 5 of b pushcurrentpicture fill r withcolor red fill g withcolor green fill b withcolor blue fill c withcolor white red fill m withcolor white green fill y withcolor white blue fill w withcolor white for i r g b c m y draw i withcolor 5whit
268. t and depth of the preceding and following text into account Preliminary Version November 11 2001 Atfew applications pointD reverse circleA intersectionpoint reverse circleB draw_dot pointC label 1lft btex C etex pointC shifted 2w 0 draw_dot pointD label 1lft btex D etex pointD shifted 2w 0 enddef stopbuffer In placing the label we must make sure that the text runs free of the lines and curves Again move the stand_out macro just prior to draw_intersection macro so that this step is highlighted in the drawing color while prior steps are drawn in the default color in this case black startbuffer 3 start_everything draw_basics draw_circles stand_out draw_intersection stop_everything stopbuffer The line drawn through points C and D will be the perpendicular bisector of the line segment connecting points A and B In the next step we will draw a line using the plain meTarpost drawdblarrow macro that draws arrowheads at each end of a path startbuf fer f def draw_bisector path lineCD lineCD origin origin shifted 2 distance 0 lineCD lineCD rotated 90 shifted 0 5 pointA pointB lineCD lineCD shifted 0 distance drawdblarrow lineCD enddef stopbuffer startbuf fer 4 start_everything draw_basics draw_circles draw_intersection stand_out draw_bisector stop_everythin
269. t one we load although delayed the jobname is as we expect So at least in WEB2C the result of the conversion comes available in the file filename pdf This conversion process is roughly compatible with texexec pdf fig c result filename filename number This uses CONT XT and is therefore slower but fortunately there is a small PERL script that does a faster job using the minimal format Given that the previously mentioned format is generated you can say mptopdf somefile mptopdf somefile 123 mptopdf mp The results are copied into files named somefile number This mechanism will also be available in a next release of TEXUTIL a TX file manipulation script that comes with CONTEXT Since ACROBAT has troubles with figures smaller than 1 inch we issue a warning When embedding graphics in documents a size less that 1 inch does not harm In order to overload runtime directives in the PDFTgx configuration file we set the offsets and output method in the macro The resulting PDF file is about as efficient as such a self contained file can be However if needed this PDF file can be converted to EPS using for instance the pdftops program in WEB2C or GHOSTSCRIPT Test case If you want to test of your installation is working properly you may construct a file called test tex that contains the following lines Preliminary Version November 11 2001
270. t with a circular line that we define as follows By using a buffer we keep things organized startbuffer circle startuseMPgraphic followtokens path RotPath RotPath reverse fullcircle BPOST Preliminary Version November 11 2001 Donald Knuth has spent the past several years working on a system allow ing him to control many aspects of the design of his forthcoming books from the typesetting and layout down to the very shapes of the letters Seldom has an au thor had anything remote ly like this power to con test 1 available In his article The Concept of a Meta Font Knuth sets forth for the first time the underlying philosophy of METAFONT as well as some of its products Not on ly is the concept exiting and clearly well executed but in my opinion the arti cle is charmingly written as well However despite my over test 3 trol the final ap pearance of his or her work Knuth s TEX typesetting system has be come well known and available in many countries around the world By contrast his METAFONT system for designing families of typefaces has not be come as well known test 2 all enthusiasm for Knuth s idea and article there are some points in it that I feel might be taken wrongly by many readers and since they are points that touch close to
271. tMPdrawing picture pic numeric wid len pos n wid 0 len 0 pos 0 n 0 stopMPdrawing We also started fresh by resetting the drawing From now on each start command will add some more to this graphic The next macro is responsible for collecting the data Each element is passed on to TEX using the btex construct So METAPOST itself will call TEX POST Preliminary Version November 11 2001 def whatever 17 appendtoks 1 to MPtoks setbox MPbox hbox bfd the MPtoks startMPdrawing n n 1 len n the wd MPbox stopMPdrawing startMPdrawing pic n btex bfd 1 etex stopMPdrawing handletokens MetaPost is Fun with whatever We use the low level CONTEXT macro appendtoks to extend the token list MPtoks The handletokens macro passes each token character of MetaPost is Fun to the macro whatever The tokens are appended to the token register MPtoks already defined Then we typeset the content of MPtoks in MPbox also already defined The width of the box is passed to metarost and stored in len By default the content of the drawing is expanded which means that the macro is replaced by its current meaning so the current width ends up in the metarost file The next part of the drawing starting with btex puts the token in a picture This time we don t expand the drawing since we want to pass font information
272. takes a few lines First we clip the correct part next we scale it up and finally we let the bounding box suit the left picture startuseMPgraphic layout 2 includeMPgraphic layout 1 clip currentpicture to unitsquare scaled 3cm shifted 0 5cm currentpicture currentpicture scaled 2 shifted 0 8cm setbounds currentpicture to unitsquare xyscaled 6cm 8cm stopuseMPgraphic This code demonstrates how you can reuse a graphic inside another one This strategy can easily be used to stepwise build or extend graphics The two graphics were put side by side with the following command Watch the use of line correction commands They optimize the white space around the graphic startlinecorrection blank hbox useMPgraphic layout 1 hskipicm useMPgraphic layout 2 stoplinecorrection Preliminary Version November 11 2001 As soon as you want to make an electronic document you will want to use different areas of the screen for different purposes text menus buttons etc For this reason CONTEXT provides not only left and right margins but also additional left and right edge areas and top and bottom margins These areas are shown in the figure on the next page When defining this graphic all areas have related dimensions Here it makes sense to let MeTAPOST Calculate these dimensions as much as possible First we define the five by five matrix of areas We pass the width and hei
273. tartuseMPgraphic page StartPage for i Top Header Text Footer Bottom for j LeftEdge LeftMargin Text RightMargin RightEdge draw Fi endfor endfor StopPage eld i j withpen pencircle scaled 2pt withcolor 625red stopuseMPgraphic We use two nested for loops to step over the areas A for loop witha step of 1 will fail because the indices are defined in a rather special way On the other hand the mechanism is rather tolerant in the sense that i j and j i are both accepted Preliminary Version November 11 2001 Page 6 5 Advanced features Coming up with some more advanced graphics is not so much a problem of definition as well as knowing how to combine features Here we will demonstrate how page backgrounds can contain foreground graphics like menus fe thrive in information thick worlds because of our marvelous and everyday capacity to select clit single out structure highlight group terge harmonize synthesize focus organize fondense reduce boil down choose categorize catalog classify list abstract scan look into dcalize isolate discriminate distinguish screen pigeonhole pick over sort integrate blend spect filter Limp skip smooth chunk average approximate cluster aggregate outline sum arize itemize review dip into flip through browse glance into leaf through skim refine snume
274. terminal and log file 2 The previous picture shows what is typeset when we also say showmakeup This command visualizes Tex s boxes skips kerns and penalties As you can see there are some boxes involved which is due to the conversion of METAPOST output to PDF startlinecorrection blank the graphic stoplinecorrection The small bar is a kern and the small rectangles are penalties More details on this debugger can be found in the CONTEXT manuals and the documentation of the modules involved Preliminary Version November 11 2001 Preliminary Version November 11 2001 11 HAI Defining styles A document style can gain a lot by using a few graphics In this chapter we will introduce some style elements and their usage Adaptive buttons So far we have seen a lot of graphic ingredients that you can use to make your documents more attractive In this chapter we will define a simple document style This style was written for the PDFTgX presentations at the TUG 2000 conference in Oxford UK This style exploits a few tricks like graphics calculated using positional information It also demonstrates how you can make menu buttons that dynamically adapt their shapes to the rest of the page layout page 1 page 2 page 3 page 4 page 5 Later we will see an instance with some more randomness in the graphics While writing this style the
275. texttexts margin uniqueMPgraphic copyright Preliminary Version November 11 2001 6 3 The graphic goes into the outer margin The second argument can be used to put something in the inner margin Multiple overlays You can stack overlays Consider the next case where we assume that you have enabled interaction support using setupinteraction state start setupbackgrounds page background color nextpage backgroundcolor darkyellow Here the page gets a colored background and a hyperlink to the next page previously defined by def ineoverlay nextpage overlaybutton nextpage An overlaybutton is just a button with all attributes color frame etc set to nothing having the dimensions of the overlay The argument is one of the permitted destinations like nextpage firstpage SearchDocument and alike For efficiency reasons the backgrounds areas like text text are calculated only when their definition has changed When a background changes per page we have to recalculate it on each page In the next example the macro overlaybutton generates a different button on each page But since we don t explicitly set the background at each page there is no way the background drawing mechanism can know that this button has changed Therefore we must force recalculation with setupbackgrounds state repeat You can test this concept yourself with the follow
276. th A third alternative is the filldraw macro From the previous examples we would expect a bounding box that matches the one of the drawn path pickup pencircle scaled 5cm filldraw unitsquare xscaled 8cm yscaled 1cm withcolor 625white path bb bboxmargin Opt bb bbox currentpicture draw bb withpen pencircle scaled ipt withcolor 625red The resulting graphic has the bounding box of the fill Note how the path because it is stroked with a 5cm pen extends beyond the border of the bounding box The way this image shows up depends on the viewer settings you use to render the graphic For example in GHOSTVIEW if you disable clipping to the bounding box only the positive quadrant of the graphic is shown Further if you enable clipping to the bounding box this image will look exactly like the previous image created with the fill command In many cases it may be best to avoid the illdraw command Preliminary Version November 11 2001 From the previous examples you can deduce that the following alternative results in a proper bounding box pickup pencircle scaled 5cm path p p unitsquare xscaled 8cm yscaled 1cm fill p withcolor 625white draw p withcolor 625white path bb bboxmargin Opt bb bbox currentpicture draw bb withpen pencircle scaled ipt withcolor 625red The CONTEXT distribution comes with a set of mMETAaPOST modules one
277. thcolor 625white fill Main withcolor 850white draw Main withcolor 625red StopPage stopuseMPgraphic Here we displace the corners randomly which leads to backgrounds like figure 6 5 The following definition would have worked as well startuseMPgraphic page StartPage path Main Main Field Text Text randomized 1cm pickup pencircle scaled 2pt fill Page withcolor 625white fill Main withcolor 850white draw Main withcolor 625red StopPage stopuseMPgraphic Edward R Tufte IVa flees nk yt ben ofr meeoe el erage Oe harmonize synthesize enumerate glean synopsize winnow the wheat from the chaff and separate the sheep from the poate Donald E Knuth Thus I came to the conclusion that the designer ofa new system must not only be the implementer and first the initial design is complete and fairly robust the real test begins as people with many different viewpoints undertake their own experiments Douglas R Hostadter Edward R Tufte We thrive in information thick worlds because of our marvelous and everyday capacity to select synthesize focus Thus I came to the conclusion that the designer ofa new system must not only be the implementer and first large scale user the designer should also write the first user manual The ern ry oar raps wll bra burt JX sie Iethad the initial design is complete and fairly robust the real test begins as people with many different viewpoints unde
278. thcolor red fill cc withcolor white red fill gg withcolor green fill mm withcolor white green fill bb withcolor blue fill yy withcolor white blue for i rr gg bb cc mm yy draw i withcolor 5white endfor currentpicture currentpicture xsized size enddef In determining the right intersection points you need to know where the path starts and in what direction it moves In case of doubt drawing the path as an arrow helps If you want to see the small paths used you need to comment the lines with the i11 s and uncomment the lines with draw s Due to the symmetry and the fact that we keep the figure centered around the origin we only need to calculate two paths since we can rotate them There are for sure more efficient ways to draw such a figure but this one demonstrates a few new tricks like grouping We use grouping here because we want to use mm to indicate the magenta path and mm normally means millimeter Within a group you can save variables These get their old values when the group is left With for we process multiple paths after each other In this case it hardly saves tokens but it looks more clever One of the more efficient methods is using the buildcycle macro This macro takes two or more paths and calculates the combined path Although this is a rather clever macro you should be prepared to help it a bit when paths have multiple intersection points Again we could follow a more secure mathemat
279. them A buffer is a container for content that is to be re used later on The main reason for their existence is that they were needed for typesetting manuals and articles on Tx By putting the code snippets in buffers we don t have to key in the code twice since we can either show the code of buffers verbatim or process the code as part of the text flow This means that the risk of mismatch between the code shown and the typeset text is minimized startbuffer You are reading the METAFUN manual stopbuffer This buffer can be typeset verbatim using typebuffer and processed using getbuffer as we will do now An other advantage of using buffers is that they help you keeping the document source clean In a many places in this manual we put table or figure definitions in a buffer and pass the buffer to another command like placefigure A very big table getbuffer Sometimes it makes sense to collect buffers in separate files In that case we give them names This time we should say typebuffer mfun to typeset the code verbatim Instead of Tex code we can put meTAaPosT definitions in buffers Buffers can be used to stepwise build graphic By putting code in multiple buffers you can selectively process this code startbuffer red drawoptions withcolor 625red stopbuffer startbuffer yellow drawoptions withcolor 625yellow stopbuffer We can now include the same graphic in two colors by simply using different bu
280. ths that are not centered around the origin and don t start at the top point We achieve this by moving the path to the center Preliminary Version November 11 2001 jaro cp center p q p shifted cp The arbitrary starting point is taken care of by a slightly more complicated path cutter First we make sure that the path runs counterclockwise if xpart directionpoint t of q lt 0 q reverse q fi Knowing this we can split the path in two using a slightly different splitter cutbefore t if xpart point 0 of q lt 0 amp q fi cutafter b cutbefore b if xpart point 0 of q gt O amp q fi cutafter t HHP HB I HOHA As always when implementing a feature like this some effort goes into a proper user interface In doing so we need some 15x trickery that goes beyond this text like collecting text and splitting of the part needed Also we want to be able to handle multiple shapes at once like the next example demonstrates The macro is included in one of the metarost libraries so we first have to say useMPlibrary txt We define four shapes They are not really beautiful but they demonstrate what happens in border cases For instance too small first lines are ignored First we define a circle Watch how the dimensions are set in the graphic The arguments passed to build_parshape are path an offset an additional horizontal and v
281. tions which means that at a lower level one can do more advanced things Here we limit ourselves to the more common cases In the previous examples we used an arrow to indicate the direction and magnitude of the shade The next macro demonstrates the principles in a different way def test_shade expr a b ra rb pickup pencircle scaled 1mm color ca ca MPcolor a color cb cb MPcolor b color cc cc MPcolor c path pa pa fullcircle scaled 2ra shifted a path pb pb fullcircle scaled 2rb shifted b sh define_circular_shade a b ra rb ca cb Preliminary Version November 11 2001 fill pb withshade sh draw pb withcolor cc draw pa withcolor cc enddef The shade is distributed between two circles each with a radius and center point All four can be set but as the next calls demonstrate we can normally do with less which is why we provided the macro with less parameters test_shade origin origin Ocm 1cm test_shade origin origin 25cm 1cm test_shade origin origin 50cm 1cm test_shade origin origin shifted 25cm 0 Ocm 1cm test_shade origin origin shifted 25cm 0 25cm 1cm test_shade origin origin shifted 25cm 0 50cm 1cm test_shade origin shifted 25cm 0 origin Ocm 1cm test_shade origin shifted 25cm 0 origin 25cm 1cm test_shade origin shifted 25cm 0 origin
282. tive The previous graphics draws exactly 1001 lines in a scratch numbers in a wall fashion In 1998 the NTG did a survey among its members and in the report we used this fuzzy counter to enhance the rather dull tables system users Atari 10 4 WWI MSDOS 49 1 IHE IHI IHT IM IHT LT TT THI OS 2 94 IMH MacOS 5 7 Mfl UNIX 51 9 LHE H LHI IHT LH UM MT HT Let WINDOWS 64 2 HIM IHT IH LAT IAT IHI IHT IHT MH Tt UH II Table 7 1 Operating system n 106 Table 7 1 demonstrates how scratch numbers can be used An interesting side effect is that when you look long enough to these kind of graphics it looks like the lines are no longer horizontal This table is defined as follows Preliminary Version November 11 2001 starttabulate 1 cl1 HL NC system NC HL NC Atari NC NC MSDOS NC NC 0S 2 NC NC MacOS NC NC UNIX NC NC WINDOWS NC HL stoptabulate You will notice that we pass a variable to the graphic using a second argument We can access this variable with MPvar The graphic is defined as usable graphic because we want to generate h 10 49 79 5 51 64 N ON Fe BA 2A E A A a NC users NC NR NC useMPgraphic fuzzycount n 11 NC NR NC useMPgraphic fuzzycount n 52 NC NR NC useMPgraphic fuzzycount n 10 NC NR NC useMPgraphic fuzzycount n 6 NC NR NC useMPgraphic fuzzycount n 55 NC NR
283. topspace 48pt backspace 48pt cutspace 12pt width 400pt margin Ocm rightedge 88pt rightedgedistance 48pt header Ocm footer 0cm height middle We use a moderate about a line height inter paragraph white space setupwhitespace big Of course we use colors since on computer displays they come for free setupcolors state start definecolor red r 75 definecolor yellow r 75 g 75 definecolor gray s 50 definecolor white s 85 Because it is an interactive document we have to enable hyperlinks and alike However in this style we disable the viewer s highlight a hyperlink when it s clicked on feature We will use a menu so we enable menus Later we will see the contract color hyperlinks gets that color when we are already on the location in action setupinteraction state start click off color red contrastcolor gray menu on The menu itself is set up as follows Because we will calculate menu buttons based on their position on the page we have to keep track of the positions Therefore we set the position variable to yes setupinteractionmenu right frame off position yes align middle topoffset 75cm bottomoffset 75cm color gray contrastcolor gray Defining siye Preliminary Version November 11 2001 style bold before after The menu content is rather sober just a list of topics and a close button Later we w
284. ue do_it 1 4 false do_it 5 4 false do_it 2 4 true do_it 3 4 true do_it 4 4 true Preliminary Version November 11 2001 edge margin text margin edge reader FI we COE vonon M Page backgrounds Preliminary Version November 11 2001 6 2 do_it 1 5 false do_it 5 5 false do_it 2 5 false do_it 3 5 false do_it 4 5 false This picture in itself is not yet explanatory so we add some labels Again we use a macro which we feed with a picture generated by Tpx Since these pictures are filtered from the source and pre processed we cannot embed the btex etex in the macro do_it and pass a string It has to be done this way def do_it expr yy tt path p p unitsquare xyscaled w 1 hlyy shifted x 1 ylLlyy label 1ft tt center p shifted w 1 2 u 25cm 0 enddef do_it 1 btex bottom etex do_it 2 btex footer etex do_it 3 btex text etex do_it 4 btex header etex do_it 5 btex top etex In the horizontal direction we have edges margins and text There are left and right edges and margins which are swapped on even pages when you typeset a double sided document def do_it expr xx tt path p p unitsquare xyscaled w lxx h 1 shifted x xx y 1 label tt center p shifted 0 height h 1 2 enddef do_it 1 btex edge etex
285. urt TEX significantly If I had iot participated fully in all these activities literally hundreds of improvements would never have een made because I would never have thought of them or perceived why they were important But rim ennot bestest fs oo strongly loaned by a tingla penton One te initial design is complete and fairly robust the real test begins as people with many different iewpoints undertake their own experiments Douglas R Hostadter mald Knuth has spent the past several years working on a system allowing him to control many sspects of the design of his forthcoming books from the typesetting and layout down to the ver hapes of the letters Seldom has an author had anything remotely like this power to control t l appearance of his or her work Knuth s TX typesetting system has become well known an wailable in many countries around the world By contrast his Mevaront system for designing families of typefaces has not become as well known or available In his article The Concept of a Meta Font Knuth sets forth for the first time the underlying hilosophy of metaronr as well as some of its products Not only is the concept exiting and clearly ell executed but in my opinion the article is charmingly written as well However despite myl werall enthusiasm for Knuth s idea and article there are some points in it that I feel might bd iken wrongly by many readers and since they are points that touch close to my deepest
286. using the same dimensions as the final picture or when you want to show only a small piece fill fullcircle scaled 2cm withcolor 625yellow setbounds currentpicture to unitsquare scaled icm draw unitsquare scaled 1cm withcolor 625red Here we set the bounding box with the command setbounds which takes a path Welcome to METAeOST Preliminary Version November 11 2001 115 raphic extends beyond the bounding box but the bounding box determines the placement and therefore the spacing around the graphic We can get rid of the artwork outside the bounding box by clipping it fill fullcircle scaled 2cm withcolor 625yellow clip currentpicture to unitsquare scaled 1cm The resulting picture is just as large but shows less of the picture Cutting and pasting When enhancing or building a graphic often parts of already constructed paths are needed The subpath cutbefore and cutafter operators can be used to split paths in smaller pieces In order to do so we must know where we are on the path that is involved For this we use points on the path Unfortunately we can only use these points when we know where they are located In this section we will combine some techniques discussed in previous sections We will define a few macros manipulate some paths and draw curves and points 2 3 e 1 e e 4 0 o8 e e 5 e 7 6 This circle is drawn by scaling the predefine
287. veryday s infinity is supposed to be With as built in MeTAPOST command that accepts curl and tension directive as described in this section you will now probably understand why plain metarost defines the following macros that way def curl 1 curl 1 enddef def tension infinity enddef def tension atleast 1 enddef Preliminary Version November 11 2001 2r These definitions also point out why you cannot add directives to the left or right side of and they are directives themselves Transformations A transform is a vector that is used in what is called an affine transformation To quote the METAPOST manual Tf p px Py is a pair and T is a transform then p transform T isa pair of the form ty txxPx tryPyrty tyxPx tyyPy where the six numeric quantities tx ty txxs txys tyx tyy determine T In literature concerning POSTSCRIPT and PDF you will find many references to such transformation matrices A matrix of s 0 0 s 0 0 is scaling by sx in the horizontal direction and s in the vertical direction while 1 0 tx 1 0 ty is a shift over tx ty Of course combinations are also possible Although these descriptions seem in conflict with each other in the nature and order of the transform components in the vectors the concepts are the same You normally populate transformation matrices using scaled shifted rotated transfo
288. ves they frequently need to indicate the direction of motion I often have need of a little macro that will put an arrow of requested length anchored at a point on the curve and bending with the curve in the direction of motion When David Arnold asked me how this could be achieved the fact that a length was requested meant that the solution should be sought in using the primitives and macros we introduced a few paragraphs before Say that we want to call for such an arrow as follows path p p fullcircle scaled 3cm pair q q point 4 along p pickup pencircle scaled 2mm draw p withcolor 625white drawarrow somearrow p q 2cm withcolor 625red draw q withcolor 625yellow Because we want to follow the path we need to construct the arrow from this path Therefore we first reduce the path by cutting off the part before the given point Next we cut off the end of the Welcome tO MET APOST Preliminary Version November 11 2001 resulting path so that we keep a slice that has the length that was asked for Since we can only cut at points we determine this point using the arctime primitive vardef somearrow expr pat loc len save p path p p pat cutbefore loc p cutafter point arctime len of p of p enddef By using a vardef we hide the intermediate assignments Such vardef is automatically sur rounded by begingroup and endgroup so the save is
289. wn using colorcircle 4cm 4 6 8 4 8 6 6 4 8 addto currentpicture also inverted currentpicture shifted 5cm 0 When we draw a path or stroke a path as it is called officially we actually perform an addition addto currentpicture doublepath somepath The i11 command is actually addto currentpicture contour somepath We will need both doublepath and contour operations in the definition of inverted When meterost has digested a path into a picture it keeps track of some characteristics We can ask for them using part operators The following operators can be applied to a transform vector one of MetarosT data types but also to a picture Say that we have drawn a circle draw fullcircle xscaled 3cm yscaled 2cm dashed dashpattern on 3mm off 3mm withpen pencircle scaled imm withcolor 625red picture p p currentpicture This circle looks like pe d s Sa We can now ask for some of the characteristics of currentpicture like its color We could write the values to the log file but it is more convenient to put them on paper label rt redpart amp decimal redpart p 4cm 5cm label rt greenpart amp decimal greenpart p 4cm Ocm label rt bluepart amp decimal bluepart p 4cm 5cm The result has no typographic beauty keep in mind that here we use meTaPosT to typeset the text but serves its purpose Preliminary Version November 11 2001
290. xpects to find it If you want to be sure that everything is done correctly you may try texexec make alone metafun Depending on how you want to process your graphic in the file cont sys tex which you can put in a place where CONT XT can find it you may set one or more of the following switches runMPgraphicstrue process graphics at run time runMPTEXgraphicstrue at run time process graphics that contain text that is to be typeset by TX by calling TEXEXEC recycleMPslotstrue use a less temporary files as possible useMETAFUNformattrue use a MetaFun format file instead of loading all modules separately It makes much sense to process the graphics directly because then Tpx will know the right dimen sions at once if you process the graphics afterwards Tex will run much faster but additional runs may be needed TREX The installation of Tpx is not trivial Fortunately the Tpx user groups distribute TEx in such a way that installation is nearly automatic There are well written manuals available for installing Tx If you are free to choose what TEX you use we advise to use PDF Tgx ConTpxt The installation of CONTEXT is described in the manual that is included in the distribution If you want to update to a more recent version you can fetch a new archive from one of the sites that Preliminary Version November 11 2001 AA A 5 host CONTEXT You ne
291. y shed some insight in what metarost is doing path p p fullcircle xscaled 4cm yscaled 3cm drawpath p drawcontrollines p drawpoints p drawcontrolpoints p drawpointlabels p The pre and post control points show up as small dots and are connected to their parent point with thin lines You can deduce the direction of a path from the way the points are numbered but using an arrow to indicate the direction is more clear Preliminary Version November 11 2001 path p p fullcircle xscaled 4cm yscaled 3cm drawarrowpath p drawcontrollines p drawpoints p drawcontrolpoints p drawpointlabels p The drawarrowpath is responsible for the arrow Especially when you are in the process of defining macros that have to calculate intersections or take subpaths knowing the direction may be of help The next table summarizes the special drawing commands drawpath the path drawarrowpath the direction of the path drawcontrollines the lines to the control points drawpoints the points that make up the path drawcontrolpoints the control points of the points drawpointlabels the numbers of the points You can set the characteristics of these like you set drawoptions The default settings are as follows drawpathoptions withpen pencircle scaled 5 withcolor 8white drawpointoptions withpen pencircle scaled 4 withcolor black drawcontroloptions with
292. ypeset documents we will define them in the document source Figure 13 2 White s illusion Unless you belong to the happy few whose visual capabilities are not distorted by neural opti mizations in figure 13 2 the gray rectangles at the left look lighter than those on the right Alas you can fool yourself but MetaPost does not cheat This graphic referred to as White s illusion is defined as follows startbuffer interim linecap butt numeric u u 1cm pickup pencircle scaled 5u for i lu step u until 5u draw 0 i 5u i endfor for i 2u step u until 4u draw u i 2u i withcolor 5white draw 3u i 4u i shifted 0 5u withcolor 5white endfor stopbuffer Watch how we include the code directly We have packaged this graphic in a buffer which we include as a floating figure placefigure here fig tricked 1 White s illusion processMPbuf fer When passed to metarost this code is encapsulated in its beginfig and endfig macros and thereby grouped But any change to a variable that is not explicitly saved migrates to the outer level In order to prevent all successive graphics to have butt d linecaps we have to change this Preliminary Version November 11 2001 A few line characteristic locally Because linecap is defined as an internal variable we have to use interim to overload its value Because u is a rather
293. z31 g h 242 z41 Now we can draw the lines but first we choose ourselves an acceptable line thickness pickup pencircle scaled 5pt The lines are draw with the following code draw z11 z12 z13 z14 cycle draw z11 z13 draw z12 z14 draw z21 z22 z23 z24 cycle draw z21 z23 draw z22 z24 draw z31 z32 z33 z34 cycle draw z31 z33 draw z32 z34 draw z41 z42 z43 z44 cycle draw z41 z43 draw z42 z44 The mid points can be calculated by meTtaPosT too The next lines define that those points are positioned halfway the extremes zi z3 0 5 z11 z13 z2 0 5 z21 z23 0 5 z31 z33 z4 0 5 z41 z43 To make them stand out we choose an alternative linestyle draw z1 z3 dashed evenly draw z2 z4 dashed evenly Just to be complete we add a symbol that marks the right angle First we determine the common point of the two lines that lays at whatever point Metarost finds suitable Preliminary Version November 11 2001 Welcome to METAR z0 whatever z1 z3 mark_rt_angle z1 z0 z2 z2 is not used at all whatever z2 z4 So far most equations were rather simple and in order to solve them metarost did not have to work real hard The only boundary condition is that in order to find a solution MeTaPosT must be able to solve all dependencies The previous lines showing the whatever variable is a typical example of a s
294. zi tension 1 z2 zi tension 1 and 1 z2 The tripple dot command is actually a macro so that the following two paths are identical Zl 22 zi tension atleast 1 z2 The atleast directive tells MetaPosT to do some magic behind the screens Both the 3 4 and the atleast lead to the question what exactly is the influence of tension directive We will try to demystify tension by drawing the next graphic u 1cm zi 0 0 z2 2u 4u z3 4u 0 def sample expr p c few nyore details Preliminary Version November 11 2001 g 4 CxS S A VNR Lavy 2 a i je SEY OR draw p withpen pencircle scaled 2 5mm withcolor white draw p withpen pencircle scaled 2 0mm withcolor c enddef for i 75 step 05 until 1 sample zl tension i z2 z3 625red endfor for i l step 05 until 2 sample zl tension i z2 z3 625yellow endfor sample zi z2 z3 625white sample zl Z2 23 625white Indeed values less than 75 give an error message but large values are okay As you can see the two gray curves are the same So here atleast 1 means 1 even if larger values are useful Curves are made up out of points and each point has two control points Since the tension specifier finaly becomes a control point it will be no surprise that you may specify two tension values If we replac

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