METAPOST and the FIIT Logo

Transcription

1 METAPOST and the FIIT Logo Matej KOŠÍK Slovak University of Technology Faclty of Informatics and Information Technologies Ilkovičova 3, Bratislava, Slovakia 1 The Tools Abstract. Yo can consider this article as a fn story which might be of interest to those who like mathematics, programming and graphics. We show how or logo can be described by means of METAPOST commands. Professor Donald E. Knth devoted significant part of his life to the area of compteraided typesetting. There are three related tools: TEX METAFONT METAPOST TEX [3] is a tool for combining glyphs to larger strctres. METAFONT [3] is a tool for defining the shapes of the glyphs we can se in TEX, their mtal kerning and possible ligatres. Sometimes we also need to inclde varios graphics (plots, diagrams etc.) in or docments. METAPOST [1, 2] can be sed for those diagrams which can somehow be conveniently compted. It is possible to define points declaratively as an intersection of two given straight lines. It is possible to declare new closed paths as areas bonded by a given set of crves. There are operators for finding ot coordinates of a point on a given path in a given time. We can find ot tangents in points belonging to some crve in particlar time and other things. An important advantage of this tool is Spervisor: prof. Jiří Šafařík, PhD, Institte of Informatics and Software Engineering, Faclty of Informatics and Information Technologies SUT in Bratislava IIT.SRC 2008, Bratislava, April 30, 2008, pp. 1 8.

2 2 Matej Košík that it is possible to embed otpt of TEX commands to or figres for varios descriptive textal labels we need to pt into or figres. We have fond ot that also the logo of or faclty is a decent mathematical object which deserves its own METAPOST definition. 2 Or Logo Or logo will be drawn to the following two-dimensional area: 0 This area will be filled with strokes of or virtal pen and ink. First we wold like to draw a contor of the logo body. We do this by the following commands: := 4cm; r := /3; draw (0,0)--(-r,0)..(,r)--(,)-- (r,)..(0,-r)--cycle; r r 0 r r Yo can see that we first define some variables which will hold some dimensions we will se over and over. Variable holds the width and the height of or logo. Variable r defines the size of the ronded corners. The last command draws a closed path composed

3 METAPOST and the FIIT Logo 3 from several segments. It begins in the point (0, 0), then it goes throgh five other points and finally it closes its voyage back in (0, 0). Some of the segments are straight (the ones where we sed -- operator) and some of them were spposed to be crved (the ones where we sed.. operator). Unfortnately, the two segments which were spposed to be ronded are straight in the above figre. METAPOST decided to se an abscissa as the most simple smooth crve connecting the two given points. This is not what we want and therefore we will change the last command to: draw (0,0)--(-r,0){right}..{p}(,r)--(,)-- (r,){left}..{down}(0,-r)--cycle; We have given METAPOST additional information abot the tangents after and before appropriate points of the crve and this time the shape of the logo body seems to be correct. r r 0 r r Now, if we change the draw command to fill, we will get: r r 0 r r So, we have a logo body. Now we wold like to ct ot parts of this logo. This can be accomplished with the ndraw command. Let s first do the small ct which goes from the left border of the logo slightly to the right. We choose the shape of or pen:

4 4 Matej Košík w := /10; pickp pencircle scaled w; and then we can do the ndrawing: x := /8; y := /2; ndraw (0,y)--(x,y); y = 2 0 x = 8 Nothing extremely complicated. So we go on to ndraw the ct which goes from the bottom border of or logo and goes p: x := r; y := /2 - w; ndraw (x,0)--(x,y); y = 2 w 0 x = r Undrawing the top-left circle is analogos. We only have to compte its path. This is done by sing the fllcircle operator. It retrns s the circle with radis of 1 point and center in the beginning of the coordinate system. We take this path, scale it and shift it. Then we ndraw it (with the crrently chosen pen).

5 METAPOST and the FIIT Logo 5 s := /2-3w/2; y := - s/2 - w/2; ndraw fllcircle scaled s shifted (x,y); The only problematic thing may be perhaps finding ot the proper center of the circle and its radis. Bt, as it trns ot, these vales can be precisely compted. The center of the circle is in point (x, y) and its radis is s. y = s 2 w x = r Now we did all the cts on the left. We cold proceed analogosly on the right. Bt, apparently, cts in the right part of the logo are the same as the ones on the left except for the fact that they are rotated by 180 degrees arond the logo center. This gives s the chance to tilize more advanced featres of METAPOST. Instead of applying the ndraw operations to the crrent pictre as we did above: % Make the left-right ct. pickp pencircle scaled w; x := /8; y := /2; ndraw (0,y)--(x,y); % Make the bottom-p ct. x := r; y := /2-w; ndraw (x,0)--(x,y); % Make the top-left circlar ct. s := /2-3w/2; y := -s/2-w/2; ndraw fllcircle scaled s shifted (x,y); we will apply them to the axiliary pictre named leftcts. % Make cts (bottom-p, left-right, % top-left circlar) which are on the left. pictre leftcts; leftcts := nllpictre;

6 6 Matej Košík % Make the left-right ct. x := /8; y := /2; pen p; p := pencircle scaled w; addto leftcts doblepath (0,y)--(x,y) withpen p withcolor backgrond; % Make the bottom-p ct. x := r; y := /2-w; addto leftcts doblepath (x,0)--(x,y) withpen p withcolor backgrond; % Make the top-left circlar ct. s := /2-3w/2; y := -s/2-w/2; addto leftcts doblepath fllcircle scaled s shifted (x,y) withpen p withcolor backgrond; If we know draw the leftcts to the crrent pictre draw leftcts; and we have what we wanted: we get the same reslt as before: y = s 2 w x = r The advantage of this approach is, that now we can easily ndraw leftcts rotated arond the logo center by 180 degrees: draw leftcts transformed identity rotatedarond((/2,/2),180); and we have what we wanted:

7 METAPOST and the FIIT Logo Conclsion METAPOST belongs to the TEX and METAFONT family. Its important virte is that it enables s to embed TEX or L A TEX labels to or figres. That is qite hard to do with other kind of drawing tools. The whole program: 7 fiitlogo.mp 7 beginfig(-1); := 4cm; r := /3; w := /10; pickp pencircle scaled 3pt; fill (0,0)--(-r,0){right}..{p}(,r)--(,)-- (r,){left}..{down}(0,-r)--cycle; pictre leftcts; leftcts := nllpictre; x := /8; y := /2; pen p; p := pencircle scaled w; addto leftcts doblepath (0,y)--(x,y) withpen p withcolor backgrond; x := r; y := /2-w; addto leftcts doblepath (x,0)--(x,y) withpen p withcolor backgrond; s := /2-3w/2; y := -s/2-w/2; addto leftcts doblepath fllcircle scaled s shifted (x,y) withpen p withcolor backgrond; draw leftcts; draw leftcts transformed identity rotatedarond((/2,/2),180); endfig; end

8 8 Matej Košík References [1] Hobby, J.D.: Introdction to MetaPost. In: EroTEX 92 Proceedings, 1992, pp [2] Hobby, J.D.: A User s manal for MetaPost. Compting Science Technical Report no. 162, AT&T Bell Laboratories, Mrray Hill, New Jersey, [3] Knth, D.E.: TEX and METAFONT: New Directions in Typesetting. Digital Press, 1979.