Some METAFONT Techniques

This paper presents a few ideas on how to solve certain geometrical problems arising very often in character design, not directly solvable by METAFONTs plain macros. The first part of the paper presents two geometrical problems: the “k problem” and the “x problem”, their solutions using dichotomy, and a different solution using path intersections. The latter was proposed earlier on the net by the author; although geometrically correct, it does not work in real-world METAFONT practice: a nice example of METAFONT code : : : to avoid. The second part of the paper presents two simple macro for drawing “loose” Bézier curves; in a sense, the opposite of the tension operator. Finally, the third part solves a problem stated by Alan Hoenig: how to extract text and data out of aMETAFONT run, without using the log file. This is done in a straightforward manner by running a Flex-generated preprocessor over the GF file: the Flex code for this utility is given in appendix B. 1 Two Geometrical Problems, Solved by Iterated Calculations 1.1 Description Suppose you want to design a character ‘K’, as on the left part of fig. 1. The character should fit inside a box of width w and height h, and should consist of three strokes: the vertical stroke z0 z00 , and the two oblique strokes z1 z2 and z10 z20 . Only constraint: the point z1l = z10r should be fixed (for example, its coordinates can be (0; h2 )). So, here is the problem: Find a stroke z1 z2 with fixed z1l; y2l; x2r . This problem is not trivial, because METAFONT cannot compute pen positions without knowing in advance the angle of the pen (this stands both for defining a new pen with command pickup pen as for defining a simulated pen with command penpos). Because it arises when designing the letter ‘K’, we will call this problem, the “k problem”. The next problem is encountered when designing an ‘X’: as on the right part of fig. 1, suppose you want to draw this letter. Once again it should fit inside the box, and should consist of two strokes. To keep the same notation as in the previous case, we have only given names to the pen positions concerning the upper right part of the letter. In this case the constraints are: z1 is fixed (and not z1l as in the previous case), as well as y2l and x2r. Here again is the problem, which we call the “x problem”: Find a stroke z1 z2 with fixed z1; y2l; x2r. Well understood, in both cases the direction of the stroke must be perpendicular to the angle of the pen: all strokes must keep the same width.