METAFONT is a programming language used to define vector fonts. It is also the name of the interpreter that executes Metafont code, generating the bitmap fonts that can be embedded into e.g. PostScript. Metafont was devised by Donald Knuth as a counterpart to his TeX typesetting system.
One of the characteristics of Metafont is that all of the shapes of the glyphs are defined with geometrical equations, e.g., one can define a given point to be the intersection of a line segment and a Bézier cubic.
Unlike more common outline font formats (such as TrueType or PostScript Type 1), a Metafont font is primarily made up of strokes with finite-width "pens", along with filled regions. Thus, rather than describing the outline of the glyph directly, a Metafont file describes the pen paths. Some simpler Metafont fonts, such as the calligraphic mathematics fonts in the Computer Modern family, use a single pen stroke with a relatively large pen to define each visual "stroke" of the glyphs. More complex fonts such as the Roman text fonts in the Computer Modern family use a small pen to trace around the outline of the visual "strokes", which are then filled; the result is much like an outline font, but with slightly softened corners defined by the pen shape.
Since the font shapes are defined by equations rather than directly-coded numbers, it is possible to treat parameters such as aspect ratio, font slant, stroke width, serif size, and so forth as input parameters in each glyph definition (which then define not a single font, but a meta-font). Thus, by changing the value of one of these parameters at one location in the Metafont file, one can produce a consistent change throughout the entire font. Computer Modern Roman illustrates many uses of this feature; a typical TeX installation includes a number of versions of the font in sizes from 5pt to 17pt, with the stroke widths the same in all sizes (rather than increasing as the font is scaled up) and aspect ratios widening in the smaller sizes for increased legibility. In addition, the Computer Modern typewriter and sans-serif fonts are defined using essentially the same Metafont file as the Roman font, but with different global parameters.
Curves in Metafont are defined as cubic splines rather than quadratic, for greater versatility with similarly simple arithmetic.
Metafont can render any kind of graphical output, not just glyphs. However, MetaPost with its PostScript output is preferred for advanced illustrations. Metafont is most commonly invoked without a direct request from the user. DVI files can only contain references to typefaces, rather than the sets of raster or vector glyphs that other formats like PostScript allow. Consequently the glyphs in the typefaces need to be accessed whenever a request is made to view, print or convert a DVI file. Most TeX distributions are configured so that any fonts not currently available at the required resolution are generated by calls to Metafont. The typefaces are then stored for later reuse.
Metafont can also be run interactively, and has commands for displaying on the screen the images it produces. Knuth has said that he uses Metafont as a kind of desk calculator for solving complicated equations, though he now uses MetaPost for mathematical illustrations.
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