Metafont and MetaPost

Metafont is a system created by Donald E. Knuth for generating fonts, in particular for use with TeX, his well-known typsetting system.¹ Expressed in a somewhat simplified way, Metafont is a system for programming curves, which are then digitized and output in the form of run-time encoded bitmaps. (See Knuth's The Metafontbook for more information).

John D. Hobby modified Metafont's source code to create MetaPost, which functions in much the same way, but outputs encapsulated PostScript (EPS) files instead of bitmaps. MetaPost is very useful for creating graphics and is a convenient interface to PostScript. It is also easy both to imbed TeX code in MetaPost programs, for instance, for typesetting labels, and to include MetaPost graphics in ordinary TeX files, e.g., by using dvips.² Apart from simply printing the PostScript file output by dvips, there are many programs that can process ordinary or encapsulated PostScript files and convert them to other formats. Just two of the many possibilities are ImageMagick and GIMP, both of which can be used to create animations from MetaPost graphics.

However, MetaPost inherited a significant limitation from Metafont: it's not possible to use it for making three-dimensional graphics, except in a very limited way. One insuperable problem is the severe limitation on the magnitude of user-defined numerical variables in Metafont and MetaPost.³ This made sense for Metafont's and MetaPost's original purposes, but they make it impossible to perform the calculations needed for 3D graphics.

Another problem is the data types defined in Metafont: Points are represented as pairs of real values and affine transformations as sets of 6 real values. This corresponds to the representation of points and affine transformations in the plane as a two-element vector on the one hand and a six element matrix on the other. While it is possible to work around the limitation imposed by having points be represented by only two values, it is impracticable in the case of the transformations.

For these reasons, I decided to write a program that would behave more or less like Metafont, but with suitable extensions, and the ability to handle three dimensional data; namely 3DLDF. It stores the data and performs the transformations and other necessary calculations and is not subject to the limitations of MetaPost and its data types. Upon output, it performs a perspective transformation, converting the 3D image into a 2D one. The latter can now be expressed as an ordinary MetaPost program, so 3DLDF writes its output as MetaPost code to a file.

In the following, it may be a little unclear why I sometimes refer to Metafont and sometimes to MetaPost. The reason is that Metafont inherited much of its functionality from Metafont. Certain operations in Metafont have no meaning in MetaPost and so have been removed, while MetaPost's function of interfacing with PostScript has caused other operations to be added. For example, in MetaPost, color is a data type, but not in Metafont. Unless otherwise stated, when I refer to Metafont, it can be assumed that what I say applies to MetaPost as well. However, when I refer to MetaPost, it will generally be in connection with features specific to MetaPost.