Fonts & Encodings

G.1. History

We can hardly imagine the connection between the splendid curves of a font like Monotype Garamond and the hood of a Renault. Yet both consist of curves, and in both cases the production process (whether the final product be a Type 1 font or a piece of metal) went through a phase of computer-assisted design.

But how were car bodies designed before the computer era? Engineers made models out of wood or plaster and approached the desired result through successive approximations. Developing one model after another was neither rapid nor efficient. Pierre Bézier (1910–1999), an engineer at Renault since 1933, started doing research on computer science in 1960 to find a system for modeling curves, or even surfaces, that would be easy to compute and also easy for the human to manipulate.

The curves that bear his name satisfy these conditions. But he was not the only one to work on these techniques. There were also Paul de Casteljau, an engineer at Citroën, and Birkhoff, Garabedian, and de Boor, at General Motors, in the United States. Bézier's work gave us the curves, which today are known around the world because they are at the heart of every computer-assisted design system; de Casteljau's work gave us the algorithm that we shall see below; Boor and his colleagues worked on B-splines ('B' as in "Bézier"), a more refined version of Bézier curves.

In the text that follows, we shall present the main properties of the Bézier curves. This text was inspired primarily by [246]. ...