Curves and Surfaces for CAGD, 5th Edition

4

The de Casteljau Algorithm

The algorithm described in this chapter is probably the most fundamental one in the field of curve and surface design, yet it is surprisingly simple. Its main attraction is the beautiful interplay between geometry and algebra: a very intuitive geometric construction leads to a powerful theory.

Historically, it is with this algorithm that the work of de Casteljau started in 1959. The only written evidence is in [145] and [146], both technical reports that are not easily accessible. De Casteljau’s work went unnoticed until W. Boehm obtained copies of the reports in 1975. Since then, de Casteljau’s work has gained more popularity.

4.1 Parabolas

We give a simple construction for the generation of a parabola; the straightforward ...