De Casteljau's geometric approach to geometric design still alive

Abstract

With great enthusiasm and admiration we would like to pay tribute to Paul de Faget de Casteljau for his essential contribution to CAGD. Motivated by the development of automated human-computer collaboration for car industry, not only was he the very first pioneer in this field, but his initial geometric approach to creating shapes from poles was even undeniably the simplest and most remarkably effective. Two crucial points in this approach are to keep in mind: firstly, the idea of splitting one variable into several variables to facilitate the algorithmic construction of curves; secondly, the possibility of controlling shapes by means of osculating flats and corner-cutting algorithms. The present article is a partial survey on Chebyshevian blossoms intended to show that his ideas are still alive.