chapter  7
Parametric Curves and Surfaces
Pages 58

The need for mathematical representations of free-form shapes, suitable for computer processing, became apparent during the 1960s in the automotive and aeronautic industries. Until that time, the specifications by the designers for the shape of cars and planes were implemented only approximately, as no exact descriptions of such shapes were in practical use. When computer-driven machinery that could produce complex-shaped objects was made available to these industries, it became essential to devise suitable mathematical descriptions. Paul de Casteljau and Pierre Be´zier, then working at Citroe¨n and Renault, respectively, developed independently the theory of polynomial curves and surfaces that now bears Be´zier’s name-de Casteljau’s work was not published early on-and constitutes the basic tool for describing and rendering free-form shapes.