27 - Bézier Curves

Summary

In the middle of the 1960's, a system for designing and manufacturing cars using free-form curves and surfaces was developed by P. Bézier at the Renault automobile company. This computerized system, named UNISURF, provides a general mathematical framework for defining arbitrarily shaped curves and surfaces.

Previously, designers of stamped parts such as car body panels had used manual tools such as French curves. (Of course, the Bézier curve could be referred to as a French curve also, but here we mean French curve in the traditional sense.) These designers defined the shape of a car body in terms of cross sections at most one hundred millimeters apart. In this process, the cross-sectional curves are carved into a three-dimensional model and interpolation is left to the experience of highly skilled pattern makers. The final standard, however, is the “master model”, whose shape no longer coincides precisely with the curves originally traced on the drawing board. This inconsistency results in expenses and delays. No significant improvement could be expected in the absence of an accurate, complete mathematical definition of free-form shape.

A good designing system must allow for the interface between the underlying mathematical techniques and the designers, who have a good knowledge of descriptive geometry but may have little training in algebra or analysis. In order to be successful, a system must appeal to designers — it must be simple, intuitive and easy to use. It is crucial that such a design system make no mathematical demands on the users other than those to which they have been accustomed through the conventional design process.