P. Bézier: How a Simple System Was Born

This chapter discusses the evolution of systems to solve mathematical problems. Most of the systems were invented by mathematicians, but UNISURF, at least at the beginning, was developed by mechanical engineers from the automotive industry. These engineers were familiar with parts mainly described by lines and circles; fillets and other blending auxiliary surfaces were scantly defined, their final shape being left to the skill and experience of the patternmakers and die-setters. The idea of UNISURF was initially oriented toward geometry rather than analysis, but kept in mind that every datum should be exclusively expressed by numbers. The basic idea of UNISURF came from a comparison with a process often used in foundries to obtain a core: sand being compacted in a box. To make the system more flexible, one might change the shape of the template at the same time as it is moved. This process could not produce a large variety of shapes, but the principle could be translated into a mathematical solution.

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