Bézier, pioneer of mathematics in car design – 10/24/2023 – Marcelo Viana

In 1933, the young Frenchman Pierre Bézier (1910–1999) got his first job in the Renault industry, as a tool fitter. He retired from the same company 42 years later as director of mechanical methods. In the meantime, he revolutionized automation in the design and production of Renault and Peugeot cars, leaving an extraordinary legacy as a pioneer of computer-aided design (CAD), which today permeates numerous sectors of activity, from industry to Art.

Bézier graduated as a mechanical engineer from the Escola Normal Superior das Artes e Ofícios, in 1930, and as an electrical engineer from the Escola Superior de Eletricidade, the following year. Much later, at the age of 67, he entered Pierre and Marie Curie University to obtain a doctorate in mathematics. Alongside his work in industry, he was a professor at the National Conservatory of Arts and Crafts in Paris between 1968 and 1979.

One of the biggest problems in the automotive industry was how to shape the shape of a new car so that it is effective from an aerodynamic point of view and beautiful, of course. One possibility would be to consider several equations, make the computer draw the corresponding surfaces, discard those that were not pleasing and improve those that were promising. But it’s not that simple.

To begin with, it would be necessary to discover reasonable equations for the surface of a car: in addition to being a lot of work, such equations would certainly be very complicated. This was even more critical at a time when computers were in their infancy: in 1964, after much insistence, Bézier managed to get Renault to acquire a second-hand computer with an incredible eight kilobytes of memory!

Furthermore, in the case where an equation gave a promising result, it would not be obvious how to modify it to improve the result. In any case, it was nonsense to spend time and money finding and improving complex equations that, frankly, were useless.

It would be much better if the computer could draw different shapes without the need for equations, and in a way that they could be easily adjusted and modified by the user, to obtain even better results.

These concerns led Bézier, from 1960 onwards, to introduce into industrial design and production the mathematical idea that we now call the Bézier curve, which he patented and popularized (although he was not the inventor) and which today forms the basis of all design. modern. I will write about this next week.

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