B-SPLINES CONTRA BÉZIERSPLINES

Abstract

P. E. Bézier, a mechanical and electrical engineer, developed his idea of interpolating given data during his work at Renault. Instead of using ordinary polynomials he introduced Bernstein polynomials in his algorithm. With the help of the Bernstein operator and a piecewise forgoing he invented a method to interpolate given data with a smooth spline curve. I. J. Schoenberg is often entitled as the father of B-Splines, although Laplace probably worked with some kind of B-Splines in 1820. They are introduced as basis for the spline functions, and this is the reason for their name. We present the basic properties of Bézier- and B-Splines including their shape preserving behaviour. In many examples we illustrate the main differences in their interpolating properties.