Efficient evaluation of multivariate polynomials

Abstract In CAGD applications, the usual way to store a polynomial defined over a triangle is in the Bernstein-Bezier form, and the accepted way to evaluate it at a given point in the triangle is by the de Casteljau algorithm. In this paper we present an algorithm for evaluating Berstein-Bezier type polynomials which is significantly faster than de Casteljau. This suggests that a modified form of Bernstein-Bezier may be preferable for CAGD applications (as well as in applications of piecewise polynomials in data fitting and numerical solution of boundary-value problems).