On Computing Zeros of a Bivariate Bernstein Polynomial

Abstract

In this paper, the problem of computing zeros of a general degree bivariate Bernstein polynomial is considered. An efficient and robust algorithm is presented that takes into full account particular properties of the function considered. The algorithm works for rectangular as well as triangular domains. The outlined procedure can also be applied for the computation of the intersection of a Bézier patch and a plane as well as in the determination of an algebraic curve restricted to a compact domain. In particular, singular points of the algebraic curve are reliably detected.