An application of fast factorization algorithms in Computer Aided Geometric Design

Abstract

Structured matrices play an important role in the numerical solution of practical problems, because it is possible to develop fast algorithms for their triangular factorization. In this paper we consider a classical problem of Computer Aided Geometric Design, namely the computation of the intersection points of two planar rational parametric curves, given in Bernstein form. For the numerical solution to this problem we propose an algebraic approach, based on a fast factorization algorithm of the resulting Bezout matrix with polynomial entries, which avoids the need for symbolic computation. This also allows us to efficiently handle high degree curves. Numerical examples and comparisons with other standard intersection methods are given.