A unified approach to resultant matrices for Bernstein basis polynomials

Resultant matrices can be used to compute the intersection points of curves that are defined by polynomials. They were originally developed for polynomials expressed in the power (monomial) basis, but the recent development of resultant matrices for Bernstein basis polynomials has increased their use in computer aided geometric design, for which the Bernstein basis is the standard polynomial basis. In this paper, the equations that relate the Sylvester, Bézout and companion resultant matrices for Bernstein basis polynomials are derived, thereby establishing their equivalence. It is shown that these equations are more complicated than their power basis equivalents.