A unified approach to resultant matrices for Bernstein basis polynomials

Authors:
Joab R. Winkler
Affiliations:
Department of Computer Science, The University of Sheffield, Regent Court, 211 Portobello Street, Sheffield S1 4DP, United Kingdom
Venue:
Computer Aided Geometric Design
Year:
2008

Citing 8
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Abstract

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, Bezout 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.