Bernstein Bezoutians and application to intersection problems
We study the Bezier curve-surface and Bezier surface-surface intersection problems avoiding the well-known unstable conversion between the Bernstein basis and the power basis. These varieties are given by parameterizations in Bernstein bases and all intermediate computations are performed in that form. For this purpose we construct an adapted resultant for generic Bernstein polynomial systems with a special shape which appear in the intersection problems. This construction is based on the expression of the Bezoutian matrix in Bernstein form. (C) 2011 Elsevier B.V. All rights reserved.
intersection problems bernstein basis resultant bezoutian matrix