Curve implicitization in the bivariate tensor-product Bernstein basis

Details Curve implicitization in the bivariate tensor-product Bernstein basis Curve implicitization in the bivariate tensor-product Bernstein basis

2005-12-19

arxiv.org/abs/math/0512448v1

Mathematics

Numerical Analysis

11 pages

Scientific paper

The approach to curve implicitization through Sylvester and Bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case of Bernstein-Bezoutian matrices constructed when the polynomials are given in the Bernstein basis. The coefficients of the implicit equation are also computed in the bivariate tensor-product Bernstein basis, and their computation involves the bidiagonal factorization of the inverses of certain totally positive matrices.

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