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Curve implicitization in the bivariate tensor-product Bernstein basis

Ana Marco·Jose-Javier Martinez
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Abstract

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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Ana Marco, Jose-Javier Martinez. 2005-12-19. Curve implicitization in the bivariate tensor-product Bernstein basis. https://arxiv.org/abs/math/0512448

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