Geometric applications of the Bezout matrix in the Lagrange basis

Authors:
D. A. Aruliah;Robert M. Corless;Laureano Gonzalez-Vega;Azar Shakoori
Affiliations:
UOIT, Oshawa, ON, Canada;ORCCA, UWO, London, ON, Canada;Universidad de Cantabria, Santander, Spain;ORCCA, UWO, London, ON, Canada
Venue:
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Year:
2007

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Abstract

Using a new formulation of the Bézout matrix, we construct bivariate matrix polynomials expressed in a tensor-product Lagrange basis. We use these matrix polynomials to solve common tasks in computer-aided geometric design. For example, we show that these bivariate polynomials can serve as stable and efficient implicit representations of plane curves for a variety of curve intersection problems.