Implicit Representation of Rational Parametric Surfaces

In many applications we need to compute the implicit representation of rational parametric surfaces. Previously, resultants and Grobner bases have been applied to this problem. However, these techniques at times result in an extraneous factors along with the implicit equation and fail altogether when a parametrization has base points. In this paper we present algorithms to implicitize rational parametric surfaces with and without base points. One of the strength of the algorithms lies in the fact that we do not use multivariate factorization. The base points blow up to rational curves on the surface and we present techniques to compute the rational parametrization of the blow up curves.

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