A univariate resultant-based implicitization algorithm for surfaces
In this paper, we present a new algorithm for computing the implicit equation of a rational surface V from a rational parametrization P((t) over bar). The algorithm is valid independent of the existence of base points, and is based on the computation of polynomial gcds and univariate resultants. Moreover, we prove that the resultant-based formula provides a power of the implicit equation. In addition, performing a suitable linear change of parameters, we prove that this power is indeed the degree of the rational map induced by the parametrization. We also present formulas for computing the partial degrees of the implicit equation. (c) 2008 Published by Elsevier Ltd
implicitization partial degrees rational surface parametrization properness