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 ¯ ) . The algorithm is valid independent of the existence of base points, and is based on the computation of polynomial gcds and univariate resultants. Moreover...

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Vydáno v:Journal of symbolic computation Ročník 43; číslo 2; s. 118 - 139
Hlavní autoři: Pérez-Díaz, Sonia, Rafael Sendra, J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.02.2008
Témata:
Implicitization
Partial degrees
Properness
Rational surface parametrization
Partial degrees
Implicitization
Rational surface parametrization
Properness
ISSN:0747-7171, 1095-855X
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Popis
Shrnutí:In this paper, we present a new algorithm for computing the implicit equation of a rational surface V from a rational parametrization P ( t ¯ ) . 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.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2007.10.001