Implicitization of rational ruled surfaces with μ-bases

Marc Dohm (1)

1 GALAAD - Geometry, algebra, algorithms

Chen, Sederberg, and Zheng introduced the notion of a µ-basis for a rational ruled surface in Chen et al. (2001) and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We generalize this result to the case of an arbitrary parametrization. We also give a new proof for the corresponding theorem in the curve case and treat the reparametrization problem for curves and ruled surfaces.

Mots clés: implicitization; µ-basis; ruled surface; reparametrization

Domaines: Géométrie algébrique [math.AG]

Marc Dohm. Implicitization of rational ruled surfaces with μ-bases. 2006. ⟨inria-00132800v1⟩