Local parametrization of cubic surfaces

Authors:
Ibolya Szilágyi;Bert Jüttler;Josef Schicho
Affiliations:
RISCLinz/RICAM, Johannes Kepler University, A-4040 Linz, Austria;Institute of Applied Geometry, Johannes Kepler University, A-4040 Linz, Austria;RICAM, Austrian Academy of Sciences, A-4040 Linz, Austria
Venue:
Journal of Symbolic Computation
Year:
2006

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Abstract

Algebraic surfaces-which are frequently used in geometric modelling-are represented either in implicit or parametric form. Several techniques for parametrizing a rational algebraic surface as a whole exist. However, in many applications, it suffices to parametrize a small portion of the surface. This motivates the analysis of local parametrizations, i.e., parametrizations of a small neighborhood of a given point P of the surface S. In this paper we introduce several techniques for generating such parametrizations for nonsingular cubic surfaces. For this class of surfaces, it is shown that the local parametrization problem can be solved for all points, and any such surface can be covered completely.