Approximate rational parameterization of implicitly defined surfaces

Authors:
Elmar Wurm;Bert Jüttler;Myung-Soo Kim
Affiliations:
Institute of Applied Geometry, Johannes Kepler University, Linz, Austria;Institute of Applied Geometry, Johannes Kepler University, Linz, Austria;Department of Computer Science, Seoul National University, Korea
Venue:
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Year:
2005

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Abstract

We present a method for approximate rational parameterization of algebraic surfaces of arbitrary degree and genus (or more general implicitly defined surfaces), based on numerical optimization techniques. The method computes patches of maximal size on these surfaces subject to certain quality constraints. It can be used to generate local low degree approximations and rational approximations of non-parameterisable surfaces.