Department of Informatics and Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
Abstract:
By exploiting the freedom in the choice of parametrization of a parametric surface, we show that there exist quadratic parametric surfaces that approximate a given parametric surface with the same approximation order as cubics, namely four, in the neighbourhood of a point where the Gaussian curvature of the surface is nonzero. This provides a first generalization to surfaces of earlier work for curves.