On geometric interpolation of parametric surfaces

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. 2005 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2005
• Where: CAGD
• Authors: Knut Mørken
• Keywords: Approximation Order, CAGD 2005, Gaussian Curvature, Parametric Surface