@MISC{Pfluger92ondegenerate, author = {P. R. Pfluger and M. Neamtu}, title = {On Degenerate Surface Patches}, year = {1992} }

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Abstract

A local construction of a GC 1 interpolating surface to given scattered data in R 3 can give rise to degenerate Bernstein--B'ezier patches. That means the parametrization at vertices is not regular in the sense that the length of the tangent vector to any curve passing through a vertex is zero at that vertex. This implies that the curvature of these curves tends to infinity whenever one approaches a vertex. This fact seems to have not a negative influence on the shape of the surface. 1 Interpolation problem We have considered the problem of interpolating scattered data points in R 3 by a geometrically smooth (GC 1 ) surface. In order to be able to handle "complicated" surfaces with many data points, methods designed for that purpose are usually local in nature. For a classification of different approaches see [4]. Various attempts to attack the interpolation problem using degenerate polynomial patches are described in [3,5,1] and also in an article in these proceedings [2]. No...