TitleData-Dependent Triangulation in the Plane with Adaptive Knot Placement (In Book)
inGeometric Modelling: Dagstuhl 1999, Computing Supplement
Author(s) Rene Schaetzl, Hans Hagen, James C. Barnes, Bernd Hamann, Ken Joy
Editor(s) Guido Brunette, H. Bieri, Silvia Noemi Crivelli
Year 2001
Abstract In many applications one is concerned with the approximation of functions from a finite set of scattered data sites with associated function values. We describe a scheme for constructing a hierarchy of triangulations that approximates a given data set at varying levels of resolution. Intermediate triangulations can be associated with a particular level of a hierarchy by considering their approximation errors. We present a data-dependent triangulation scheme using a Sobolev norm to measure error instead of the more commonly used root-mean-square (RMS) error. Triangles are split by selecting points in a triangle, or its neighbors, that are in areas of potential discontinuites or areas of hight gradients. We call such points “significant points.”