TitleAn Edge-Preserving, Data-Dependent Triangulation Scheme for Hierarchical Rendering (In Book)
inScientific Visualization - Methods and Applications
Author(s) James C. Barnes, Bernd Hamann, Ken Joy
Editor(s) Hans Hagen, G. M. Nielson, F. Post
Year 1999
AddressNew York, New York
Abstract In many applications one is concerned with the approximation of functions from a finite set of given data sites with associated functions values. We describe a construction of a hierarchy of triangulations which approximate the given data at varying levels of detail. Intermediate triangulations can be associated with a particular level of the hieracrchy by considering their approximation errors. This paper presents a new data-dependent triangulation scheme for multi-valued scattered data in the plane. We perform piecewise linear approximation based on data-dependent triangulations. Our scheme preserves edges (discontinuities) that might exist in a given data set by placing vertices close to edges. We start with a coarse, data-dependent triangulation of the convex hull of the given data sites and subdivide triangles until the error of the piecewise linear approximation implied by a triangulation is smaller than some tolerance.