An Edge-Preserving, Data-Dependent Triangulation Scheme for Hierarchical Rendering

Abstract

In many applications one is concerned with the approximation of functions from a finite set of given data sites with associated function 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 hierarchy 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.