Linear Approximation of Trimmed Surfaces

Abstract

Introduction Parametric surfaces in various representations, such as B'ezier-and B-spline-tensorproduct patches, triangular patches etc., play an important role in CAGD-applications. Connecting patches with different degree of continuity and trimming surfaces are well-known techniques to construct a variety of shapes like ship hulls, car bodys, etc. For finite element analysis, stereolithography, rendering and other areas, techniques for approximating such surfaces by a piecewise linear set of elements (mostly triangles) are required. The aim of these techniques is to obtain a triangulation that ffl approximates the initial surface within a predefined tolerance ffl; ffl consists of well-shaped triangles, ffl avoids cracks between the triangles of different surface patches and ffl delivers an easy method to get multiple resolutions of the approximation. After shortly presenting some of the most relevant