Piecewise Linear Approximation of Trimmed Surfaces

Abstract

Stereolithography applications require a surface model of the modeled object consisting of a mesh of triangular facets. This model can also be used for mechanical analysis through finite element methods. In this paper, a new algorithm for the piecewise linear approximation of trimmed surfaces is presented. The algorithm generates a triangulation that approximates the initial surface within a predefined tolerance. The approximation is conformai, without cracks in edges: a closed polyhedron is obtained in the case of a closed initial surface. The algorithm first builds a quadtree-structured bound on the patch curvatures for every surface patch, and then works by first discretizing trimming curves and afterwards relaxing the location of a sufficient number of vertices inside the trimmed region in every patch. The resulting triangulation satisfies the max-min criterion in parametric space.