Geometry‐based fully automatic mesh generation and the delaunay triangulation

Abstract

Abstract One approach to fully automatic mesh generation in two and three dimensions is to generate and triangulate a set of points within and on the boundary of a geometry using the properties of the Delaunay triangulation. Because the point data generate mesh topology of greater dimension, it is necessary to insure topological compatibility and perform classification of the resulting mesh with respect to the original geometry. Necessary and sufficient conditions for classification of mesh topology on three‐dimensional planar geometry are given, as well as a discussion of the more complex case of curved geometry. This paper also presents conditions to insure topological compatibility along with techniques for identifying and resolving cases of incompatibility.