Tetrahedral mesh generation by Delaunay refinement

Abstract

Given a complex of vertices, constraining segments, and planar straight-line constraining facets in E 3 , with no input angle less than 90 ffi , an algorithm presented herein can generate a conforming mesh of Delaunay tetrahedra whose circumradius-to-shortest edge ratios are no greater than two. The sizes of the tetrahedra can provably grade from small to large over a relatively short distance. An implementation demonstrates that the algorithm generates excellent meshes, generally surpassing the theoretical bounds, and is effective in eliminating tetrahedra with small or large dihedral angles, although they are not all covered by the theoretical guarantee. 1 Introduction Meshes of triangles or tetrahedra have many applications, including interpolation, rendering, and numerical methods such as the finite element method. Most such applications demand more than just a triangulation of the object or domain being rendered or simulated. To ensure accurate results, the triangles or tetr...