Guaranteed-quality Delaunay meshing in 3D

Abstract

A mesh generating technique for producing three dimensional tetrahedral meshes based on Delaunay triangulation (DT) is presented. This Delaunay-based method avoids slivers, tetrahedral mesh-elements that are almost flat, and maximizes the minimum angle between a given point set. The Empty Circle Property defines the DT of a set of point sites, the circumsphere of each triangle is empty of all other sites, and if the analogous property holds in three dimension, the circumsphere of each tetrahedron is empty of all other sites. Theorems for three dimensional meshing algorithms are presented.