Delaunay Refinement for Piecewise Smooth Complexes

Abstract

We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions. The algorithm protects edges with weighted points to avoid the difficulty posed by small angles between adjacent input elements. These weights are chosen to mimic the local feature size and to satisfy a Lipschitz-like property. A Delaunay refinement algorithm using the weighted Voronoi diagram is shown to terminate with the recovery of the topology of the input. Guaranteed bounds on the aspect ratios, normal variation, and dihedral angles are also provided. To this end, we present new concepts and results including a new definition of local feature size and a proof for a generalized topological ball property.