Delaunay refinement for piecewise smooth complexes

Abstract

We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions with correct topology. The small angles between the tangents of two meeting manifold patches pose difficulty. We protect these regions with weighted points. The weights are chosen to mimic the local feature size and to satisfy a Lipschitz-like property. A Delaunay refinement using the weighted Voronoi diagram is shown to terminate with the recovery of the topology of the input. 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.