Localized delaunay refinement for piecewise-smooth complexes

• Authors: Tamal Krishna Dey;Andrew G. Slatton
• Venue: Proceedings of the twenty-ninth annual symposium on Computational geometry
• Year: 2013

Delaunay refinement, a versatile method of mesh generation, is plagued by memory thrashing when required to generate large output meshes. To address this space issue, a localized version of Delaunay refinement was proposed for generating meshes for smooth surfaces and volumes bounded by them. The method embodies a divide-and-conquer paradigm in that it maintains the growing set of sample points with an octree and produces a local mesh within each individual node, and stitches these local meshes seamlessly. The proofs of termination and global consistency for localized methods exploit recently developed sampling theory for smooth surfaces. Unfortunately, these proofs break down for a larger class called piecewise smooth complexes (PSCs) that allow smooth surface patches that are joined along ridges and corners. In this work, we adapt a recently developed sampling and meshing algorithm for PSCs into the localization framework. This requires revisiting the original algorithm, and more importantly re-establishing the correctness proofs to accommodate the localization framework. Our implementation of the algorithm exhibits that it can indeed generate large meshes with significantly less time and memory than the original algorithm without localization. In fact, it beats a state-of-the-art meshing tool of CGAL for generating large meshes.