Theoretically Guaranteed Mesh Generation—In Practice

Jonathan R. Shewchuk (University of California at Berkeley)

This short course is an introduction to triangular and tetrahedral mesh generation algorithms, especially those based on Delaunay triangulations. Coverage is restricted to algorithms that have two desirable qualities at once: they are mathematically guaranteed to generate high-quality meshes, and they work well enough in practice to compete with traditional, heuristic algorithms in engineering applications.

Topics covered include a short review of Delaunay triangulations and constrained Delaunay triangulations; extensive coverage of Delaunay refinement algorithms for triangular and tetrahedral mesh generation, including methods by Chew, Ruppert, Ungor, Boivin/Ollivier-Gooch, Miller/Walkington/Pav, and me; handling of 2D domains with curved boundaries; handling of 2D and 3D domains with small angles; sliver elimination; anisotropy; and the octree-based isosurface stuffing algorithm.

This document was translated from L^AT_EX by H^EV^EA.