Delaunay Meshing of Surfaces

Abstract

Meshing of surfaces is an ubiquitous problem in many applications of science and engineering. Among different approaches available for meshing surfaces, Delaunay meshing is often favored because of its directional independence and good quality in general. As application varies, so does the input form of the surface to be meshed. We present algorithms to compute Delaunay meshes for various forms of input surfaces. Specifically, we consider surfaces input with (i) point cloud data, (ii) implicit equations, and (iii) polyhedra. These algorithms come with theoretical guarantees and some of them have been successfully implemented. In this talk we detail the algorithms, provide the mathematical reasoning behind their designs, and show the results of some experiments.