Mesh sizing with additively weighted Voronoi diagrams

Abstract

We address the problem of generating mesh sizing functions from a set of points with specified sizing values. The sizing functions are shown to be maximal and K-Lipschitz, with arbitrary parameter K provided by the user. These properties allow generating low complexity meshes with adjustable gradation. After constructing an additively weighted Voronoi diagram, our algorithm provides fast and accurate answers to arbitrary point queries. We have implemented our mesh sizing technique as a sizing criterion for the 2D triangle meshing component from the CGAL library. We demonstrate the performance advantages of our technique through experimental results on various inputs.