Face-centred Voronoi Refinement for Surface Mesh Generation

Abstract

A Frontal-Delaunay surface meshing algorithm for closed 2-manifolds embedded in R3 is presented. This new algorithm is an extension of existing restricted Delaunay-refinement techniques, in which the point-placement scheme is modified to improve element quality in the presence of mesh size constraints. Specifically, it is shown that the use of off-centre Steiner vertices, positioned along facets in the associated Voronoi diagram, typically leads to an improvement in the shape- and size-quality of the resulting surface tessellation. The new method can be viewed as a hybridisation of conventional Delaunay-refinement and advancing-front techniques, in which new vertices are positioned to satisfy both element size and shape constraints. It is shown that by restricting point-placement to faces of the associated Voronoi diagram, the new Frontal-Delaunay algorithm maintains many of the theoretical guarantees commonly associated with conventional restricted Delaunay-refinement techniques. The performance of the new Frontal-Delaunay scheme is investigated experimentally, via a series of comparative studies designed to contrast the performance of the new algorithm with a typical Delaunay-refinement technique. It is shown that the new Frontal-Delaunay algorithm inherits many of the benefits of both Delaunay-refinement and advancing-front type methods, typically leading to the construction of very high quality triangulations in practice. Experiments are conducted using a range of complex benchmarks, verifying the robustness and practical performance of the proposed scheme.