Delaunay Mesh Generation of Three Dimensional Domains

Delaunay meshes are used in various applications such as finite element analysis, computer graphics rendering, geometric modeling, and shape analysis. As the applications vary, so do the domains to be meshed. Although meshing of geometric domains with Delaunay simplices have been around for a while, provable techniques to mesh various types of three dimensional domains have been developed only recently. We devote this article to presenting these techniques. We survey various related results and detail a few core algorithms that have provable guarantees and are amenable to practical implementation. Delaunay refinement, a paradigm originally developed for guaranteeing shape quality of mesh elements, is a common thread in these algorithms. We finish the article by listing a set of open questions. Research supported by NSF, USA (CCF-0430735 and CCF-0635008). Department of Computer Science and Engineering, Ohio State University, Ohio, USA. Email: [email protected]