Fast Delaunay triangulation in three dimensions

An efficient algorithm for Delaunay triangulation of a given set of points in three dimensions based on the point insertion technique is presented. Various steps of the triangulation algorithm are reviewed and many acceleration procedures are devised to speed up the triangulation process. New features include the search of a neighbouring point by the layering scheme, locating the containing tetrahedron by random walk, formulas of important geometrical quantities of a new tetrahedron based on those of an existing one, a novel approach in establishing the adjacency relationship, the use of adjacency table and the management of memory. The resulting scheme is one of the fastest triangulation algorithms known to the authors, which is able to generate tetrahedra generation rate of 15 000 tetrahedra per second for randomly generated points on a HP 735 machine.