Post-optimization of Delaunay tetrahedrization

The paper brings results of post-optimization of Delaunay tetrahedrization. Delaunay triangulation is a very popular method to create 2D meshes, but in 3D its properties are not as good as in 2D and can be improved. For this improvement an already existing method was used: local transformations, so called flips, performed in order to improve different geometrical properties of tetrahedra and applied to the finished 3D Delaunay triangulation. We examined this method by using various criteria to compare their benefits and losses in the area of the tetrahedra shape or time demand. We found out that the greatest benefit comes from the so called compound criteria and from the criterion which minimizes the numbers of tetrahedra. Other criteria have no positive influence on mesh improvement, they rather degrade the quality of the Delaunay mesh. The question of time is not so important, because all criteria are fast enough (they take at most 10 percent of time needed to construct a Delaunay mesh).