Optimal tetrahedral mesh generation for three-dimensional point set

Three-dimensional (3D) triangulation is a basic topic in computer graphics. It is considered very difficult to obtain the global optimal 3D triangulation, such as the triangulation which satisfies the max-min solid angle criterion. A new method called genetic tetrahedral mesh generation algorithm (GTMGA for short) is presented. GTMGA is based on the principle of genetic algorithm and aims at the global optimal triangulation. With a multi-objective fitness function, GTMGA is able to perform optimizations for different requirements. New crossover operator and mutation operator, polyhedron crossover and polyhedron mutation, are used in GTMGA. It is shown by the experimental results that GTMGA works better than both the 3D Delaunay triangulation and the algorithm based on local transformations.