Abstract:
Delaunay triangulation is a mainly used method for tetrahedral mesh generation, but the initial mesh generated by this method cannot include all boundary constraints, so the boundary recovery is a necessary step for the generation of Delaunay tetrahedral mesh. The difficulty of boundary recovery lies in determining the number and location of auxiliary points (Steiner points) and reducing the negative effects caused by Steiner points. In this study, an improved boundary recovery method for Delaunay tetrahedral mesh generation is proposed, which aims to increase the success rate of constrained recovery and reduce the number of Steiner points added during the boundary recovery. The overall process of this method is composed of a double iteration with two rounds inside, which fully utilizes the advantages of the constrained boundary recovery method and the interior Steiner point insertion method, and reduces the number of broken boundary constraints caused by boundary restoration. This method firstly solves the problem that the recursive shell transformation algorithm tends to fall into the local optimum, by introducing the simulated annealing algorithm, and an improved constrained boundary recovery method is proposed. Then, three key methods, including the AABB tree, the geometrically accurate "line and surface intersection" function, and a hash algorithm for intersection count query, are introduced or proposed to improve the efficiency and robustness of finding the intersection between mesh entities and boundary entities. Finally, for boundaries that cannot be recovered by topological transformation, the interior and boundary Steiner points are inserted. The proposed method is tested on more than 4,000 surface mesh samples of the Thingi10k dataset, which shows that the success rate of constrained boundary recovery is effectively improved, and meanwhile the number of Steiner points introduced by the boundary recovery is generally reduced.