Abstract: A stable tetrahedral mesh generation algorithm is presented, which improves the present three dimensional Delaunay tetrahedral mesh generation methods with the following techniques: Random perturbation and lazy inserting techniques are introduced to improve the robustness with less speed decrease; Constrained segments restoration and constrained facet restoration algorithm are improved to deal with curved boundary and carry out boundary consistency; Mesh optimization combining the facet flipping and vertex insertion methods and Sliver elimination method are proposed to im-prove the mesh quality. Several examples are given to validate the proposed algorithm.

Key words: Boundary consistency, Delaunay, Mesh generation, Tetrahedral mesh