Tetrahedron Model Reconstruction and Optimization

Three dimensional geometric modeling plays an important role in virtual surgery simulation. One of difficulties is how to construct well-shaped tetrahedral models. Delaunay tetrahedral reconstruction is an effective method in virtual surgery simulations. However, it is difficult to satisfy the quality requirements of the finite element method because of the bad shaped elements existed. This paper describes a method to construct quality 3D tetrahedral model directly from surface mesh, and a new hybrid sliver-element elimination method for Delaunay tetrahedral is proposed in this paper. Numerical examples are provided to demonstrate the effectiveness of the algorithm. The experimental results show that the tetrahedron model reconstruction method can improve the quality and solve the missing boundary problem, and the Delaunay tetrahedral sliver element elimination method can not only maintain the geometry shape of original model, but also solve the randomness problem for point selecting in Delaunay refinement method.