基于投影法的四面体网格切割算法

四面体网格切割算法是有限元仿真中的重要组成部分，切割的结果决定了刚度矩阵的更新速度和精度。本文在研究Cotin算法和Bielser算法的基础上，采用了预投影的方法，将部分顶点投影到切割平面上，使原先的四面体分割转化为相邻四面体分离，以达到简化分割的目的。与Cotin算法和Bielser算法相比，由该算法得到的网格切割边界更加合理，剖分比更低，提高了刚度矩阵更新的速度和精度。

Tetrahedron Mesh-Cut Algorithm Based on Projective Method

The tetrahedron mesh-cut algorithm is an important part of finite element method(FEM).The mesh-cut result determines the speed and the precision of stiff matrix regeneration.Based on the Cotin and the Bielser algorithms,the algorithm proposed in this paper projects the original mesh before mesh-cutting.Parts of the vertexes are projected on the segmented face.After being projected,the mesh segmenting is changed as mesh separating,so that the mesh-cut algorithm becomes easier.Compared with Cotin and Bielser algorithms,the algorithm makes the mesh-cut results more reasonable.Meanwhile,the increasing of the tetrahedron number is lower,thus improving the speed and the precision of stiff matrix regeneration.