基于B-rep边界约束的Delaunay四面体剖分

摘要

为实现B-rep的三维实体的四面体剖分,研究了网格划分过程中的关键问题.基于B-rep数据结构的拓扑关系,提出一种在网格划分过程中约束实体边界的策略.研究了包含插入点的包含域的合法性检验方法,并对其改进扩展以保证生成单元的有效性.在对点和面的拓扑关系进行预处理的基础上,提出了判断四面体单元是否被实体边界包围的面法向法和基于单元边的加密点生成算法.最后使用Delaunay逐点插入法结合以上算法实现对以B-rep为模型的三维实体的四面体单元网格划分,并通过实例得到验证.%To make the solid based on B-rep modal tetrahedrization, the key problems making mesh are studied. The strategy of constrainting the solid's bounary while making mesh is puted forward with respect to the topological relationships of the data structure in the B-rep Modal,In order to get right elements, the validity of space containing the nodes is judged. By way of buliding the topological relationships between the faces and the vertexes, the face-normal method that points out whether a tetrahedron is in the solid and the nodes generation algorithm on the tetrahedrons are proposed. In process of tetrahedrizations of the B-rep modalbased 3D solid, the methods are realized using Delaunay point by point insertion and the examples are offered.