四面体网格生成方法的研究与实现

摘要

针对四面体网格生成过程中需要人工构造背景网格和指定尺寸信息的问题,提出了一种自动计算网格尺寸的方法.该方法通过按层次推进产生四面体网格,根据周围前沿面的尺寸和法线信息,计算新生成四面体的尺寸,使四面体网格在尺寸上能够均匀分布.在网格生成过程中,无需人工指定相关信息,并能保证新生成四面体的质量.联立直线和平面的参数方程,根据方程组解的情况判断线段和三角形是否相交,并对相交的条件作了详细的分析.使用空间八叉树管理前沿面,降低与前沿面相关操作的复杂度.数值算例表明,该方法能够生成较高质量的四面体网格.%To address the issue that background mesh is constructed and mesh size is specified manually in the process of mesh generation, a method of automatically calculating mesh size is proposed. Though tetrahedral mesh generation by each layer, based on the surrounding front and normal information, the size of tetrahedron is calculated and smooth mesh is generated. In the process of mesh generation, related information specified by manually is unnecessary and the quality is also guaranteed. Though simultaneous parameter equations of the line and plane, the relationship between a segment and a triangle is judged, the intersection condition is given in detail. Octree space division is employed to manage the front, which reduce complexity of operations associated with front. The examples demonstrate that high quality tetrahedral mesh is generated.