任意多面体边界一致四面体网格生成方法

摘要

A conforming boundary recovery algorithm to solve the problem of arbitrary polyhedral tetrahedral mesh generation is presented,which can satisfy the boundary geometry and topology constraints.This method is based on boundary recovery algorithm of 3D Delaunay Tetrahedralization.Firstly,a dynamic programming method is employed to suppress the Steiner points on the boundary facets;and then the related tetrahedrons is repaired in order to maintain the integrity of the original polyhedron boundary topology;finally,an extended Laplacian smoothing method is utilized to improve the elements with poor quality.This algorithm can guarantee a complete recovery of arbitrary polyhedral boundary in theory.Moreover,it has a robust performance in practice.%提出一种能够满足多面体边界几何与拓扑约束的边界一致恢复算法,解决了任意多面体的边界一致四面体网格生成问题。在恢复多面体的几何约束时,边界上可能会引入Steiner点,这样就不满足拓扑约束。对此,本文采用动态规划方法将Steiner点从边界上消除,修复与其相关四面体单元的拓扑关系,以保持原多面体边界的拓扑完整性,并采用扩展的Laplacian光顺算法优化劣质单元。在理论上,本文算法能够保证完整地恢复任意多面体的边界。算例表明,本文提出的边界一致恢复算法鲁棒性高,可应用于复杂多面体模型。