基于简化和细分技术的三角形网格拓扑优化方法  

Topological Optimization for Triangular Mesh Based on Simplification and Subdivision

作　　者：吕书明[1] 张明磊[1] 孙树立[1,2] 

机构地区：[1]北京大学工学院力学与工程科学系,北京100871 [2]湍流与复杂系统国家重点实验室,北京100871

出　　处：《计算机辅助设计与图形学学报》2014年第8期1225-1231,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11172004;11172005;10772004);北京市自然科学基金(1102020)

摘　　要：由于采用自动生成技术得到的网格往往不能满足数值模拟和仿真的要求,为此基于网格简化和细分技术,提出一种简单、高效的三角形网格拓扑优化方法.首先根据边折叠简化算法对三角形网格进行简化,得到具有较好拓扑连接关系的粗网格;然后对简化后的粗网格进行细分,引入具有良好节点度的新节点;最后再进行简化,直到网格的节点数达到给定的阈值.实验结果表明,该方法可以很好地改善网格的拓扑连接关系,与网格修匀技术结合能够大幅度提高网格的质量.The quality of mesh generated by automatic meshing techniques sometimes cannot satisfy the requirements for numerical analysis and simulation.A simple and efficient approach for triangular mesh topological optimization is developed based on mesh simplification and subdivision.First a coarse mesh with good topological connectivity is obtained by edge collapse with topological improvement.Then the coarse mesh is refined by subdivision to introduce vertices with good valance.Finally the mesh simplification with topological improvement is performed again until a predefined threshold for number of vertices is reached.The testing results demonstrate that the proposed approach can greatly improve the mesh topological connectivity as well as the mesh quality when combining with mesh smoothing.

关 键 词：拓扑优化 网格简化 网格细分 节点度 边折叠 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]