基于凸凹性的网格细分综合优化

Mesh Subdivision for Optimizing both Shape and Topology

实际工程中希望表示物体的三角形网格形状优良,同时拓扑逼近真实曲面。但是对非均匀离散点云重建得到的网格进行优化时,这两个标准常常是相互矛盾的。该文针对在实际工程中遇见的这个问题,提出一种结合全局特征以及局部特性的细分算法。该算法避免了一般细分方法对凹区域处理出现的折叠现象,可以获取三角形形状和空间拓扑的综合优化解。最后通过对于工程应用实例的细分计算,得到了与原始网格拓扑一致,但更逼近真实曲面的细分优化网格,表明了所提出简化算法的有效性。

In engineering,the mesh with both uniform shape and excellent topology is expected.But in fact,the criterion optimizing shape is contrary with other one optimizing topology.In this paper,one subdivision algorithm is presented for getting the mesh with excellent both shape and topology.This algorithm combines the local geometric feature of pair-tri-angles and whole topological express of mesh to get the mesh with integrated excellent shape and topology.At last,some experimental results--meshes with excellent triangle and topology,which is the same topology as the original meshes--in reverse engineering are afforded and prove the usefulness of this mesh subdivision method.