基于Gmsh的Voronoi结构参数化生成算法  

Parameterized generation algorithm of Voronoi structures based on Gmsh

作　　者：胡健 薛振宇 董培梅 HU Jian;XUE Zhenyu;Dong Peimei(College of Information Engineering,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学信息工程学院,浙江杭州310018

出　　处：《中国计量大学学报》2024年第4期635-646,共12页Journal of China University of Metrology

基　　金：浙江省自然科学基金项目(No.LQ23F010014)。

摘　　要：目的:构建Voronoi(泰森多边形)的三维结构。方法:使用Gmsh中的几何实体和网格生成功能,将Voronoi结构的生成转化为网格生成问题,之后基于骨架模型构建三维Voronoi结构的体积参数化。通过非线性优化过程,生成内六面体群。将其分成两部分,并根据设计的算法生成不同类型的体积参数化节点。与B-spline曲线结合,生成B-spline曲面。结果:曲面与Voronoi节点数据相结合,构建了完整的三维Voronoi结构。结论:提出的结构生成算法实现了高效、精准且可控的Voronoi结构生成方式,借助骨架模型成功构建了三维晶格结构的体积参数化.Aims:This paper aims to construct a three-dimensional structure of Voronoi.Methods:By using the geometric entities and mesh generation function in Gmsh,the generation of Voronoi structures was transformed into a mesh generation problem.Then the volume parameterization of 3D Voronoi structures was constructed based on the skeleton model.Through a nonlinear optimization process,an inner hexahedron group was generated and divided into two parts.And different types of volume parameterized nodes were generated based on the designed algorithm.Combined with the B-spline curve,a B-spline surface was generated.The surface was combined with Voronoi node data to construct a complete three-dimensional Voronoi structure.Results:A complete three-dimensional Voronoi structure was constructed by combining surface and Voronoi node data.Conclusions:The proposed structure generation algorithm achieves an efficient,accurate,and controllable Voronoi structure generation method,and successfully constructs the volume parameterization of three-dimensional lattice structures using a skeleton model.

关 键 词：泰森多边形 三维有限元网格生成器 德洛内三角网 非线性优化 六面体群 

分 类 号：TP311.1[自动化与计算机技术—计算机软件与理论]