密度场控制的四面体网格自适应生成算法

doi:10.16182/j.issn1004731x.joss.201801006

摘要/Abstract

摘要： 通过构造表面模型的密度场,提出一种四面体网格自适应生成算法。在表面模型的轴向包围盒内均匀点采样;以模型表面为边界定义一个非均匀的密度场来构建采样点集的质心Voronoi结构,同时动态地增删采样点以优化点集分布;以模型内部的采样点为基础,以模型表面为边界约束,进行四面体网格划分。实验表明,算法能够处理具有不同拓扑和几何复杂度的表面模型,生成的体网格整体质量较高,网格单元形状规整、尺寸自适应且疏密可调。算法可用于有限元分析、动态仿真等领域。

关键词: 计算几何, 四面体网格化, 密度场, 质心Voronoi结构, 网格优化

Abstract: We present an algorithm for adaptively generating tetrahedral mesh by constructing the density field of a surface model. A uniform sampled point set is first generated inside the axial bounding box of the surface model. A non-uniform density field is defined according to the surface boundary of the model. Under the control of the density field, the centroidal Voronoi tessellation of the point set is constructed by using iterative method, and the distribution of the point set is optimized adaptively via dynamically adding or deleting points. Taking the points inside the surface model as the insertion points, a tetrahedral mesh is generated with the surface mode being the boundary-constraint condition. The experimental results show that our algorithm can handle a variety of surface models with different complexity of topology and geometry, and can adaptively generate tetrahedral mesh with different density distribution by adjusting the density field. Most of the generated tetrahedral cells are more regular and the overall quality of the mesh is higher. Our algorithm can be used for finite element analysis, dynamic simulation, and so on.

Key words: computational geometry, tetrahedral meshing, density field, centroidal Voronoi tessellation, mesh optimization

中图分类号:

TP391

王继东,范丽鹏,庞明勇 . 密度场控制的四面体网格自适应生成算法[J]. 系统仿真学报, 2018, 30(1): 45-52.

Wang Jidong,Fan Lipeng,Pang Mingyong . Adaptive Generation Algorithm of Tetrahedral Meshes Based on Density Field[J]. Journal of System Simulation, 2018, 30(1): 45-52.

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