四面体网格边界恢复改进算法

曾寅家; 陈建军; 傅珂杰

doi:10.7638/kqdlxxb-2022.0192

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四面体网格边界恢复改进算法

研究论文 | 更新时间：2026-05-28

- 四面体网格边界恢复改进算法
- Improved boundary recovery method for tetrahedral mesh generation
- 空气动力学学报 2023年41卷第10期页码：42-51
- 作者机构：
  
  浙江大学航空航天学院,杭州,310027
- 作者简介：
  
  曾寅家（1998-），浙江丽水人，硕士研究生，研究方向：网格生成. E-mail：wingerzeng@zju.edu.cn
  陈建军*（1979-），江西铅山人，教授，博导，研究方向：计算力学，高性能计算. E-mail：chenjj@zju.edu.cn
- 基金信息：
- DOI：10.7638/kqdlxxb-2022.0192
  中图分类号： TP301.6
- 纸质出版：2023
- 稿件说明：
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曾寅家, 陈建军, 傅珂杰. 四面体网格边界恢复改进算法[J]. 空气动力学学报, 2023, 41(10): 42−51.

ZENG Yinjia, CHEN Jianjun, FU Kejie. Improved boundary recovery method for tetrahedral mesh generation[J]. 2023, 41(10): 42-51.
曾寅家, 陈建军, 傅珂杰. 四面体网格边界恢复改进算法[J]. 空气动力学学报, 2023, 41(10): 42−51. DOI： 10.7638/kqdlxxb-2022.0192

ZENG Yinjia, CHEN Jianjun, FU Kejie. Improved boundary recovery method for tetrahedral mesh generation[J]. 2023, 41(10): 42-51. DOI： 10.7638/kqdlxxb-2022.0192.

摘要

Delaunay三角化是生成四面体网格的主流方法，而通过该方法生成的初始网格无法保留所有边界约束，因此边界恢复是Delaunay四面体网格生成的必要步骤。边界恢复的难点在于确定辅助点（Steiner点）的数量和位置，以及降低Steiner点引发的负面效应。为此，本文提出了一种改进的四面体网格边界恢复方法，旨在提高约束边界恢复成功率，并减少加入的Steiner点数量。该方法总体流程由“两层+两轮”迭代构成，流程充分利用了约束边界恢复方法和体内Steiner点插入方法的优势，降低了边界恢复对边界约束的破坏。方法首先针对递归壳变换算法容易陷入局部最优解的问题，通过引入模拟退火算法加以解决，提出了一种改进的约束边界恢复方法；然后对于方法中的“网格实体—边界实体求交”关键环节，引入或实现了AABB树、几何精确的“线面相交”函数、交点数查询哈希算法三个关键方法加以优化；最后对于拓扑变换无法恢复的边界，实现了体内、边界两种Steiner点插入方法。实验阶段取用了Thingi10k数据集的4000余例面网格样本进行测试，结果表明该方法有效提高了约束边界恢复的成功率，并能普遍性地减少边界恢复引入的Steiner点数量。

Abstract

Delaunay triangulation is a mainly used method for tetrahedral mesh generation

but the initial mesh generated by this method cannot include all boundary constraints

so the boundary recovery is a necessary step for the generation of Delaunay tetrahedral mesh. The difficulty of boundary recovery lies in determining the number and location of auxiliary points (Steiner points) and reducing the negative effects caused by Steiner points. In this study

an improved boundary recovery method for Delaunay tetrahedral mesh generation is proposed

which aims to increase the success rate of constrained recovery and reduce the number of Steiner points added during the boundary recovery. The overall process of this method is composed of a double iteration with two rounds inside

which fully utilizes the advantages of the constrained boundary recovery method and the interior Steiner point insertion method

and reduces the number of broken boundary constraints caused by boundary restoration. This method firstly solves the problem that the recursive shell transformation algorithm tends to fall into the local optimum

by introducing the simulated annealing algorithm

and an improved constrained boundary recovery method is proposed. Then

three key methods

including the AABB tree

the geometrically accurate "line and surface intersection" function

and a hash algorithm for intersection count query

are introduced or proposed to improve the efficiency and robustness of finding the intersection between mesh entities and boundary entities. Finally

for boundaries that cannot be recovered by topological transformation

the interior and boundary Steiner points are inserted. The proposed method is tested on more than 4

000 surface mesh samples of the Thingi10k dataset

which shows that the success rate of constrained boundary recovery is effectively improved

and meanwhile the number of Steiner points introduced by the boundary recovery is generally reduced.

关键词

Keywords

references

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