一种基于模型域分割的规则六面体网格生成方法

doi:10.11996/JG.j.2095-302X.2026030589

图学学报 ›› 2026, Vol. 47 ›› Issue (3): 589-597.DOI: 10.11996/JG.j.2095-302X.2026030589

• 计算机图形学与虚拟现实 • 上一篇下一篇

一种基于模型域分割的规则六面体网格生成方法

张天瑞¹^,², 王爱增¹^,²(), 宁涛¹, 张凤全³

¹ 北京航空航天大学机械工程及自动化学院，北京 100191
² 北京航空航天大学虚拟现实技术与系统国家重点实验室，北京 100191
³ 北京邮电大学数字媒体与设计艺术学院，北京 100876

收稿日期:2025-10-22 接受日期:2026-01-22 出版日期:2026-06-30 发布日期:2026-06-30
通讯作者:王爱增，E-mail：azwang@buaa.edu.cn
基金资助:
北京市自然科学基金(1252014);航空科学基金(2023Z068051002);科创甬江2035(2024Z162);国家重点研发计划(2023YFB3309002);北京市社会科学基金规划项目(24YTB014)

Hexahedral mesh generation algorithm based on domain decomposition

ZHANG Tianrui¹^,², WANG Aizeng¹^,²(), NING Tao¹, ZHANG Fengquan³

¹ School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
² State Key Laboratory of Virtual Reality Technology & Systems, Beihang University, Beijing 100191, China
³ School of Digital Media and Design Arts, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received:2025-10-22 Accepted:2026-01-22 Published:2026-06-30 Online:2026-06-30
Contact: WANG Aizeng，E-mail：azwang@buaa.edu.cn
Supported by:
Beijing Natural Science Foundation(1252014);Aeronautical Science Foundation of China(2023Z068051002);Sci-Tech Innovation Yongjiang 2035(2024Z162);National Key Research and Development Program of China(2023YFB3309002);Humanities and Social Sciences Foundation of Beijing(24YTB014)

摘要/Abstract

摘要：

为解决规则六面体网格的自动生成问题，提出一种基于模型域分割的规则六面体网格自动生成方法。首先利用模型几何属性构建属性邻接图，提取模型域特征并生成分割面，将模型域分割为多个结构简单的子域；对各子域特征进行自动分类与匹配，应用预设子域网格模板生成子域网格；最后通过网格合并获得整体全六面体网格。并将特征驱动的域分割与模板化生成相结合，在保证拓扑一致性与几何特征保持的同时，减少人工干预，提高网格生成的稳定性与可重复性。模板生成阶段结合特征保持的参数化映射与拓扑约束扫掠方法，实现了六面体网格生成，形成了由域分割、模板生成到网格合并的自动化流程，可应用于典型机械类模型的网格生成，为数字化仿真分析提供参考。

关键词: 有限元分析, 属性邻接图, 模型域分割, 六面体网格

Abstract:

To address automatic generation of structured hexahedral meshes, an automatic hexahedral mesh generation algorithm based on model-domain segmentation was proposed. This method constructed an attribute-adjacency graph from geometric attribute of the model to extract domain features and generate partitioning surfaces, thereby decomposing a model domain into multiple simpler subdomains. The subdomains were then automatically classified and matched based on their features, and predefined subdomain mesh templates were applied to generate subdomain meshes. Finally, the subdomain meshes were merged to obtain an all-hexahedral mesh for the entire model. By combining feature-driven domain segmentation with template-based mesh generation, the proposed method reduced manual intervention while ensuring both topological consistency and geometric feature preservation, thereby improving the stability and repeatability of mesh generation. In the template-generation stage, feature-preserving parameterized mapping was combined with topology-constrained sweeping to generate the hexahedral meshes, forming an automated pipeline from domain segmentation to template generation and mesh merging. The method was applied to meshing typical mechanical models, providing a reference for digital simulation and analysis.

Key words: finite element analysis, attributed adjacency graph, domain decomposition, hexahedral mesh

中图分类号:

TP391.7

张天瑞, 王爱增, 宁涛, 张凤全. 一种基于模型域分割的规则六面体网格生成方法[J]. 图学学报, 2026, 47(3): 589-597.

ZHANG Tianrui, WANG Aizeng, NING Tao, ZHANG Fengquan. Hexahedral mesh generation algorithm based on domain decomposition[J]. Journal of Graphics, 2026, 47(3): 589-597.

图/表 18

图1 三维模型(其中Fi为模型面)

Fig. 1 3D model (where Fi denotes a model face)

图2 三维模型的AAG

Fig. 2 AAG of the 3D model

表1 属性信息

Table 1 Attribute information

属性	属性值
边类型	1 直线 0 弧线
边的凹凸性	1 凸边 0 光顺边 -1 凹边
边的闭合性	0 闭合 1 开放
面类型	平面柱面环面 …
面的凹凸性	1 凸面 0 平面 -1 凹面

图3 子域结构示意((a) 可映射；(b)~(d) 不可映射)

Fig. 3 Schematic of subdomain structures ((a) Mappable; (b)-(d) Non-mappable)

图4 闭环分割环，直接生成分割面

Fig. 4 Closed-loop splitting ring for direct generation of the partitioning surface

图5 开环分割面，通过构造虚拟边闭合

Fig. 5 Open-loop partitioning surface closed by constructing virtual edges

图6 对AAG添加分割面

Fig. 6 Adding partitioning surfaces to the AAG

图7 三维模型及其分割面，加粗环为分割面的边界

Fig. 7 3D model and its partitioning surface; the bold loop indicates the boundary of the partitioning surface

图8 模型分割((a) 原始模型域；(b) 模型子域)

Fig. 8 Model domain decomposition ((a) Initial domain; (b) Partitioned subdomains)

表2 部分属性编码信息

Table 2 Partial attribute encoding information

维度	特征	编码数值
1	平面	1
1	圆柱面	2
1	圆锥面	3
1	椭球面	4
1	自由曲面	5
2	凸面	1
2	凹面	2
2	光顺面	3
3	闭合面	1
3	开放面	2

表3 典型子图的表示

Table 3 Representation of typical subgraphs

模板	几何表示	属性图	编码
矩形毛坯+圆形通孔
矩形毛坯+方形通孔
圆柱(实心)
圆柱(空心)
矩形毛坯+圆柱凸台
矩形毛坯+四棱柱凸台

图9 算法流程图

Fig. 9 Flowchart of the algorithm

图10 映射法

Fig. 10 Mapping method

图11 六面体网格的映射过程((a) 参数域网格；(b) 物理域网格)

Fig. 11 Mapping process of the hexahedral mesh ((a) Parametric-domain mesh; (b) Physical-domain mesh)

图12 前处理软件六面体主导的网格生成结果((a) 轴承盖模型；(b) 轴承盖模型的网格；(c) 轴承座模型；(d) 轴承座模型的网格)

Fig. 12 Result of hexahedral-dominant meshing in a preprocessing software ((a) Bearing cover model; (b) Mesh of bearing cover; (c) Bearing pedestal model; (d) Mesh of bearing pedestal)

图13 轴承座模型网格生成((a) 原始模型；(b) 算法结果；(c) 网格切面)

Fig. 13 Mesh generation for the bearing pedestal model ((a) Original model; (b) The algorithm result; (c) Mesh cross-section)

图14 矩形弯头模型网格生成((a) 原始模型；(b) 算法结果；(c) 网格切面)

Fig. 14 Mesh generation for the rectangular elbow model ((a) Original model; (b) The algorithm result; (c) Mesh cross-section)

图15 轴承盖模型网格生成((a) 原始模型；(b) 算法结果；(c) 网格切面)

Fig. 15 Mesh generation for the bearing cover model ((a) Original model; (b) The algorithm result; (c) Mesh cross-section)

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一种基于模型域分割的规则六面体网格生成方法

Hexahedral mesh generation algorithm based on domain decomposition

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