基于各向异性四叉树网格的CAD模型快速三角化算法  

Fast tessellation algorithm for CAD models on anisotropic quadtree grids

作　　者：徐璟潮 倪浩楠 刘陶然 魏祥利 陈建军[1] XU Jingchao;NI Haonan;LIU Taoran;WEI Xiangli;CHEN Jianjun(School of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]浙江大学航空航天学院,杭州310027

出　　处：《空气动力学学报》2025年第3期1-13,I0001,共14页Acta Aerodynamica Sinica

基　　金：冲压发动机技术全国重点实验室基金(2022-JCJQ-LB-020-05);浣江实验室专项项目(KM20220616)。

摘　　要：计算机辅助设计(computer-aided design,CAD)模型的三角化在工程和科学研究领域中有重要应用,它为模型可视化提供底层数据表征,也可作为计算机辅助工程、计算机辅助制造等CAD下游应用的输入,支持诸如网格生成、数值模拟、快速原型设计等关键领域的研究与应用。本研究提出了一种基于各向异性四叉树背景网格的CAD模型快速三角化算法。该算法通过自底向上构建的算法流程,确保结果的二维流形;在可控容差的曲线离散阶段,通过设计一种基于曲率和曲率一阶导的尺寸函数有效识别特征;而在自适应四叉树快速曲面三角化阶段,通过设计各向异性四叉树,使得三角化的结果满足最小化网格单元的要求。此外,通过后验的混合多阶容差条件实现了与原始CAD输入在不同连续性上的一致性。复杂CAD模型输入下的数值对比实验表明,相比OCC、Gmsh等开源软件以及Ansys等商业软件中同类算法,该算法在几何保形精度、背景网格规模、算法时间效率等方面均体现出不同程度的优势,具有实际工程应用的潜力。Tessellation of computer-aided design(CAD)models plays a crucial role in engineering and scientific domains,offering foundational data for model visualization and serving as input for downstream CAD applications,including computer-aided engineering(CAE)and computer-aided manufacturing(CAM).This research presented a rapid tessellation algorithm for CAD models that employs an anisotropic quadtree background grid.The algorithm,constructed from the ground up,guaranteed the output as two-dimensional manifolds.It featureed a size function reliant on curvature and its first derivative to accurately identify geometric featureed within a controllable tolerance during curve discretization.During the adaptive quadtree phase for swift surface tessellation,it minimized mesh elements,ensuring alignment with the original CAD input through a posteriori hybrid multi-order tolerance criteria.Comparative numerical experiments indicate that this algorithm outperforms existing open-source software,such as OCC and Gmsh,and commercial solutions like Ansys,in geometric accuracy,background grid scale,and computational efficiency,highlighting its potential for practical engineering applications.

关 键 词：各向异性 四叉树三角化 几何自适应 特征保形 网格生成 

分 类 号：O242[理学—计算数学]