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基于混合几何建模的可靠一致曲面网格生成

Reliable and Conforming Surface Mesh Generation Based on Hybrid Geometry Modelling

  • 摘要: 复杂CAD模型中存在的几何退化、拓扑模糊等特征, 会使曲面的映射参数域产生边界畸变, 进而导致网格质量下降、特征丢失甚至生成失败. 为了提升曲面网格生成的可靠性和网格结果的几何一致性, 提出一种基于解析曲面和离散STL网格混合输入的高质量曲面网格生成方法. 首先基于曲面的B-rep生成多曲面协同对齐的自适应曲线网格; 然后分类判别曲面的映射参数域畸变, 对于存在边界畸变的曲面, 修复和重参数化输入的离散STL网格, 并以曲线网格结果为约束重构曲面的参数域; 最后在重构的参数域生成网格, 再插值获得物理域网格. 在实际工程模型上的实验结果表明, 所提方法在单元质量与可靠性方面展现出明显优势, 最小角小于45°的单元占比平均下降了43.27%; 半径比在0.9~1.0的单元占比达66.46%, 优于对比商业软件的56.10%和59.63%; 在包含薄片曲面、退化曲面和周期性曲面的复杂CAD模型中, 均可生成几何一致的曲面网格.

     

    Abstract: Geometric degeneracies and topological ambiguities in complex CAD models often distort parametric domain mappings, leading to poor mesh quality, feature loss, or even generation failure. To improve mesh reliability and geometric consistency, this study proposes a robust high-quality surface mesh generation framework that combines both analytic surfaces and discrete STL meshes as input. First, the method generates adaptive curve-aligned meshes from B-rep surfaces while ensuring multi-surface coordination. It then classifies parametric domain distortions. For surfaces with boundary distortions, the algorithm repairs and reparameterizes input STL meshes, reconstructing their parametric domains under curve-aligned mesh constraints. Finally, it regenerates the mesh in the corrected parametric domain and interpolates it back to the physical space. Experimental results on practical engineering models show that the proposed method exhibits significant advantages in element quality and reliability. The average proportion of elements with a minimum angle less than 45° reduces by 43.27%; the proportion of elements with a radius ratio between 0.9 and 1.0 reaches 66.46%, which outperforms the 56.10% and 59.63% of comparative commercial software. For complex CAD models containing thin-walled surfaces, degraded surfaces and periodic surfaces, the method can generate geometrically consistent surface meshes.

     

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