This paper presents an effective framework to automatically construct 3D quadrilateral meshes of complicated geometry and arbitrary topology adapted for parametric studies. The input is a triangulation of the solid 3D model’s boundary provided from B-Rep CAD models or scanned geometry. The triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. This workflow includes an integration of a geometry-feature-aware pants-to-cuboids decomposition algorithm. This set of cuboids perfectly replicates the input surface topology. Using aligned global parameterization, patches are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. Based on the cuboid decomposition and global parameterization, a 3D quadrilateral mesh is extracted. For different parametric instances with the same topology but different geometries, the MEG-IsoQuad method allows to have the same representation: isotopological meshes holding the same connectivity where each point on a mesh has an analogous one into all other meshes. Faithful 3D numerical charts of parametric geometries are then built using standard data-based techniques. Geometries are then evaluated in real-time. The efficiency and the robustness of the proposed approach are illustrated through a few parametric examples.

中文翻译：

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3D B-Rep网格划分，用于基于数据的实时几何参数分析

本文提出了一个有效的框架，可以自动构建适用于参数研究的复杂几何形状和任意拓扑的3D四边形网格。输入是从B-Rep CAD模型或扫描的几何图形提供的实体3D模型边界的三角剖分。通过两个步骤将三角网格分解为一组长方体：裤子分解和长方体分解。此工作流程包括几何特征感知的裤子到立方体分解算法的集成。这组长方体完美地复制了输入表面拓扑。使用对齐的全局参数化，可将贴片重新定位在表面上，以实现较低的总体失真以及与主曲率方向和锋利特征对齐的方式。基于长方体分解和全局参数化，提取3D四边形网格。对于具有相同拓扑但几何形状不同的不同参数实例，MEG-IsoQuad方法允许具有相同的表示形式：保持相同连通性的等拓扑网格，其中网格上的每个点都与所有其他网格类似。然后使用基于标准数据的技术构建真实的3D数字几何图形图表。然后实时评估几何形状。通过几个参数示例说明了所提出方法的效率和鲁棒性。然后使用基于标准数据的技术构建真实的3D数字几何图形图表。然后实时评估几何形状。通过几个参数示例说明了所提出方法的效率和鲁棒性。然后使用基于标准数据的技术构建真实的3D数字几何图形图表。然后实时评估几何形状。通过几个参数示例说明了所提出方法的效率和鲁棒性。