3D B-Rep meshing for real-time data-based geometric parametric analysis

• Published in: Advanced modeling and simulation in engineering sciences 2021-04, Vol.8 (1), p.1-28, Article 8
• Main Authors: Maquart, Tristan, Elguedj, Thomas, Gravouil, Anthony, Rochette, Michel
• Format: Article
• Language: English
• Subjects: 3D quadrilateral meshes; Algorithms; Classical and Continuum Physics; Computational Science and Engineering; Data-based models; Decomposition; Engineering; Engineering Sciences; Finite element method; Geometry; Global parameterization; Model testing; Parameterization; Parametric analysis; Parametric geometry; Parametric statistics; Quadrilaterals; Real time; Research Article; Robustness (mathematics); Standard data; Theoretical and Applied Mechanics; Three dimensional models; Topology; Triangulation; Workflow
• ISSN: 2213-7467; 2213-7467
• DOI: 10.1186/s40323-021-00194-5

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.