Quadrilateral and hexahedral mesh generation based on surface foliation theory
内容提要： For the purpose of isogeometric analysis, one of the most common ways is to construct structured hexahedral meshes, which have regular tensor product structure, and fit them by volumetric T-Splines. This theoretic work proposes a novel surface quadrilateral meshing method, colorable quad-mesh, which leads to the structured hexahedral mesh of the enclosed volume for high genus surfaces. The work proves the equivalence relations among colorable quad-meshes, finite measured foliations and Strebel differentials on surfaces. This trinity theorem lays down the theoretic foundation for quadrilateral/hexahedral mesh generation, and leads to practical, automatic algorithms. The work proposes the following algorithm: the user inputs a set of disjoint, simple loops on a high genus surface, and specifies a height parameter for each loop; a unique Strebel differential is computed with the combinatorial type and the heights prescribed by the user’s input; the Strebel differential assigns a flat metric on the surface and decomposes the surface into cylinders; a colorable quad-mesh is generated by splitting each cylinder into two quadrilaterals, followed by subdivision; the surface cylindrical decomposition is extended inward to produce a solid cylindrical decomposition of the volume; the hexahedral meshing is generated for each volumetric cylinder and then glued together to form a globally consistent hex-mesh. 报告人简介： Na Lei is a Professor in the School of Software and Technology at Dalian University of Technology. She completed her PhD in Computer Algebra in Institute of Mathematics at Jilin University in 2002. Her research focuses on Computational Conformal Geometry, Computational Topology, Computer Algebra and their applications on Computer Graphics, Computer Vision, Geometric Modeling and Medical Imaging.