报告时间：1月10日星期二下午14:30
报告地点：浙江大学紫金港校区蒙民伟楼402室
报告题目：Quadrilateral and hexahedral mesh generation based on surface foliation theory
报告人：雷娜 教授
主持人：黄劲 教授

Abstract: 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.

个人简介：雷娜，大连理工大学软件学院教授，博士生导师. 2002年于吉林大学数学研究所获得博士学位，开始在吉林大学数学学院从事教学科研工作，2009年被聘为教授。2016年加入大连理工大学软件学院。中国工业与应用数学学会几何设计与计算专业委员会委员，中国数学会计算机数学专业委员会委员，美国数学会Math Review评论员。研究方向为计算几何，主要研究兴趣为应用微分几何、代数几何的理论与方法，解决计算机图形学、计算机视觉、可视化等领域的问题。