﻿ Quadrilateral and hexahedral mesh generation based on surface foliation theory-大连理工大学数学科学学院（新）

# Quadrilateral and hexahedral mesh generation based on surface foliation theory

2017年10月30日 16:23  点击：[]

学术报告

报告题目：Quadrilateral and hexahedral mesh generation based on surface foliation theory

报告时间：2017112日（周四）下午15:00-16:00

报告地点：创新园大厦A1101

报告人：雷娜 教授

报告校内联系人：于波  联系电话：84708351-8016

报告摘要：

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：

雷娜，大连理工大学国际信息与软件学院教授，博士生导师，兼任北京成像技术高精尖创新中心研究员；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 Mathematical Review评论员。纽约州立大学石溪分校计算机系访问教授；德克萨斯大学奥斯汀分校计算工程与科学研究所research fellow；清华大学数学科学中心访问教授；中科院数学与系统科学研究院访问学者。研究方向为：应用现代微分几何和代数几何的理论与方法解决工程及医学领域的问题，主要聚焦于计算共形几何、计算拓扑、符号计算及其在计算机图形学、计算机视觉、几何建模和医学图像中的应用。

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