GAMES Webinar 2020 – 128期(几何处理专题) | Xianzhong Fang(Zhejiang University), Na Lei(Dalian University of Technology)
【GAMES Webinar 2020-128期】（几何处理专题）
报告嘉宾1：Xianzhong Fang, Zhejiang University
报告题目：Frame Field-driven Quad and Hex Remeshing
High-quality meshes, i.e. pure quad and hex meshes, are attractive for many applications. Automatic, robust and controllable generations of them are important problems both in academic and industrial domain. Now there exist many methods for quadrangulation. Thereinto, multi-chart parameterization-based methods achieve great success in these years, which provide flexible control for quadrangulation when using frame fields as guiding fields.But such method has no guarantee. Applying the similar strategy for hex-meshing is a natural and promising idea. However, from the guiding field creation to the singularity structure analysis, many important steps in hex remeshing are much more difficult than the quad counterpart. This talk will introduce some background knowledge about frame fields, parametrization and so on for remeshing at first. Then introduce our attempts for robustly controllable quadrangulation by combining Morse-Smale complex and parametrization, and hex remeshing by using closed-form polycube under frame field control.
Xianzhong Fang received his doctoral degree in computer science from Zhejiang University in 2019, supervised by Prof. Jin Huang and Prof. Hujun Bao. He currently is a post-doctor at the State Key Lab of CAD&CG, Zhejiang University. His research interests include parametrization, field generation and remeshing.
报告嘉宾2：Na Lei ，Dalian University of Technology
报告题目：Quadrilateral Mesh Generation : Meromorphic Quartic Differentials and Abel-Jacobi Condition
This work discovers the equivalence relation between quadrilateral meshes and meromorphic quartic differentials. Each quad-mesh induces a conformal structure of the surface, and a meromorphic quartic differential, where the conguration of singular vertices corresponds to the congurations of the poles and zeros (divisor) of the meroromorphic differential. Due to Riemann surface theory, the conguration of singularities of a quad-mesh satisfies the Abel-Jacobi condition. Inversely, if a divisor satifises the Abel-Jacobi condition, then there exists a meromorphic quartic differential whose divisor equals to the given one. Furthermore, if the meromorphic quadric differential is with finite trajectories, then it also induces a quad-mesh, the poles and zeros of the meromorphic differential correspond to the singular vertices of the quad-mesh.
Dr. Na Lei is currently a professor of DUT-RU International School of Information Science and Engineering in Dalian University of Technology, director of Institute of Geometric Computing and Inteligent Media Technology, affiliated professor of Beijing Advanced Innovation Center for Imaging Technology, Mathematical Review reviewer of American Mathematical Society. Dr. Na Lei got her Ph. D. from Jilin University in 2002. Then she spent one year in Institute for Computational Engineering and Sciences of University of Texas at Austin, working with Dr. Bajaj as a JTO research fellow, and another year in Computer Science Department of the State University of New York at Stony Brook, working with Dr. David Xianfeng Gu as a visiting professor. She is a reviewer for many distinguished journals and a PC member for many important international conferences. Dr. Na Lei’s research interest is to deal with the practical problem in engineering and medical fields by applying the theory and methods of modern differential geometry and topology.
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