GAMES Webinar 2020 – 153期(几何专题) | Caigui Jiang (KAUST)
【GAMES Webinar 2020-153期】(几何专题)
报告嘉宾：Caigui Jiang (KAUST)
报告题目：Geometric Modeling from Flat Sheet Material
In this presentation, I will talk about our recent work on geometric modeling based on planar material which consists of two major parts.
Curve-pleated structures. In this paper we study pleated structures generated by folding paper along curved creases. We discuss their properties and the special case of principal pleated structures. A discrete version of pleated structures is particularly interesting because of the rich geometric properties of the principal case, where we are able to establish a series of analogies between the smooth and discrete situations, as well as several equivalent characterizations of the principal property. These include being a conical mesh, and being flat-foldable. This structure-preserving discretization is the basis of computation and design. We propose a new method for designing pleated structures and reconstructing reference shapes as pleated structures: we first gain an overview of possible crease patterns by establishing a connection to pseudo-geodesics, and then initialize and optimize a quad mesh so as to become a discrete pleated structure. We conclude by showing applications in design and reconstruction, including cases with combinatorial singularities. Our work is relevant to fabrication in so far as the offset properties of principal pleated structures allow us to construct curved sculptures of finite thickness.
Quad-Mesh Based Isometric Mappings and Developable Surfaces. We discretize isometric mappings between surfaces as correspondences between checkerboard patterns derived from quad meshes. This method captures the degrees of freedom inherent in smooth isometries and enables a natural definition of discrete developable surfaces. This definition, which is remarkably simple, leads to a class of discrete developables which is much more flexible in applications than previous concepts of discrete developables. In this paper, we employ optimization to efficiently compute isometric mappings, conformal mappings and isometric bending of surfaces. We perform geometric modeling of developables, including cutting, gluing and folding. The discrete mappings presented here have applications in both theory and practice: We propose a theory of curvatures derived from a discrete Gauss map as well as a construction of watertight CAD models consisting of developable spline surfaces.
Caigui Jiang is a research scientist at Visual Computing Center (VCC) of King Abdullah University of Science and Technology (KAUST). Before that, he worked as a research scientist and Postdoc at ICSI, UC Berkeley and the Max Planck Institute for Informatics from Jun. 2016 to Jan. 2019. He obtained his Ph.D. from KAUST under the supervision of Prof. Dr. Helmut Pottmann and Prof. Dr. Peter Wonka and his B.S. and M.S. degrees from Xi’an Jiaotong University (XJTU) in 2008 and 2011 respectively. His research interests are in geometric modeling, geometry processing, architectural geometry, computer graphics, and computer vision.
张举勇，中国科学技术大学数学科学学院副教授，博士生导师。2006年于中科大计算机系获得学士学位，2011年于新加坡南洋理工大学计算机工程学院获得博士学位，2011年至2012年于瑞士联邦理工学院洛桑分校从事博士后研究，2012年至今工作于中国科学技术大学数学科学学院。研究兴趣包括计算机图形学、计算机视觉、数值最优化算法。现担任The Visual Computer期刊编委。于2018年获得”几何设计与计算青年学者奖”，“安徽省青年数学奖”。
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