Seminars on Numerical Algorithms, Analyses, and Applications：Real-time Locally Injective Harmonic Deformation

：陈仁杰（中国科学技术大学）
：2022-11-10 10:30
：腾讯会议ID：581-4735-3770（无密码）

报告人：陈仁杰（中国科学技术大学）

时  间：11月10日上午10:30-12:00

地  点：腾讯会议ID：581-4735-3770（无密码）

内容摘要:

We present a highly efficient method for interactive shape deformation. Our method operates within a low dimensional subspace of shape-aware 𝐶∞ harmonic maps, and is the first method that is guaranteed to produce a smooth locally injective deformation in 3D. Unlike mesh-based methods in which local injectivity is enforced on tetrahedral elements, our method enforces injectivity on a sparse set of domain samples. The main difficulty is then to certify the map as locally injective throughout the entire domain. This is done by utilizing the Lipschitz continuity property of the harmonic basis functions. We show a surprising relation between the Lipschitz constant of the smallest singular value of the map Jacobian and the norm of the Hessian. We further carefully derive a Lipschitz constant for the Hessian, and develop a sufficient condition for the injectivity certification. This is done by utilizing the special structure of the harmonic basis functions combined with a novel regularization term that pushes the Lipschitz constants further down. As a result, the injectivity analysis can be performed on a relatively sparse set of samples. Combined with a parallel GPU-based implementation, our method can produce superior deformations with unique quality guarantees at real-time rates.

个人简介：

陈仁杰, 中国科学技术大学数学科学学院特任教授。2005获得浙江大学学士学位，2010年获得浙江大学博士学位。2011年至2015年于以色列理工大学和美国北卡罗来纳大学教堂山分校从事博士后研究，2015年至2019年在德国马普计算机所任高级研究员，2019年入选国家创新人才计划青年项目并加入中国科学技术大学。担任The Visual Computer期刊编委，GMP2021会议联合主席和SGP2021 Graduate School联合主席。在ACM TOG,CAD,CAGD等计算机图形学与计算机辅助几何设计领域顶级期刊上发表论文三十余篇。

 

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