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Digital Differential Geometry Processing

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Abstract

The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.

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Authors and Affiliations

  1. State Key Lab of CAD & CG, Zhejiang University, Hangzhou, 310027, P.R. China

    Xin-Guo Liu, Hu-Jun Bao & Qun-Sheng Peng

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  1. Xin-Guo Liu
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  2. Hu-Jun Bao
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  3. Qun-Sheng Peng
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Correspondence to Xin-Guo Liu.

Additional information

Survey: The research work of this paper is supported by the National Natural Science Foundation of China under Grant No. 60021201, the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China under Grant No. 705027, and the National Grand Fundamental Research 973 Program of China under Grant No. 2002CB312101.

Xin-Guo Liu received the B.Sc. and the Ph.D. degrees in applied mathematics from Zhejiang University in 1995 and 2001. He is currently in the State Key Lab of CAD&CG, and is a professor of the Computer Science School in Zhejiang University. Before joining CAD&CG Lab in 2006, he was a researcher of the Internet Graphics Group in Microsoft Research Asia. His main research interests are in geometry processing, appearance modeling, real-time rendering, and deformable objects.

Hu-Jun Bao received his Bachelor’s and Ph.D. degrees in applied mathematics from Zhejiang University in 1987 and 1993. His research interests include modeling and rendering techniques for large scale of virtual environments and their applications. He is currently the director of State Key Laboratory of CAD&CG of Zhejiang University. He is also the principal investigator of the virtual reality project sponsored by Ministry of Science and Technology of China.

Qun-Sheng Peng is a professor of computer graphics in Zhejiang University. His research interests include realistic image synthesis, computer animation, scientific data visualization, virtual reality, bio-molecule modeling. Prof. Peng graduated from Beijing Mechanical College in 1970 and received the Ph.D. degree from the Department of Computing Studies, University of East Anglia in 1983. He is currently in the editorial boards of several international and Chinese journals.

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Liu, XG., Bao, HJ. & Peng, QS. Digital Differential Geometry Processing. J Comput Sci Technol 21, 847–860 (2006). https://doi.org/10.1007/s11390-006-0847-5

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