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Estimating subdivision depth of Catmull-Clark surfaces

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Abstract

In this paper, both general and exponential bounds of the distance between a uniform Catmull-Clark surface and its control polyhedron are derived. The exponential bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Based on the exponential bound, we can predict the depth of subdivision within a user-specified error tolerance. This is quite useful and important for pre-computing the subdivision depth of subdivision surfaces in many engineering applications such as surface/surface intersection, mesh generation, numerical control machining and surface rendering.

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, 100084, Beijing, P.R. China

    Hua-Wei Wang & Kai-Huai Qin

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  1. Hua-Wei Wang
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  2. Kai-Huai Qin
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Correspondence to Hua-Wei Wang.

Additional information

Supported by the National Natural Science Foundation of China (Grant No.60273013), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20010003048) and the 985 Fundamental Research Fund of Tsinghua University (Grant No.JC2002023).

Hua-Wei Wang is currently a Ph.D. candidate in Department of Computer Science and Technology at Tsinghua University, Beijing, P.R. China. He received his B.S. and B.E. degrees from Department of Applied Mathematics and Department of Computer Science and Technology, respectively, Tsinghua University in 1998. His research interests include computer graphics, computer aided geometric design, curves and surfaces, etc.

Kai-Huai Qin is a professor of computer science and technology, Tsinghua University. He was a postdoctoral fellow from 1990 to 1992, then joined the Department of Computer Science and Technology of Tsinghua University as an associate professor. He received his Ph.D. and M.Eng. from Huazhong University of Science and Technology in 1990 and 1984, and his B.Eng. from South China University of Technology in 1982. His research interests include computer graphics, computer aided geometric design, wavelets, virtual reality and intelligent and smart CAD/CAM.

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Wang, HW., Qin, KH. Estimating subdivision depth of Catmull-Clark surfaces. J. Comput. Sci. & Technol. 19, 657–664 (2004). https://doi.org/10.1007/BF02945592

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  • DOI: https://doi.org/10.1007/BF02945592

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