[1] Zhou Hai, Zhou Laishui,. Novel method for exactly evaluating the energyof Catmull-Clark subdivision surfaces [J]. Journal of Southeast University (English Edition), 2005, 21 (4): 453-458. [doi:10.3969/j.issn.1003-7985.2005.04.016]

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Novel method for exactly evaluating the energyof Catmull-Clark subdivision surfaces()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

21

Issue:

2005 4

Page:

453-458

Research Field:

Computer Science and Engineering

Publishing date:

2005-12-30

Info

Title:

Novel method for exactly evaluating the energyof Catmull-Clark subdivision surfaces

Author(s):

Zhou Hai¹;  Zhou Laishui²

¹ School of Mechanical Engineering, Yancheng Institute of Technology, Yancheng 224003, China
²Research Center of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Keywords:

Catmull-Clark subdivision;  energy of surface;  fairing of surface

PACS:

TP391

DOI:

10.3969/j.issn.1003-7985.2005.04.016

Abstract:

A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh.A closed-form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces.Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision.Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology.The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.

References:

[1] Wang Guojin, Wang Guozhao, Zheng Jianmin.Computer aided geometric design [M].Beijing:Higher Education Press, 2001.362-367.(in Chinese)
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[4] Friedel I.Data dependent energy operators for subdivision surfaces [D].Caltech:Department of Computer Science of California Institute of Technology, 2002.
[5] Halstead M, Kass M, DeRose T.Efficient, fair interpolation using Catmull-Clark surfaces[J].Computer Graphics, 1993, 27(3):35-44.
[6] Catmull E, Clark J.Recursively generated B-spline surfaces on arbitrary topological meshes[J].Computer Aided Design, 1978, 10(6):350-355.
[7] Zorin D.Overview of subdivision schemes [A].In:Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH[C].New York:ACM Press, 2000.65-84.
[8] Stam J.Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values [A].In:Computer Graphics Proceedings, ACM SIGGRAPH[C].New York:ACM Press, 1998.395-404.
[9] Hanos V, Ralph R, Tamas V.A survey of blending methods that use parametric surfaces[J].Computer Aided Design, 1994, 26(5):341-365.
[10] Li Guiqing, Li Hua.Blending parametric patches with subdivision surfaces[J].Journal of Computer Science and Technology, 2001, 17(4):498-506.

Memo

Memo:

Biographies: Zhou Hai(1965—), male, doctor, associate professor, zhouhai@ycit.cn;Zhou Laishui(1962—), male, doctor, professor, zlsme@nuaa.edu.cn.

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