[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(
)
Catmull-Clark 细分曲面能量精确分析方法
)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
- Catmull-Clark 细分曲面能量精确分析方法
- 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
- 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.
- 提出了一种新的精确计算包含奇异顶点的Catmull-Clark细分曲面能量的方法.通过把Catmull-Clark细分曲面片转化成双3次B样条曲面片, 导出了任意拓扑结构的细分曲面完整的能量计算公式.该方法不需要对细分曲面进行递归细分, 就能计算出细分曲面的膜能量和薄板能量, 与现有方法相比, 该方法能快速准确地计算出细分曲面的能量.曲面光顺实例表明, 用该方法计算细分曲面能量高效可行.
References:
[1] Wang Guojin, Wang Guozhao, Zheng Jianmin.Computer aided geometric design [M].Beijing:Higher Education Press, 2001.362-367.(in Chinese)
[2] Zorin D, Schröder P.Subdivision for modeling and animation [A]. In:Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH[C].New York:ACM Press, 1999.65-87.
[3] Terzopoulos D, Platt J.Elastically deformable models [J].Computer Graphics, 1987, 24(4):205-214.
[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.