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A bound on the distance between Loop subdivision surface and its control mesh

A bound on the distance between Loop subdivision surface and its control mesh
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摘要 By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions, we obtain a bound on the distance between Loop subdivision surface patch and its control mesh. The bound can be used to compute the numbers of subdivision for a given tolerance. Finally, two examples are listed in this paper to demon- strate the applications of the bound. By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions, we obtain a bound on the distance between Loop subdivision surface patch and its control mesh. The bound can be used to compute the numbers of subdivision for a given tolerance. Finally, two examples are listed in this paper to demon- strate the applications of the bound.
作者 Zhang Yuhua Zhao Chong Cui Zhenlu Zeng Xiaoming
机构地区 Department of Mathematics Department of Computer Science Department of Mathematics and Computer Science
出处 《Computer Aided Drafting,Design and Manufacturing》 2012年第1期27-30,共4页 计算机辅助绘图设计与制造（英文版）
基金 Supported by the National Natural Science Foundation of China (No.61170324) the Natural Science Foundation of Fujian Province of China (No.2010J01012) the National Defense Basic Scientific Research Program of China (No.B1420110155)
关键词 Loop surface control mesh BOUND SUBDIVISION basis functions Loop surface control mesh bound subdivision basis functions
分类号 TP391.7 [自动化与计算机技术—计算机应用技术] TP391.41 [自动化与计算机技术—计算机应用技术]
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参考文献9

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  • 3Moncayo, M., Amat, S.. Error bounds for a class of subdi- vision schemes based on the two-scale refinement equation [J]. Journal of Computational and Applied Mathematics, 2011, 236: 265-278.
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  • 5Narin, D., Peters, J., Lutterkort, D.. Sharp quantitative bounds on the distance between a polynomial piece and its Bezier control polygon [J]. Computer Aided Geometric Design, 1999, 16: 613-631.
  • 6Reif., U.. Best bounds on the approximation of polynomi- als and splines by their control structure [J]. Computer Aided Geometric Design, 2000,17:579-589.
  • 7Stam, J.. Evaluation of Loop subdivision surfaces [C] // Proceedings of SIGGRAPH'98, ACM Inc., 1999: 395-400.
  • 8Ying H.. Conditions for parametric and geometric coinci- dence of two rational curves [J]. Computer Aided Drafting, Design and Manufacturing, 2007,17(1).
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Computer Aided Drafting,Design and Manufacturing
2012年 第1期

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