Progressive-Iterative Approximation by Extension of Cubic Uniform B-spline Curves

被引：0
|
作者：
Liu C. [1 ,2 ]
Han X. [1 ]
Li J. [2 ]
机构：
[1] School of Mathematics and Statistics, Central South University, Changsha
[2] College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi
来源：
Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics | 2019年 / 31卷 / 06期
关键词：
Extension of cubic uniform B-spline curve; Progressive-iterative approximation; Shape parameter; Spectral radius;
D O I：
10.3724/SP.J.1089.2019.17399
中图分类号：
学科分类号：
摘要：
In order to obtain faster convergence rate, we proposed the (weighted) progressive-iterative approximation by the extension of the cubic uniform B-spline curves with shape parameters. Firstly, we presented the (weighted) progressive-iterative approximation expression, and then studied the optimal shape parameters and the optimal weight by analyzing the spectral radius of the iterative matrix of the progressive-iterative approximation. Finally, we also proposed the (weighted) progressive-iterative approximation by the extension of bicubic uniform B-spline surfaces, and pointed out that the initial surface also has the (weighted) progressive iteration approximation property. Numerical results show that the optimal shape parameters and the optimal weight make the iterative methods have the fastest convergence rate. © 2019, Beijing China Science Journal Publishing Co. Ltd. All right reserved.
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页码：899 / 910
页数：11
相关论文
共 17 条
  • [1] Lin H.W., Bao H.J., Wang G.J., Totally positive bases and progressive iteration approximation, Computers and Mathematics with Applications, 50, 3, pp. 575-586, (2005)
  • [2] Maekawa T., Matsumoto Y., Namiki K., Interpolation by geometric algorithm, Computer-Aided Design, 39, 4, pp. 313-323, (2007)
  • [3] Lin H.W., The convergence of the geometric interpolation algorithm, Computer-Aided Design, 42, 6, pp. 505-508, (2010)
  • [4] Lin H., Survey on geometric iterative methods with applications, Journal of Computer-Aided Design & Computer Graphics, 27, 4, pp. 582-589, (2015)
  • [5] Lin H.W., Maekawa T., Deng C.Y., Survey on geometric iterative methods and their applications, Computer-Aided Design, 95, pp. 40-51, (2017)
  • [6] Delgado J., Pena J.M., Progressive iterative approximation and bases with the fastest convergence rates, Computer Aided Geometric Design, 24, 1, pp. 10-18, (2007)
  • [7] Han X., Liu S., An extension of the cubic uniform B-spline curve, Journal of Computer-Aided Design & Computer Graphics, 15, 5, pp. 576-578, (2003)
  • [8] Han X.L., Piecewise quartic polynomial curves with a local shape parameter, Journal of Computational and Applied Mathematics, 195, 1-2, pp. 34-45, (2006)
  • [9] Xu G., Wang G., Extensions of uniform cubic B-spline curve with local shape parameters, Journal of Computer Research and Development, 44, 6, pp. 1032-1037, (2007)
  • [10] Cao J., Wang G.Z., Non-uniform B-spline curves with multiple shape parameters, Journal of Zhejiang University Science C, 12, pp. 800-808, (2011)
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