Chinagraph 2016-几何计算 |
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带互异权值的渐进迭代逼近算法及其应用 |
张莉1, 赵林1, 檀结庆1,2 |
1. 合肥工业大学 数学学院, 安徽 合肥 230009; 2. 合肥工业大学 计算机与信息学院, 安徽 合肥 230009 |
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Progressive iterative approximation with different weights and its application |
ZHANG Li1, ZHAO Lin1, TAN Jieqing1,2 |
1. School of Mathematics, Hefei University of Technology, Hefei 230009, China; 2. School of Computer and Information, Hefei University of Technology, Hefei 230009, China |
[1] 齐东旭,田自贤,张玉心,等.曲线拟合的数值磨光方法[J].数学学报,1975,18(3):173-184. QI D X, TIAN Z X, ZHANG Y X, et al. The method of numeric polish in curve fitting[J]. Acta Mathematica Sinica,1975,18(3):173-184. [2] DE BOOR C. How does Agee's smoothing method work[J/OL].[2016-7-10]. http://ftp.cs.wisc.edu/debooron/agee.pdf. [3] 蔺宏伟,王国瑾,董辰世.用迭代非均匀B-spline曲线(曲面)拟合给定点集[J].中国科学:E辑,2004,33:315-331. LIN H W, WANG G J, DONG C S. Constructing iterative non-uniform B-spline curve and surface to fit data points[J]. Science in China:Ser E,2004,33:315-331. [4] LIN H W, BAO H J, WANG G J. Totally positive bases and progressive iteration approximation[J]. Computers and Mathematics with Applications,2005,50(3/4):575-586. [5] DELGADO J, PENA J M. Progressive iterative approximation and bases with the fastest convergence rates[J]. Computer Aided Geometric Design,2007,24(1):10-18. [6] CHEN J, WANG G J. Progressive iterative approximation for triangular Bézier surfaces[J]. Computer-Aided Design,2011,43(8):889-895. [7] 邓少辉,汪国昭.渐进迭代逼近方法的数值分析[J].计算机辅助设计与图形学学报,2012,24(7):879-884. DENG S H, WANG G Z. Numerical analysis of the progressive iterative approximation method[J]. Journal of Computer-Aided Design and Graphics,2012,24(7):879-884. [8] LIN H W. Local progressive-iterative approxim-ation format for blending curves and patches[J]. Computer Aided Geometric Design,2010,27(4):322-339. [9] LIN H W. Adaptive fitting by the progressive-iterative approximation[J]. Computer Aided Geometric Design,2012,29(7):463-473. [10] LU L Z. Weighted progressive iteration approximation and convergence analysis[J]. Computer Aided Geometric Design,2010,27:129-137. [11] 陈杰,王国瑾,金聪健.两类推广的渐近迭代逼近[J].自动化学报,2012,38(1):135-139. CHEN J, WANG G J, JIN C J. Two kinds of generalized progressive iterative approximations[J]. Acta Automatica Sinica,2012,38(1):135-139. [12] 刘晓艳,邓重阳.非均匀三次B样条曲线插值的Jacobi-PIA算法[J].计算机辅助设计与图形学学报,2015,27(3):484-491. LIU X Y, DENG C Y. Jacobi-PIA algorithm for non-uniform cubic B-spline curve interpola-tion[J]. Journal of Computer-Aided Design& Graphics,2015,27(3):484-491. [13] LIN H W, ZHANG Z Y. An extended iterative format for the progressive-iteration approximation[J]. Computers & Graphics,2011,35:967-975. [14] DENG C Y, LIN H W. Progressive and iterative approximation for least squares B-spline curve and surface fitting[J]. Computer-Aided Design,2014,47(1):32-44. [15] 蔺宏伟.几何迭代法及其应用综述[J].计算机辅助设计与图形学学报,2015,27(4):582-589. LIN H W. Survey on geometric iterative methods with applications[J]. Journal of Computer-Aided Design& Graphics,2015,27(4):582-589. [16] DUNLL C, XU Y. Orthogonal Polynomials of Several Variables[M]. Cambridge:Cambridge University Press,2001. |
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