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浙江大学学报(理学版)  2017, Vol. 44 Issue (1): 22-27    DOI: 10.3785/j.issn.1008-9497.2017.01.003
Chinagraph 2016-几何计算     
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
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
 全文: PDF(1942 KB)   HTML  
摘要: 在计算机辅助几何设计(CAGD)领域,渐进迭代逼近(PIA)算法因其具有很好的自适应性和收敛稳定性,被广泛应用于插值与逼近问题.其中带权渐进迭代逼近(WPIA)算法通过调整向量加权明显加快了收敛速度.提出了一种带互异权值的渐进迭代逼近算法,不仅操作灵活,还可根据需要对各控制顶点进行调整,实现不同的迭代效果;同时通过引入一个参数,给出了可调权值迭代算法,当参数取合适值时,该算法的收敛速度比带权PIA算法更快,且权值取法不依赖于配置矩阵的特征值.最后用数值实例,通过对Bézier曲线、张量积Bézier曲面,以及三角Bézier曲面进行迭代,展示了该算法的有效性.
关键词: 渐进迭代逼近带权渐进迭代逼近插值与逼近zier曲线曲面三角Bézier曲面    
Abstract: In CAGD, progressive iterative approximation (PIA) method is widely used to solve interpolation and approximation problems due to its perfect adaptability and convergence stability. Weighted progressive iterative approximation (WPIA) can accelerate the convergence rate by assigning an appropriate weight for each adjusting vectors. One new PIA method with mutually different weights is presented. It not only provides more flexibility in operation, but also achieves satisfactory iterative result for different control vertices. A set of weights with an adjustable parameter has also been put forward, which can be obtained without resorting to the eigenvalue of collocation matrices and can speed up the convergence rate compared with the WPIA method. Numerical examples of Bézier curves, tensor-product Bézier surfaces and triangular Bézier surfaces demonstrate the effectiveness of the method.
Key words: progressive iterative approximation(PIA)    weighted progressive iterative approximation (WPIA)    interpolation and approximation    Bézier curves and surfaces    triangular Bézier surfaces
收稿日期: 2016-07-15 出版日期: 2017-01-22
CLC:  TP391.41  
基金资助: 国家自然科学基金重点资助项目(U1135003);国家自然科学基金资助项目(61472466,61100126);中国博士后科学基金面上资助项目(2015M571926);浙江大学CAGD&CG国家重点实验室开放课题(A1607)
作者简介: 张莉(1976-),ORCID:http://orcid.org/0000-0002-9208-1949,女,博士,教授,主要从事CAGD研究,E-mail:lizhang@hfut.edu.cn.
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张莉, 赵林, 檀结庆. 带互异权值的渐进迭代逼近算法及其应用[J]. 浙江大学学报(理学版), 2017, 44(1): 22-27.

ZHANG Li, ZHAO Lin, TAN Jieqing. Progressive iterative approximation with different weights and its application. Journal of Zhejiang University (Science Edition), 2017, 44(1): 22-27.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.01.003        https://www.zjujournals.com/sci/CN/Y2017/V44/I1/22

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