三次均匀B样条扩展曲线的渐进迭代逼近法  

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

作　　者：刘成志 韩旭里[1] 李军成 Liu Chengzhi;Han Xuli;Li Juncheng(School of Mathematics and Statistics, Central South University, Changsha 410083;College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000)

机构地区：[1]中南大学数学与统计学院,长沙410083 [2]湖南人文科技学院数学与金融学院,娄底417000

出　　处：《计算机辅助设计与图形学学报》2019年第6期899-910,共12页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11771453);湖南省自然科学基金(2017JJ3124);中南大学中央高校基本科研业务费(2018zzts005)

摘　　要：为了得到收敛速度更快的几何迭代法,提出带形状参数的三次均匀B样条扩展曲线的(加权)渐进迭代逼近法.首先基于三次均匀B样条扩展曲线提出(加权)渐进迭代逼近法的迭代格式;然后通过分析迭代矩阵的谱半径,探讨迭代法的最优形状参数及加权渐进迭代逼近法的最优权系数;最后指出双三次均匀B样条扩展曲面同样具有(加权)渐进迭代逼近性质.数值实例结果表明,所求的最优形状参数及权系数使得迭代法具有最快的收敛速度.In order to obtain faster convergence rate, we proposed the (weighted) progressive-iterative ap- proximation by the extension of the cubic uniform B-spline curves with shape parameters. Firstly, we pre- sented 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 progres- sive-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 pa- rameters and the optimal weight make the iterative methods have the fastest convergence rate.

关 键 词：三次均匀B样条的扩展曲线 形状参数 渐进迭代逼近法 谱半径 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]