三次均匀B样条扩展曲线的渐进迭代逼近法

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.

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

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.