带互异权值的B样条曲线的最小二乘渐进迭代逼近

Least Square Progressive Iterative Approximation of B-spline Curves with Different Weights

为使B样条拟合目标曲线的迭代过程中单独控制部分数据点,调整局部曲线形状,减小局部曲线迭代误差,提出带互异权值的最小二乘渐进迭代逼近法.首先赋统一初始权值于每个数据点,用最小二乘渐进迭代逼近法生成B样条拟合曲线;其次调整部分数据点对应的权值,运用带互异权值的最小二乘渐进迭代逼近法生成B样条拟合曲线;最后比较调整前后拟合误差.实例结果表明,本文所提出方法可调整局部拟合曲线形状,减小拟合误差.

In order to control part data points independently,adjust the shape of local curves and reduce the iterative errors of local curves in the process of fitting B-spline to the target curve,we propose a least square progressive iterative approximation with different weights.Firstly,the unified initial weights are assigned to all data points,and the B-spline fitting curve is generated by the least square progressive iterative approximation.Secondly,the weights corresponding to some data points are adjusted,and the B-spline fitting curve is generated by using the least square progressive iterative approximation with different weights.Finally,the fitting errors before and after adjustment are compared.The example results show that the method proposed in this paper can adjust the shape of local fitting curves and reduce fitting errors.