数据点加权最小二乘渐进迭代逼近及其B样条曲线拟合

为了使B样条拟合曲线插值部分数据点且逼近其余数据点,提出数据点加权的最小二乘渐进迭代逼近(DW-LSPIA)算法,证明了其收敛性并以它为基础提出一种B样条曲线拟合算法.首先赋初始权重于每个数据点,用DW-LSPIA算法生成初始拟合曲线;然后根据待插值点与拟合曲线上对应点的误差调整待插值点的权重,并重新运用DW-LSPIA算法生成新的拟合曲线;如此迭代,直至拟合曲线达到插值要求.实例结果表明,该拟合算法鲁棒、高效,也可使拟合曲线保形.

Data-Weighted Least Square Progressive and Iterative Approximation and Related B-Spline Curve Fitting

In order to make the fitting curves interpolate some data points and approximate others,we propose the data-weighted least square progressive and iterative approximation(DW-LSPIA)algorithm and prove its convergence.Based on DW-LSPIA,we present a B-spline curve fitting scheme.First,we define initial weights for all data points to be interpolated and get a B-spline fitting curve by DW-LSPIA.Then we update all weights according to the errors between data points to be interpolated and their corresponding points on the fitting curve and update the B-spline fitting curve by DW-LSPIA again.We update the weights and fitting curves iteratively until the interpolation accuracy is satisfied.Examples showed that the B-spline fitting algorithm is robust,efficient and can obtain shape-preserving fitting curves.