曲线曲面局部最小二乘渐进迭代逼近  

Local Progressive and Iterative Approximation for Least Squares B-spline Curve and Surface Fitting

作　　者：高杨[1] 蒋旖旎 蔺宏伟[1,2] GAO Yang;JIANG Yini;LIN Hongwei(School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China;State Key Laboratory of CAD&CG,Zhejiang University,Hangzhou 310058,China)

机构地区：[1]浙江大学数学科学学院,杭州310058 [2]浙江大学CAD&CG国家重点实验室,杭州310058

出　　处：《计算机科学》2024年第1期225-232,共8页Computer Science

摘　　要：作为一种有效的大数据拟合方法,曲线曲面最小二乘渐进迭代逼近方法(LSPIA)吸引了众多研究者的关注,并获得了广泛的应用。针对LSPIA算法拟合局部数据点效果较差的问题,提出了一种局部的LSPIA算法,称为LOCAL-LSPIA。首先,给定初始曲线(曲面)并从给定的数据点中选择部分数据点;然后在初始曲线(曲面)上选择需要调整的控制点;最后,LOCAL-LSPIA通过迭代调整这一部分控制点来生成一系列局部变化的拟合曲线(曲面),并且保证生成的曲线(曲面)的极限是在仅调整这部分控制点的情况下拟合部分数据点的最小二乘结果。在多个曲线曲面拟合上的实验结果表明,为达到相同的拟合精度,LOCAL-LSPIA算法比LSPIA算法需要的步骤和运算时间更少。因此,LOCAL-LSPIA是有效的,而且在拟合局部数据的情况下比LSPIA算法的收敛速度更快。Progressive and iterative approximation for least squares B-spline curve and surface fitting(LSPIA),as an effective method for fitting large data,has attracted the attention of many researchers.To address the problem that the LSPIA algorithm is less effective in fitting local data points,a local LSPIA algorithm,called LOCAL-LSPIA,is proposed.Firstly,the initial curve is given and some of the data points are selected from the given data points.Then,the control points to be adjusted are selected on the initial curve.Finally,LOCAL-LSPIA is used to generate a series of locally varying fitted curves(surfaces)by iteratively adjusting this part of the control points and ensuring that the limits of the generated curves(surfaces)are the least-squares results of fitting some of the data points while adjusting only this part of the control points.Experimental results on multiple curve-surface fitting show that the LOCAL-LSPIA algorithm requires fewer steps and shorter time than the LSPIA algorithm to achieve the same local fitting accuracy.Therefore,LOCAL-LSPIA is effective and has a faster convergence rate than LSPIA algorithm in the case of fitting local data.

关 键 词：渐进迭代逼近 数据拟合 局部 最小二乘 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]