计算机科学

计算机科学 ›› 2024, Vol. 51 ›› Issue (1): 225-232.doi: 10.11896/jsjkx.230700152

• 计算机图形学&多媒体 • 上一篇    下一篇

曲线曲面局部最小二乘渐进迭代逼近

高杨1, 蒋旖旎1, 蔺宏伟1,2   

  1. 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
  • 收稿日期:2023-07-20 修回日期:2023-09-21 出版日期:2024-01-15 发布日期:2024-01-12
  • 通讯作者: 蔺宏伟(hwlin@zju.edu.cn)
  • 作者简介:(22235072@zju.edu.cn)

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

GAO Yang1, JIANG Yini1, LIN Hongwei1,2   

  1. 1 School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China
    2 State Key Laboratory of CAD&CG,Zhejiang University,Hangzhou 310058,China
  • Received:2023-07-20 Revised:2023-09-21 Online:2024-01-15 Published:2024-01-12
  • About author:GAO Yang,born in 2000,postgraduate.His main research interest is computer aided geometric design.
    LIN Hongwei,born in 1973,professor.His main research interests include computer aided geometric design,computer aided topology design and quantum graphics.

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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。

关键词: 渐进迭代逼近, 数据拟合, 局部, 最小二乘

Abstract: 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.

Key words: Progressive-iterative approximation, Data fitting, Local, Least squares

中图分类号: 

  • TP391.41
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