浙江大学学报（理学版）2025，Vol.52Issue(3)：346-356,370,12.DOI:10.3785/j.issn.1008-9497.2025.03.006
加速的B样条曲线曲面拟合最小二乘渐进迭代逼近
Accelerated least squares progressive-iterative approximation for B-spline curve and surface fittings
摘要
Abstract
The least squares progressive-iterative approximation(LSPIA)method can approximate curves or surfaces to fit given data point sets.The standard LSPIA method employs the Landweber iterative format to calculate the control points,but it converges relatively slowly.In this paper,an accelerated LSPIA method is proposed based on the Chebyshev semi-iterative scheme.The main idea is to use the extrapolation form of Chebyshev polynomials,taking into account the historical information of the control points of the fitting curve or surface,as well as an adaptive step size parameter selection strategy to update the control points(denoted by CLSPIA).The convergence analysis indicates that the CLSPIA method for cubic B-spline curve and surface fitting has a faster convergence rate than the standard LSPIA method.Numerical examples further validate the theoretical results and demonstrate that the CLSPIA method is feasible and effective.关键词
三次B样条曲线曲面/最小二乘拟合/渐进迭代逼近法/切比雪夫多项式Key words
ubic B-spline curve and surface/least squares fitting/progressive-iterative approximation/Chebyshev polynomial分类
计算机与自动化引用本文复制引用
刘成志,吴念慈,李军成..加速的B样条曲线曲面拟合最小二乘渐进迭代逼近[J].浙江大学学报（理学版）,2025,52(3):346-356,370,12.基金项目
国家自然科学基金资助项目(12101225,12201651) （12101225,12201651）
湖南省自然科学基金资助项目(2023JJ50080) （2023JJ50080）
中南民族大学中央高校基本科研业务费专项资金资助项目(CZQ23004). （CZQ23004）
