摘要
混合曲线曲面的拟合常应用于计算机辅助设计与制造中,但传统的数据拟合方法缺乏明显的几何意义.最小二乘渐进迭代逼近算法(progressive-iterative approximation for least square fitting, LSPIA)能通过迭代地调整控制点得到原始数据点的最小二乘拟合结果,具有明显的几何意义,但收敛速度较慢.为解决这个问题,本文提出一种基于共轭梯度法的最小二乘渐进迭代逼近算法(conjugate-gradient progressive-iterative approximation for least square fitting, CG-LSPIA).该算法首先计算共轭曲线曲面,再更新混合曲线曲面,在没有数值误差的情况下,迭代至多n步即可生成给定数据点的最小二乘拟合曲线曲面.此外,本文给出了CG-LSPIA算法收敛性证明.最后,以B样条曲线曲面为例,与LSPIA算法进行了比较,实验表明该算法有效,并且减少了达到相同拟合误差限所需的迭代次数与时间.
The fitting of curves and surfaces has been widely used in computer-aided design and computeraided manufacturing(CAD/CAM). However, traditional data fitting methods lack clear geometric meaning.By iteratively adjusting control points, the progressive-iterative approximation for least square fitting(LSPIA)algorithm can obtain the least square fitting results for given data points with intuitive geometric meaning, but the convergence rate is prolonged. Here, we design a novel LSPIA algorithm based on the conjugate-gradient method, named CG-LSPIA. First, the conjugate-gradient vector is constructed, and then the control points are precisely updated. The algorithm converges in at most n iterations. We also demonstrate the convergence of CG-LSPIA. In the absence of numerical error, the numerical examples show that our method is effective and greatly reduces the iteration time for reaching the fitting error limit compared with the LSPIA.
作者
蒋旖旎
蔺宏伟
Yini JIANG;Hongwei LIN(School of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China;State Key Laboratory of CAD&CG,Zhejiang Unwversity,Hangzhou 310058,China)
出处
《中国科学:信息科学》
CSCD
北大核心
2022年第7期1251-1271,共21页
Scientia Sinica(Informationis)
基金
国家自然科学基金(批准号:61872316,61932018)
重点研发计划(批准号:2020YFB1708900)资助项目。
关键词
渐进迭代逼近
最小二乘拟合
共轭梯度法
数据拟合
几何设计
progressive-iterative approximation algorithm
least square fitting
conjugate-gradient method
data fitting
geometric design