用四点插值细分曲线拟合离散点列  

Fitting discrete data points by the 4-point interpolation subdivision curve

作　　者：邱慧 李亚娟 邓重阳 QIU Hui;LI Yajuan;DENG Chongyang(School of Science,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第5期36-43,共8页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61872121);浙江省重点研发计划资助项目(2021c001103)。

摘　　要：提出一种用四点插值细分曲线拟合有序离散点列的算法。首先,对离散数据点列参数化;然后,利用四点插值细分法的极限曲线上的点的计算公式,并结合离散点列参数化和最小二乘法求解拟合曲线的初始控制点;最后,根据初始控制点得到逼近离散点列的四点插值细分曲线。算法实例表明,相比于三次均匀B样条曲线的拟合算法,该算法在一定的拟合误差下,拟合曲线的初始控制点的数目较少。在实际应用中,该算法可以通过少量的初始控制点拟合大量离散数据点列,达到数据简化的效果。在多分辨率分析方面,该算法利用初始控制点逐次细分,得到任意个数点列构成的拟合曲线。An algorithm for fitting the discrete data points with the four-point interpolation subdivision curve is proposed.Firstly,the discrete data point sequence is parameterized.Then,the limit point calculation formula of the four-point interpolation subdivision method is used,and the initial control points of the fitting curve are solved by parameterization of the discrete data points sequence and the least square method.Finally,the four-point interpolation subdivision curve approximating the discrete data points is obtained according to the initial control points.Examples show that compared with the fitting algorithm of cubic uniform B-spline curve,the algorithm in this paper has a smaller number of initial control points of the fitted curve under given fitting error.In practical applications,the algorithm can fit a large number of discrete data points through a small number of initial control points,to achieve the effect of data simplification.In multi-resolution analysis,the algorithm uses the initial control points to subdivide step by step to get the fitting curve composed of any decimal point column.

关 键 词：四点插值细分法 曲线拟合 最小二乘法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]