步长加速法优化B样条参数的离散数据点拟合  

Discrete Data Points Fitting Based on Optimization of B-Spline Parameters Using Step-Acceleration Method

作　　者：张莉[1] 张能俊 姚红丽 檀结庆[1,2] Zhang Li;Zhang Nengjun;Yao Hongli;Tan Jieqing(School of Mathematics,Hefei University of Technology,Hefei 230009;School of Computer and Information,Hefei University of Technology,Hefei 230009)

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]合肥工业大学计算机与信息学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2021年第2期169-176,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61972131);国家重点研发计划(2018YFB2100301).

摘　　要：采用迭代法拟合离散数据点时,数据点的参数化会同时影响逼近的效果和逼近的速度,为此,提出一种通过迭代调整优化控制顶点和数据点参数的方法,其收敛速度较快且拟合得到曲线更贴合控制点.首先,选取初始控制顶点,通过自适应的BFGS方法优化控制顶点得到拟合曲线;其次,保持控制顶点不变,利用步长加速法优化数据点对应的参数;最后,利用新参数值重新优化控制顶点并得到新的拟合曲线.数值实例表明,所提方法在迭代前期步骤中,收敛速度快于现有的基于控制顶点迭代法,且优化后的曲线更加逼近离散的数据点,拟合误差更小.When fitting discrete data points by iterative method,the parameterization of data points will affect the approximation effect and speed at the same time.A method of optimizing the parameters of control vertices and data points by iterative adjustment is proposed,which converges faster and fits the original data points better.Firstly,the initial control vertices are selected,and the adaptive BFGS method is used to optimize the control vertices and obtain the fitting curve.Secondly,the parameters corresponding to data points are optimized by the step-size acceleration method while the control vertices are kept unchanged.Finally,the new parameters are used to re-optimize the control vertices and a new fitting curve is obtained.Numerical examples show that the convergence speed in the early iteration stage of the given algorithm is faster than most existing iterative methods.Furthermore,the optimized curves are much closer to discrete data points and fitting error are much smaller.

关 键 词：无约束优化 BFGS方法 B样条 步长加速法 曲线拟合 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]