步长加速法优化B样条参数的离散数据点拟合

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...

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

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.