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.