Bilateral Scaling Jacobi-PIA Algorithm Based On The Jacobi-PIA Algorithm For Non-Uniform Cubic B-Spline Curve Interpolation

The problem of data fitting has always been one of the important research topics in computer aided geometry design and computer graphics.So far,there are many methods of data fitting.Progressive iterative approximation is an efficient and intuitive data fitting method,which is widely used in the field of CAGD and has good adaptability and convergence.It can not only reduce the computational cost of solving large linear equations,but also generate a series of fitting curves or surfaces.In industrial production,the problem of fitting given data points using B-spline curves has a wide range of applications,and has some research significance up to now.As the geometric meaning of PIA is clear,its calculation is simple,stable,and easy to program,it has been recognized by industry experts once proposed.Considering that the convergence speed of the jacobi iteration will become faster after bilateral scaling preprocessing,the thesis proposes a bilateral scaling Jacobi-PIA algorithm based on the Jacobi-PIA algorithm for non-uniform cubic B-spline curve interpolation.This algorithm combines the bilateral scaled jacobi iteration method with the progressive iterative approximation method to obtain a series of non-uniform cubic B-spline curves that gradually approximate a given data point.Firstly,we introduce the bilateral scaling preprocessing of the jacobi iteration.Secondly,based on this theory,we describe the basic process of the bilateral scaling Jacobi-PIA algorithm,and then provide a theoretical proof of the convergence of the algorithm.Finally,several numerical examples are given to illustrate the corresponding images and error analysis.Numerical examples show that the convergence speed of the bilateral scaling JacobiPIA algorithm is better than that of the Jacobi-PIA algorithm.