Anderson Acceleration For B-spline Curve Fitting

In recent years,curve fitting technology has been widely used in image processing,engineering experiments and other fields.It is an important research topic in computer graphics and computer-aided geometric design.In this paper,the existing b-spline curve fitting method of unordered point cloud is introduced and summarized,and on this basis,a fast b-spline fitting method is proposed based on the Anderson acceleration method.B-spline curve fitting is the most common method in curve fitting,the method of B-spline curve fitting has the advantages of locality,continuity but there are some problems in accuracy and efficiency.At present,the widely used B-spline fitting algo-rithm mainly includes PDM algorithm,TDM algorithm,SDM algorithm and L-BFGS algorithm.These algorithms have some limitations and defects in terms of stability,ef-ficiency and data processing scale.In practical application,B-spline curve fitting requires higher accuracy and speed.In order to increase the speed of planar B-spline curve fitting,Anderson acceleration is applied to the method of planar B-spline curve fitting.And then a quasi-Newton method based on Anderson acceleration is proposed.Anderson acceleration is an algorithm for accelerating fixed point iteration.In recent years,it has been widely used in engineering due to its simple implementation and good acceleration effect.Firstly,an initial shape is set,and then the position parameters of the projection point of each data point are found according to the initial shape.Then,the corresponding position of control points is calculated by Anderson acceleration,and the above two steps are iterated until the result converges.The experimental results show that the proposed method in this paper outperforms other methods with respect to convergence speed and iteration time.