Research On Smooth Reconstruction Of B-spline Curves

Aiming at the problem that it is difficult to consider the approximation error and curve fairing of the reconstructed curve at the same time in the existing curve fairing reconstruction technology of reverse engineering,the paper combines the advantages of particle swarm optimization algorithm,launches a systematic research on curve fairing reconstruction method,and proposes a cubic B-spline curve fairing reconstruction algorithm and an arbitrary number of B-spline curve fairing reconstruction algorithm.Firstly,according to the least square fitting model of B-spline curve,the problems existing in the existing B-spline curve smooth reconstruction technique are analyzed,and then the smooth reconstruction model of the curve is established by setting different smoothness pointers.The least square fitting model is adopted to fit the initial curve whose curve error meets the approximation accuracy and the error value is small enough to obtain the initial curvature.Then,based on the sign change before the initial curvature value of the curve,the bad points and areas of curvature signs that may lead to inflection points on the curve are found out,and the bad points and areas of curvature signs are preferentially smoothed.Finally,based on the curvature change,the curvature change smoothing is carried out for the points with sharp curvature change.Based on the curvature difference and the basis function value at the most difference,a fairing strategy is proposed to adjust the main and auxiliary control points simultaneously,which effectively improves the fairing efficiency in the fairing process of the reconstructed curve.The approximation accuracy is taken as the constraint condition of the particle swarm optimization algorithm,the search space of particles in the algorithm is limited,and the curve error of the reconstructed curve generated in the whole fairing process is controlled.Based on the arbitrary order B-Spline curve,a new improvement is made on the basis of the improved cubic B-Spline Curve fairing Reconstruction algorithm.The fairing function describing smoothness is added to the objective function of constructing the initialcurve,and the coefficient factor is added before the approximation function and fairing function.By selecting the appropriate combination of coefficient factors,the initial curve which not only meets the requirements of accuracy but also has good smoothness can be outputted.As the input of algorithm smoothing process,the time of curve smoothing process can be shortened.And based on the distribution of the basis function values of the points on the curve,a more flexible control point adjustment strategy is given,which further improves the smoothing efficiency of the curve smoothing process.The algorithms proposed in this paper have been successfully programmed in MATLAB software.Several examples of curve reconstruction are given to demonstrate and demonstrate the effectiveness and practicability of the algorithm in curve and surface reconstruction.