The Curves Research Of The Approximation Algorithm Based On B-Spline

With the development of technology, both manufacturing industry and industrial production have higher requirements to curves and surfaces in precision, meanwhile, the requirement of computing speed for modeling and animation has reached a higher level. The traditional interpolation spline is difficult to add or delete the points, and it is not easy to deal with the post processing, while the approximation spline can not meet the accuracy requirements. So that both methods are unable to meet the actual needs of production.To avoid these disadvantages, an approximation algorithm based on the cubic B-spline curves and surfaces have been presented. The algorithm, which is based on the cubic B-spline, avoids the shortcoming of the traditional interpolation and the approximation spline, and combines the advantages of both, which improves the calculation speed and precision.Based on the algorithm, the study of his paper contains the following points:1) Study the background, development trend and the current situation of the free curves and surfaces.2) Based on the periodic cubic B spline curve, the algorithm extends to wider boundary conditions in this paper. Thus the approximation algorithm is more general and practical. At the same time, the iteration point is changed and the number of control points at the boundary is reduced, which further improves the accuracy of the algorithm.3) Apply this algorithm on the curves approximation. For the different boundary conditions, the proof of the convergence of the algorithm is given out respectively. The numerical experiments using Matlab show that the improved algorithm has a faster convergence speed, higher accuracy and program easier.4) Based on the cubic B-spline curves, the algorithm extends to Quartic B-spline in this paper. Because the Quartic B-spline is third derivative, this algorithm meets the needs of industrial production with higher precision.5) Apply the Quartic B-spline algorithm to the field of the curve approximation. Prove the convergence theoretical feasibility of the algorithm in curve in the case of the uniform step and the general step. The numerical approximation experiments using Matlab on the common functions show that the algorithm in this paper have a faster convergence speed and could meet the higher practical industrial needs.