Interpolation Method And Experimental Research Spline Surfaces Based On Particle Swarm Global Bicubic B

Curve and curved surface reconstruction of geometric theory system is made of three techniques, they are interpolation, fitting and approximation. In the case of the known sample data, the approximation method is to make the constructor infinite close to them, the interpolation method and fitting method belongs to the category of reverse engineering, Fitting is only asking for reconstruction of curve and curved surface close to the sample data, and the interpolation method is that curve and curved surface are required to strictly through sample data. The Bezier, B spline and NURBS method in Computer aided design (CAGD) is widely research on free curve and surface design, the cubic B spline curve interpolation and double cubic B spline curved surface interpolation are less needed information, has the advantages of simple calculation, easy programming, so as to get more researchers’ attention.B-spline interpolation process can be described as:first, through the given sample points and B spline order to determine the parameters of the vector and the node vector. Then, according to theory of B-spline interpolation, control points or control grid was calculated out. Parameter vector and node vector directly affects the b-spline curve interpolation, and is closely related to the selection of them. When B spline surface node vector is determined according to the characteristics of sample points, b-spline curve interpolation becomes orderly data points of nonlinear parameter optimization problem. Due to Particle Swarm Optimization (PSO) can effectively solve the problem of nonlinear Optimization, and the Particle Swarm algorithm has simple rules, fast convergence rate, not easy to fall into local optimum, less adjustable parameters, and mature theory research results has been given for the choice of parameters, etc. In this paper, the nonlinear parameter optimization in b-spline curve interpolation can be effectively solved by using the particle swarm algorithm, cubic B spline curve interpolation based on Particle Swarm Optimization is successfully realized. On the basis of the idea, the one-dimensional plane curve interpolation was expanded to the two-dimensional curved surface interpolation and global double cubic B spline surface interpolation based on particle swarm algorithm is finally achieved.The experimental platform was set up in this paper, these two methods of program design is successfully achieved. Through selecting several representative complexes function, a large number of grouping experiment and comparative experiments are completed. The experiment result shows that under the less number of iterations the two methods proposed in this paper can get smaller interpolation error and the optimal curve and curved surface reconstruction of graphics. Also shows that for a variety of complex curved surface interpolation under the imperfect sample set, global double cubic B spline surface interpolation based on particle swarm algorithm can obtain good effect. Therefore, the proposed approach has a positive significance on curve and curved surface interpolation.