Scattered Data Points Fitting Using Ball B-Spline Curves Based on Particle Swarm Optimization

Scattered data fitting is always a challenging problem in the fields of geometric modeling and computer aided design. As the skeleton based three-dimensional solid model representation, the Ball B-Spline Curve is suitable to fit the tubular scattered data points. We study the problem of fitting the scattered data points with Ball B-spline curves (BBSCs) and propose the corresponding fitting algorithm based on the Particle Swarm Optimization (PSO) algorithm. In this process, we face three critical and difficult sub problems: (1) parameterization of the data points, (2) determination of the knot vector and (3) calculation of the control radii. All of them are multidimensional and nonlinear, especially the calculation of the parametric values. The parallelism of the PSO algorithm provides a high optimization, which is more suitable for solving nonlinear, nondifferentiable and multi-modal optimization problems. So we use it to solve the scattered data fitting problem. The PSO is applied in three steps to solve them. Firstly, we determine the parametric values of the data points with PSO. Then we compute the knot vector based on the parametric values of the data points. At last, we get the radius function. The experiments on the shell surface, the crescent surface and the real-world models verify the accuracy and flexibility of the method. The research can be widely used in the computer aided design, animation and model analysis.