基于粒子群优化的球 B-样条曲线拟合分散数据点

Xingce Wang, Zhongke Wu, Junchen Shen, Qianqian Jiang, Yuanshuai Zhu, Mingquan Zhou
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引用次数: 3

摘要

散点数据拟合一直是几何建模和计算机辅助设计领域的难题。作为基于骨架的三维实体模型表示方法,球 B 样条曲线(Ball B-Spline Curve)适用于拟合管状散点数据。我们研究了用球 B 样条曲线(BBSC)拟合散乱数据点的问题,并基于粒子群优化(PSO)算法提出了相应的拟合算法。在这一过程中,我们面临三个关键和困难的子问题:(1) 数据点的参数化;(2) 节向量的确定;(3) 控制半径的计算。所有这些问题都是多维和非线性的,尤其是参数值的计算。PSO 算法的并行性提供了高优化性,更适合解决非线性、无差异和多模式优化问题。因此,我们用它来解决分散数据拟合问题。PSO 分三步进行求解。首先,我们用 PSO 确定数据点的参数值。然后,根据数据点的参数值计算节点向量。最后,得到半径函数。在贝壳表面、月牙表面和实际模型上的实验验证了该方法的准确性和灵活性。这项研究可广泛应用于计算机辅助设计、动画制作和模型分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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