求解NURBS曲面间最小距离的人工势场算法
An Artificial Potential Field Method of Calculating Minimum Distance between NURBS Surfaces
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摘要: 针对Newton-Raphson（NR）法对初值要求苛刻的缺点,结合人工势场法和Verlet算法,提出一种求解NURBS曲面间最小距离的人工势场算法.该算法构建了小球势力场模型,通过分析小球受力情况,采用Verlet算法模拟小球在势力场中的运动过程,两球平衡位置即为曲面间最小距离处.将曲面边界问题用统一的算法描述,通过拓展算法来求解点、NURBS曲线和曲面3种不同对象之间的最小距离.仿真实验结果表明,文中算法通用性强、鲁棒性好、实时性高.Abstract: A novel algorithm to calculate minimum distance between NURBS surfaces is proposed with the combination of artificial potential field method and Verlet algorithm.The minimum distance between equilibrium positions obtained via the Verlet algorithm can be determined,while the boundary problems can be addressed by artificial potential field（APF）.The algorithm is extended to calculate minimum distances between points,NURBS curves or surfaces,and simulation results demonstrate its generalization,robustness and high performance.
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