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| 基于B样条自由曲面体间最短距离计算算法研究 | |
| 引用本文： | 陈国振,刘静华,丑武胜. 基于B样条自由曲面体间最短距离计算算法研究[J]. 工程图学学报, 2006, 27(1): 82-86 |
| 作者姓名： | 陈国振 刘静华 丑武胜 |
| 作者单位： | 1. 北京航空航天大学工业设计系,北京,100083 2. 北京航空航天大学机器人研究所,北京,100083 |
| 摘 要： | 提出了一种快速求解B样条曲线间最短距离的算法。该算法首先运用ULB方法,计算出两条NUBS曲线控制多边形间一对距离为极小值的点,以此对极小值点的连线方向作为曲线间最短距离的矢量方向,然后用爬山法求出两曲线在该矢量方向上的一对极值点,并以此对极值点作为拟牛顿迭代法求解非线性方程组的初始值,这样大大减少了求解方程组根的迭代次数,可快速求出精确解。最后把该算法扩展到NURBS自由曲面。 |
| 关 键 词： | 计算机应用 最短距离计算 ULB算法 拟牛顿迭代法 B样条 |
| 文章编号： | 1003-0158（2006）01-0082-05 |
| 收稿时间： | 2005-07-28 |
| 修稿时间： | 2005-07-28 |
Minimum Distance Algorithm Based on Free-Form B-Spline Surface Objects |
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| CHEN Guo-zhen,LIU Jing-hua,CHOU Wu-sheng. Minimum Distance Algorithm Based on Free-Form B-Spline Surface Objects[J]. Journal of Engineering Graphics, 2006, 27(1): 82-86 | |
| Authors: | CHEN Guo-zhen LIU Jing-hua CHOU Wu-sheng |
| Affiliation: | 1. Department of Industrial Design, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; 2. Robotics Institute, Beijing University of Aeronautics and Astronautics, Beijing 100083, China |
| Abstract: | An algorithm which can rapidly calculate the minimum distance between two B-spline curves is presented.Firstly,a pair of minimum distance points between two control polyhedron of NUBS curves is calculated by using ULB algorithm.The line connecting the pair of points is regarded as the direction of minimum distance vector.Then two extreme points are calculated on the vector using hill-climbing method and the two extreme points are regarded as initial values of Quasi Newton iterative method to resolute non-linear equations.This algorithm can greatly reduce the times of iterative and rapidly gain the precise values.Finally the algorithm is extended to NURBS surfaces. |
| Keywords: | computer application minimum distance calculation ULB algorithm Quasi-Newton iterative method B-spline |
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