Calculating the minimum distance between two NURBS curves
A novel method is proposed to compute the minimum distance between two 2D or 3D NURBS curves using control polygons in an efficient and robust way. The first step is to decompose both of NURBS curves into their piecewise Bzier forms. The second step is to use a two level selection process to select a subset of all possible pairs. The first level selection uses upper-lower bounding boxes of Bzier subcurves to remove pairs. The second level selection is based on the spatial relationship test between a pair of Bzier subcurves. The third step is to use a multidimensional Newton-Raphson method to compute the approximate local minimum distances of pairs of Bzier subeurves. By comparing all local minimum distances between a pair of Bzier subcurves, it is able to find the global minimum distance. The final step is to use the multidimensional Newton-Raphson method to improve the accuracy.
Minimum Distance Control Polygon NURBS Curve Newton-raphson Method
Ping He Caiming Zhang Jingbo Zhou Yingliang Ma
School of Computer Science and Technology Shandong University Jinan, PR China
国际会议
温州
英文
643-648
2009-11-26（万方平台首次上网日期，不代表论文的发表时间）