Computing the minimum distance between a point and a NURBS curve

Xiao-Diao Chen (1, 2) , Jun-Hai Yong (3) , Guozhao Wang (4, 5) , Jean-Claude Paul (2, 3) , Gang Xu (1, 4, 5)

1 HDU - Hangzhou Dianzi University
2 CAD - Computer Aided Design
3 THSS - School of Software
4 Department of Mathematics [Hangzhou]
5 Institute of Computer Graphics and Image Processing

A new method is presented for computing the minimum distance between a point and a NURBS curve. It utilizes a circular clipping technique to eliminate the curve parts outside a circle with the test point as its center point. The radius of the elimination circle becomes smaller and smaller during the subdivision process. A simple condition for terminating the subdivision process is provided, which leads to very few subdivision steps in the new method. Examples are shown to illustrate the efficiency and robustness of the new method.

Domaines: Géométrie algorithmique [cs.CG]

Xiao-Diao Chen, Jun-Hai Yong, Guozhao Wang, Jean-Claude Paul, Gang Xu. Computing the minimum distance between a point and a NURBS curve. Computer-Aided Design, 2008, 40 (10-11), pp.1051-1054. ⟨10.1016/j.cad.2008.06.008⟩. ⟨inria-00518359⟩