HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Computing minimum distance between two implicit algebraic surfaces

Xiao-Diao Chen 1 Jun-Hai Yong 1 Guo-Qin Zheng 1 Jean-Claude Paul 1 Jia-Guang Sun 1
1 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : The minimum distance computation problem between two surfaces is very important in many applications such as robotics, CAD/CAM and computer graphics. Given two implicit algebraic surfaces, a new method based on the offset technique is presented to compute the minimum distance and a pair of points where the minimum distance occurs. The new method also works where there are an implicit algebraic surface and a parametric surface. Quadric surfaces, tori and canal surfaces are used to demonstrate our new method. When the two surfaces are a general quadric surface and a surface which is a cylinder, a cone or an elliptic paraboloid, the new method can produce two bivariate equations where the degrees are lower than those of any existing method.
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/inria-00124255
Contributor : Chine Publications Liama Connect in order to contact the contributor
Submitted on : Friday, January 12, 2007 - 4:52:50 PM
Last modification on : Friday, February 4, 2022 - 3:10:20 AM

Links full text

Identifiers

Collections

Citation

Xiao-Diao Chen, Jun-Hai Yong, Guo-Qin Zheng, Jean-Claude Paul, Jia-Guang Sun. Computing minimum distance between two implicit algebraic surfaces. Computer-Aided Design, Elsevier, 2006, Computer-Aided Design, 38 (10), pp.1053--1061. ⟨10.1016/j.cad.2006.04.012⟩. ⟨inria-00124255⟩

Share

Metrics

Record views

121