Computing minimum distance between two implicit algebraic surfaces

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. c 2006 Elsevier Ltd. All rights reserved.

• Type: Journal
• Year: 2006
• Where: CAD
• Authors: Xiao-Diao Chen, Jun-Hai Yong, Guo-Qin Zheng, Jean-Claude Paul, Jia-Guang Sun
• Keywords: CAD 2006, Minimum Distance, Minimum Distance Computation, Surfaces, Theoretical Computer Science