Computing minimum distance between two implicit algebraic surfaces

✍ Scribed by Xiao-Diao Chen; Jun-Hai Yong; Guo-Qin Zheng; Jean-Claude Paul; Jia-Guang Sun

• Book ID: 104006402
• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 932 KB
• Volume: 38
• Category: Article
• ISSN: 0010-4485
• DOI: 10.1016/j.cad.2006.04.012

✦ Synopsis

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.