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Computing minimum distance between two implicit algebraic surfaces

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.
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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, 38 (10), pp.1053-1061. ⟨10.1016/j.cad.2006.04.012⟩. ⟨inria-00518397⟩

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