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Computing the minimum distance between a point and a clamped B-spline surface

Xiao-Diao Chen 1, 2 Gang Xu 2, 3 Jun-Hai Yong 1, 4 Guozhao Wang 3 Jean-Claude Paul 1, 4 
1 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : The computation of the minimum distance between a point and a surface is important for the applications such as CAD/CAM, NC verification, robotics and computer graphics. This paper presents a spherical clipping method to compute the minimum distance between a point and a clamped B-spline surface. The surface patches outside the clipping sphere which do not contain the nearest point are eliminated. Another exclusion criterion whether the nearest point is on the boundary curves of the surface is employed, which is proved to be superior to previous comparable criteria. Examples are also shown to illustrate efficiency and correctness of the new method.
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Xiao-Diao Chen, Gang Xu, Jun-Hai Yong, Guozhao Wang, Jean-Claude Paul. Computing the minimum distance between a point and a clamped B-spline surface. Graphical Models, Elsevier, 2009, 71 (3), pp.107-112. ⟨10.1016/j.gmod.2009.01.001⟩. ⟨inria-00518353⟩

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