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Computing the minimum distance between two Bézier curves

Xiao-Diao Chen 1 Linqiang Chen 2 Yigang Wang 2 Gang Xu 2 Jun-Hai Yong 1, 3 Jean-Claude Paul 3, 1
3 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : A sweeping sphere clipping method is presented for computing the minimum distance between two Bézier curves. The sweeping sphere is constructed by rolling a sphere with its center point along a curve. The initial radius of the sweeping sphere can be set as the minimum distance between an end point and the other curve. The nearest point on a curve must be contained in the sweeping sphere along the other curve, and all of the parts outside the sweeping sphere can be eliminated. A simple sufficient condition when the nearest point is one of the two end points of a curve is provided, which turns the curve/curve case into a point/curve case and leads to higher efficiency. Examples are shown to illustrate efficiency and robustness of the new method.
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Xiao-Diao Chen, Linqiang Chen, Yigang Wang, Gang Xu, Jun-Hai Yong, et al.. Computing the minimum distance between two Bézier curves. Journal of Computational and Applied Mathematics, Elsevier, 2009, 229 (1), pp.194-301. ⟨10.1016/j.cam.2008.10.050⟩. ⟨inria-00518351⟩

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