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Journal Articles Journal of Computational and Applied Mathematics Year : 2009

Computing the minimum distance between two Bézier curves

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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Dates and versions

inria-00518351 , version 1 (17-09-2010)

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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, 2009, 229 (1), pp.194-301. ⟨10.1016/j.cam.2008.10.050⟩. ⟨inria-00518351⟩
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