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Computing the minimum distance between two planar algebraic curves

Abstract :  Through geomet ric observation , it is found that the nearest point on a curve is a tangent point between the curve and an off set curve of the other curve. Based on this observation , an off set method is presented for computing the minimum distance between two planar algebraic curves. The new method is geomet rically inst ructive , and can be used for computing the minimum distance between an algebraic curve and a parametric one on the same plane. For planar quadratic curves , the degree of the resulting univariate polynomial equation by our method is much lower than that of the equations in previous comparable methods , which may lead to lower computation complexity or higher robustness of the solutions.
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https://hal.inria.fr/inria-00518427
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  • HAL Id : inria-00518427, version 1

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Xiao-Diao Chen, Jun-Hai Yong, Guozhao Wang. Computing the minimum distance between two planar algebraic curves. Journal of Computer Aided Design & Computer Graphics, Hujun Bao, 2008. ⟨inria-00518427⟩

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