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arXiv · 1806.06805

Classification of the relative positions between an ellipsoid and an elliptic paraboloid

Miguel Brozos-Vázquez·María José Pereira-Sáez·María José Souto-Salorio·Ana D. Tarrío-Tobar
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Abstract

We classify all the relative positions between an ellipsoid and an elliptic paraboloid when the ellipsoid is small in comparison with the paraboloid ({\it small} meaning that the ellipsoid cannot be tangent to the paraboloid at two points simultaneously). This provides an easy way to detect contact between the two surfaces by a direct analysis of the coefficients of a fourth degree polynomial.

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Miguel Brozos-Vázquez, María José Pereira-Sáez, María José Souto-Salorio, Ana D. Tarrío-Tobar. 2018-06-14. Classification of the relative positions between an ellipsoid and an elliptic paraboloid. https://arxiv.org/abs/1806.06805

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