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

06/14/2018

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by   Miguel Brozos-Vázquez, et al.

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We classify all the relative positions between an ellipsoid and an elliptic paraboloid when the ellipsoid is small in comparison with the paraboloid ( 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.