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Points massiques, espace des sphères et « hyperbole »

Abstract : The use of massic points permits to define a branch of a hyperbola in the Euclidean plane using a Rational Quadratic Bézier Curve. In the space of spheres, a circular cone, a circular cylinder, a torus, a pencil of spheres or a Dupin cyclide is represented by a conic. If the kind of the pencil is Poncelet or if the canal surface is a circular cone, a spindle torus, a spindle or a horned Dupin cyclide, the curve is a circle which is seen as a hyperbole. The limit points of the pencil or the singular points of the Dupin cyclide can be determined using the asymptotes of this circle. In this article, we show that the use of massic points simplifies the modelization of these pencils or these Dupin cyclides in the space of spheres.
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Lionel Garnier, Lucie Druoton, Jean-Paul Becar. Points massiques, espace des sphères et « hyperbole ». Journées du Groupe de Travail en Modélisation Géométrique 2015, 2015, POITIERS, France. ⟨hal-02513124⟩

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