Abstract
The use of mass points eases the definition of a branch of a hyperbola in the Euclidean plane based on a Rational Quadratic Bézier Curve. In the space of spheres, any circular cone, circular cylinder, torus, pencil of spheres or Dupin cyclide is represented by a rational quadratic Bézier curve that is conic arc seen as circle arc. The limit points of the Poncelet pencil or the singular points of the Dupin cyclide can be determined using the asymptotes of this circle. This article shows that the use of mass points simplifies the modelling of these pencils or these Dupin cyclides in the space of spheres. The determination of the Dandelin spheres ends this work as an application.
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