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The non-degenerate Dupin cyclides in the space of spheres using Geometric Algebra

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Résumé

Dupin cyclides are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century and \textcolor{black}{were} introduced in CAD by R. Martin in 1982. A Dupin cyclide can be defined, in two different ways, as the envelope of a one-parameter family of oriented spheres. So, it is very interesting to model the Dupin cyclides in the space of spheres, space wherein each family of spheres can be seen as a conic curve. In this paper, we model the non-degenerate Dupin cyclides and the space of spheres using Conformal Geometric Algebra. This new approach permits us to benefit from the advantages of the use of Geometric Algebra.
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Dates et versions

hal-00785317 , version 1 (05-02-2013)

Identifiants

  • HAL Id : hal-00785317 , version 1

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Lucie Druoton, Laurent Fuchs, Lionel Garnier, Rémi Langevin. The non-degenerate Dupin cyclides in the space of spheres using Geometric Algebra. AGACSE, Jul 2012, La Rochelle, France. ⟨hal-00785317⟩
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