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

Lucie Druoton 1 Laurent Fuchs 2 Lionel Garnier 3 Rémi Langevin 4
1 MGSI
IMB - Institut de Mathématiques de Bourgogne [Dijon], Le2i - Laboratoire Electronique, Informatique et Image
2 XLIM-SIC - SIC
Université de Poitiers, XLIM - XLIM
Abstract : 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.
Type de document :
Communication dans un congrès
AGACSE, Jul 2012, La Rochelle, France
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00785317
Contributeur : Lionel Garnier <>
Soumis le : mardi 5 février 2013 - 19:19:38
Dernière modification le : mardi 6 février 2018 - 15:56:21

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  • 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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