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 [UMR6303]
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.
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Conference papers
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00785317
Contributor : Lionel Garnier <>
Submitted on : Tuesday, February 5, 2013 - 7:19:38 PM
Last modification on : Wednesday, September 12, 2018 - 1:27:46 AM

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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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