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

Lucie Druoton (1, 2, 3) , Laurent Fuchs (4) , Lionel Garnier (2) , Rémi Langevin (3)

1 DAM/VALDUC - VALDUC
2 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]
4 XLIM-SIC - SIC

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.

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

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⟩