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Advances in Applied Clifford Algebras

, Volume 24, Issue 2, pp 515–532 | Cite as

The Non-Degenerate Dupin Cyclides in the Space of Spheres Using Geometric Algebra

  • Lucie Druoton
  • Laurent Fuchs
  • Lionel Garnier
  • Rémi Langevin
Article

Abstract

Dupin cyclides are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century and were introduced in CAD by R. Martin in 1982. A Dupin cyclide can be defined, in two different ways, as the envelope of a oneparameter 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 nondegenerate 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.

Keywords

Dupin cyclide space of spheres Conformal Geometric Algebra 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Lucie Druoton
    • 1
    • 2
    • 3
  • Laurent Fuchs
    • 4
  • Lionel Garnier
    • 3
  • Rémi Langevin
    • 2
  1. 1.C.E.A. DAM, ValducIs Sur TilleFrance
  2. 2.Institut de Mathématique de Bourgogne, UMR CNRS 5584 University of Burgundy, Faculté MirandeDijonFrance
  3. 3.LE2I, UMR CNRS 6306, University of Burgundy, faculté MirandeDijonFrance
  4. 4.XLIM-SIC, UMR CNRS 7252, University of PoitiersFuturoscope ChasseneuilFrance

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