6533b826fe1ef96bd1283cdc
RESEARCH PRODUCT
The non-degenerate Dupin cyclides in the space of spheres using Geometric Algebra
Lucie DruotonLionel GarnierRémi LangevinLaurent Fuchssubject
[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]Dupin cyclideDupin cyclide[INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR]010103 numerical & computational mathematics02 engineering and technologySpace (mathematics)[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]01 natural sciencesGeometric algebra[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]space of spheresAlgebraic surface0202 electrical engineering electronic engineering information engineering0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsconformal geometric algebraApplied MathematicsDegenerate energy levelsConformal geometric algebra020207 software engineering[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR][INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]AlgebraConic section[ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG]SPHERESdescription
International audience; 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-07-04 |