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

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.