General cyclides Original Research Article

In this paper we consider the problem of joining circles with prescribed tangencies, i.e., along given cones or spheres. The joining surfaces are envelopes of quadratic 1-parameter families of spheres which generalize the family of Dupin cyclides, but still their algebraic degree is four. They are represented with conics in 4-space. Given a conic in Bézier form the implicit equation of the corresponding surface is exhibited.