Studying cyclides with Laguerre geometry

Abstract We develop a theory of Dupin cyclides (including natural quadrics) using associated isotropic hypersurfaces and their control points in the 4-dimensional cyclographic model of Laguerre geometry. In the framework of this approach the classification of cyclides and their parametric and implicit equations are easily re-derived. These results enable us to detect in a constructive way all cases of G 1 -continuous compositions of cyclide patches along rational quadratic, cubic and quartic curves.