Canal surfaces defined by quadratic families of spheres

Abstract

This paper is devoted to quadratic canal surfaces, i.e. surfaces that are envelopes of quadratic families of spheres. They are generalizations of Dupin cyclides but are more flexible as blending surfaces between natural quadrics. The classification of quadratic canal surfaces is given from the point of view of Laguerre geometry. Their properties that are important for geometric modeling are studied: rational parametrizations of minimal degree, Bézier representations, and implicit equations. © 2008 Springer-Verlag Berlin Heidelberg.