  We derive parametrizations of the Delaunay constant mean curvature surfaces
of revolution that follow directly from parametrizations of the conics that
generate these surfaces via the corresponding roulette. This uniform treatment
exploits the natural geometry of the conic (parabolic, elliptic or hyperbolic)
and leads to simple expressions for the mean and Gaussian curvatures of the
surfaces as well as the construction of new surfaces.
