In this paper we develop a method to parameterize tubular surfaces onto the cylinder. The cylinder can be seen
as the natural parameterization domain for tubular surfaces since they share the same topology. Most present
algorithms are designed to parameterize disc-like surfaces onto the plane. Surfaces with a different topology are cut
into disc-like patches and the patches are parameterized separately. This introduces discontinuities and constrains
the parameterization. Also the semantics of the surface are lost. We avoid this by parameterizing tubular surfaces
on, their natural domain, the cylinder. Since the cylinder is locally isometric to the plane we can do calculations
on the cylinder without loosing efficiency. For speeding up the calculation we use a progressive parameterization
technique, as suggested in recent literature. Together, this results in a robust, efficient, continuous, and semantics
preserving parameterization method for arbitrary tubular surfaces