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.