Parameterization of tubular surfaces on the cylinder

Abstract

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