A subdivision scheme for surfaces of revolution

This paper describes a simple and efficient non-stationary subdivision scheme of order 4. This curve scheme unifies known subdivision rules for cubic B-splines, splines-in-tension and a certain class of trigonometric splines capable of reproducing circles. The curves generated by this unified subdivision scheme are C2 splines whose segments are either polynomial, hyperbolic or trigonometric functions, depending on a single tension parameter. This curve scheme easily generalizes to a surface scheme over quadrilateral meshes. The authors hypothesize that this surface scheme produces limit surfaces that are C2 continuous everywhere except at extraordinary vertices where the surfaces are C1 continuous. In the particular case where the tension parameters are all set to 1, the scheme reproduces a variant of the Catmull–Clark subdivision scheme. As an application, this scheme is used to generate surfaces of revolution from a given profile curve.  2001 Published by Elsevier Science B.V.