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 C^2 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 C^2 continuous everywhere except at extraordinary vertices where the surfaces are C^1 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.

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