A symmetric, non-uniform, refine and smooth subdivision algorithm for general degree B-splines

Subdivision surfaces would find a greater number of applications if there was a scheme that included general degree NURBS as a special case. As a step towards such a scheme, we present a univariate refine and smooth subdivision algorithm that applies directly to regular regions of a surface and might, in future work, be generalised to incorporate extraordinary points. The algorithm is symmetric and non-uniform, is defined for general degree, and has similar properties to the uniform Lane-Riesenfeld refine and smooth construction.