Subdivision surfaces would be useful in a greater number of applications if an arbitrary-degree, non-uniform scheme existed that was a generalisation of NURBS. As a step towards building such a scheme, we investigate non-uniform analogues of the Lane-Riesenfeld 'refine and smooth' subdivision paradigm. We show that the assumptions made in constructing such an analogue are critical, and conclude that Schaefer's global knot insertion algorithm is the most promising route for further investigation in this area.
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