Non-uniform recursive Doo-Sabin surfaces

This paper presents a generalization of Catmull-Clark-variant Doo-Sabin surfaces and non-uniform biquadratic B-spline surfaces called NURDSes (Non-Uniform Recursive Doo-Sabin Surfaces). One step of NURDS refinement can be factored into one non-uniform linear subdivision step plus one dual step. Compared to the prior non-uniform Doo-Sabin surfaces (i.e., quadratic NURSSes), NURDSes are convergent for arbitrary n-sided faces. Closed form limit point rules, which are important for applications in adaptive rendering and NC machining, are given as well.