Adjustable speed surface subdivision

We introduce a non-uniform subdivision algorithm that partitions the neighborhood of an extraordinary point in the ratio σ:1−σ, where σ(0,1). We call σ the speed of the non-uniform subdivision and verify C¹ continuity of the limit surface. For σ=1/2, the Catmull–Clark limit surface is recovered. Other speeds are useful to vary the relative width of the polynomial spline rings generated from extraordinary nodes.