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 C 1 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