The subdivision algorithm for generating curves and its properties (Q1335410)

The authors study properties of subdivision algorithms for Bézier splines following the general scheme \(p_{2j}^{l+1}=\sum a_ k p_{j-k}^ l\), \(p_{2j+1}^{l+1}=\sum b_ k p_{j-k}^ l\). The nontrivial properties studied are convexity preservation, polynomial reproduction, convergence, and order of continuity. The last two criteria, derived by Fourier methods, seem to be rather complicated for practical use.