Convergence analysis of corner cutting algorithms refining points and refining nets of functions
Theoretical contribution for researchers in geometric modeling and subdivision surfaces, but incremental as it extends existing convergence proofs.
The paper provides an elementary proof of convergence for corner cutting algorithms refining points under general weights, and extends the proof to nets of functions under stricter weight conditions.
In this paper we give an elementary proof of the convergence of corner cutting algorithms refining points, in case the corner cutting weights are taken from the rather general class of weights considered by Gregory and Qu (1996). We then use similar ideas, adapted to nets of functions, to prove the convergence of corner cutting algorithms refining nets of functions, in case the corner cutting weights are taken from a stricter class of weights than in the refinement of points.