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In this paper we give an elementary proof of the convergence of cornercutting algorithms refining points, in case the corner cutting weights aretaken 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 theconvergence of corner cutting algorithms refining nets of functions, in casethe corner cutting weights are taken from a stricter class of weights than inthe refinement of points.

Convergence analysis of corner cutting algorithms refining points and refining nets of functions