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

TL;DR

This paper provides an elementary proof of the convergence of corner cutting algorithms for points and nets of functions, expanding understanding of their behavior with different classes of weights.

Contribution

It introduces a simplified convergence proof for corner cutting algorithms refining points and extends it to nets of functions with stricter weight conditions.

Findings

Convergence proven for point-refining corner cutting algorithms.

Extension of convergence proof to nets of functions.

Applicable to a broader class of weights than previous studies.

Abstract

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.