Improving the stability bound for the PPH nonlinear subdivision scheme for data coming from strictly convex functions

Abstract

Subdivision schemes are widely used in the generation of curves and surfaces, and therefore they are applied in a variety of interesting applications from geological reconstructions of unaccessible regions to cartoon film productions or car and ship manufacturing. In most cases dealing with a convexity preserving subdivision scheme is needed to accurately reproduce the required surfaces. Stability respect to the initial input data is also crucial in applications. The so called PPH nonlinear subdivision scheme is proven to be both convexity preserving and stable. The tighter the stability bound the better controlled is the final output error. In this article a more accurate stability bound is obtained for the nonlinear PPH subdivision scheme for strictly convex data coming from smooth functions. Numerical experiments are included to show the potential applications of the derived theory.