Department of Applied Mathematics, University of Twente
Abstract
Stationary interpolatory subdivision schemes which preserve shape properties such as convexity or monotonicity are constructed. The schemes are rational in the data and generate limit functions that are at least C2. The emphasis is on a class of six-point convexity preserving subdivision schemes that generate C2 limit functions. In addition, a class of six-point monotonicity preserving schemes that also leads to C2 limit functions is introduced. As the algebra is far too complicated for an analytical proof of smoothness, validation has been performed by a simple numerical methodology