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 $C^2$. The emphasis is on a class of six-point convexity preserving subdivision schemes that generate $C^2$ limit functions. In addition, a class of six-point monotonicity preserving schemes that also leads to $C^2$ 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.
|Place of Publication||Enschede|
|Number of pages||18|
|Publication status||Published - 1998|
|Name||Memorandum Faculteit TW|
|Publisher||Department of Applied Mathematics, University of Twente|
- Shape preservation
- Rational stationary subdivision