### 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 $C^2$. 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.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | Universiteit Twente |

Number of pages | 18 |

Publication status | Published - 1998 |

### Publication series

Name | Memorandum Faculteit TW |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1452 |

ISSN (Print) | 0169-2690 |

### Keywords

- METIS-141121
- IR-65649
- Convexity
- Shape preservation
- Rational stationary subdivision
- positivity
- MSC-65D15
- EWI-3272
- monotonicity
- smoothness
- MSC-65D07
- MSC-41A15
- MSC-41A29

### Cite this

Kuijt, F., & van Damme, R. M. J. (1998).

*Shape preserving C*. (Memorandum Faculteit TW; No. 1452). Enschede: Universiteit Twente.^{2}interpolatory subdivision schemes