### Abstract

Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness conditions known from the literature are discussed. In order to allow a simpler construction of suitable nonlinear Hermite subdivision schemes, these conditions are posed as assumptions. For linear Hermite subdivision, explicit schemes that satisfy sufficient conditions for $C^2$-convergence are constructed. This leads to larger classes of $C^2$ schemes than known from the literature. Finally, convexity preserving Hermite-interpolatory subdivision is examined, and some explicit rational schemes that generate $C^1$ limit functions are presented.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | Universiteit Twente |

Number of pages | 17 |

Publication status | Published - 1998 |

### Publication series

Name | Memorandum Faculteit TW |
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Publisher | Universiteit Twente |

No. | 1461 |

### Keywords

- MSC-41A05
- MSC-65D05
- stationary linear subdivision
- Stationary non-linear subdivision
- MSC-65D17
- Hermite interpolation
- Convexity preservation
- IR-30467
- METIS-141107
- MSC-41A29
- EWI-3281

## Cite this

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

*Hermite-interpolatory subdivision schemes*. (Memorandum Faculteit TW; No. 1461). Enschede: Universiteit Twente.