## Abstract

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form {Mathematical expression} The convergence of the control polygons to a C° curve is analysed in terms of the convergence to zero of a derived scheme for the differences f_{i+1}^{k}-f_{i}^{k}. The analysis of the smoothness of the limit curve is reduced to the convergence analysis of "differentiated" schemes which correspond to divided differences of f_{i}^{k}:i∈ Z with respect to the diadic parametrization t_{i}^{k}=i/2^{k}. The inverse process of "integration" provides schemes with limit curves having additional orders of smoothness.

Original language | English |
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Pages (from-to) | 127-147 |

Number of pages | 21 |

Journal | Constructive Approximation |

Volume | 7 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1991 |

## Keywords

- AMS classification: 41A15, 65Q05, 68U05, 65D10
- Control polygon
- Curve design
- Limit curve
- Subdivision scheme