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A smoothness criterion for monotonicity-preserving subdivision

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Abstract

In this paper we study subdivision schemes that both interpolate and preserve the monotonicity of the input data, and we derive a simple ratio condition that guarantees the continuous differentiability of the limit function. We then show that the condition holds for both a scheme of Kuijt and van Damme, based on rational functions, and a scheme of Sabin and Dodgson, based on square roots.

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Authors and Affiliations

  1. Centre of Mathematics for Applications, Department of Informatics, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    M. Floater

  2. Dipartimento di Matematica, Università di Bologna, P.zza di Porta S. Donato 5, 40127, Bologna, Italy

    C. Beccari

  3. University of Cambridge, Cambridge, UK

    T. Cashman

  4. Faculty of Informatics, University of Lugano, Via Giuseppe Buffi 13, 6904, Lugano, Switzerland

    T. Cashman

  5. Dept. of Mathematics and Applications, University of Milano-Bicocca, Via R. Cozzi 53, 20125, Milano, Italy

    L. Romani

Authors
  1. M. Floater
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  2. C. Beccari
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  3. T. Cashman
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  4. L. Romani
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Corresponding author

Correspondence to M. Floater.

Additional information

Communicated by: Raymond H. Chan.

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Floater, M., Beccari, C., Cashman, T. et al. A smoothness criterion for monotonicity-preserving subdivision. Adv Comput Math 39, 193–204 (2013). https://doi.org/10.1007/s10444-012-9275-y

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  • DOI: https://doi.org/10.1007/s10444-012-9275-y

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