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Taylorian fields and subdivision algorithms

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Abstract

Some recents papers [3,8] provide a new approach for the concept of subdivision algorithms, widely used in CAGD: they develop the idea of interpolatory subdivision schemes for curves. In this paper, we show how the old results of H. Whitney [13,14] on Taylorian fields giving necessary and sufficient conditions for a function to be of classC k on a compact provide also necessary and sufficient conditions which can be used to construct interpolatory subdivision schemes, in order to obtain, at the limit, aC 1 (orC k,k>1 eventually) function. Moreover, we give general results for the approximation properties of these schemes, and error bounds for the approximation of a given function.

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique et d'Optimisation, Université de Lille 1 Flandres-Artois, 59655, Villeneuve d'Ascq Cedex, France

    A. Le Méhauté

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  1. A. Le Méhauté
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Communicated by M. Gasca

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Le Méhauté, A. Taylorian fields and subdivision algorithms. Numer Algor 1, 225–235 (1991). https://doi.org/10.1007/BF02142324

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  • DOI: https://doi.org/10.1007/BF02142324

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