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Characterization of covergent subdivision schemes

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Approximation Theory and its Applications

Abstract

Subdivision schemes provide important techniques for the fast generation of curves and surfaces. A recusive refinement of a given control polygon will lead in the limit to a desired visually smooth object. These methods play also an important role in wavelet analysis. In this paper, we use a rather simple way to characterize the convergence of subdivision schemes for multivariate cases. The results will be used to investigate the regularity of the solutions for dilation equations.

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Authors and Affiliations

  1. Department of Mathematics, University of Duisburg, D-47057, Duisburg, Germany

    Zhou Xinlong

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  1. Zhou Xinlong
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Correspondence to Zhou Xinlong.

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Xinlong, Z. Characterization of covergent subdivision schemes. Approx. Theory & its Appl. 14, 11–24 (1998). https://doi.org/10.1007/BF02836764

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  • DOI: https://doi.org/10.1007/BF02836764

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