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Smoothness of subdivision surfaces at extraordinary points

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Abstract

A stationary subdivision scheme such as Catmull and Clark's is described by a matrix iteration around an extraordinary point. We show how higher order smoothness of a limiting surface obtained by a stationary subdivision algorithm for tri- or quadrilateral nets depends on the spectral properties of the matrix and give necessary and sufficient conditions. The results are also useful to construct subdivision algorithms for surfaces of any smoothness order at extraordinary points.

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  1. IBDS, Universität Karlsruhe, D-76128, Karlsruhe, Germany

    Hartmut Prautzsch

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  1. Hartmut Prautzsch
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Prautzsch, H. Smoothness of subdivision surfaces at extraordinary points. Advances in Computational Mathematics 9, 377–389 (1998). https://doi.org/10.1023/A:1018945708536

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