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The Importance of Polynomial Reproduction in Piecewise-Uniform Subdivision

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Mathematics of Surfaces XI

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3604))

Abstract

We survey a number of related methods, which have been published by the author and collaborators, in the field of subdivision schemes for curves and surfaces. The theory presented in these works relies mainly on the notion of polynomial reproduction, i.e. the ability of a scheme to reproduce all polynomials up to a certain degree as limit functions. We demonstrate that the study of polynomial reproduction is central to smoothness analysis and to approximation. In particular, we show how to exploit polynomial reproduction in the context of piecewise-uniform stationary subdivision. The applications include boundary treatments for subdivision surfaces, interpolation of curves by surfaces, subdivision stencils around extraordinary vertices (construction of C 2 schemes), as well as schemes that involve different kinds of grids (triangular / quadrilateral).

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Author information

Authors and Affiliations

  1. Cadent Ltd, Hata’asiya 17, Or-Yehuda, Israel

    Adi Levin

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  1. Adi Levin
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Editor information

Editors and Affiliations

  1. School of Computer Science, Cardiff University, Cardiff, UK

    Ralph Martin

  2. Department of Computer Science, Loughborough University, LE11 3TU, Leicestershire, UK

    Helmut Bez

  3. Numerical Geometry Ltd., UK

    Malcolm Sabin

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© 2005 Springer-Verlag Berlin Heidelberg

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Levin, A. (2005). The Importance of Polynomial Reproduction in Piecewise-Uniform Subdivision. In: Martin, R., Bez, H., Sabin, M. (eds) Mathematics of Surfaces XI. Lecture Notes in Computer Science, vol 3604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537908_17

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  • DOI: https://doi.org/10.1007/11537908_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28225-9

  • Online ISBN: 978-3-540-31835-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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