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Numerical Checking of C 1 for Arbitrary Degree Quadrilateral Subdivision Schemes

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Mathematics of Surfaces XIII (Mathematics of Surfaces 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5654))

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Abstract

We derive a numerical method to confirm that a subdivision scheme based on quadrilateral meshes is C 1 at the extraordinary points. We base our work on Theorem 5.25 in Peters and Reif’s book “Subdivision Surfaces”, which expresses it as a condition on the derivatives within the characteristic ring around the EV. This note identifies instead a sufficient condition on the control points in the natural configuration from which the conditions of Theorem 5.25 can be established.

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Author information

Authors and Affiliations

  1. The Computer Laboratory, University of Cambridge, UK

    U. H. Augsdörfer, T. J. Cashman & N. A. Dodgson

  2. Numerical Geometry Ltd., UK

    M. A. Sabin

Authors
  1. U. H. Augsdörfer
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  2. T. J. Cashman
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  3. N. A. Dodgson
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  4. M. A. Sabin
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Editor information

Editors and Affiliations

  1. Computer Vision and Pattern Recognition Group,Computer Science, University of York Heslington, YO10-5DD, York, United Kingdom

    Edwin R. Hancock

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

    Ralph R. Martin

  3. Numerical Geometry Ltd, 26 Abbey Lane, Lode, CB5 9EP, Cambridge, UK

    Malcolm A. Sabin

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© 2009 Springer-Verlag Berlin Heidelberg

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Augsdörfer, U.H., Cashman, T.J., Dodgson, N.A., Sabin, M.A. (2009). Numerical Checking of C 1 for Arbitrary Degree Quadrilateral Subdivision Schemes. In: Hancock, E.R., Martin, R.R., Sabin, M.A. (eds) Mathematics of Surfaces XIII. Mathematics of Surfaces 2009. Lecture Notes in Computer Science, vol 5654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03596-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-03596-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03595-1

  • Online ISBN: 978-3-642-03596-8

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