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Bounded Curvature Subdivision Without Eigenanalysis

  • Malcolm A. Sabin
  • Thomas J. Cashman
  • Ursula H. Augsdorfer
  • Neil A. Dodgson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4647)

Abstract

It has long been known how to achieve bounded curvature at extraordinary points of a subdivision scheme by using eigenanalysis and then adjusting the mask of each extraordinary point. This paper provides an alternative insight, based on the use of second divided differences, and applies it to three familiar schemes. A single concept is shown to work in three different contexts. In each case a bounded curvature variant results, with a very simple and elegant implementation.

Keywords

Fourier Component Subdivision Scheme Regular Case Dominant Eigenvalue Subdivision Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Malcolm A. Sabin
    • 1
  • Thomas J. Cashman
    • 2
  • Ursula H. Augsdorfer
    • 2
  • Neil A. Dodgson
    • 2
  1. 1.Numerical Geometry Ltd.UK
  2. 2.Computer Laboratory, University of Cambridge, CB3 0FDUK

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