Chapter

Mathematics of Surfaces XII

Volume 4647 of the series Lecture Notes in Computer Science pp 391-411

Bounded Curvature Subdivision Without Eigenanalysis

  • Malcolm A. SabinAffiliated withNumerical Geometry Ltd.
  • , Thomas J. CashmanAffiliated withComputer Laboratory, University of Cambridge, CB3 0FD
  • , Ursula H. AugsdorferAffiliated withComputer Laboratory, University of Cambridge, CB3 0FD
  • , Neil A. DodgsonAffiliated withComputer Laboratory, University of Cambridge, CB3 0FD

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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.