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Constructive Approximation

, Volume 31, Issue 3, pp 395–415 | Cite as

Nonlinear Subdivision Schemes on Irregular Meshes

  • Andreas WeinmannEmail author
Article

Abstract

The present article deals with convergence and smoothness analysis of geometric, nonlinear subdivision schemes in the presence of extraordinary points. We discuss when the existence of a proximity condition between a linear scheme and its nonlinear analogue implies convergence of the nonlinear scheme (for dense enough input data). Furthermore, we obtain C 1 smoothness of the nonlinear limit function in the vicinity of an extraordinary point over Reif’s characteristic parametrization. The results apply to the geometric analogues of well-known subdivision schemes such as Doo–Sabin or Catmull–Clark schemes.

Keywords

Nonlinear subdivision Extraordinary point Irregular mesh 

Mathematics Subject Classification (2000)

65D17 68U05 53A99 58C07 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of GeometryTU GrazGrazAustria

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