Constructive Approximation

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

Nonlinear Subdivision Schemes on Irregular Meshes

  • Andreas WeinmannEmail author


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.


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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