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Advances in Computational Mathematics

, Volume 27, Issue 4, pp 375–400 | Cite as

A non-linear circle-preserving subdivision scheme

  • Pavel ChalmovianskýEmail author
  • Bert Jüttler
Article

We describe a new method for constructing a sequence of refined polygons, which starts with a sequence of points and associated normals. The newly generated points are sampled from circles which approximate adjacent points and the corresponding normals. By iterating the refinement procedure, we get a limit curve interpolating the data. We show that the limit curve is \(G^1\), and that it reproduces circles. The method is invariant with respect to group of Euclidean similarities (including rigid transformations and scaling). We also discuss an experimental setup for a \(G^2\) construction and various possible extensions of the method.

Keywords

subdivision techniques fitting of algebraic curves 

Mathematics subject classification (2000)

65D17 68U05 53A04 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Johann Radon Institute of Computational and Applied MathematicsAustrian Academy of ScienceLinzAustria
  2. 2.Institute of Applied GeometryJohannes Kepler UniversityLinzAustria

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