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A non-linear circle-preserving subdivision scheme

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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.

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Authors and Affiliations

  1. Johann Radon Institute of Computational and Applied Mathematics, Austrian Academy of Science, Linz, Austria

    Pavel Chalmovianský

  2. Institute of Applied Geometry, Johannes Kepler University, Linz, Austria

    Bert Jüttler

Authors
  1. Pavel Chalmovianský
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  2. Bert Jüttler
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Correspondence to Pavel Chalmovianský.

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Communicated by Tomas Sauer

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Chalmovianský, P., Jüttler, B. A non-linear circle-preserving subdivision scheme. Adv Comput Math 27, 375–400 (2007). https://doi.org/10.1007/s10444-005-9011-y

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  • DOI: https://doi.org/10.1007/s10444-005-9011-y

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