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Approximation by planar elastic curves

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Abstract

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient-driven optimization is then used to find the approximating elastic curve.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet, Building 303 B, DK-2800 Kgs., Lyngby, Denmark

    David Brander, Jens Gravesen & Toke Bjerge Nørbjerg

Authors
  1. David Brander
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  2. Jens Gravesen
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  3. Toke Bjerge Nørbjerg
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Correspondence to David Brander.

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Communicated by: Helmut Pottmann.

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Brander, D., Gravesen, J. & Nørbjerg, T.B. Approximation by planar elastic curves. Adv Comput Math 43, 25–43 (2017). https://doi.org/10.1007/s10444-016-9474-z

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  • DOI: https://doi.org/10.1007/s10444-016-9474-z

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