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On parametric polynomial circle approximation

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Abstract

In the paper, the uniform approximation of a circle arc (or a whole circle) by a parametric polynomial curve is considered. The approximant is obtained in a closed form. It depends on a parameter that should satisfy a particular equation, and it takes only a couple of tangent method steps to compute it. For low degree curves, the parameter is provided exactly. The distance between a circle arc and its approximant asymptotically decreases faster than exponentially as a function of polynomial degree. Additionally, it is shown that the approximant could be applied for a fast evaluation of trigonometric functions too.

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Authors and Affiliations

  1. FGG and IMFM, University of Ljubljana, Jamova 2, 1000, Ljubljana, Slovenia

    Gašper Jaklič

  2. IAM, University of Primorska, Muzejski trg 2, 6000, Koper, Slovenia

    Gašper Jaklič

  3. FMF and IMFM, University of Ljubljana, Jadranska 21, 1000, Ljubljana, Slovenia

    Jernej Kozak

Authors
  1. Gašper Jaklič
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  2. Jernej Kozak
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Correspondence to Gašper Jaklič.

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Jaklič, G., Kozak, J. On parametric polynomial circle approximation. Numer Algor 77, 433–450 (2018). https://doi.org/10.1007/s11075-017-0322-0

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  • DOI: https://doi.org/10.1007/s11075-017-0322-0

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