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Multifocus lemniscates: Approximation of curves

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Abstract

A focal method for the continuous approximation of smooth closed plane curves is proposed. Multifocus lemniscates are used as the approximating functions. The curve to be approximated is represented by a finite set of foci inside the curve; the number and the location of the foci provide the degrees of freedom for the focal approximation. An algorithmic solution of this problem in various modifications is constructed. Proximity criteria for curves are proposed. A comparative analysis of the approximative capabilities of the focal method with the capabilities of the classical harmonic approximation method is performed.

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Authors and Affiliations

  1. Institute of Engineering Science, Russian Academy of Sciences, Malyi Khariton’evskii per. 4, Moscow, 101990, Russia

    T. A. Rakcheeva

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  1. T. A. Rakcheeva
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Correspondence to T. A. Rakcheeva.

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Original Russian Text © T.A. Rakcheeva, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 11, pp. 2060–2072.

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Rakcheeva, T.A. Multifocus lemniscates: Approximation of curves. Comput. Math. and Math. Phys. 50, 1956–1967 (2010). https://doi.org/10.1134/S0965542510110187

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  • DOI: https://doi.org/10.1134/S0965542510110187

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