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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 11, Pages 2060–2072 (Mi zvmmf4973)  
This article is cited in 8 scientific papers (total in 8 papers)

Multifocus lemniscates: Approximation of curves

T. A. Rakcheeva

Institute of Engineering Science, Russian Academy of Sciences, Malyi Khariton'evskii per. 4, Moscow, 101990 Russia
Full-text PDF (293 kB) Citations (8)
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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.
Key words: multifocus lemniscates, curves, invariant, approximation by lemniscates, proximity criterion, computational algorithm, interactive lemniscate control.
Received: 07.04.2009
Revised: 05.06.2010
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 11, Pages 1956–1967
DOI: https://doi.org/10.1134/S0965542510110187
Bibliographic databases:
Document Type: Article
UDC: 519.674
Language: Russian
Citation: T. A. Rakcheeva, “Multifocus lemniscates: Approximation of curves”, Zh. Vychisl. Mat. Mat. Fiz., 50:11 (2010), 2060–2072; Comput. Math. Math. Phys., 50:11 (2010), 1956–1967
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:54
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