Geodesic
Multifocus lemniscates: Approximation of curves
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 2060-2072

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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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     author = {T. A. Rakcheeva},
     title = {Multifocus lemniscates: {Approximation} of curves},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2060--2072},
     publisher = {mathdoc},
     volume = {50},
     number = {11},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a17/}
}
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T. A. Rakcheeva. Multifocus lemniscates: Approximation of curves. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 2060-2072. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a17/