Geodesic
On approximation of plane curves by conics
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1576-1594

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This paper presents methods for a plane curve approximation by conics. The paper is divided into two parts: 1) approximation methods for fixed ends and fixed angles conditions 2) local curve approximation at a point. In the first part, for a given arc of a plane curve with monotonic curvature, we construct a conic approximation of the same length and give a criterion for the type of this conic. In the second part, we investigate the osculating conic and obtain formulae for its geometric parameters. We also derive the characteristic differential equation for conics and derive the necessary and sufficient condition on conic's type.
Keywords: Plane curve approximation, osculating conics. 
@article{SEMR_2018_15_a54,
     author = {A. V. Slovesnov},
     title = {On approximation of plane curves by conics},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1576--1594},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a54/}
}
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A. V. Slovesnov. On approximation of plane curves by conics. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1576-1594. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a54/