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Geometry and topology
On approximation of plane curves by conics
A. V. Slovesnov Lomonosov Moscow State University,
1, Leninskie Gory,
Moscow, 119991, Russia
Abstract:
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.
Received April 15, 2018, published December 7, 2018
Citation:
A. V. Slovesnov, “On approximation of plane curves by conics”, Sib. Èlektron. Mat. Izv., 15 (2018), 1576–1594
Linking options:
https://www.mathnet.ru/eng/semr1016 https://www.mathnet.ru/eng/semr/v15/p1576
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