• 1987 (Vol.1)

Recognition of projectively transformed planar figures. XV. Methods for searching for axes and centers of ovals with symmetries, using a set of dual pairs of cevian triads

© 2021 P. P. Nikolaev

Institute for Information Transmission Problems “Kharkevich Institute” RAS, 127994 Moscow, Bolshoy Karetny per., 19, Russia
Smart Engines Service LLC, 117312 Moscow, Prospect 60-Letiya Oktyabrya, 9, Russia

Received 02 Nov 2020

A number of new enumeration-type procedures for searching symmetry elements of oval curves (their axes or centers) are suggested and modelled, which are based on alternative methods involving one of the two projectively invariant structures on the figure field: a set of so-called dual pairs (DP) or a cevian triad (CT) having the property of their intersection at the common interior point c of the oval (o). In this paper, each of the two DPs is specified on a Plucker polar curve determined by its external pole P, for the position of which conditions are formulated that are satisfied in the enumeration scheme, according to the properties of P to belong either the symmetry axis of o or a chord intersecting the desired center of o (for the cases of radial or rotational symmetry of an odd index). Similarly, CTs with the node c are used when searching for the positions of projectively symmetric pairs of points of the contour o, which, when iterating over the vertices, satisfy certain relations that are valid for the central (two kinds) or axial structure of o.

Key words: oval, center and axis of symmetry, Plucker pole and polar curve, dual pairs, harmonic wurf, wurf function, projectively invariant W-mapping, cevian

DOI: 10.31857/S0235009221010054

Cite: Nikolaev P. P. Raspoznavanie proektivno preobrazovannykh ploskikh figur. xv. metody poiska osei i tsentrov ovalov s simmetriyami, ispolzuyushchie set dualnykh par libo triady chevian [Recognition of projectively transformed planar figures. xv. methods for searching for axes and centers of ovals with symmetries, using a set of dual pairs of cevian triads]. Sensornye sistemy [Sensory systems]. 2021. V. 35(1). P. 55–78 (in Russian). doi: 10.31857/S0235009221010054

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