Geodesic
A method for projectively-invariant description of ovals having axial or central symmetry
Informacionnye tehnologii i vyčislitelnye sistemy, no. 2 (2014), pp. 46-59 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a method for projectively-invariant description of ovals (planar convex figures of a continuous curvature) having implicit axial or central symmetry (the Cartesian attributes of which are lost as a result of a projective transformation of the figure). In the discussed numerical model of the method, new objects are used for figure analysis. These objects, which are called dual polar lines, are based on projectively-invariant structures, so-called H- and T-polar lines, earlier proposed by the author. The dual polar lines allow localizing the images of the axis and/or the center of the oval within a single computational procedure. The developed procedures for detecting the symmetry elements of figures are shown to be in conceptual connection with Plucker’s pole-polar duality of conics. The proposed algorithm of searching for implicit elements of symmetry allows building-up a projectively-invariant description of planar figures having no geometric peculiarities except for their hidden symmetry properties (of any of the two types).
Keywords: oval, wurf, polar line, harmonic correspondence.
Mots-clés : projective transformation, tangent line, pole 
@article{ITVS_2014_2_a5,
     author = {P. P. Nikolayev},
     title = {A method for projectively-invariant description of ovals having axial or central symmetry},
     journal = {Informacionnye tehnologii i vy\v{c}islitelnye sistemy},
     pages = {46--59},
     year = {2014},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ITVS_2014_2_a5/}
}
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P. P. Nikolayev. A method for projectively-invariant description of ovals having axial or central symmetry. Informacionnye tehnologii i vyčislitelnye sistemy, no. 2 (2014), pp. 46-59. http://geodesic.mathdoc.fr/item/ITVS_2014_2_a5/