Global invariants of paths and curves for the group of orthogonal transformations in the two-dimensional Euclidean space


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Khadjiev D., ÖREN İ.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.27, no.2, pp.37-65, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.2478/auom-2019-0018
  • Title of Journal : ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Page Numbers: pp.37-65

Abstract

In this paper, for the orthogonal group G = O(2) and special orthogonal group G = O+ (2) global G-invariants of plane paths and plane curves in two-dimensional Euclidean space E-2 are studied. Using complex numbers, a method to detect G-equivalences of plane paths in terms of the global G-invariants of a plane path is presented. General evident form of a plane path with the given G-invariants are obtained. For given two plane paths x(t) and y(t) with the common G-invariants, evident forms of all transformations g is an element of G, carrying x(t) to y(t), are obtained. Similar results have obtained for plane curves.