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


Creative Commons License

Khadjiev D., ÖREN İ.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.27, ss.37-65, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 27 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2478/auom-2019-0018
  • Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Sayfa Sayıları: ss.37-65

Özet

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.