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

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Atıf İçin Kopyala

Khadjiev D., ÖREN İ.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.27, sa.2, ss.37-65, 2019 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 27 Sayı: 2
• Basım Tarihi: 2019
• Doi Numarası: 10.2478/auom-2019-0018
• Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.37-65
• Anahtar Kelimeler: Curve, Invariant, Euclidean geometry, DIFFERENTIAL INVARIANTS, COMPLETE SYSTEMS
• Karadeniz Teknik Üniversitesi Adresli: Evet

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.