A new method to detect projective equivalences and symmetries of rational 3D curves

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GÖZÜTOK U., ÇOBAN H. A., SAĞIROĞLU Y., Alcázar J. G.

Journal of Computational and Applied Mathematics, cilt.419, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 419
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.cam.2022.114782
  • Dergi Adı: Journal of Computational and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Projective equivalences, Projective symmetries, Rational 3D curves, Differential invariants, ALGEBRAIC-CURVES, PLANE
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

© 2022 Elsevier B.V.We present a new approach to detect projective equivalences and symmetries between two rational parametric 3D curves properly parametrized. In order to do this, we introduce two rational functions that behave nicely for Möbius transformations, which are the transformations in the parameter space associated with the projective equivalences between the curves. The Möbius transformations are found by first computing the gcd of two polynomials built from these two functions, and then searching for a special type of factors, “Möbius-like”, of this gcd. The projective equivalences themselves are easily computed from the Möbius transformations. In particular, and unlike previous approaches, we avoid solving big polynomial systems. The algorithm has been implemented in Maple™ (2021), and evidences of its efficiency as well as a comparison with previous approaches are given.