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, vol.419, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 419
  • Publication Date: 2023
  • Doi Number: 10.1016/j.cam.2022.114782
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: 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
  • Keywords: Projective equivalences, Projective symmetries, Rational 3D curves, Differential invariants, ALGEBRAIC-CURVES, PLANE
  • Karadeniz Technical University Affiliated: Yes

Abstract

© 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.