SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2020 / Volume: 69 Issue: 2

Recognition of complex polynomial Bezier curves under similarity transformations

İdris Ören(KARADENİZ TEKNİK ÜNİVERSİTESİ)0000-0003-2716-3945
Muhsin İncesu(MUŞ ALPARSLAN ÜNİVERSİTESİ)0000-0003-2515-9627
Pages
—
Publication Date
2020-12-31
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, in case two polynomial curve (complex Bezier curve) are similar for the similarity group, a general form of all similarity transformations, carrying one curve into the other curve, are obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, similarity groups in the complex plane C, polynomial curves and complex Bezier curves in C are introduced.
📊
Key Findings & Data:Global similarity invariants of polynomial curves and complex Bezier curves in C are given in terms of complex functions.
💡
Conclusion & Impact:Moreover, in case two polynomial curve (complex Bezier curve) are similar for the similarity group, a general form of all similarity transformations, carrying one curve into the other curve, are obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bezier curve · Invariant · similarity

Abstract

In this paper, similarity groups in the complex plane C, polynomial curves and complex Bezier curves in C are introduced. Global similarity invariants of polynomial curves and complex Bezier curves in C are given in terms of complex functions. The problem of similarity of two polynomial curves in C are solved. Moreover, in case two polynomial curve (complex Bezier curve) are similar for the similarity group, a general form of all similarity transformations, carrying one curve into the other curve, are obtained.

🔖

Cite This Article

Ören, İ., İncesu, M. (2020). Recognition of complex polynomial Bezier curves under similarity transformations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 2. https://doi.org/10.31801/cfsuasmas.692608

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (27)

  1. Zhang, C., Du, S., Liu, J.,Li, Y., Xue,J., Liu, Y., Robust iterative closest point algorithm with bounded rotation angle for 2D registration, Neurocomputing, 195(2016),172-180.
  2. Besl, P. J., McKay, N. D., A method for registration of 3-D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2) (1992), 239-256.
  3. Du, S., Zheng, N., Ying, S., Liu, J., Affine iterative closest point algorithm for point set registration, Pattern Recognition Letters, 31(2010),791-799.
  4. Chen, H., Zhang, X., Du, S., Wu, Z., Zheng, N., A Correntropy-based affine iterative closest point algorithm for robust point set registration, IEEE/CAA J. Autom. Sin., 6 (4) (2019), 981-991.
  5. Weiss, I., Geometric invariants and object recognition, J. Math. Imaging Vision, 10 (3) (1993), 201-231.
  6. Sanchez-Reyes, J., Complex rational Bézier curves, Comput. Aided Geom. Design, 26(8) (2009), 865-876.
  7. Tsianos, K. I., Goldman, R., Bézier and B-spline curves with knots in the complex plane, Fractals, 19(1) (2011), 67-86.
  8. Ait-Haddou, R., Herzog, W., Nomura, T., Complex Bézier curves and the geometry of polygons, Comput. Aided Geom. Design, 27(7) (2010), 525-537.
  9. Ören, İ., On the control invariants of planar Bézier curves for the groups M(2) and SM(2), Turk. J. Math. Comput. Sci.,10 (2018), 74-81.
  10. Khadjiev, D., Ören, İ., Pekşen,Ö., Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space, Int. J. Geom. Methods Mod. Phys., 15(6)(2018), 1-28.
  11. Alcazar, J. G., Hermoso, C., Muntingh, G., Detecting similarity of rational plane curves, J. Comput. Appl. Math., 269 (2014), 1-13.
  12. Alcazar, J. G., Hermoso, C,, Muntingh, G., Similarity detection of rational space curves, J. Symbolic Comput., 85 (2018), 4-24.
  13. Alcazar, J. G., Gema, M. Diaz-Toca, Hermoso, C., On the problem of detecting when two implicit plane algebraic curves are similar, Internat. J. Algebra Comput, 29 (5) (2019),775-793.
  14. Hauer, M., Jüttler, B., Detecting affine equivalences of planar rational curves, EuroCG 2016, Lugano, Switzerland, March 30-April 1, 2016.
  15. Ören, İ., Equivalence conditions of two Bézier curves in the Euclidean geometry, Iran J Sci Technol Trans Sci, 42(3) (2016),1563-1577.
  16. Reyes, J. S., Detecting symmetries in polynomial Bézier curves,J. Comput. Appl. Math., 288 (2015), 274-283.
  17. Mozo-Fernandez, J., Munuera, C., Recognition of polynomial plane curves under affine transformations, AAECC, 13 (2002), 121-136.
  18. Gürsoy, O., İncesu,., LS(2)-Equivalence conditions of control points and application to planar Bézier curves, New Trends in Mathematical Science, 3 (2017), 70-84.
  19. Bez, H.E., Generalized invariant-geometry conditions for the rational Bézier paths, Int J Comput Math, 87 (2010), 793-811.
  20. Encheva, R. P., Georgiev, G. H., Similar Frenet curves, Result. Math, 55 (2009), 359-372.
  21. Khadjiev, D., Ören, İ., Global invariants of paths and curves for the group of orthogonal transformations in the two-dimensional Euclidean space, An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat., 27(2) (2019), 37-65.
  22. Marsh, D., Applied Geometry For Computer Graphics and CAD, Springer-Verlag, London,1999.
  23. Berger, M., Geometry I, Springer-Verlag, Berlin, Heidelberg, 1987.
  24. Zhang, C., Du, S., Liu, J.,Li, Y., Xue,J., Liu, Y., Robust iterative closest point algorithm with bounded rotation angle for 2D registration, Neurocomputing, 195(2016),172-180.
  25. Weiss, I., Geometric invariants and object recognition, J. Math. Imaging Vision, 10 (3) (1993), 201-231.
  26. Gürsoy, O., İncesu,., LS(2)-Equivalence conditions of control points and application to planar Bézier curves, New Trends in Mathematical Science, 3 (2017), 70-84.
  27. Bez, H.E., Generalized invariant-geometry conditions for the rational Bézier paths, Int J Comput Math, 87 (2010), 793-811.