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Year 2019, Volume: 2 Issue: 2, 129 - 133, 25.11.2019

İdris Ören , Muhsin İncesu

Abstract

References

  • [1] R. P. Encheva and G. H. Georgiev, Similar Frenet curves, Result.Math, 55 (2009), 359-372.
  • [2] D. Khadjiev, İ. Ören, Ö. Pekşen, , Global invariants of path and curves for the group of all linear similarities in the two-dimensional Euclidean space, Int.J.Geo. Modern Phys, 15(6) (2018),1-28.
  • [3] M. İncesu, LS(2)􀀀Equivalence conditions of control points and application to planar Bézier curves, NTMSCI 5(3) (2017), 70-84.
  • [4] M. İncesu, Düzlemsel Bézier e˘grilerinin S(2) denklik ¸sartları, MSU J. of Sci., 5(2) (2018), 471-477.
  • [5] İ. Ören, , Equivalence conditions of two Bézier curves in the Euclidean geometry, Iran J Sci Technol Trans Sci., 42 (2018), 1563-1577.
  • [6] D. Marsh , Applied geometry for computer graphics and CAD, Springer-Verlag, London,1999.
  • [7] M. Berger, Geometry I, Springer-Verlag, Berlin Heidelberg, 1987.
  • [8] WK. Wang, H. Zhang, XM. Liu, JC. Paul, Conditions for coincidence of two cubic Bézier curves, J. Comput. Appl. Math.,235 (2011), 5198-5202 .
  • [9] J. Sanchez-Reyes, On the conditions for the coincidence of two cubic Bézier curves. J. Comput. Appl. Math.,236 (2011), 1675-1677.
  • [10] X.Chen, W. Ma, C. Deng, Conditions for the coincidence of two quartic Bézier curves. Appl Math Comput 225 (2013),731-736 .
  • [11] XD. Chen, C. Yang, W. Ma, Coincidence condition of two Bézier curves of an arbitrary degree, Comput. Graph 54 (2016),121-126 .

Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$

Year 2019, Volume: 2 Issue: 2, 129 - 133, 25.11.2019

İdris Ören , Muhsin İncesu

Abstract

In this paper, for linear similarity groups, global invariants of plane Bezier  curves ( plane polynomial curves) in $E_{2}$ are introduced. Using complex numbers and the global $G$-invariants of a plane Bezier  curve( a plane polynomial curve),  for given two plane Bezier  curves (plane polynomial curves) $x(t)$ and $y(t)$, evident forms of all transformations $g\in G$, carrying $x(t)$ to $y(t)$,  are obtained.

Keywords

Polynomial curve B\'{e}zier curve Invariant Linear similarity group

References

  • [1] R. P. Encheva and G. H. Georgiev, Similar Frenet curves, Result.Math, 55 (2009), 359-372.
  • [2] D. Khadjiev, İ. Ören, Ö. Pekşen, , Global invariants of path and curves for the group of all linear similarities in the two-dimensional Euclidean space, Int.J.Geo. Modern Phys, 15(6) (2018),1-28.
  • [3] M. İncesu, LS(2)􀀀Equivalence conditions of control points and application to planar Bézier curves, NTMSCI 5(3) (2017), 70-84.
  • [4] M. İncesu, Düzlemsel Bézier e˘grilerinin S(2) denklik ¸sartları, MSU J. of Sci., 5(2) (2018), 471-477.
  • [5] İ. Ören, , Equivalence conditions of two Bézier curves in the Euclidean geometry, Iran J Sci Technol Trans Sci., 42 (2018), 1563-1577.
  • [6] D. Marsh , Applied geometry for computer graphics and CAD, Springer-Verlag, London,1999.
  • [7] M. Berger, Geometry I, Springer-Verlag, Berlin Heidelberg, 1987.
  • [8] WK. Wang, H. Zhang, XM. Liu, JC. Paul, Conditions for coincidence of two cubic Bézier curves, J. Comput. Appl. Math.,235 (2011), 5198-5202 .
  • [9] J. Sanchez-Reyes, On the conditions for the coincidence of two cubic Bézier curves. J. Comput. Appl. Math.,236 (2011), 1675-1677.
  • [10] X.Chen, W. Ma, C. Deng, Conditions for the coincidence of two quartic Bézier curves. Appl Math Comput 225 (2013),731-736 .
  • [11] XD. Chen, C. Yang, W. Ma, Coincidence condition of two Bézier curves of an arbitrary degree, Comput. Graph 54 (2016),121-126 .
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

İdris Ören 0000-0003-2716-3945

Muhsin İncesu 0000-0003-2515-9627

Publication Date November 25, 2019
Acceptance Date September 18, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Ören, İ., & İncesu, M. (2019). Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$. Conference Proceedings of Science and Technology, 2(2), 129-133.
AMA Ören İ, İncesu M. Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$. Conference Proceedings of Science and Technology. November 2019;2(2):129-133.
Chicago Ören, İdris, and Muhsin İncesu. “Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$”. Conference Proceedings of Science and Technology 2, no. 2 (November 2019): 129-33.
EndNote Ören İ, İncesu M (November 1, 2019) Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$. Conference Proceedings of Science and Technology 2 2 129–133.
IEEE İ. Ören and M. İncesu, “Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$”, Conference Proceedings of Science and Technology, vol. 2, no. 2, pp. 129–133, 2019.
ISNAD Ören, İdris - İncesu, Muhsin. “Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$”. Conference Proceedings of Science and Technology 2/2 (November 2019), 129-133.
JAMA Ören İ, İncesu M. Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$. Conference Proceedings of Science and Technology. 2019;2:129–133.
MLA Ören, İdris and Muhsin İncesu. “Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$”. Conference Proceedings of Science and Technology, vol. 2, no. 2, 2019, pp. 129-33.
Vancouver Ören İ, İncesu M. Detecting Similarities of Bezier Curves for the Groups $LSim(E_{2}), LSim^{+}( E_{2})$. Conference Proceedings of Science and Technology. 2019;2(2):129-33.
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