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Year 2021, , 245 - 250, 01.12.2021
https://doi.org/10.33401/fujma.941439

Abstract

References

  • [1] C. Huygens, Horologium Oscillatorium Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricæ, 1673.
  • [2] Ş. Kılıçoğlu, S. Şenyurt, On the involute of the cubic Bezier curve by using matrix representation in E3, Eur. J. Pure Appl. Math., (13), 216-226, 2020.
  • [3] Z. Duman, Involute-Evolute curve couples of Bezier curve, MSc. Thesis, Sakarya University, 2021.
  • [4] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer, 2006.
  • [5] A. Gray, E. Abbena, S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
  • [6] B. O’Neill, Elementary Differential Geometry, Academic Press, Rev. 2nd.ed., Elsevier, USA, 2006.
  • [7] J. W. Rutter, Geometry of Curves, Chapman & Hall/CRC, 2000.
  • [8] M. Özdemir, Diferansiyel Geometri, Altın Nokta Basın Yayın, 2020.
  • [9] E. Erkan, S. Yüce, Serret-Frenet frame and curvatures of Bezier curves, Mathematics, 6(12), 321, 1-20, 2018.

Curve Couples of Bézier Curves in Euclidean 2-Space

Year 2021, , 245 - 250, 01.12.2021
https://doi.org/10.33401/fujma.941439

Abstract

The goal of this paper is to characterize the evolute, involute and parallel curves of a Bezier curve which is applicable to computer graphics and related subjects. Especially, these curve couples are investigated at the endpoints. Moreover, the curvatures of these curve couples are given.

References

  • [1] C. Huygens, Horologium Oscillatorium Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricæ, 1673.
  • [2] Ş. Kılıçoğlu, S. Şenyurt, On the involute of the cubic Bezier curve by using matrix representation in E3, Eur. J. Pure Appl. Math., (13), 216-226, 2020.
  • [3] Z. Duman, Involute-Evolute curve couples of Bezier curve, MSc. Thesis, Sakarya University, 2021.
  • [4] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer, 2006.
  • [5] A. Gray, E. Abbena, S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
  • [6] B. O’Neill, Elementary Differential Geometry, Academic Press, Rev. 2nd.ed., Elsevier, USA, 2006.
  • [7] J. W. Rutter, Geometry of Curves, Chapman & Hall/CRC, 2000.
  • [8] M. Özdemir, Diferansiyel Geometri, Altın Nokta Basın Yayın, 2020.
  • [9] E. Erkan, S. Yüce, Serret-Frenet frame and curvatures of Bezier curves, Mathematics, 6(12), 321, 1-20, 2018.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ayşe Yılmaz Ceylan 0000-0002-8051-2879

Publication Date December 1, 2021
Submission Date May 23, 2021
Acceptance Date October 1, 2021
Published in Issue Year 2021

Cite

APA Ceylan, A. Y. (2021). Curve Couples of Bézier Curves in Euclidean 2-Space. Fundamental Journal of Mathematics and Applications, 4(4), 245-250. https://doi.org/10.33401/fujma.941439
AMA Ceylan AY. Curve Couples of Bézier Curves in Euclidean 2-Space. Fundam. J. Math. Appl. December 2021;4(4):245-250. doi:10.33401/fujma.941439
Chicago Ceylan, Ayşe Yılmaz. “Curve Couples of Bézier Curves in Euclidean 2-Space”. Fundamental Journal of Mathematics and Applications 4, no. 4 (December 2021): 245-50. https://doi.org/10.33401/fujma.941439.
EndNote Ceylan AY (December 1, 2021) Curve Couples of Bézier Curves in Euclidean 2-Space. Fundamental Journal of Mathematics and Applications 4 4 245–250.
IEEE A. Y. Ceylan, “Curve Couples of Bézier Curves in Euclidean 2-Space”, Fundam. J. Math. Appl., vol. 4, no. 4, pp. 245–250, 2021, doi: 10.33401/fujma.941439.
ISNAD Ceylan, Ayşe Yılmaz. “Curve Couples of Bézier Curves in Euclidean 2-Space”. Fundamental Journal of Mathematics and Applications 4/4 (December 2021), 245-250. https://doi.org/10.33401/fujma.941439.
JAMA Ceylan AY. Curve Couples of Bézier Curves in Euclidean 2-Space. Fundam. J. Math. Appl. 2021;4:245–250.
MLA Ceylan, Ayşe Yılmaz. “Curve Couples of Bézier Curves in Euclidean 2-Space”. Fundamental Journal of Mathematics and Applications, vol. 4, no. 4, 2021, pp. 245-50, doi:10.33401/fujma.941439.
Vancouver Ceylan AY. Curve Couples of Bézier Curves in Euclidean 2-Space. Fundam. J. Math. Appl. 2021;4(4):245-50.

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