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On Pedal and Contrapedal Curves of Bézier Curves

Year 2021, Volume: 9 Issue: 2, 217 - 221, 15.10.2021
https://izlik.org/JA99WM63EJ

Abstract

The aim of this paper is to charaterize pedal and contrapedal curves of a Bézier curve which has many applications in computer graphics and related areas. Moreover, the pedal and contrapedal curve of a planar Bézier curve at the starting and the ending points are investigated.

References

  • 1) Do Carmo, M. P., \textit{Differential Geometry of Curves and Surfaces}, Prentice-Hall, Englewood Cliffs, NJ, 1976.
  • 2) Erkan, E. and Yüce, S., Serret-Frenet Frame and Curvatures of Bézier Curves, Mathematics, Vol:6, No.12 (2018), 321, 1-20.
  • 3) Gray, A., Abbena, E. and Salamon, S., \textit{Modern Differential Geometry of Curves and Surfaces with Mathematica}, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
  • 4) Li Y, Pei D. Pedal curves of frontals in the Euclidean plane, Math. Meth. Appl. Sci., 41, (2018), 1988–1997.
  • 5) Marsh, D., \textit{Applied geometry for computer graphics and CAD}, Springer, 2006.
  • 6) O'Neill, B., \textit{Elemantary Differential Geometry}, Academic Oress, Rev. 2nd.ed., Elsevier, USA, 2006.
  • 7) Tuncer OO, Ceyhan H, Gök İ, Ekmekci FN. Notes on pedal and contrapedal curves of fronts in the Euclidean plane, Math. Meth. Appl. Sci., 41, (2018), 5096–5111.

Year 2021, Volume: 9 Issue: 2, 217 - 221, 15.10.2021
https://izlik.org/JA99WM63EJ

Abstract

References

  • 1) Do Carmo, M. P., \textit{Differential Geometry of Curves and Surfaces}, Prentice-Hall, Englewood Cliffs, NJ, 1976.
  • 2) Erkan, E. and Yüce, S., Serret-Frenet Frame and Curvatures of Bézier Curves, Mathematics, Vol:6, No.12 (2018), 321, 1-20.
  • 3) Gray, A., Abbena, E. and Salamon, S., \textit{Modern Differential Geometry of Curves and Surfaces with Mathematica}, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
  • 4) Li Y, Pei D. Pedal curves of frontals in the Euclidean plane, Math. Meth. Appl. Sci., 41, (2018), 1988–1997.
  • 5) Marsh, D., \textit{Applied geometry for computer graphics and CAD}, Springer, 2006.
  • 6) O'Neill, B., \textit{Elemantary Differential Geometry}, Academic Oress, Rev. 2nd.ed., Elsevier, USA, 2006.
  • 7) Tuncer OO, Ceyhan H, Gök İ, Ekmekci FN. Notes on pedal and contrapedal curves of fronts in the Euclidean plane, Math. Meth. Appl. Sci., 41, (2018), 5096–5111.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ayşe Yılmaz Ceylan

Merve Kara This is me

Submission Date August 20, 2021
Acceptance Date September 16, 2021
Publication Date October 15, 2021
IZ https://izlik.org/JA99WM63EJ
Published in Issue Year 2021 Volume: 9 Issue: 2

Cite

APA Ceylan, A. Y., & Kara, M. (2021). On Pedal and Contrapedal Curves of Bézier Curves. Konuralp Journal of Mathematics, 9(2), 217-221. https://izlik.org/JA99WM63EJ
AMA 1.Ceylan AY, Kara M. On Pedal and Contrapedal Curves of Bézier Curves. Konuralp J. Math. 2021;9(2):217-221. https://izlik.org/JA99WM63EJ
Chicago Ceylan, Ayşe Yılmaz, and Merve Kara. 2021. “On Pedal and Contrapedal Curves of Bézier Curves”. Konuralp Journal of Mathematics 9 (2): 217-21. https://izlik.org/JA99WM63EJ.
EndNote Ceylan AY, Kara M (October 1, 2021) On Pedal and Contrapedal Curves of Bézier Curves. Konuralp Journal of Mathematics 9 2 217–221.
IEEE [1]A. Y. Ceylan and M. Kara, “On Pedal and Contrapedal Curves of Bézier Curves”, Konuralp J. Math., vol. 9, no. 2, pp. 217–221, Oct. 2021, [Online]. Available: https://izlik.org/JA99WM63EJ
ISNAD Ceylan, Ayşe Yılmaz - Kara, Merve. “On Pedal and Contrapedal Curves of Bézier Curves”. Konuralp Journal of Mathematics 9/2 (October 1, 2021): 217-221. https://izlik.org/JA99WM63EJ.
JAMA 1.Ceylan AY, Kara M. On Pedal and Contrapedal Curves of Bézier Curves. Konuralp J. Math. 2021;9:217–221.
MLA Ceylan, Ayşe Yılmaz, and Merve Kara. “On Pedal and Contrapedal Curves of Bézier Curves”. Konuralp Journal of Mathematics, vol. 9, no. 2, Oct. 2021, pp. 217-21, https://izlik.org/JA99WM63EJ.
Vancouver 1.Ayşe Yılmaz Ceylan, Merve Kara. On Pedal and Contrapedal Curves of Bézier Curves. Konuralp J. Math. [Internet]. 2021 Oct. 1;9(2):217-21. Available from: https://izlik.org/JA99WM63EJ
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