EN
On Pedal and Contrapedal Curves of Bézier Curves
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.
Keywords
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
October 15, 2021
Submission Date
August 20, 2021
Acceptance Date
September 16, 2021
Published in Issue
Year 2021 Volume: 9 Number: 2
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
