EN
Curve Couples of Bézier Curves in Euclidean 2-Space
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.
Keywords
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Publication Date
December 1, 2021
Submission Date
May 23, 2021
Acceptance Date
October 1, 2021
Published in Issue
Year 1970 Volume: 4 Number: 4
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
1.Ceylan AY. Curve Couples of Bézier Curves in Euclidean 2-Space. Fundam. J. Math. Appl. 2021;4(4):245-250. doi:10.33401/fujma.941439
Chicago
Ceylan, Ayşe Yılmaz. 2021. “Curve Couples of Bézier Curves in Euclidean 2-Space”. Fundamental Journal of Mathematics and Applications 4 (4): 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
[1]A. Y. Ceylan, “Curve Couples of Bézier Curves in Euclidean 2-Space”, Fundam. J. Math. Appl., vol. 4, no. 4, pp. 245–250, Dec. 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 1, 2021): 245-250. https://doi.org/10.33401/fujma.941439.
JAMA
1.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, Dec. 2021, pp. 245-50, doi:10.33401/fujma.941439.
Vancouver
1.Ayşe Yılmaz Ceylan. Curve Couples of Bézier Curves in Euclidean 2-Space. Fundam. J. Math. Appl. 2021 Dec. 1;4(4):245-50. doi:10.33401/fujma.941439
Cited By
How to Find a Bezier Curve in $\mathbf{E}^{3}$
Communications in Advanced Mathematical Sciences
https://doi.org/10.33434/cams.1021878A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\'{e}zier Curve in Plane
Communications in Advanced Mathematical Sciences
https://doi.org/10.33434/cams.1228730
