[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
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.
[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.
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.