A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\'{e}zier Curve in Plane

Year 2023, Volume: 6 Issue: 2, 67 - 77, 30.06.2023

Şeyda Kılıçoglu , Semra Yurttançıkmaz

https://doi.org/10.33434/cams.1228730

Cited By: 3

Abstract

In this study, it has been researched the exponential curve as a $3^{rd},$ $5^{th}$ and $7^{th}$ order B\'{e}zier curve in $\mathbf{E}^{2}$. Also, the numerical matrix representations of these curves have been calculated using the Maclaurin series in the plane via the control points.

Keywords

Bézier curves , Exponential curve , Maclaurin series , $5^{th}$ and $7^{th}$ $order$ B\

References

• [1] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006.
• [2] E. Cohen, R. F. Riesenfeld, General matrix representations for B´ezier and B-spline curves, Computers in Industry, 3(1-2) (1982), 9-15.
• [3] T.A. Aydin, A matrix presentation of higher order derivatives of Bezier curves and surfaces, Journal of Science and Art, 21(1) (2021), 77-90.
• [4] Ş. Kılışoğlu, S. Şenyurt, On the Matrix Representation of 5th order B´ezier Curve and derivatives, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 71(1) (2022), 133-152.
• [5] Ş. Kılıçoğlu, On Approximation of Helix by 3rd; 5th and 7th order B´ezier curves in E3, Thermal Science, 26(2) (2023), 525-538.
• [6] Ş. Kılıçoğlu, On approximation sine wave with the 5th and 7th order B´ezier paths in E2, Thermal Science, 26(2) (2023), 539-550.
• [7] Ş. Kılıçoğlu, S. Yurttançıkmaz, How to approximate cosine curve with 4th and 6th order B´ezier curve in plane?, Thermal Science, 26(2) (2023), 559-570.
• [8] F. Tas, K. Ilarslan, A new approach to design the ruled surface, Int. J. Geom. Methods Mod. Phys., 16(6) (2019), Article ID 1950093, doi: 10.1142/S0219887819500932.
• [9] H. Hagen, Bezier-curves with curvature and torsion continuity, Rocky Mountain J. Math., 16(3) (1986), 629-638.
• [10] A. Y. Ceylan, Curve Couples of B´ezier Curves in Euclidean 2-Space, FUJMA, 4(4) (2021), 245-250.
• [11] H. Zhang, F. Jieqing, Bezier Curves and Surfaces, State Key Lab of CAD&CG Zhejiang University, 2006.
• [12] S.Michael, B´ezier curves and surfaces, Lecture 8, Floater Oslo Oct., 2003.
• [13] G. Farin, Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
• [14] S¸ . Kılıc¸o˘glu, S. S¸enyurt, On the cubic bezier curves in E3, Ordu University Journal of Science and Technology, 9(2) (2019), 83-97.
• [15] A. Levent, B. Sahin, Cubic Bezier-like transition curves with new basis function, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 44(2) (2008), 222-228.
• [16] Ş. Kılıçoğlu, S. Şenyurt, On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3, European Journal of Pure and Applied Mathematics, 13(2020), 216-226.
• [17] Ş. Kılıçoğlu, S. Şenyurt, On the Bertrand mate of a cubic Bezier curve by using matrix representation in E3, 18th International Geometry Sym., 2021.
• [18] Ş. Kılıçoğlu, S. Şenyurt, On the Mannheim partner of a cubic Bezier curve in E3, International Journal of Maps in Mathematics, 5(2) (2022), 182-197.
• [19] Ş. Kılıçoğlu, S. Şenyurt, How to Find B´ezier Curves in E3, Commun. Adv. Math. Sci, 5(1) (2022), 12-24.
• [20] ”Derivatives of a B´ezier Curve” https://pages.mtu.edu/˜shene/COURSES/ cs3621/NOTES/spline /Bezier/ bezier-der. html.
• [21] Ş. Kılıçoğlu, S. Şenyurt, On the matrix representation of Bezier curves and derivatives in E3, Sigma J. Engineering and Natural Sci., (in press).