Research Article

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

Volume: 6 Number: 2 June 30, 2023
EN

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

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. [1] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006.
  2. [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. [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. [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. [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. [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. [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. [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. [9] H. Hagen, Bezier-curves with curvature and torsion continuity, Rocky Mountain J. Math., 16(3) (1986), 629-638.
  10. [10] A. Y. Ceylan, Curve Couples of B´ezier Curves in Euclidean 2-Space, FUJMA, 4(4) (2021), 245-250.
APA
Kılıçoglu, Ş., & Yurttançıkmaz, S. (2023). A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane. Communications in Advanced Mathematical Sciences, 6(2), 67-77. https://doi.org/10.33434/cams.1228730
AMA
1.Kılıçoglu Ş, Yurttançıkmaz S. A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane. Communications in Advanced Mathematical Sciences. 2023;6(2):67-77. doi:10.33434/cams.1228730
Chicago
Kılıçoglu, Şeyda, and Semra Yurttançıkmaz. 2023. “A Modelling on the Exponential Curves As $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane”. Communications in Advanced Mathematical Sciences 6 (2): 67-77. https://doi.org/10.33434/cams.1228730.
EndNote
Kılıçoglu Ş, Yurttançıkmaz S (June 1, 2023) A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane. Communications in Advanced Mathematical Sciences 6 2 67–77.
IEEE
[1]Ş. Kılıçoglu and S. Yurttançıkmaz, “A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane”, Communications in Advanced Mathematical Sciences, vol. 6, no. 2, pp. 67–77, June 2023, doi: 10.33434/cams.1228730.
ISNAD
Kılıçoglu, Şeyda - Yurttançıkmaz, Semra. “A Modelling on the Exponential Curves As $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane”. Communications in Advanced Mathematical Sciences 6/2 (June 1, 2023): 67-77. https://doi.org/10.33434/cams.1228730.
JAMA
1.Kılıçoglu Ş, Yurttançıkmaz S. A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane. Communications in Advanced Mathematical Sciences. 2023;6:67–77.
MLA
Kılıçoglu, Şeyda, and Semra Yurttançıkmaz. “A Modelling on the Exponential Curves As $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane”. Communications in Advanced Mathematical Sciences, vol. 6, no. 2, June 2023, pp. 67-77, doi:10.33434/cams.1228730.
Vancouver
1.Şeyda Kılıçoglu, Semra Yurttançıkmaz. A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\’{e}zier Curve in Plane. Communications in Advanced Mathematical Sciences. 2023 Jun. 1;6(2):67-7. doi:10.33434/cams.1228730