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BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 6 Sayı: 2, 67 - 77, 30.06.2023

Şeyda Kılıçoglu Semra Yurttançıkmaz

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

Öz

Kaynakça

  • [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).

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

Yıl 2023, Cilt: 6 Sayı: 2, 67 - 77, 30.06.2023

Şeyda Kılıçoglu Semra Yurttançıkmaz

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Şeyda Kılıçoglu 0000-0003-0252-1574

Semra Yurttançıkmaz 0000-0001-6712-3687

Yayımlanma Tarihi 30 Haziran 2023
Gönderilme Tarihi 3 Ocak 2023
Kabul Tarihi 17 Mayıs 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 2

Kaynak Göster

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 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. Haziran 2023;6(2):67-77. doi:10.33434/cams.1228730
Chicago Kılıçoglu, Şeyda, ve 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 6, sy. 2 (Haziran 2023): 67-77. https://doi.org/10.33434/cams.1228730.
EndNote Kılıçoglu Ş, Yurttançıkmaz S (01 Haziran 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 Ş. Kılıçoglu ve 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, c. 6, sy. 2, ss. 67–77, 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 (Haziran 2023), 67-77. https://doi.org/10.33434/cams.1228730.
JAMA 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 ve 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, c. 6, sy. 2, 2023, ss. 67-77, doi:10.33434/cams.1228730.
Vancouver 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):67-7.
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