Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 5 Sayı: 1, 12 - 24, 17.03.2022
https://doi.org/10.33434/cams.1021878

Öz

Destekleyen Kurum

yok

Proje Numarası

yok

Teşekkür

Dergi yönetimine ve makaleye hakemlik yapacak değerli hakemlere teşekkür ederiz.

Kaynakça

  • [1] H. Hagen, Bezier-curves with curvature and torsion continuity, Rocky Mountain J. Math., 16(3), (1986), 629-638.
  • [2] D. Marsh, Applied Geometry for Computer Graphics and CAD. Springer Science and Business Media., 2006.
  • [3] G. Farin, Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
  • [4] H. Zhang, F. Jieqing, Bezier Curves and Surfaces (2), State Key Lab of CAD&CG Zhejiang University, 2006.
  • [5] S. Michael, Bezier Curves and Surfaces, Lecture 8, Floater Oslo Oct., 2003.
  • [6] E. Erkan, S. Yüce, Serret-Frenet frame and curvatures of B´ezier curves, Mathematics, 6 (12) (2018), 321.
  • [7] H. K. Samanci, S. Celik, M. Incesu, The Bishop frame of B´ezier curves, Life Sci. J, 12(6) 2015, 175-180.
  • [8] H. K. Samanci, M. Incesu, Investigating a quadratic Bezier curve due to NCW and N-Bishop frames, Turk. J. Math. Compu. Sci., 12(2) (2020), 120-127.
  • [9] Ş. Kılıçoğlu, S. Şenyurt, On the cubic bezier curves in E3, Ordu Uni. J. Sci. Techno., 9(2) (2019), 83-97.
  • [10] Ş. Kılıçoğlu, S. Şenyurt, On the involute of the cubic B´ezier curve by using matrix representation in E3, European J. Pure App. Math., 13 (2020), 216-226.
  • [11] A. Levent, B. Sahin, Cubic bezier-like transition curves with new basis function, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 44(2) (2008) , 222-228.
  • [12] Ş. Kılıçoğlu, S. Şenyurt, On the matrix representation of 5th order B´ezier curve and derivatives, Comm. Fac. Sci. Uni. Ankara Series A1 Math. Stat., in press 2021.
  • [13] Ş. Kılıçoğlu, S. Şenyurt, On the Bertrand mate of a cubic B´ezier curve by using matrix representation in E3, 18th International Geometry Sym. 2021.
  • [14] Ş. Kılıçoğlu, S. Şenyurt, On the Mannheim partner of a cubic Bezier curve in E3, 10th International Eurasian Conference on Mathematical Sciences and Applications, 2021.
  • [15] A. Y. Ceylan, Curve couples of Bezier curves in Euclidean 2-space, Fundamental J. Math. App., 4(4) (2021), 245-250.
  • [16] Ş. Kılıçoğlu, S. Şenyurt, On the matrix representation of Bezier curves and derivatives in E3, Sigma J. Engineering and Natural Sci., in Press 2021

How to Find a Bezier Curve in $\mathbf{E}^{3}$

Yıl 2022, Cilt: 5 Sayı: 1, 12 - 24, 17.03.2022
https://doi.org/10.33434/cams.1021878

Öz

"How to find any $n^{th}$ order B\'{e}zier curve if we know its first, second, and third derivatives?" Hence we have examined the way to find the B\'{e}zier curve based on the control points with matrix form, while derivatives are given in $\mathbf{E}^{3}$. Further, we examined the control points of a cubic B\'{e}zier curve with given derivatives as an example. In this study first we have examined how to find any $n^{th}$ order Bezier curve with known its first, second and third derivatives, which are inherently, the $\left( n-1\right) ^{th}$ order, the $\left(n-2\right) ^{th}$ and the $\left( n-3\right) ^{th}$ Bezier curves in respective order. There is a lot of the number of B\'{e}zier curves with known the derivatives with control points. Hence to find a B\'{e}zier curve we have to choose any control point of any derivation\. In this study we have chosen two special points which are the initial point $P_{0}$ and the endpoint $P_{n}$.

Proje Numarası

yok

Kaynakça

  • [1] H. Hagen, Bezier-curves with curvature and torsion continuity, Rocky Mountain J. Math., 16(3), (1986), 629-638.
  • [2] D. Marsh, Applied Geometry for Computer Graphics and CAD. Springer Science and Business Media., 2006.
  • [3] G. Farin, Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
  • [4] H. Zhang, F. Jieqing, Bezier Curves and Surfaces (2), State Key Lab of CAD&CG Zhejiang University, 2006.
  • [5] S. Michael, Bezier Curves and Surfaces, Lecture 8, Floater Oslo Oct., 2003.
  • [6] E. Erkan, S. Yüce, Serret-Frenet frame and curvatures of B´ezier curves, Mathematics, 6 (12) (2018), 321.
  • [7] H. K. Samanci, S. Celik, M. Incesu, The Bishop frame of B´ezier curves, Life Sci. J, 12(6) 2015, 175-180.
  • [8] H. K. Samanci, M. Incesu, Investigating a quadratic Bezier curve due to NCW and N-Bishop frames, Turk. J. Math. Compu. Sci., 12(2) (2020), 120-127.
  • [9] Ş. Kılıçoğlu, S. Şenyurt, On the cubic bezier curves in E3, Ordu Uni. J. Sci. Techno., 9(2) (2019), 83-97.
  • [10] Ş. Kılıçoğlu, S. Şenyurt, On the involute of the cubic B´ezier curve by using matrix representation in E3, European J. Pure App. Math., 13 (2020), 216-226.
  • [11] A. Levent, B. Sahin, Cubic bezier-like transition curves with new basis function, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 44(2) (2008) , 222-228.
  • [12] Ş. Kılıçoğlu, S. Şenyurt, On the matrix representation of 5th order B´ezier curve and derivatives, Comm. Fac. Sci. Uni. Ankara Series A1 Math. Stat., in press 2021.
  • [13] Ş. Kılıçoğlu, S. Şenyurt, On the Bertrand mate of a cubic B´ezier curve by using matrix representation in E3, 18th International Geometry Sym. 2021.
  • [14] Ş. Kılıçoğlu, S. Şenyurt, On the Mannheim partner of a cubic Bezier curve in E3, 10th International Eurasian Conference on Mathematical Sciences and Applications, 2021.
  • [15] A. Y. Ceylan, Curve couples of Bezier curves in Euclidean 2-space, Fundamental J. Math. App., 4(4) (2021), 245-250.
  • [16] Ş. Kılıçoğlu, S. Şenyurt, On the matrix representation of Bezier curves and derivatives in E3, Sigma J. Engineering and Natural Sci., in Press 2021
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Süleyman Şenyurt 0000-0003-1097-5541

Şeyda Kılıçoglu 0000-0003-0252-1574

Proje Numarası yok
Yayımlanma Tarihi 17 Mart 2022
Gönderilme Tarihi 10 Kasım 2021
Kabul Tarihi 17 Ocak 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 1

Kaynak Göster

APA Şenyurt, S., & Kılıçoglu, Ş. (2022). How to Find a Bezier Curve in $\mathbf{E}^{3}$. Communications in Advanced Mathematical Sciences, 5(1), 12-24. https://doi.org/10.33434/cams.1021878
AMA Şenyurt S, Kılıçoglu Ş. How to Find a Bezier Curve in $\mathbf{E}^{3}$. Communications in Advanced Mathematical Sciences. Mart 2022;5(1):12-24. doi:10.33434/cams.1021878
Chicago Şenyurt, Süleyman, ve Şeyda Kılıçoglu. “How to Find a Bezier Curve in $\mathbf{E}^{3}$”. Communications in Advanced Mathematical Sciences 5, sy. 1 (Mart 2022): 12-24. https://doi.org/10.33434/cams.1021878.
EndNote Şenyurt S, Kılıçoglu Ş (01 Mart 2022) How to Find a Bezier Curve in $\mathbf{E}^{3}$. Communications in Advanced Mathematical Sciences 5 1 12–24.
IEEE S. Şenyurt ve Ş. Kılıçoglu, “How to Find a Bezier Curve in $\mathbf{E}^{3}$”, Communications in Advanced Mathematical Sciences, c. 5, sy. 1, ss. 12–24, 2022, doi: 10.33434/cams.1021878.
ISNAD Şenyurt, Süleyman - Kılıçoglu, Şeyda. “How to Find a Bezier Curve in $\mathbf{E}^{3}$”. Communications in Advanced Mathematical Sciences 5/1 (Mart 2022), 12-24. https://doi.org/10.33434/cams.1021878.
JAMA Şenyurt S, Kılıçoglu Ş. How to Find a Bezier Curve in $\mathbf{E}^{3}$. Communications in Advanced Mathematical Sciences. 2022;5:12–24.
MLA Şenyurt, Süleyman ve Şeyda Kılıçoglu. “How to Find a Bezier Curve in $\mathbf{E}^{3}$”. Communications in Advanced Mathematical Sciences, c. 5, sy. 1, 2022, ss. 12-24, doi:10.33434/cams.1021878.
Vancouver Şenyurt S, Kılıçoglu Ş. How to Find a Bezier Curve in $\mathbf{E}^{3}$. Communications in Advanced Mathematical Sciences. 2022;5(1):12-24.

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