Research Article
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Year 2022, , 376 - 383, 30.12.2022
https://doi.org/10.47000/tjmcs.984372

Abstract

References

  • Aydin, T.A., A matrix presentation of higher order derivatives of bezier curve and surface journal, Journal of Science and Arts, 21(1)(2021), 77–90.
  • Evren, S. Y., On the Bertrand Nurbs Curves, Master Thesis, Mus¸ Alparslan University, 2020.
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  • Incesu, M., Evren, S.Y., Gursoy, O., On the Bertrand pairs of open non-uniform rational B-spline curves, In Mathematical Analysis and Applications, Springer, Singapore, (2021), 167–184.
  • Kılıçoğlu, Ş, Şenyurt, S., On the cubic Bezier curves in E3, Ordu University Journal of Science and Technology, 9(2)(2019), 83–97.
  • Kılıçoğlu, Ş, Şenyurt, S., 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.
  • Kılıçoğlu, Ş, Şenyurt, S., On the Mannheim partner of a cubic Bezier curve in E3, International Journal of Maps in Mathematics, 5(2)(2022), 182–197.
  • Kılıçoğlu, Ş, Şenyurt, S., On the matrix representation of 5th order Bezier curve and its derivatives in E3, Communications Series A1 Mathematics & Statistics, 71(1)(2022), 133–152.
  • Marsh, D., Applied Geometry for Computer Graphics and CAD Springer Science and Business Media, 2006.
  • Michael, S., Bezier curves and surfaces, Lecture 8, Floater Oslo Oct., 2003.
  • Tas, F., Ilarslan, K., A new approach to design the ruled surface, International Journal of Geometric Methods in Modern Physics, 16(6)(2019).
  • Zhang, H., Jieqing, F., Bezier Curves and Surfaces (2), State Key Lab of CAD&CG Zhejiang University, 2006

On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$

Year 2022, , 376 - 383, 30.12.2022
https://doi.org/10.47000/tjmcs.984372

Abstract

In this study, we have examined Bertrand mate of a cubic Bezier curve based on the control points with matrix form in $E^3$. Frenet vector fields and also curvatures of Bertrand mate of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in $E^3$.

References

  • Aydin, T.A., A matrix presentation of higher order derivatives of bezier curve and surface journal, Journal of Science and Arts, 21(1)(2021), 77–90.
  • Evren, S. Y., On the Bertrand Nurbs Curves, Master Thesis, Mus¸ Alparslan University, 2020.
  • Farin, G., Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
  • Hagen, H., Bezier-curves with curvature and torsion continuity, Rocky Mountain J. Math., 16(3)(1986), 629–638.
  • Incesu, M., Gursoy, O., LS(2)-Equivalence conditions of control points and application to planar Bezier curves, New Trends in Mathematical Sciences, 5(3)(2017) , 70–84.
  • Incesu, M., Evren, S.Y., Gursoy, O., On the Bertrand pairs of open non-uniform rational B-spline curves, In Mathematical Analysis and Applications, Springer, Singapore, (2021), 167–184.
  • Kılıçoğlu, Ş, Şenyurt, S., On the cubic Bezier curves in E3, Ordu University Journal of Science and Technology, 9(2)(2019), 83–97.
  • Kılıçoğlu, Ş, Şenyurt, S., 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.
  • Kılıçoğlu, Ş, Şenyurt, S., On the Mannheim partner of a cubic Bezier curve in E3, International Journal of Maps in Mathematics, 5(2)(2022), 182–197.
  • Kılıçoğlu, Ş, Şenyurt, S., On the matrix representation of 5th order Bezier curve and its derivatives in E3, Communications Series A1 Mathematics & Statistics, 71(1)(2022), 133–152.
  • Marsh, D., Applied Geometry for Computer Graphics and CAD Springer Science and Business Media, 2006.
  • Michael, S., Bezier curves and surfaces, Lecture 8, Floater Oslo Oct., 2003.
  • Tas, F., Ilarslan, K., A new approach to design the ruled surface, International Journal of Geometric Methods in Modern Physics, 16(6)(2019).
  • Zhang, H., Jieqing, F., Bezier Curves and Surfaces (2), State Key Lab of CAD&CG Zhejiang University, 2006
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Şeyda Kılıçoglu 0000-0003-0252-1574

Süleyman Şenyurt 0000-0003-1097-5541

Publication Date December 30, 2022
Published in Issue Year 2022

Cite

APA Kılıçoglu, Ş., & Şenyurt, S. (2022). On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$. Turkish Journal of Mathematics and Computer Science, 14(2), 376-383. https://doi.org/10.47000/tjmcs.984372
AMA Kılıçoglu Ş, Şenyurt S. On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$. TJMCS. December 2022;14(2):376-383. doi:10.47000/tjmcs.984372
Chicago Kılıçoglu, Şeyda, and Süleyman Şenyurt. “On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$”. Turkish Journal of Mathematics and Computer Science 14, no. 2 (December 2022): 376-83. https://doi.org/10.47000/tjmcs.984372.
EndNote Kılıçoglu Ş, Şenyurt S (December 1, 2022) On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$. Turkish Journal of Mathematics and Computer Science 14 2 376–383.
IEEE Ş. Kılıçoglu and S. Şenyurt, “On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$”, TJMCS, vol. 14, no. 2, pp. 376–383, 2022, doi: 10.47000/tjmcs.984372.
ISNAD Kılıçoglu, Şeyda - Şenyurt, Süleyman. “On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$”. Turkish Journal of Mathematics and Computer Science 14/2 (December 2022), 376-383. https://doi.org/10.47000/tjmcs.984372.
JAMA Kılıçoglu Ş, Şenyurt S. On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$. TJMCS. 2022;14:376–383.
MLA Kılıçoglu, Şeyda and Süleyman Şenyurt. “On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 2, 2022, pp. 376-83, doi:10.47000/tjmcs.984372.
Vancouver Kılıçoglu Ş, Şenyurt S. On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in $\mathbf{E}^{3}$. TJMCS. 2022;14(2):376-83.