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

Yıl 2022, Cilt: 14 Sayı: 2, 376 - 383, 30.12.2022

Şeyda Kılıçoglu , Süleyman Şenyurt

https://doi.org/10.47000/tjmcs.984372

Cited By: 5

Öz

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 $E^3$.

Anahtar Kelimeler

Bezier curves, Bertrand mate, cubic Bezier curve

Kaynakça

• 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