Süleyman ŞENYURT, Şeyda KILIÇOĞLU

An Examination on to Find 5th Order B´ezier Curve in E3

In this study, we have examined how to find any 5th order B´ezier curve with its known first, second and third derivatives, which are the 4th order, the cubic and the quadratic B´ezier curves, respectively, based on the control points of given the derivatives. Also we give an example to find the 5th order B´ezier curve with the given derivatives.

PDF

___

[1] H. Hagen, B´ezier-Curves with Curvature and Torsion Continuity, The Rocky Mountain Journal of Mathematics 16(3) (1986) 629–638.
[2] F. Ta¸s, K. Ilarslan, A New Approach to Design the Ruled Surface, International Journal of Geometric Methods in Modern Physics 16(6) (2019).
[3] G. Farin, Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
[4] S¸. Kılı¸co˘glu, S. S¸enyurt, On the Cubic B´ezier Curves in E3, Ordu University Journal of Science and Technology 9(2) (2019) 83–97.
[5] S¸. Kılı¸co˘glu, S. S¸enyurt, On the Involute of the Cubic B´ezier Curve by Using Matrix Representation in E3, European Journal of Pure and Applied Mathematics 13 (2020) 216–226.
[6] S¸. Kılı¸co˘glu, S. S¸enyurt, On the Matrix Representation of 5th order B´ezier Curve and derivatives, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistic (2021) In press.
[7] S¸. Kılı¸co˘glu, S. S¸enyurt, On the Matrix Representation of B´ezier Curves and Derivatives in E3, Sigma Journal of Engineering and Natural Sciences (2021) In press.
[8] S¸. Kılı¸co˘glu, S. S¸enyurt, On the Bertrand Mate of a Cubic B´ezier Curve by Using Matrix Representation in E3, 18th International Geometry Symposium in Honour of Prof. Dr. Sadık Kele¸s, Malatya, Turkey, 2021, pp. 129.
[9] S¸. Kılı¸co˘glu, S. S¸enyurt, On the Mannheim Partner of a Cubic B´ezier Curve in E3, 10th International Eurasian Conference on Mathematical and Applications, Sakarya, Turkey, 2021, pp. 154.
[10] M. Incesu, S. Y. Evren, The Selection of Control Points for Two Open Non Uniform B-Spline Curves to Form Bertrand Pairs, Tblisi Journal of Mathematics, Special Issue 8 (2021) 195–208.
[11] H. K. Samanci, M. Incesu, Investigating a Quadratic B´ezier Curve Due to NCW and N-Bishop Frames, Turkish Journal of Mathematics and Computer Science 12(2) (2020) 120–127.