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HOW TO APPROXIMATE COSINE CURVE WITH 4TH AND 6TH ORDER BEZIER CURVE IN PLANE?

ABSTRACT
There are many ways to approximate cosine curve. In this study we have examined the way how the cosine curve can be written as any order Bezier curve. As a result using the Maclaurin series we have examined cosine curve as the 4th and the 6th order Bezier curve based on the control points with matrix form in E2. We give the control points of the 4th and the 6th order Bezier curve based on the coefficients. Also we give the coefficients based on the the control points of the 4th and the 6th order Bezier curve too.
KEYWORDS
PAPER SUBMITTED: 2021-08-10
PAPER REVISED: 2022-09-10
PAPER ACCEPTED: 2022-09-25
PUBLISHED ONLINE: 2023-01-29
DOI REFERENCE: https://doi.org/10.2298/TSCI22S2559K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 2, PAGES [559 - 570]
REFERENCES
  1. ***, Derivatives of a Bezier Curve, pages.mtu.edu/shene/COURSES/cs362n/NOTES/spline/Bezier/bezier-der. html.
  2. Marsh, D., Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006
  3. Tas, F., Ilarslan, K., A New Approach to Design the Ruled Surface, International Journal of Geometric Methods in Modern Physics, 16 (2019), 6, 1950093
  4. Hagen, H., Bezier-Curves with Curvature and Torsion Continuity, Rocky Mountain J. Math., 16 (1986), 3, pp. 629-638
  5. Zhang, H., Jieqing, F., Bezier Curves and Surfaces (2), State Key Lab of CAD&CG Zhejiang University, 2006
  6. Michael, S. F., Bezier Curves and Surfaces, in: Enciclopedia of Applied and Computational Mathematics, pp. 113-115, Springer, New York, USA, 2003
  7. Farin, G., Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, New York, USA, 1996
  8. Kilicoglu, S., Senyurt, S., On the Cubic Bezier Curves in E3, Ordu University Journal of Science and Technology, 9 (2019), 2, pp. 83-97
  9. Levent, A., Sahin, B., Cubic Bezier-Like Transition Curves with New Basis Function, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 44 (2008), 2, pp. 222-228
  10. Kilicoglu, S., Senyurt, S., On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3, European Journal of Pure and Applied Mathematics, 13 (2020), 2, pp. 216-226
  11. Kilicoglu, S., Senyurt, S., An Examination on to Find 5th Order Bezier Curve in E3, Journal of New Theory, 37 (2021), Dec., pp. 35-44
  12. Kilicoglu, S., Senyurt, S., On the Mannheim Partner of a Cubic Bezier Curve in E3, International Journal of Maps in Mathematics, 5 (2022), 2, pp. 182-197
  13. Kilicoglu, S., Senyurt, S., On the Matrix Representation of 5th order Bezier Curve and Derivatives, Commun .Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 71 (2022), 1, pp. 133-152
  14. Kilicoglu, S., Senyurt, S., How to Find Bezier Curves in E3, Communications in Advanced Mathematical Sciences, 5 (2022), 1, pp. 12-24
  15. Kilicoglu, S., Senyurt, S., On the Matrix Representation of Bezier Curves and Derivatives in E3, Sigma . Engineering and Natural Sci., 71 (2022), 1, pp. 133-152

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence