Research Article
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Year 2023, , 7 - 14, 28.03.2023
https://doi.org/10.32323/ujma.1238898

Abstract

References

  • [1] B. O’Neill, Semi-Riemann Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • [2] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44-107.
  • [3] G. Farin, History of Curves and Surfaces in CAGD, in: Handbook of CAGD, 2002.
  • [4] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer- Verlag, Berlin, 2nd ed, 2005.
  • [5] M. ˙Incesu, O. G¨ursoy, B´ezier E˘grilerinde Esas Formlar ve Eg˘rilikler, XVII Ulusal Matematik Sempozyumu, Bildiriler, Abant I˙zzet Baysal U¨ niversitesi, (2004), 146-157.
  • [6] G. H. Geoergiev, Shapes of Plane B´ezier Curves in Curve and Surface Design, Avignon, edited by P. Chenin, T. Lyche and L. L Schumaker, Nashboro Prees, Brentwood, TN, (2006) 143-152.
  • [7] G. H. Georgiev, On the shape of the cubic B´ezier Curve, Proc. Of International Congress Pure and Applied Differential Geometry- Brussels, edited by F. Dillen and I. Van de Woestyne, Shaker Verlag, Aachen,(2007), 98-106.
  • [8] G. H. Georgiev, Spacelike B´ezier curves in the three-dimensional Minkowski space, Proceedings of AIP Conference, 1067(1) (2008), 373-380.
  • [9] G. H. Georgiev, Constructions of spacelike B´ezier surfaces in the three-dimensional Minkowski space, Proceedings of AIP Conference 1184 (1)(2009), 199-206.
  • [10] P. Chalmoviansky, B. Pokorna, Quadratic space-like B´ezier curves in the three dimensional Minkowski space, Proceeding of Symposium on Computer Geometry, 20 (2011), 104-110.
  • [11] B. Pokorna, P. Chalmoviansky, Planar cubic spacelike B´ezier curves in three dimensional Minkowski space, Proceeding of Symposium on Computer Geometry, 23 (2012), 93-98.
  • [12] H. Ugail, M. C. Marquez, A. Yilmaz, On B´ezier surfaces in three-dimensional Minkowski space, Computers and Mathematics with Applications, 62 (2011), 2899-2912.
  • [13] H. Kus¸ak Samancı, S. C¸ elik, The curvatures of the spacelike B´ezier curve with a spacelike principal normal in Minkowski 3􀀀Space, International Journal of Mathematics and Computation, 29(4) (2018).
  • [14] S. C¸ elik, Investigation of B´ezier curves and surfaces from computer aided geometric design elements in Minkowski space, Master Thesis, Bitlis Eren University, 2017.
  • [15] H. Kus¸ak Samancı, Some geometric properties of the spacelike B´ezier curve with a timelike principal normal in Minkowski 3􀀀space, Cumhuriyet Science Journal, 39(1) (2018), 71-79.
  • [16] H. Kus¸ak Samancı, O¨ . Kalkan, S. C¸ elik, The timelike Be´zier spline in Minkowski 3􀀀space, Journal of Science and Art,47(2) (2019), 357-374.
  • [17] Y. U¨ nlu¨tu¨rk, Z. Savcı, On non-unit speed curves in Minkowski 3􀀀space, Scientia Magna, 8(4) (2012), 66-74.
  • [18] S. Birman, K. Nomuzi, Trigonometry in Lorentzian geometry, Am. Math. Monthly, 91 (1984).
  • [19] W. H. Greub, Linear Algebra, Academic Press, New York, 434 p., 1963.

The Geometry of Bezier Curves in Minkowski 3−Space

Year 2023, , 7 - 14, 28.03.2023
https://doi.org/10.32323/ujma.1238898

Abstract

The scope of this paper is to look at some aspects of the differential geometry of Bezier curves in Minkowski space. For that purpose, we firstly introduce Frenet Bezier curve in Minkowski 3-space. Especially, we investigate the Serret-Frenet frame, curvature and torsion of the Frenet Bezier curves at all points. Moreover, we give the Frenet apparatus of these curves at the end points.

References

  • [1] B. O’Neill, Semi-Riemann Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • [2] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44-107.
  • [3] G. Farin, History of Curves and Surfaces in CAGD, in: Handbook of CAGD, 2002.
  • [4] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer- Verlag, Berlin, 2nd ed, 2005.
  • [5] M. ˙Incesu, O. G¨ursoy, B´ezier E˘grilerinde Esas Formlar ve Eg˘rilikler, XVII Ulusal Matematik Sempozyumu, Bildiriler, Abant I˙zzet Baysal U¨ niversitesi, (2004), 146-157.
  • [6] G. H. Geoergiev, Shapes of Plane B´ezier Curves in Curve and Surface Design, Avignon, edited by P. Chenin, T. Lyche and L. L Schumaker, Nashboro Prees, Brentwood, TN, (2006) 143-152.
  • [7] G. H. Georgiev, On the shape of the cubic B´ezier Curve, Proc. Of International Congress Pure and Applied Differential Geometry- Brussels, edited by F. Dillen and I. Van de Woestyne, Shaker Verlag, Aachen,(2007), 98-106.
  • [8] G. H. Georgiev, Spacelike B´ezier curves in the three-dimensional Minkowski space, Proceedings of AIP Conference, 1067(1) (2008), 373-380.
  • [9] G. H. Georgiev, Constructions of spacelike B´ezier surfaces in the three-dimensional Minkowski space, Proceedings of AIP Conference 1184 (1)(2009), 199-206.
  • [10] P. Chalmoviansky, B. Pokorna, Quadratic space-like B´ezier curves in the three dimensional Minkowski space, Proceeding of Symposium on Computer Geometry, 20 (2011), 104-110.
  • [11] B. Pokorna, P. Chalmoviansky, Planar cubic spacelike B´ezier curves in three dimensional Minkowski space, Proceeding of Symposium on Computer Geometry, 23 (2012), 93-98.
  • [12] H. Ugail, M. C. Marquez, A. Yilmaz, On B´ezier surfaces in three-dimensional Minkowski space, Computers and Mathematics with Applications, 62 (2011), 2899-2912.
  • [13] H. Kus¸ak Samancı, S. C¸ elik, The curvatures of the spacelike B´ezier curve with a spacelike principal normal in Minkowski 3􀀀Space, International Journal of Mathematics and Computation, 29(4) (2018).
  • [14] S. C¸ elik, Investigation of B´ezier curves and surfaces from computer aided geometric design elements in Minkowski space, Master Thesis, Bitlis Eren University, 2017.
  • [15] H. Kus¸ak Samancı, Some geometric properties of the spacelike B´ezier curve with a timelike principal normal in Minkowski 3􀀀space, Cumhuriyet Science Journal, 39(1) (2018), 71-79.
  • [16] H. Kus¸ak Samancı, O¨ . Kalkan, S. C¸ elik, The timelike Be´zier spline in Minkowski 3􀀀space, Journal of Science and Art,47(2) (2019), 357-374.
  • [17] Y. U¨ nlu¨tu¨rk, Z. Savcı, On non-unit speed curves in Minkowski 3􀀀space, Scientia Magna, 8(4) (2012), 66-74.
  • [18] S. Birman, K. Nomuzi, Trigonometry in Lorentzian geometry, Am. Math. Monthly, 91 (1984).
  • [19] W. H. Greub, Linear Algebra, Academic Press, New York, 434 p., 1963.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ayşe Yılmaz Ceylan 0000-0002-8051-2879

Publication Date March 28, 2023
Submission Date January 18, 2023
Acceptance Date March 28, 2023
Published in Issue Year 2023

Cite

APA Ceylan, A. Y. (2023). The Geometry of Bezier Curves in Minkowski 3−Space. Universal Journal of Mathematics and Applications, 6(1), 7-14. https://doi.org/10.32323/ujma.1238898
AMA Ceylan AY. The Geometry of Bezier Curves in Minkowski 3−Space. Univ. J. Math. Appl. March 2023;6(1):7-14. doi:10.32323/ujma.1238898
Chicago Ceylan, Ayşe Yılmaz. “The Geometry of Bezier Curves in Minkowski 3−Space”. Universal Journal of Mathematics and Applications 6, no. 1 (March 2023): 7-14. https://doi.org/10.32323/ujma.1238898.
EndNote Ceylan AY (March 1, 2023) The Geometry of Bezier Curves in Minkowski 3−Space. Universal Journal of Mathematics and Applications 6 1 7–14.
IEEE A. Y. Ceylan, “The Geometry of Bezier Curves in Minkowski 3−Space”, Univ. J. Math. Appl., vol. 6, no. 1, pp. 7–14, 2023, doi: 10.32323/ujma.1238898.
ISNAD Ceylan, Ayşe Yılmaz. “The Geometry of Bezier Curves in Minkowski 3−Space”. Universal Journal of Mathematics and Applications 6/1 (March 2023), 7-14. https://doi.org/10.32323/ujma.1238898.
JAMA Ceylan AY. The Geometry of Bezier Curves in Minkowski 3−Space. Univ. J. Math. Appl. 2023;6:7–14.
MLA Ceylan, Ayşe Yılmaz. “The Geometry of Bezier Curves in Minkowski 3−Space”. Universal Journal of Mathematics and Applications, vol. 6, no. 1, 2023, pp. 7-14, doi:10.32323/ujma.1238898.
Vancouver Ceylan AY. The Geometry of Bezier Curves in Minkowski 3−Space. Univ. J. Math. Appl. 2023;6(1):7-14.

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