Research Article

The Geometry of Bezier Curves in Minkowski 3−Space

Volume: 6 Number: 1 March 28, 2023
EN

The Geometry of Bezier Curves in Minkowski 3−Space

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.

Keywords

Curvature, Serret-Frenet frame, Minkowski ´ 3−Space., Bezier Curve

References

  1. [1] B. O’Neill, Semi-Riemann Geometry with Applications to Relativity, Academic Press, New York, 1983.
  2. [2] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44-107.
  3. [3] G. Farin, History of Curves and Surfaces in CAGD, in: Handbook of CAGD, 2002.
  4. [4] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer- Verlag, Berlin, 2nd ed, 2005.
  5. [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. [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. [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. [8] G. H. Georgiev, Spacelike B´ezier curves in the three-dimensional Minkowski space, Proceedings of AIP Conference, 1067(1) (2008), 373-380.
  9. [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. [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.
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
1.Ceylan AY. The Geometry of Bezier Curves in Minkowski 3−Space. Univ. J. Math. Appl. 2023;6(1):7-14. doi:10.32323/ujma.1238898
Chicago
Ceylan, Ayşe Yılmaz. 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.
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
[1]A. Y. Ceylan, “The Geometry of Bezier Curves in Minkowski 3−Space”, Univ. J. Math. Appl., vol. 6, no. 1, pp. 7–14, Mar. 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 1, 2023): 7-14. https://doi.org/10.32323/ujma.1238898.
JAMA
1.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, Mar. 2023, pp. 7-14, doi:10.32323/ujma.1238898.
Vancouver
1.Ayşe Yılmaz Ceylan. The Geometry of Bezier Curves in Minkowski 3−Space. Univ. J. Math. Appl. 2023 Mar. 1;6(1):7-14. doi:10.32323/ujma.1238898