Research Article

Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space

Volume: 39 Number: 1 March 16, 2018
EN TR

Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space

Abstract

The aim of present paper is to introduce and investigate the spacelike Bezier curve with a timelike principal normal in Minkowski 3-space. The Serret-Frenet frame, curvatures and the derivation formulas of the curve at the starting and ending points are studied.

Keywords

Bezier,spacelike,timelike,curvature,torsion

References

  1. [1]. Ratcliffe J.G., Foundations of hyperbolic manifolds, Graduate texts in mathematics, vol. 149, 2nd edition, 2006.
  2. [2]. Lopez R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int. Electron. J. Geom., 7-1 (2014) 44-107.
  3. [3]. Farin G., Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
  4. [4]. Marsh D., Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006.
  5. [5]. İncesu M., Gursoy, O., Bezier Eğrilerinde Esas Formlar ve Eğrilikler, XVII Ulusal Matematik Sempozyumu, Bildiriler, Abant İzzet Baysal Üniversitesi, (2004) 146-157.
  6. [6]. Georgiev G.H. Spacelike Bezier Curves in the Three-dimensional Minkowski space, Proceedings of AIP Conference, 1067-1 (2008) .
  7. [7]. Chalmoviansky P., Pokorna B., Quadratic Spacelike Bezier Curves in the three dimensional Minkowski Space, Proceeding of Symposium on Computer Geometry, 20 (2011) 104-110.
  8. [8]. Pokorna B., Chalmovianski P., Planar Cubic Spacelike Bezier Curves in Three Dimensional Minkowski Space, Proceeding of Syposium on Computer Geometry, SCG, 23 (2012).93-98.
  9. [9]. Bükcü B., Karacan M., Bishop Frame of the Spacelike Curve with a Spacelike Principal Normal in Minkowski 3-space , Commun. Fac. Sci. Univ. Ank. Series, A1, 57-1 (2008) 13-22.
APA
Kuşak Samancı, H. (2018). Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space. Cumhuriyet Science Journal, 39(1), 71-79. https://doi.org/10.17776/csj.344353
AMA
1.Kuşak Samancı H. Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space. CSJ. 2018;39(1):71-79. doi:10.17776/csj.344353
Chicago
Kuşak Samancı, Hatice. 2018. “Some Geometric Properties of The Spacelike Bezier Curve With a Timelike Principal Normal in Minkowski 3-Space”. Cumhuriyet Science Journal 39 (1): 71-79. https://doi.org/10.17776/csj.344353.
EndNote
Kuşak Samancı H (March 1, 2018) Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space. Cumhuriyet Science Journal 39 1 71–79.
IEEE
[1]H. Kuşak Samancı, “Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space”, CSJ, vol. 39, no. 1, pp. 71–79, Mar. 2018, doi: 10.17776/csj.344353.
ISNAD
Kuşak Samancı, Hatice. “Some Geometric Properties of The Spacelike Bezier Curve With a Timelike Principal Normal in Minkowski 3-Space”. Cumhuriyet Science Journal 39/1 (March 1, 2018): 71-79. https://doi.org/10.17776/csj.344353.
JAMA
1.Kuşak Samancı H. Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space. CSJ. 2018;39:71–79.
MLA
Kuşak Samancı, Hatice. “Some Geometric Properties of The Spacelike Bezier Curve With a Timelike Principal Normal in Minkowski 3-Space”. Cumhuriyet Science Journal, vol. 39, no. 1, Mar. 2018, pp. 71-79, doi:10.17776/csj.344353.
Vancouver
1.Hatice Kuşak Samancı. Some Geometric Properties of The Spacelike Bezier Curve with a Timelike Principal Normal in Minkowski 3-Space. CSJ. 2018 Mar. 1;39(1):71-9. doi:10.17776/csj.344353