Research Article
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.
References
- [1]. Ratcliffe J.G., Foundations of hyperbolic manifolds, Graduate texts in mathematics, vol. 149, 2nd edition, 2006.
- [2]. Lopez R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int. Electron. J. Geom., 7-1 (2014) 44-107.
- [3]. Farin G., Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
- [4]. Marsh D., Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006.
- [5]. İncesu M., Gursoy, O., Bezier Eğrilerinde Esas Formlar ve Eğrilikler, XVII Ulusal Matematik Sempozyumu, Bildiriler, Abant İzzet Baysal Üniversitesi, (2004) 146-157.
- [6]. Georgiev G.H. Spacelike Bezier Curves in the Three-dimensional Minkowski space, Proceedings of AIP Conference, 1067-1 (2008) .
- [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]. 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]. 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.
Year 2018,
Volume: 39 Issue: 1, 71 - 79, 16.03.2018
Abstract
Bu çalışmanın amacı Minkowski 3-uzayında
zamanımsı asal normalli uzayımsı Bezier eğrisini tantmak ve incelemektir.
Eğrinin başlangıç ve bitiş noktasındaki Serret-Frenet çatısı, eğrilikleri ve
türev formülleri çalışılmıştır.
References
- [1]. Ratcliffe J.G., Foundations of hyperbolic manifolds, Graduate texts in mathematics, vol. 149, 2nd edition, 2006.
- [2]. Lopez R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int. Electron. J. Geom., 7-1 (2014) 44-107.
- [3]. Farin G., Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
- [4]. Marsh D., Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006.
- [5]. İncesu M., Gursoy, O., Bezier Eğrilerinde Esas Formlar ve Eğrilikler, XVII Ulusal Matematik Sempozyumu, Bildiriler, Abant İzzet Baysal Üniversitesi, (2004) 146-157.
- [6]. Georgiev G.H. Spacelike Bezier Curves in the Three-dimensional Minkowski space, Proceedings of AIP Conference, 1067-1 (2008) .
- [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]. 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]. 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.
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | March 16, 2018 |
| Submission Date | October 14, 2017 |
| Acceptance Date | December 10, 2017 |
| Published in Issue | Year 2018Volume: 39 Issue: 1 |
