Research Article
BibTex RIS Cite

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

Year 2018, Volume: 39 Issue: 1, 71 - 79, 16.03.2018

Hatice Kuşak Samancı

https://doi.org/10.17776/csj.344353
https://izlik.org/JA88RU46HB

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]. 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.

Zamanımsı Asal Normalli Uzayımsı Bezier Eğrisinin Bazı Geometrik Özellikleri

Year 2018, Volume: 39 Issue: 1, 71 - 79, 16.03.2018

Hatice Kuşak Samancı

https://doi.org/10.17776/csj.344353
https://izlik.org/JA88RU46HB

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.

Keywords

Bezier uzayımsı zamanımsı eğrilik burulma

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 Research Article
Authors

Hatice Kuşak Samancı

Submission Date October 14, 2017
Acceptance Date December 10, 2017
Publication Date March 16, 2018
DOI https://doi.org/10.17776/csj.344353
IZ https://izlik.org/JA88RU46HB
Published in Issue Year 2018 Volume: 39 Issue: 1

Cite

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

Cited By

Minkowski-3 Uzayında Timelike Rasyonel Bezier Eğrilerinin Eğrilikleri Üzerine
Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
Hatice KUŞAK SAMANCI
https://doi.org/10.17798/bitlisfen.420286
R3 de Açık B-Spline Eğrilerinin G-Benzerlikler
Muş Alparslan Üniversitesi Fen Bilimleri Dergisi
Muhsin İNCESU
https://doi.org/10.18586/msufbd.807153
The new characterization of ruled surfaces corresponding dual Bézier curves
Mathematical Methods in the Applied Sciences
Muhsin Incesu
https://doi.org/10.1002/mma.7398
THE SERRET-FRENET FRAME OF THE RATIONAL BEZIER CURVES IN THE EUCLIDEAN-3 SPACE BY ALGORITHM METHOD
Journal of Science and Arts
https://doi.org/10.46939/J.Sci.Arts-21.3-a12
Asymptotic Frame Fields of Rational Bézier Curves
Düzce Üniversitesi Bilim ve Teknoloji Dergisi
https://doi.org/10.29130/dubited.1016157
The Geometry of Bezier Curves in Minkowski 3−Space
Universal Journal of Mathematics and Applications
https://doi.org/10.32323/ujma.1238898
The quasi-frame of the rational and polynomial Bezier curve by algorithm method in Euclidean space
Engineering Computations
https://doi.org/10.1108/EC-04-2022-0193
Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space
Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.21597/jist.1243458

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December