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Year 2018, Volume: 6 Issue: 1, 144 - 148, 15.04.2018

Abstract

References

  • [1] P. Bezier, Essai de definition numerique des courbes et des surfaces experimentales: contributions a l'etude des proprietes des courbes et des surfaces parametriques polynominales à coefficients vectoriels. Textes (Doctoral dissertation,)1977.
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  • [8] Planar cubic space-like Bézier curves in three dimensional Minkowski space, Proceedings of Symposium on Computer Geo. 21(2012)93-98.
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  • [10] A. Yilmaz, Bezier Curves and Surfaces. Master Thesis, Akdeniz Unv., Antalya, Turkey, 2009.

Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal

Year 2018, Volume: 6 Issue: 1, 144 - 148, 15.04.2018

Abstract

Rational Bezier curves are one of the most important computer graphics for the computer-aided geometric design (CAGD). This paper presents certain metric properties of a space-like rational Bezier curve with time-like principal normal in Minkowski 3-space. First, the Bezier curve is defined in Minkowski space. Then, Serret-Frenet frames, the curvatures, and the torsions of the curve are obtained for each space-like condition. Finally, the derivative formulas of the curve are calculated, and a numerical example is given.

References

  • [1] P. Bezier, Essai de definition numerique des courbes et des surfaces experimentales: contributions a l'etude des proprietes des courbes et des surfaces parametriques polynominales à coefficients vectoriels. Textes (Doctoral dissertation,)1977.
  • [2] De Casteljau, Shape mathematics and CAD (Vol. 2), Kogan Page, 1986.
  • [3] G. Farin, Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
  • [4] G.H. Georgiev, Spacelike Bezier curves in the three-dimensional Minkowski space, Proceedings of AIP Conference 1067 (1)(2008).
  • [5] M.Incesu and O.G\"{u}rsoy, Bezier Eğrilerinde Esas Formlar ve Eğrilikler, XVII Ulusal Matematik Sempozyumu, Bildiriler, Abant İzzet Baysal Ün.,(2004)146-157.
  • [6] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space”, arXiv preprint arXiv:0810.3351,(2008).
  • [7] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer-Verlag, Berlin, 2nd edn, 2005.
  • [8] Planar cubic space-like Bézier curves in three dimensional Minkowski space, Proceedings of Symposium on Computer Geo. 21(2012)93-98.
  • [9] B. Pokorn\'{a}, P. Chalmoviansk\'{y}, Quadratic space-like Bézier curves in the three dimensional Minkowski space, Proceedings of Symposium on Computer Geo. 20(2011) 104-110.
  • [10] A. Yilmaz, Bezier Curves and Surfaces. Master Thesis, Akdeniz Unv., Antalya, Turkey, 2009.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Hatice Kuşak Samancı

Publication Date April 15, 2018
Submission Date December 25, 2017
Acceptance Date April 6, 2018
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Kuşak Samancı, H. (2018). Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp Journal of Mathematics, 6(1), 144-148.
AMA Kuşak Samancı H. Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp J. Math. April 2018;6(1):144-148.
Chicago Kuşak Samancı, Hatice. “Metric Properties of a Space-Like Rational Bezier Curve With a Time-Like Principal Normal”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 144-48.
EndNote Kuşak Samancı H (April 1, 2018) Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp Journal of Mathematics 6 1 144–148.
IEEE H. Kuşak Samancı, “Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal”, Konuralp J. Math., vol. 6, no. 1, pp. 144–148, 2018.
ISNAD Kuşak Samancı, Hatice. “Metric Properties of a Space-Like Rational Bezier Curve With a Time-Like Principal Normal”. Konuralp Journal of Mathematics 6/1 (April 2018), 144-148.
JAMA Kuşak Samancı H. Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp J. Math. 2018;6:144–148.
MLA Kuşak Samancı, Hatice. “Metric Properties of a Space-Like Rational Bezier Curve With a Time-Like Principal Normal”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 144-8.
Vancouver Kuşak Samancı H. Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp J. Math. 2018;6(1):144-8.
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