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

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.

Keywords:

Bezier curve, CAGD, Minkowski space space-like curve,

PDF

___

[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.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

Arşiv