| | | |

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

#### Hatice Kuşak Samancı [1]

##### 55 228

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.

Bezier curve, CAGD, Minkowski space, space-like curve
• [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.
Primary Language en Engineering Articles Author: Hatice Kuşak SamancıCountry: Turkey Publication Date: April 15, 2018
 Bibtex @research article { konuralpjournalmath370669, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2018}, volume = {6}, pages = {144 - 148}, doi = {}, title = {Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal}, key = {cite}, author = {Kuşak Samancı, Hatice} } APA Kuşak Samancı, H . (2018). Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp Journal of Mathematics (KJM), 6 (1), 144-148. Retrieved from http://dergipark.org.tr/konuralpjournalmath/issue/31478/370669 MLA Kuşak Samancı, H . "Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal". Konuralp Journal of Mathematics (KJM) 6 (2018): 144-148 Chicago Kuşak Samancı, H . "Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal". Konuralp Journal of Mathematics (KJM) 6 (2018): 144-148 RIS TY - JOUR T1 - Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal AU - Hatice Kuşak Samancı Y1 - 2018 PY - 2018 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 144 EP - 148 VL - 6 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2018 ER - EndNote %0 Konuralp Journal of Mathematics (KJM) Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal %A Hatice Kuşak Samancı %T Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal %D 2018 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 6 %N 1 %R %U ISNAD Kuşak Samancı, Hatice . "Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal". Konuralp Journal of Mathematics (KJM) 6 / 1 (April 2018): 144-148. AMA Kuşak Samancı H . Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp J. Math.. 2018; 6(1): 144-148. Vancouver Kuşak Samancı H . Metric Properties of a Space-like Rational Bezier Curve with a Time-like Principal Normal. Konuralp Journal of Mathematics (KJM). 2018; 6(1): 148-144.