Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space

Öz

In this paper Gaussian, Mean and total curvature formulae of Rational Bezier Curves with asymptotic frame field are calculated by using its curvatures in 3- dimensional lightlike cone in Minkowski 4- Space. Our main intention is to introduce and investigate some differential geometric properties of the the Rational Bezier Curves with asymptotic frame field in 3- dimensional lightlike cone in Minkowski 4- Space by using its curvatures.

Anahtar Kelimeler

• Gauss Curvature
• Mean Curvature
• Total Curvature
• Minkowski 4-Space
• Rational Bezier Curves

Minkowski 4-Uzayda Rasyonel Bezier Eğrilerinin Gauss, Ortalama ve Total Eğriliklerinin Formüleri

Öz

Bu makale Minkowski 4-Uzayda 3-boyutlu ışıksı konide asimtotik çatılı Rasyonel Bezier eğrilerinin eğriliklerini kullanarak Gauss, Ortalama ve Total eğriliklerinin hesaplanmasını sunmaktadır.

Anahtar Kelimeler

• Gauss eğriliği
• ortalama eğrilik
• total eğrilik

Kaynakça

1. Almaz F., Külahcı, M. A. and Yılmaz, M. Y. (2020). Approximation To The Smarandache Curves in the The Null Cone, Palestine Journal of Mathematics, Vol. 9(1), 527-536.
2. Georgiev, G.H. (2008). Spacelike Bezier Curves in the Three-dimensional Minkowski Space, Proceedings of AIP Conference, 1067(1): 373-380.
3. Farin, G. (2002). Curves and Surfaces for CAGD: a practical guide, Morgan Kaufmann Publications, USA.
4. Kulahci, M., Bektas, M. and Ergüt, M. (2007). Curves of AW(k)-Type in 3-Dimensional Null Cone, Physics Letters A 371, 275-277.
5. Kulahci, M and Almaz, F.(2017). Some Characterizations of Osculating in the Lightlike Cone, Bol. Soc. Paran. Math. 35(2), 39-48.
6. Marsh, D. (2005). Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, USA, 2005.
7. Liu, H. (2004). Curves in the Lightlike Cone. Contributions to Algebra and Geometry, 45(1), pp. 291-303, 2004.
8. Liu, H. and Qingxian, M. (2011). Representation Formulas of Curves in a Two-and Three dimensional Lightlike Cone. Results in Mathematics, 59 (3), pp. 437-451.

9. López, R. (2014). Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. International Electronic Journal of Geometry, 7(1), pp. 44-107.
10. Kuşak Samancı, H. (2018). Minkowski 3-uzayında Timelike Rasyonel Bézier Eğrilerinin Eğrilikleri Üzerine. Bitlis Üniversitesi Fen Bilimleri Dergisi, 7(2), pp. 243-255.
11. Kuşak Samancı, H.(2018). Some Geometric Properties of the Spacelike Bézier Curve with a Timelike Principal Normal in Minkowski 3-space. Cumhuriyet Science Journal, 39(1), pp. 71-79.
12. Çelik, S. (2017). Investigation of Bezier curve and surfaces in Minkowski space from computer aided geometric design elements, Master Thesis, Bitlis Eren University.
13. 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, 2018.
14. Kuşak Samancı, H. and Çelik, S. (2018). “The Curvatures of the Spacelike Bezier Curve with a Spacelike Principal Normal in Minkowski 3-space”, International Journal of Mathematics and Computation, (29)4.
15. Kuşak Samancı, H., Kalkan, O. and Celik, S. (2019). The Timelike Bezier Spline in Minkowski 3-Space. Journal of Science and Arts, 19(2), 357-374.
16. Kuşak Samancı, H., Çelik S. and İncesu, M. (2020), The Shape Operator of The Bezier Surfaces in Minkowski 3 space, Journal of Science and Arts, vol. 4, no. 53, pp. 865–880.
17. Ugail, H., Márquez, MC and Yılmaz A, 2011. On Bézier surfaces in three-dimensional Minkowski space. Computers & Mathematics with Applications, 62 (8): 2899-2912.
18. Özkan Tükel, G. and Yücesan, A. (2015). Elastic Curves in a Two-dimensional Lightlike Cone. International Electronic Journal of Geometry, 8(2), pp. 1-8.
19. Özkan Tükel, G., Yücesan, A. and Yılmaz Ceylan, A. (2021). Asymtotic frame field Rational Bezier curves. Düzce University Journal of Science & Technology, 9, pp. 259-268.
20. Yılmaz Ceylan, A., Turhan, T. and Özkan Tükel, (2021), G. On the Geometry of Rational Bézıer Curves. Honam Mathematical Journal, 43(1), pp. 88-99.
21. Turhan, T., Yılmaz Ceylan, A. and Özkan Tükel, G. (2021). Rational Bézier Curves on 2-dimensional Anti de Sitter Space. International Asian Congress on Contemporary Sciences-V, Nakhchivan, Azerbaijan, pp. 467-473.
22. Yılmaz Ceylan, A., Turhan, T. and Özkan Tükel, G. (2020). On Non-null Rational Bézier Curves on 2-dimensional de Sitter Space. 4th International Conference on Mathematics ”An İstanbul Meeting for World Mathematicians,” İstanbul, Turkey, pp. 132.
23. Ertem Kaya, F. (2022). A special calculations of Rational Bezier curves in Minkowski 3 and 4-Spaces. 1. International Conference on Engineering and Applied Naturel Science [online], 10-13 May.
24. Ertem Kaya, F. (2022). Total Curvature Integral Equation type of Spacelike Quadratic Rational Bezier curves in Minkowski 3- Space, IV. International Turkıc World Congress on Science and Engineering, June 23-24, 2022, Niğde - TURKEY.