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

Year 2023, Volume: 13 Issue: 4, 2926 - 2933, 01.12.2023
https://doi.org/10.21597/jist.1243458

Abstract

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.

References

  • 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.
  • Georgiev, G.H. (2008). Spacelike Bezier Curves in the Three-dimensional Minkowski Space, Proceedings of AIP Conference, 1067(1): 373-380.
  • Farin, G. (2002). Curves and Surfaces for CAGD: a practical guide, Morgan Kaufmann Publications, USA.
  • Kulahci, M., Bektas, M. and Ergüt, M. (2007). Curves of AW(k)-Type in 3-Dimensional Null Cone, Physics Letters A 371, 275-277.
  • Kulahci, M and Almaz, F.(2017). Some Characterizations of Osculating in the Lightlike Cone, Bol. Soc. Paran. Math. 35(2), 39-48.
  • Marsh, D. (2005). Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, USA, 2005.
  • Liu, H. (2004). Curves in the Lightlike Cone. Contributions to Algebra and Geometry, 45(1), pp. 291-303, 2004.
  • 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.
  • López, R. (2014). Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. International Electronic Journal of Geometry, 7(1), pp. 44-107.
  • Kuşak Samancı, H. (2018). Minkowski 3-uzayında Timelike Rasyonel Bézier Eğrilerinin Eğrilikleri Üzerine. Bitlis Üniversitesi Fen Bilimleri Dergisi, 7(2), pp. 243-255.
  • 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.
  • Çelik, S. (2017). Investigation of Bezier curve and surfaces in Minkowski space from computer aided geometric design elements, Master Thesis, Bitlis Eren University.
  • 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.
  • 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.
  • 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.
  • 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.
  • Ugail, H., Márquez, MC and Yılmaz A, 2011. On Bézier surfaces in three-dimensional Minkowski space. Computers & Mathematics with Applications, 62 (8): 2899-2912.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

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

Year 2023, Volume: 13 Issue: 4, 2926 - 2933, 01.12.2023
https://doi.org/10.21597/jist.1243458

Abstract

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

References

  • 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.
  • Georgiev, G.H. (2008). Spacelike Bezier Curves in the Three-dimensional Minkowski Space, Proceedings of AIP Conference, 1067(1): 373-380.
  • Farin, G. (2002). Curves and Surfaces for CAGD: a practical guide, Morgan Kaufmann Publications, USA.
  • Kulahci, M., Bektas, M. and Ergüt, M. (2007). Curves of AW(k)-Type in 3-Dimensional Null Cone, Physics Letters A 371, 275-277.
  • Kulahci, M and Almaz, F.(2017). Some Characterizations of Osculating in the Lightlike Cone, Bol. Soc. Paran. Math. 35(2), 39-48.
  • Marsh, D. (2005). Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, USA, 2005.
  • Liu, H. (2004). Curves in the Lightlike Cone. Contributions to Algebra and Geometry, 45(1), pp. 291-303, 2004.
  • 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.
  • López, R. (2014). Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. International Electronic Journal of Geometry, 7(1), pp. 44-107.
  • Kuşak Samancı, H. (2018). Minkowski 3-uzayında Timelike Rasyonel Bézier Eğrilerinin Eğrilikleri Üzerine. Bitlis Üniversitesi Fen Bilimleri Dergisi, 7(2), pp. 243-255.
  • 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.
  • Çelik, S. (2017). Investigation of Bezier curve and surfaces in Minkowski space from computer aided geometric design elements, Master Thesis, Bitlis Eren University.
  • 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.
  • 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.
  • 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.
  • 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.
  • Ugail, H., Márquez, MC and Yılmaz A, 2011. On Bézier surfaces in three-dimensional Minkowski space. Computers & Mathematics with Applications, 62 (8): 2899-2912.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Filiz Ertem Kaya 0000-0003-1538-9154

Early Pub Date November 30, 2023
Publication Date December 1, 2023
Submission Date January 27, 2023
Acceptance Date August 14, 2023
Published in Issue Year 2023 Volume: 13 Issue: 4

Cite

APA Ertem Kaya, F. (2023). Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space. Journal of the Institute of Science and Technology, 13(4), 2926-2933. https://doi.org/10.21597/jist.1243458
AMA Ertem Kaya F. Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space. J. Inst. Sci. and Tech. December 2023;13(4):2926-2933. doi:10.21597/jist.1243458
Chicago Ertem Kaya, Filiz. “Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space”. Journal of the Institute of Science and Technology 13, no. 4 (December 2023): 2926-33. https://doi.org/10.21597/jist.1243458.
EndNote Ertem Kaya F (December 1, 2023) Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space. Journal of the Institute of Science and Technology 13 4 2926–2933.
IEEE F. Ertem Kaya, “Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space”, J. Inst. Sci. and Tech., vol. 13, no. 4, pp. 2926–2933, 2023, doi: 10.21597/jist.1243458.
ISNAD Ertem Kaya, Filiz. “Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space”. Journal of the Institute of Science and Technology 13/4 (December 2023), 2926-2933. https://doi.org/10.21597/jist.1243458.
JAMA Ertem Kaya F. Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space. J. Inst. Sci. and Tech. 2023;13:2926–2933.
MLA Ertem Kaya, Filiz. “Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space”. Journal of the Institute of Science and Technology, vol. 13, no. 4, 2023, pp. 2926-33, doi:10.21597/jist.1243458.
Vancouver Ertem Kaya F. Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space. J. Inst. Sci. and Tech. 2023;13(4):2926-33.