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Frenet Frames of Trigonometric B'ezier Curves

Year 2022, Volume: 14 Issue: 1, 124 - 128, 30.06.2022
https://doi.org/10.47000/tjmcs.1015220

Abstract

The geometry of curves and surfaces plays a very important role in computer-aided geometric design (CAGD). The goal of this paper is to construct the Frenet frames of trigonometric B\'ezier curves in Euclidean $ 2 $ and $ 3- $space. Especially, the curvatures of these curves are investigated at the beginning and the ending points.

References

  • Ammad, M., Misro, M.Y., Construction of local shape adjustable surfaces using quintic trigonometric B\'ezier curve, Symmetry, 12(2020), 1205.
  • Bashir, U., Abas, M., Awang, M., Ali, J., The quadratic trigonometric B\'ezier curve with single shape parameter, J. Basic Appl. Sci. Res., 2(2012), 2541-2546.
  • Dube, M., Sharma, R., Quartic trignometric B\'ezier curve with a shape parameter, Int. J. Math. Comput. Appl. Res., 3(2013), 89-96.
  • Gray, A., Abbena, E., Salamon, S., Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
  • Han, X.A., Ma, Y.C., Huang, X.L., The cubic trigonometric B\'ezier curve with two shape parameters, Applied Mathematics Letters, 22(2009), 226-231.
  • Han, X.A., Huang, X.L., Ma, Y.C., Shape analysis of cubic trigonometric B\'ezier curves with a shape parameter, Appl. Math. Comput., 217(2010), 2527-2533.
  • Misro, M., Ramli, A., Ali, J., Quintic trigonometric B\'ezier curve with two shape parameters, Sains Malaysiana, 46(2017), 825-831.
  • O'Neill, B., Elemantary Differential Geometry, Academic Press, Rev. 2nd.ed., Elsevier, USA, 2006.
  • Sharma, R., Quartic trigonometric B\'ezier curves and surfaces with shape parameter, Int. J. Innov. Res. Comput. Commun. Eng., 3297(2016), 7712–7717.
  • Sun, X., Ji, X., Parametric model for kitchen product based on cubic T-Bézier curves with symmetry, Symmetry, 12(2020), 505.
Year 2022, Volume: 14 Issue: 1, 124 - 128, 30.06.2022
https://doi.org/10.47000/tjmcs.1015220

Abstract

References

  • Ammad, M., Misro, M.Y., Construction of local shape adjustable surfaces using quintic trigonometric B\'ezier curve, Symmetry, 12(2020), 1205.
  • Bashir, U., Abas, M., Awang, M., Ali, J., The quadratic trigonometric B\'ezier curve with single shape parameter, J. Basic Appl. Sci. Res., 2(2012), 2541-2546.
  • Dube, M., Sharma, R., Quartic trignometric B\'ezier curve with a shape parameter, Int. J. Math. Comput. Appl. Res., 3(2013), 89-96.
  • Gray, A., Abbena, E., Salamon, S., Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
  • Han, X.A., Ma, Y.C., Huang, X.L., The cubic trigonometric B\'ezier curve with two shape parameters, Applied Mathematics Letters, 22(2009), 226-231.
  • Han, X.A., Huang, X.L., Ma, Y.C., Shape analysis of cubic trigonometric B\'ezier curves with a shape parameter, Appl. Math. Comput., 217(2010), 2527-2533.
  • Misro, M., Ramli, A., Ali, J., Quintic trigonometric B\'ezier curve with two shape parameters, Sains Malaysiana, 46(2017), 825-831.
  • O'Neill, B., Elemantary Differential Geometry, Academic Press, Rev. 2nd.ed., Elsevier, USA, 2006.
  • Sharma, R., Quartic trigonometric B\'ezier curves and surfaces with shape parameter, Int. J. Innov. Res. Comput. Commun. Eng., 3297(2016), 7712–7717.
  • Sun, X., Ji, X., Parametric model for kitchen product based on cubic T-Bézier curves with symmetry, Symmetry, 12(2020), 505.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ayşe Yılmaz Ceylan 0000-0001-7635-0830

Tunahan Turhan 0000-0002-9632-2180

Gözde Özkan Tükel 0000-0003-1800-5718

Publication Date June 30, 2022
Published in Issue Year 2022 Volume: 14 Issue: 1

Cite

APA Ceylan, A. Y., Turhan, T., & Özkan Tükel, G. (2022). Frenet Frames of Trigonometric B’ezier Curves. Turkish Journal of Mathematics and Computer Science, 14(1), 124-128. https://doi.org/10.47000/tjmcs.1015220
AMA Ceylan AY, Turhan T, Özkan Tükel G. Frenet Frames of Trigonometric B’ezier Curves. TJMCS. June 2022;14(1):124-128. doi:10.47000/tjmcs.1015220
Chicago Ceylan, Ayşe Yılmaz, Tunahan Turhan, and Gözde Özkan Tükel. “Frenet Frames of Trigonometric B’ezier Curves”. Turkish Journal of Mathematics and Computer Science 14, no. 1 (June 2022): 124-28. https://doi.org/10.47000/tjmcs.1015220.
EndNote Ceylan AY, Turhan T, Özkan Tükel G (June 1, 2022) Frenet Frames of Trigonometric B’ezier Curves. Turkish Journal of Mathematics and Computer Science 14 1 124–128.
IEEE A. Y. Ceylan, T. Turhan, and G. Özkan Tükel, “Frenet Frames of Trigonometric B’ezier Curves”, TJMCS, vol. 14, no. 1, pp. 124–128, 2022, doi: 10.47000/tjmcs.1015220.
ISNAD Ceylan, Ayşe Yılmaz et al. “Frenet Frames of Trigonometric B’ezier Curves”. Turkish Journal of Mathematics and Computer Science 14/1 (June 2022), 124-128. https://doi.org/10.47000/tjmcs.1015220.
JAMA Ceylan AY, Turhan T, Özkan Tükel G. Frenet Frames of Trigonometric B’ezier Curves. TJMCS. 2022;14:124–128.
MLA Ceylan, Ayşe Yılmaz et al. “Frenet Frames of Trigonometric B’ezier Curves”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 1, 2022, pp. 124-8, doi:10.47000/tjmcs.1015220.
Vancouver Ceylan AY, Turhan T, Özkan Tükel G. Frenet Frames of Trigonometric B’ezier Curves. TJMCS. 2022;14(1):124-8.