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Dergiler / Journal of Engineering Technology and Applied Sciences / 2020 / Cilt: 5 Sayı: 3

Some Notes on Geometry of Bézier Curves in Euclidean 4-Space

Esra Erkan(HARRAN ÜNİVERSİTESİ)0000-0003-0456-6418
Salim Yüce(YILDIZ TEKNİK ÜNİVERSİTESİ)0000-0002-8296-6495
Sayfa
93–101
Yayın Tarihi
2020-12-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

For this purpose, the Serret-Frenet elements at every point, starting point and ending points are computed.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The main purpose of this paper is to investigate Bézier curves in the Euclidean space $E^4$ with respect to differential geometry.
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Temel Bulgular & Veri:The main purpose of this paper is to investigate Bézier curves in the Euclidean space $E^4$ with respect to differential geometry.
💡
Sonuç & Katkı:For this purpose, the Serret-Frenet elements at every point, starting point and ending points are computed.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bezier curve · Serret-Frenet frame · triple (ternary) product

Abstract

The main purpose of this paper is to investigate Bézier curves in the Euclidean space $E^4$ with respect to differential geometry. For this purpose, the Serret-Frenet elements at every point, starting point and ending points are computed.

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Bu Makaleye Atıf Yap

Erkan, E., Yüce, S. (2020). Some Notes on Geometry of Bézier Curves in Euclidean 4-Space. Journal of Engineering Technology and Applied Sciences, Cilt: 5 Sayı: 3, 93–101. https://doi.org/10.30931/jetas.837921

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Kaynakça (18)

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  5. Kenmotsu, K. “Periodic mean curvature and Bézier curves. Differential geometry and related topics”, World Sci. Publ., River Edge, NJ, (2002): 135-146.
  6. Georgiev, G. H. “On the shape of of the cubic Bézier curve. Pure and applied differential geometry—PADGE”, Ber. Math. Shaker Verlag, Aachen, (2007): 98-106.
  7. Samanci, H. K., Celik, S., Incesu, M., “The Bishop Frame of Bezier Curves”, Life Science Journal, 12(6), (2015).
  8. Erkan, E., Yüce, S., “Serret-Frenet Frame and Curvatures of Bézier Curves”, Mathematics, 6(12), (2018): 321-321.
  9. Aléssio, O., Düldül, M., Düldül B. U., Badr S. A., Abdel-All N. H., “Differential geometry of non-transversal intersection curves of three parametric hypersurfaces in Euclidean 4-space”, Comput. Aided Geom. Des., 31 (2014): 712-727.
  10. Williams, M. Z., Stein, F. M., “A triple product of vectors in four-space”, Math Mag 37 (1964): 230-235.
  11. Shaw, R., “Vector cross products in dimensions”, Int. J. Math. Educ. Sci. Technol., 18(6), (1987): 803-816.
  12. Aléssio, O., “Differential geometry of intersection curves in R^4 three implicit surfaces”, Comput. Aided Geom. Des., 26 (2009): 455-471.
  13. Kenmotsu, K. “Periodic mean curvature and Bézier curves. Differential geometry and related topics”, World Sci. Publ., River Edge, NJ, (2002): 135-146.
  14. Georgiev, G. H. “On the shape of of the cubic Bézier curve. Pure and applied differential geometry—PADGE”, Ber. Math. Shaker Verlag, Aachen, (2007): 98-106.
  15. Erkan, E., Yüce, S., “Serret-Frenet Frame and Curvatures of Bézier Curves”, Mathematics, 6(12), (2018): 321-321.
  16. Williams, M. Z., Stein, F. M., “A triple product of vectors in four-space”, Math Mag 37 (1964): 230-235.
  17. Shaw, R., “Vector cross products in dimensions”, Int. J. Math. Educ. Sci. Technol., 18(6), (1987): 803-816.
  18. Aléssio, O., “Differential geometry of intersection curves in R^4 three implicit surfaces”, Comput. Aided Geom. Des., 26 (2009): 455-471.