Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 5 Sayı: 3, 93 - 101, 31.12.2020
https://doi.org/10.30931/jetas.837921

Öz

Kaynakça

  • Forrest, A. R., “Curves and surfaces for computer-aided design”, University of Cambridge, United Kingdom, Cambridge, (1968).
  • Anand, V. B., “Computer graphics and geometric modeling for engineers”, John Wiley and Sons Inc. (First Edition), New York, (1992).
  • Farin, G., “Curves and surfaces for computer aided geometric design a practical guide”, Academic Press (Fourth Edition), San Diego, (1996).
  • Marsh, D., “Applied geometry for computer graphics and CAD”, Springer-Verlag London Berlin Heidelberg (Second Edition), (2000).
  • Kenmotsu, K. “Periodic mean curvature and Bézier curves. Differential geometry and related topics”, World Sci. Publ., River Edge, NJ, (2002) : 135-146.
  • 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.
  • Samanci, H. K., Celik, S., Incesu, M., “The Bishop Frame of Bezier Curves”, Life Science Journal, 12(6), (2015).
  • Erkan, E., Yüce, S., “Serret-Frenet Frame and Curvatures of Bézier Curves”, Mathematics, 6(12), (2018) : 321-321.
  • 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.
  • Williams, M. Z., Stein, F. M., “A triple product of vectors in four-space”, Math Mag 37 (1964) : 230-235.
  • Shaw, R., “Vector cross products in dimensions”, Int. J. Math. Educ. Sci. Technol., 18(6), (1987) : 803-816.
  • Aléssio, O., “Differential geometry of intersection curves in R^4 three implicit surfaces”, Comput. Aided Geom. Des., 26 (2009) : 455-471.

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

Yıl 2020, Cilt: 5 Sayı: 3, 93 - 101, 31.12.2020
https://doi.org/10.30931/jetas.837921

Öz

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.

Kaynakça

  • Forrest, A. R., “Curves and surfaces for computer-aided design”, University of Cambridge, United Kingdom, Cambridge, (1968).
  • Anand, V. B., “Computer graphics and geometric modeling for engineers”, John Wiley and Sons Inc. (First Edition), New York, (1992).
  • Farin, G., “Curves and surfaces for computer aided geometric design a practical guide”, Academic Press (Fourth Edition), San Diego, (1996).
  • Marsh, D., “Applied geometry for computer graphics and CAD”, Springer-Verlag London Berlin Heidelberg (Second Edition), (2000).
  • Kenmotsu, K. “Periodic mean curvature and Bézier curves. Differential geometry and related topics”, World Sci. Publ., River Edge, NJ, (2002) : 135-146.
  • 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.
  • Samanci, H. K., Celik, S., Incesu, M., “The Bishop Frame of Bezier Curves”, Life Science Journal, 12(6), (2015).
  • Erkan, E., Yüce, S., “Serret-Frenet Frame and Curvatures of Bézier Curves”, Mathematics, 6(12), (2018) : 321-321.
  • 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.
  • Williams, M. Z., Stein, F. M., “A triple product of vectors in four-space”, Math Mag 37 (1964) : 230-235.
  • Shaw, R., “Vector cross products in dimensions”, Int. J. Math. Educ. Sci. Technol., 18(6), (1987) : 803-816.
  • Aléssio, O., “Differential geometry of intersection curves in R^4 three implicit surfaces”, Comput. Aided Geom. Des., 26 (2009) : 455-471.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Esra Erkan 0000-0003-0456-6418

Salim Yüce 0000-0002-8296-6495

Yayımlanma Tarihi 31 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 5 Sayı: 3

Kaynak Göster

APA Erkan, E., & Yüce, S. (2020). Some Notes on Geometry of Bézier Curves in Euclidean 4-Space. Journal of Engineering Technology and Applied Sciences, 5(3), 93-101. https://doi.org/10.30931/jetas.837921
AMA Erkan E, Yüce S. Some Notes on Geometry of Bézier Curves in Euclidean 4-Space. JETAS. Aralık 2020;5(3):93-101. doi:10.30931/jetas.837921
Chicago Erkan, Esra, ve Salim Yüce. “Some Notes on Geometry of Bézier Curves in Euclidean 4-Space”. Journal of Engineering Technology and Applied Sciences 5, sy. 3 (Aralık 2020): 93-101. https://doi.org/10.30931/jetas.837921.
EndNote Erkan E, Yüce S (01 Aralık 2020) Some Notes on Geometry of Bézier Curves in Euclidean 4-Space. Journal of Engineering Technology and Applied Sciences 5 3 93–101.
IEEE E. Erkan ve S. Yüce, “Some Notes on Geometry of Bézier Curves in Euclidean 4-Space”, JETAS, c. 5, sy. 3, ss. 93–101, 2020, doi: 10.30931/jetas.837921.
ISNAD Erkan, Esra - Yüce, Salim. “Some Notes on Geometry of Bézier Curves in Euclidean 4-Space”. Journal of Engineering Technology and Applied Sciences 5/3 (Aralık 2020), 93-101. https://doi.org/10.30931/jetas.837921.
JAMA Erkan E, Yüce S. Some Notes on Geometry of Bézier Curves in Euclidean 4-Space. JETAS. 2020;5:93–101.
MLA Erkan, Esra ve Salim Yüce. “Some Notes on Geometry of Bézier Curves in Euclidean 4-Space”. Journal of Engineering Technology and Applied Sciences, c. 5, sy. 3, 2020, ss. 93-101, doi:10.30931/jetas.837921.
Vancouver Erkan E, Yüce S. Some Notes on Geometry of Bézier Curves in Euclidean 4-Space. JETAS. 2020;5(3):93-101.