Research Article
Year 2020,
Volume: 5 Issue: 3, 93 - 101, 31.12.2020
Abstract
References
- 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.
Year 2020,
Volume: 5 Issue: 3, 93 - 101, 31.12.2020
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.
References
- 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.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 31, 2020 |
| Published in Issue | Year 2020 Volume: 5 Issue: 3 |