Araştırma Makalesi
Yıl 2023,
Cilt: 15 Sayı: 2, 414 - 422, 31.12.2023
Öz
The first and second derivatives of a curve provide us fundamental
information in the study of the behavior of curve near a point. However,
if a curve is a polynomial space curve of degree n, we don’t know what
is the geometric meaning of the n-th derivative of the curve? There is no
doubt that the Frenet frame is not suitable for this purpose because it is
constructed by using first and second derivatives of a curve. On the other
hand, in this paper by using a new frame called as Flc-frame we are able
to give the geometric meaning of the n-th derivative of a curve. Moreover,
we explore some basic concepts regarding polynomial space curves from
point of view of Flc-frame in three dimensional Euclidean space.
Anahtar Kelimeler
Kaynakça
- Ayvacı, K.H., Senyurt, S., Canlı, D., Some characterizations of spherical indicatrix curves generated by Flc frame, Turk. J. Math. Comput. Sci., 13(2021), 379–387.
- Bishop, R.L., There is more than one way to frame a curve, Amer. Math. Monthly, 82(1975), 246–251.
- Dede, M., A new representation of tubular surfaces, Houston Journal of Mathematics, 45(2018), 707–720.
- Dede, M., Ekici, C., Görgülü, A., Directional q-frame along a space curve, IJARCSSE, 5(2015), 775–780.
- Farouki, R. T., Pythagorean-Hodograph Curves: Algebra and Geometry, Springer, 2008.
- Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition, CRC Press, Boca Raton, 1998.
- Guggenheimer, H., Computing frames along a trajectory, Comput. Aided Geom. Des., 6(1989), 77–78.
- Jüttler, B., Maurer, C., Cubic Pythagorean Hodograph spline curves and applications to sweep surface modeling, Comput. Aided Design, 31(1999), 73–83.
- Li, Y., Eren, K., Ayvacı, K.H., Ersoy, S., Simultaneous characterizations of partner ruled surfaces using Flc frame, AIMS Math., 7(2022), 20213–20229.
- Ravani, R., Meghdari A., Ravani, B., Rational Frenet-Serret curves and rotation minimizing frames in spatial motion design, IEEE international conference on Intelligent engineering systems, (2004), 186–192.
- Schot, S.H., Geometry of the third derivative, Mathematics Magazine, 51(1978), 259–275.
- Schot, S.H., Geometrical properties of the penosculating tonics of a plane curve, Amer. Math. Monthly, 82(1979), 449–457.
- Senyurt, S., Ayvacı, K.H., On geometry of focal surfaces due to Flc frame in Euclidean 3-space, Authorea, (2022).
- Wang, W., Juttler, B., Zheng, D., Liu, Y., Computation of rotation minimizing frame, ACM Trans. Graph., 27(2008), article no. 2.
Yıl 2023,
Cilt: 15 Sayı: 2, 414 - 422, 31.12.2023
Öz
Kaynakça
- Ayvacı, K.H., Senyurt, S., Canlı, D., Some characterizations of spherical indicatrix curves generated by Flc frame, Turk. J. Math. Comput. Sci., 13(2021), 379–387.
- Bishop, R.L., There is more than one way to frame a curve, Amer. Math. Monthly, 82(1975), 246–251.
- Dede, M., A new representation of tubular surfaces, Houston Journal of Mathematics, 45(2018), 707–720.
- Dede, M., Ekici, C., Görgülü, A., Directional q-frame along a space curve, IJARCSSE, 5(2015), 775–780.
- Farouki, R. T., Pythagorean-Hodograph Curves: Algebra and Geometry, Springer, 2008.
- Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition, CRC Press, Boca Raton, 1998.
- Guggenheimer, H., Computing frames along a trajectory, Comput. Aided Geom. Des., 6(1989), 77–78.
- Jüttler, B., Maurer, C., Cubic Pythagorean Hodograph spline curves and applications to sweep surface modeling, Comput. Aided Design, 31(1999), 73–83.
- Li, Y., Eren, K., Ayvacı, K.H., Ersoy, S., Simultaneous characterizations of partner ruled surfaces using Flc frame, AIMS Math., 7(2022), 20213–20229.
- Ravani, R., Meghdari A., Ravani, B., Rational Frenet-Serret curves and rotation minimizing frames in spatial motion design, IEEE international conference on Intelligent engineering systems, (2004), 186–192.
- Schot, S.H., Geometry of the third derivative, Mathematics Magazine, 51(1978), 259–275.
- Schot, S.H., Geometrical properties of the penosculating tonics of a plane curve, Amer. Math. Monthly, 82(1979), 449–457.
- Senyurt, S., Ayvacı, K.H., On geometry of focal surfaces due to Flc frame in Euclidean 3-space, Authorea, (2022).
- Wang, W., Juttler, B., Zheng, D., Liu, Y., Computation of rotation minimizing frame, ACM Trans. Graph., 27(2008), article no. 2.
Toplam 14 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 15 Sayı: 2 |