Yıl: 2022 Cilt: 71 Sayı: 1 Sayfa Aralığı: 39 - 50 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.878766 İndeks Tarihi: 29-07-2022

MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA

Öz:
Geometric algebra is a useful tool to overcome some problems in kinematics. Thus, the geometric algebra has attracted the attention of many researchers. In this paper, quaternion operators on curves and surfaces in Euclidean 3-space are defined by using geometric algebra. These operators generate the curves or the surfaces from the points, curves or surfaces. Using quaternion operators, we obtain motions that have orbits along the generated curve or surface. Also, these motions are expressed as 1-parameter or 2-parameter homothetic motions.
Anahtar Kelime: rotation matrices Geometric algebra homothetic motions curves quaternions surfaces

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Bottema, O., Roth, B., Theoretical Kinematics, North Holland Publ. Com., 1979.
  • [2] Karger, A., Nov´ak, J., Space Kinematics and Lie Groups, Breach Science Publishers, S.A. Switzerland, 1985.
  • [3] Yaylı, Y., Homothetic Motions at R4 , Mech. Mach. Theory, 27(3) (1992), 303-305. https://doi.org/10.1016/0094-114X(92)90020-I
  • [4] Hamilton, W. R., On quaternions; or on a new system of imaginaries in algebra, London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 25(3) (1844), 489– 495.
  • [5] Shoemake, K., Animating rotation with quaternion curves, in Proceedings of the Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques (SIG-GRAPH ’85), vol. 19, ACM, New York, NY, USA, (1985), 245–254. https://doi.org/10.1145/325334.325242
  • [6] Bayro-Corrochano, E., Modeling the 3D kinematics of the eye in the geometric algebra framework, Pattern Recognition, 36(12) (2003), 2993-3012. https://doi.org/10.1016/S0031- 3203(03)00180-8
  • [7] Leclercq, G., Lef`evre, P., Blohm, G., 3D kinematics using dual quaternions: theory and applications in neuroscience, Frontiers in Behavioral Neuroscience, (2013), p. 7. https://doi.org/10.3389/fnbeh.2013.00007
  • [8] Bekar, M., Yaylı, Y., Semi-Euclidean quasi-elliptic planar motion, International Journal of Geometric Methods in Modern Physics, 13(7) (2016), p. 11. https://doi.org/10.1142/S0219887816500894
  • [9] Aslan, S., Yaylı, Y., Canal surfaces with quaternions, Advanced in Applied Clifford Algebras, 26(1) (2016), 31-38. https://doi.org/10.1007/s00006-015-0602-5
  • [10] Aslan, S., Yaylı, Y., Split quaternions and canal surfaces in Minkowski 3-space, Int. J. Geom., 5(2) (2016), 51-61.
  • [11] Aslan, S., Yaylı, Y., Generalized constant ratio surfaces and quaternions, Kuwait J. Sci., 44(1) (2017), 42–47.
  • [12] Babaarslan, M., Yayli, Y., A new approach to constant slope surfaces with quaternion, ISRN Geom., Article ID 126358, (2012), p. 8 . https://doi.org/10.5402/2012/126358
  • [13] Gok, I., Quaternionic Approach of canal surfaces constructed by some new ideas, Advanced in Applied Clifford Algebras, 27(2) (2017), 1175-1190. https://doi.org/10.1007/s00006-016-0703-9
  • [14] Babaarslan, M. , Yaylı, Y., Split Quaternions and spacelike constant slope surfaces in Minkowski 3-space, International Journal of Geometry, 2(1) (2013), 23-33.
  • [15] Babaarslan, M. , Yaylı, Y., Split quaternions and time-like constant slope surfaces in Minkowski 3-space, International Journal of Geometry, 8(1) (2019), 57-71.
  • [16] Aslan, S., Yaylı, Y., Quaternionic shape operator, Advanced in Applied Clifford Algebras, 27(4) (2017), 2921-2931. https://doi.org/10.1007/s00006-017-0804-0
  • [17] Hacisaliho˘glu, H. H., Geometry of Motions and Theory of Quaternions, Gazi Unv. Publishing, 1983
APA Aslan S, yaylı y (2022). MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. , 39 - 50. 10.31801/cfsuasmas.878766
Chicago Aslan Selahattin,yaylı yusuf MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. (2022): 39 - 50. 10.31801/cfsuasmas.878766
MLA Aslan Selahattin,yaylı yusuf MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. , 2022, ss.39 - 50. 10.31801/cfsuasmas.878766
AMA Aslan S,yaylı y MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. . 2022; 39 - 50. 10.31801/cfsuasmas.878766
Vancouver Aslan S,yaylı y MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. . 2022; 39 - 50. 10.31801/cfsuasmas.878766
IEEE Aslan S,yaylı y "MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA." , ss.39 - 50, 2022. 10.31801/cfsuasmas.878766
ISNAD Aslan, Selahattin - yaylı, yusuf. "MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA". (2022), 39-50. https://doi.org/10.31801/cfsuasmas.878766
APA Aslan S, yaylı y (2022). MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71(1), 39 - 50. 10.31801/cfsuasmas.878766
Chicago Aslan Selahattin,yaylı yusuf MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71, no.1 (2022): 39 - 50. 10.31801/cfsuasmas.878766
MLA Aslan Selahattin,yaylı yusuf MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.71, no.1, 2022, ss.39 - 50. 10.31801/cfsuasmas.878766
AMA Aslan S,yaylı y MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(1): 39 - 50. 10.31801/cfsuasmas.878766
Vancouver Aslan S,yaylı y MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(1): 39 - 50. 10.31801/cfsuasmas.878766
IEEE Aslan S,yaylı y "MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71, ss.39 - 50, 2022. 10.31801/cfsuasmas.878766
ISNAD Aslan, Selahattin - yaylı, yusuf. "MOTIONS ON CURVES AND SURFACES USING GEOMETRIC ALGEBRA". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71/1 (2022), 39-50. https://doi.org/10.31801/cfsuasmas.878766