Research Article
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Year 2022, Volume: 71 Issue: 1, 39 - 50, 30.03.2022

Selahattin Aslan Yusuf Yaylı

https://doi.org/10.31801/cfsuasmas.878766
Cited By: 3

Abstract

References

  • Bottema, O., Roth, B., Theoretical Kinematics, North Holland Publ. Com., 1979.
  • Karger, A., Novak, J., Space Kinematics and Lie Groups, Breach Science Publishers, S.A. Switzerland, 1985.
  • Yaylı, Y., Homothetic Motions at R4, Mech. Mach. Theory, 27(3) (1992), 303-305. https://doi.org/10.1016/0094-114X(92)90020-I
  • 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.
  • 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
  • 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
  • Leclercq, G., Lefevre, 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
  • 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
  • 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
  • Aslan, S., Yaylı, Y., Split quaternions and canal surfaces in Minkowski 3-space, Int. J. Geom., 5(2) (2016), 51-61.
  • Aslan, S., Yaylı, Y., Generalized constant ratio surfaces and quaternions, Kuwait J. Sci., 44(1) (2017), 42–47.
  • 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
  • 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
  • Babaarslan, M. , Yaylı, Y., Split Quaternions and spacelike constant slope surfaces in Minkowski 3-space, International Journal of Geometry, 2(1) (2013), 23-33.
  • 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.
  • 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
  • Hacisalihoglu, H. H., Geometry of Motions and Theory of Quaternions, Gazi Unv. Publishing, 1983.

Motions on curves and surfaces using geometric algebra

Year 2022, Volume: 71 Issue: 1, 39 - 50, 30.03.2022

Selahattin Aslan Yusuf Yaylı

https://doi.org/10.31801/cfsuasmas.878766
Cited By: 3

Abstract

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.

Keywords

Geometric algebra curves surfaces quaternions rotation matrices homothetic motions

References

  • Bottema, O., Roth, B., Theoretical Kinematics, North Holland Publ. Com., 1979.
  • Karger, A., Novak, J., Space Kinematics and Lie Groups, Breach Science Publishers, S.A. Switzerland, 1985.
  • Yaylı, Y., Homothetic Motions at R4, Mech. Mach. Theory, 27(3) (1992), 303-305. https://doi.org/10.1016/0094-114X(92)90020-I
  • 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.
  • 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
  • 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
  • Leclercq, G., Lefevre, 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
  • 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
  • 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
  • Aslan, S., Yaylı, Y., Split quaternions and canal surfaces in Minkowski 3-space, Int. J. Geom., 5(2) (2016), 51-61.
  • Aslan, S., Yaylı, Y., Generalized constant ratio surfaces and quaternions, Kuwait J. Sci., 44(1) (2017), 42–47.
  • 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
  • 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
  • Babaarslan, M. , Yaylı, Y., Split Quaternions and spacelike constant slope surfaces in Minkowski 3-space, International Journal of Geometry, 2(1) (2013), 23-33.
  • 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.
  • 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
  • Hacisalihoglu, H. H., Geometry of Motions and Theory of Quaternions, Gazi Unv. Publishing, 1983.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Selahattin Aslan 0000-0001-5322-3265

Yusuf Yaylı 0000-0003-4398-3855

Publication Date March 30, 2022
Submission Date February 11, 2021
Acceptance Date July 28, 2021
Published in Issue Year 2022 Volume: 71 Issue: 1

Cite

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. https://doi.org/10.31801/cfsuasmas.878766
AMA Aslan S, Yaylı Y. Motions on curves and surfaces using geometric algebra. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2022;71(1):39-50. doi:10.31801/cfsuasmas.878766
Chicago Aslan, Selahattin, and Yusuf Yaylı. “Motions on Curves and Surfaces Using Geometric Algebra”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 39-50. https://doi.org/10.31801/cfsuasmas.878766.
EndNote Aslan S, Yaylı Y (March 1, 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.
IEEE S. Aslan and Y. Yaylı, “Motions on curves and surfaces using geometric algebra”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 39–50, 2022, doi: 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 (March 2022), 39-50. https://doi.org/10.31801/cfsuasmas.878766.
JAMA Aslan S, Yaylı Y. Motions on curves and surfaces using geometric algebra. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:39–50.
MLA Aslan, Selahattin and Yusuf Yaylı. “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, pp. 39-50, doi:10.31801/cfsuasmas.878766.
Vancouver Aslan S, Yaylı Y. Motions on curves and surfaces using geometric algebra. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):39-50.

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