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Double and Type (3,0) Minkowski Pythagorean Hodograph Curves

Year 2022, Volume: 11 Issue: 2, 660 - 665, 30.06.2022
https://doi.org/10.17798/bitlisfen.1083043

Abstract

In present paper, Double Minkowski Pythagorean Hodograph (DMPH) curves and type (3,0) Minkowski Pythagorean Hodograph (MPH) curves. Firstly, we obtained the conditions for a MPH curve to be a DMPH curve. Then, we examined these conditions in split quaternion form. Finally, a special class of seventh degree MPH curves is characterized and illustrative examples are given.

References

  • Choi, H. I., Lee, D. S., Moon, H. P. 2002. Clifford Algebra, Spin Representation and Rational Parameterization of Curves and Surfaces. Advances in Computational Mathematics, 17(1-2), 5-48.
  • Dospra, P. 2015. Quaternion Polynomials and Rational Rotation-Minimizing Frame Curves. Ph.D. Thesis, Agricultural University of Athens, 2015.
  • Farouki, R. T., Sakkalis, T. 1990. Pythagorean Hodographs. IBM Journal of Research and Development, 34(5), 736-752.
  • Farouki, R. T. 1994. The Conformal Map z→z² of the Hodograph Plane. Computer Aided Geometric Design, 11(4), 363-390.
  • Farouki, R. T., Sakkalis, T. 1994. Pythagorean-Hodograph Space Curves. Advances in Computational Mathematics, 2(1), 41-66.
  • Farouki, R. T. 2008. Pythagorean-Hodograph Curves. Springer.
  • Han, C. Y. 2008. Nonexistence of Rational Rotation-Minimizing Frames on Cubic Curves. Computer Aided Geometric Design, 25(4-5), 298-304
  • Inoguchi, J. I. 1998. Timelike Surfaces of Constant Mean Curvature in Minkowski 3-Space, Tokyo Journal of Mathematics, 21(1), 141-152.
  • Ramis, Ç. 2013. PH Curves and Applications. M.S. Thesis, Ankara University.
  • Yazla, A., Sariaydin, M. T. 2019. Applications of the Fermi-Walker derivative. Journal of Science and Arts, 19(3), 545-560.
  • Yazla, A., Sariaydin, M. T. 2020. On Surfaces Constructed by Evolution According to Quasi Frame. Facta Universitatis, Series: Mathematics and Informatics, 605-619.
  • Yazla, A., Sariaydin, M. T. Modeling with Double Minkowski Pythagorean Hodograph Curves. (Submitted)

Double and Type (3,0) Minkowski Pythagorean Hodograph Curves

Year 2022, Volume: 11 Issue: 2, 660 - 665, 30.06.2022
https://doi.org/10.17798/bitlisfen.1083043

Abstract

In present paper, Double Minkowski Pythagorean Hodograph (DMPH) curves and type (3,0) Minkowski Pythagorean Hodograph (MPH) curves are studied. Firstly, the conditions for a MPH curve to be a DMPH curve are obtained. Then, these conditions are
examined in split quaternion form. Finally, a special class of seventh degree MPH curves is characterized and illustrative examples are given.

References

  • Choi, H. I., Lee, D. S., Moon, H. P. 2002. Clifford Algebra, Spin Representation and Rational Parameterization of Curves and Surfaces. Advances in Computational Mathematics, 17(1-2), 5-48.
  • Dospra, P. 2015. Quaternion Polynomials and Rational Rotation-Minimizing Frame Curves. Ph.D. Thesis, Agricultural University of Athens, 2015.
  • Farouki, R. T., Sakkalis, T. 1990. Pythagorean Hodographs. IBM Journal of Research and Development, 34(5), 736-752.
  • Farouki, R. T. 1994. The Conformal Map z→z² of the Hodograph Plane. Computer Aided Geometric Design, 11(4), 363-390.
  • Farouki, R. T., Sakkalis, T. 1994. Pythagorean-Hodograph Space Curves. Advances in Computational Mathematics, 2(1), 41-66.
  • Farouki, R. T. 2008. Pythagorean-Hodograph Curves. Springer.
  • Han, C. Y. 2008. Nonexistence of Rational Rotation-Minimizing Frames on Cubic Curves. Computer Aided Geometric Design, 25(4-5), 298-304
  • Inoguchi, J. I. 1998. Timelike Surfaces of Constant Mean Curvature in Minkowski 3-Space, Tokyo Journal of Mathematics, 21(1), 141-152.
  • Ramis, Ç. 2013. PH Curves and Applications. M.S. Thesis, Ankara University.
  • Yazla, A., Sariaydin, M. T. 2019. Applications of the Fermi-Walker derivative. Journal of Science and Arts, 19(3), 545-560.
  • Yazla, A., Sariaydin, M. T. 2020. On Surfaces Constructed by Evolution According to Quasi Frame. Facta Universitatis, Series: Mathematics and Informatics, 605-619.
  • Yazla, A., Sariaydin, M. T. Modeling with Double Minkowski Pythagorean Hodograph Curves. (Submitted)
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Araştırma Makalesi
Authors

Aziz Yazla This is me 0000-0003-3720-9716

Muhammed Talat Sarıaydın 0000-0002-3613-4276

Publication Date June 30, 2022
Submission Date March 4, 2022
Acceptance Date May 27, 2022
Published in Issue Year 2022 Volume: 11 Issue: 2

Cite

IEEE A. Yazla and M. T. Sarıaydın, “Double and Type (3,0) Minkowski Pythagorean Hodograph Curves”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 2, pp. 660–665, 2022, doi: 10.17798/bitlisfen.1083043.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS