Skip to main content
SpringerLink
Log in

Spline Split Quaternion Interpolation in Minkowski Space

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

Spherical spline quaternion interpolation has been done on sphere in Euclidean space using quaternions. In this paper, we have done the spline split quaternion interpolation on hyperbolic sphere in Minkowski space using split quaternions and metric Lorentz. This interpolation curve is called spherical spline split quaternion interpolation in Minkowski space (MSquad).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. B. Dam, M. Koch and M. Lillholm, Quaternions, interpolation and animation. Technical Report DIKU-TR-98/5 Institute of computer science University of Copenhagen, Denmark, July 17, 1998.

  2. P. Edward and W. Jon A, Quaternions in computer vision and robotics. Technical Report Department of Computer Science, Carnegie-Mellon University, 1982.

  3. D. Eberly, Quaternion Algebra and Calculus. http://www.geometrictools.com/Documentation/Documentation.html

  4. R. Ghadami, J. Rahebi and Y. Yaylı, Linear interpolation in Minkowski space. International Journal of Pure and Applied Mathematics, vol. 77, no. 4 (2012), pp. 469–484.

  5. Hamilton W. R.: Researches respecting quaternions. Transactions of the Royal Irish Academy 21, 199–296 (1848)

    Google Scholar 

  6. D. Kincaid andW. Cheney, Numerical Analysis. Brooks/Cole Publishing Company, Pacific Grove, California, 1991.

  7. L. Noakes, A Note on Spherical Splines. Journal of the Royal Statistical Society. Series B, vol. 47, no. 3 (1985), pp. 482–488.

  8. M. Özdemir and A. A. Ergin, Rotations with unit timelike quaternion in Minkowski 3-space. Journal of Geometry and Physics, vol. 56, no. 2 (2006) pp. 322–336.

  9. B. O’Neill, Semi Riemannian Geometry with applications Storelativity. Academic Press Inc., London, 1983.

  10. D. Pletinckx, Quaternion calculus as a basic tool in Computer graphics. The Visual Computer, vol. 5, no. 2 (1989), pp. 2–13.

  11. K. Shoemake, Animating rotation with quaternion curves. ACM siggraph, vol.19, no. 3 (1985), pp. 245–254.

  12. J. Inoguchi, Timelike Surfaces of Constant Mean Curvature in Minkowski 3- Space. Tokyo J. Math. vol. 21, no. 1 (1998), pp. 140–152.

  13. M. Özdemir, The roots of a split quaternion. Applied Mathematics Letters, vol. 22, no. 2 (2009), pp. 258–263.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Ankara, Ankara, Turkey

    Raheleh Ghadami & Yusuf Yaylı

  2. Department of Electrical & Electronics, University of Gazi, Ankara, Turkey

    Javad Rahebi

Authors
  1. Raheleh Ghadami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Javad Rahebi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yusuf Yaylı
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raheleh Ghadami.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghadami, R., Rahebi, J. & Yaylı, Y. Spline Split Quaternion Interpolation in Minkowski Space. Adv. Appl. Clifford Algebras 23, 849–862 (2013). https://doi.org/10.1007/s00006-013-0410-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-013-0410-8

Keywords

Search

Navigation