Skip to main content
SpringerLink
Log in

Fast Methods for Spherical Linear Interpolation in Minkowski Space

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

Abstract

Spherical linear interpolation in Minkowski space has got a number of important applications in computer graphics, physics and kinematics. Spherical linear interpolation in Minkowski space involves the computation of trigonometric functions, which are computationally expensive. The computation will be fast since the implementation does not need to evaluate any trigonometric functions in the inner loop. Furthermore, no renormalization is necessary and therefore it is a true spherical interpolation in Minkowski space. We propose that incremental Slerp in Minkowski space. In this paper we demonstrate four different methods for incremental Slerp in Minkowski space.

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

  2. Ghadami R., Rahebi J., Yayli Y.: Linear interpolation in Minkowski space. International Journal of Pure and Applied Mathematics 77 No. (4), 469–484 (2012)

    MATH  Google Scholar 

  3. O’Neill B.: Semi Riemannian Geometry with applications Storelativity. Academic Press Inc., London (1983)

    Google Scholar 

  4. Özdemir M.: The roots of a split quaternion. Applied Mathematics Letters 22, 258–263 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

  6. Ghadami R., Rahebi J., Yayli Y.: Spline Split Quaternion Interpolation in Minkowski Space. Advances in Applied Clifford Algebras 23 No. (4), 849–862 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Mandic and V. Su Lee Goh, The Magic of Complex Numbers. Complex Valued Nonlinear Adaptive Filters (2009).

  8. Özdemir M., Ergin A. A.: Rotations with unit timelike quaternion in Minkowski 3-space. Journal of Geometry and Physics 56, 322–336 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Raheleh Ghadami & Yusuf Yayly

  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 Yayly
    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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghadami, R., Rahebi, J. & Yayly, Y. Fast Methods for Spherical Linear Interpolation in Minkowski Space. Adv. Appl. Clifford Algebras 25, 863–873 (2015). https://doi.org/10.1007/s00006-015-0536-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-015-0536-y

Keywords

Search

Navigation