Skip to main content

Conformal Geometric Algebra

  • Chapter
  • First Online:
Geometric Algebra Applications Vol. II

Abstract

The geometric algebra of a 3D Euclidean space \(G_{3,0,0}\) has a point basis and the motor algebra \(G_{3,0,1}\) a line basis. In the latter geometric algebra, the lines expressed in terms of Plücker coordinates can be used to represent points and planes as well.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Li, H., Hestenes, D., & Rockwood, A. (2001). Generalized homogeneous coordinates for computational geometry. In G. Sommer (Ed.), Geometric computing with Clifford algebra (pp. 27–59). New York: Springer-Verlag.

    Chapter  Google Scholar 

  2. Bayro-Corrochano, E. (1995). Robot perception and action using conformal geometry. In E. Bayro-Corrochano (Ed.), Handbook of geometric computing. Applications in pattern recognition, computer vision, neurocomputing and robotics (Chap. 13, pp. 405–458). Heidelberg: Springer-Verlag.

    Google Scholar 

  3. Hestenes, D. (2001). Old wine in new bottles: A new algebraic framework for computational geometry. In E. Bayro-Corrochano & G. Sobczyk (Eds.), Geometric algebra applications with applications in science and engineering (pp. 3–17). Boston: Birkhäuser.

    Chapter  Google Scholar 

  4. Hestenes, D. (2009). New tools for computational geometry and rejuvenation of screw theory. In E. Bayro-Corrochano & G. Sheuermann (Eds.), Geometric algebra computing for engineering and computer science (pp. 3–33). London: Springer.

    Google Scholar 

  5. Dress, A., & Havel, T. (1993). Distance geometry and geometric algebra. Foundations of Physics, 23(10), 1357–1374.

    Article  MathSciNet  Google Scholar 

  6. Perwass, C. B. U. (2009). Geometric algebra with applications in engineering. Berline, Heidelberg: Springer Verlag.

    MATH  Google Scholar 

  7. Perwass, C. B. U. (2000). Applications of geometric algebra in computer vision. Ph.D. Thesis, University of Cambridge.

    Google Scholar 

  8. Needham, T. (1997). Visual complex analysis. New York: Oxford University Press (Reprinted 2003)

    Google Scholar 

  9. Rosenhan, B., Perwass, C., & Sommer, G. (2005). Pose estimation of 3D free-form curves. Journal of Computer Vision, 62(3), 267–289.

    Article  Google Scholar 

  10. Lounesto, P. (1987). CLICAL software packet and user manual. Helsinki University of Technology of Mathematics, Research report A248.

    Google Scholar 

  11. Ablamowicks, R. eCLIFFORD Software packet using Maple for Clifford algebra. Computations. http://math.tntech.edu/rafal.

  12. Perwass, C. B. U. (2006). CLUCal. http://www.clucal.info/.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eduardo Bayro-Corrochano .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bayro-Corrochano, E. (2020). Conformal Geometric Algebra. In: Geometric Algebra Applications Vol. II. Springer, Cham. https://doi.org/10.1007/978-3-030-34978-3_6

Download citation

Publish with us

Policies and ethics