Advertisement

The Geometric Algebras \(G_{6,0,2}^+\), \(G_{6,3}\), \(G_{9,3}^+\), \(G_{6,0,6}^+\)

  • Eduardo Bayro-CorrochanoEmail author
Chapter
  • 54 Downloads

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, the lines expressed are expressed in terms of Plücker coordinates and the points and planes in terms of bivectors.

References

  1. 1.
    Bayro-Corrochano, E., Daniilidis, K., & Sommer, G. (2000). Motor algebra for 3D kinematics. The case of the hand–eye calibration. International Journal of Mathematical Imaging and Vision, 13(2), 79–99.Google Scholar
  2. 2.
    Bayro-Corrochano, E. (2001). Geometric computing for perception action systems. New York: Springer Verlag.CrossRefGoogle Scholar
  3. 3.
    Selig, J., & Bayro-Corrochano, E. (2010). Rigid body dynamics using Clifford algebra. Advances in Applications of Clifford algebras, 20, 141–154.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Eaester, R. B., & Hitzer, E. (2017). Double conformal geometric algebra. Advances in Applied Clifford Algebras, 27, 2175–2199.MathSciNetCrossRefGoogle Scholar
  5. 5.
    White, N. (1994). Grassmann-Cayley algebras in robotics. Journal of Intelligent Robot Systems, 11, 97–187.Google Scholar
  6. 6.
    Zamora-Esquivel, J. (2014). \(G_{6,3}\) Geometric algebra: Decription and implementation. Advances in Applied Clifford Algebras, 24, 493–514.MathSciNetCrossRefGoogle Scholar
  7. 7.
    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.CrossRefGoogle Scholar
  8. 8.
    Ablamowicks, R. eCLIFFORD Software packet using Maple for Clifford algebra. Computations. http://math.tntech.edu/rafal.

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Electrical Engineering and Computer Science DepartmentCINVESTAVGuadalajaraMexico

Personalised recommendations