Quaternion Function Reference

cdpolar

Polar Cayley-Dickson form

Syntax

[A, B] = cdpolar(q)

Description

Computes a polar form inspired by the Cayley-Dickson construction of a quaternion from two complex numbers. A and B are complex numbers equivalent to q, such that: q = A exp(B j) in mathematical notation. In Matlab/QTFM, we must convert the complex numbers into equivalent quaternions like this:

q = (real(A) + imag(A) .* qi) .* exp((real(B) .* imag(B) .* qi) .* qj)
or by using the dc function (the inverse of the cd function):
q = dc(A) .* exp(dc(B) .* qj)

Examples

>> [A, B] = cdpolar(1 + qi + qj + qk)

A = 1.4142 + 1.4142i

B = 0.7854

>>  dc(A) .* exp(dc(B) .* qj)
 
ans = 1 + 1 * I + 1 * J + 1 * K

See Also

QTFM function: cd

References

  1. Stephen J. Sangwine and Nicolas Le Bihan, 'Quaternion polar representation with a complex modulus and complex argument inspired by the Cayley-Dickson form', Advances in Applied Clifford Algebras, 20 (1), March 2010, 111-120, DOI: 10.1007/s00006-008-0128-1.
  2. Stephen J. Sangwine and Nicolas Le Bihan, 'Quaternion polar representation with a complex modulus and complex argument inspired by the Cayley-Dickson form', preprint arXiv:0802.0852, 6 February 2008, available at http://arxiv.org/abs/arxiv:0802.0852.

© 2008-2013 Stephen J. Sangwine and Nicolas Le Bihan

License terms.