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
- 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.
- 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.