2008-05-01 16:59:36 UTC
I have the suspicion that the equation that converts euler angle rotations to quaternions using the arbitrary vectors e1, e2 and e3 seem not only to work with arbitrary permutation of the X, Y, Z axes, but also works if you combine axes that are aligned in the same direction.
If you check the equation for two successive rotations of, say theta1 and -theta1 around the same axis, then you'll see that these rotations nicely cancel each other. So I guess it would work also with angles theta1 and theta2 that don't cancel.
In this case, the equation would work with the combinations:
XXY
XXZ
YYX
YYZ
ZZX
ZZY
I guess it could very well work with any rotations. If I have more time, I'll test the equation validity for arbitrary rotations.
Cheers,
Nicolas
P.S.: Thank you very much for letting all this information publicly available. This site has proved to be very useful to me, especially for the Euler angles conversion, the quaternions, and the different conventions.
