On Thu, Jul 28, 2011 at 09:48:29PM -0500, Robert Love wrote: > > Quaternions have a "handedness" or a sign convention. The recently > departed Space Shuttle used a Left versor convention while most > things, including Space Station, use the right versor convention, in > their flight software. Made for frequent confusion. > > Let me see if I can illustrate by showing the functions I use for > converting a matrix to a quaternion. > > [snip]
OK, the difference here is between quaternion conjugates. Your two matrix-to-quaternion functions return the conjugate of each other, and one of your rotate-vector-by-quaternion functions uses the conjugate of the quaternion. When quaternions are used to represent rotations, quaternion conjugates represent "opposite" rotations. E.g. if you have two spacecraft A and B and are considering the rotation between them, you can describe this as the rotation from A->B or as the rotation from B->A. The two quaternions will be the conjugate of each other. Similarly, if two systems describe the same rotation on the same axes but one defines rotation using the right-hand rule and the other the left-hand rule, their two quaternions will be the conjugate of each other. What this is all about is a matter of what co-ordinate frames you choose to interpret things in, not something about a "handedness" of quaternions. Quaternions themselves do not have a "handedness", they are just numbers. If you have systems using opposite co-ordinate frames, or indeed any other differing co-ordinate systems, then the best approach is to explicitly convert everything into a single chosen co-ordinate frame before doing any calculations. Don't entangle your representation changes (e.g. matrix to quaternion) and transforms (e.g. rotate vector) with co-ordinate frame changes. Your 'left versor' functions are the correct ones. Your 'right versor' functions create and use the opposite rotations. I don't know where you got this 'left versor' and 'right versor' terminology from. This thread seems to be the only hit for these terms together on Google. Martin _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
