Quaternions and fries (multiplying quats)

[mmeijer]

I've got my three quaternions all lined up to rotate my point or vector, works well like this..

pt1 = qrA * pt0 * qrA^-1
pt2 = qrB * pt1 * qrB^-1
pt3 = qrC * pt2 * qrC^-1

where my original point is pt0, and the rotated point is pt3.

But I want to combine the quaternions, so I can store it as a single rotation, like this..

qrAll = qrC * qrB * qrA
qrAllInverse = qrA^-1 * qrB^-1 * qrC^-1

pt3 = qrAll * pt0 * qrAllInverse

But there's something wrong.

I know order is important and I've tried a lot of different ways! I'm using the Maya API MQuaternion class.

thanks for any quaternion wisdom!

Mark

[jdj]

Hello mmeijer,

Just a few observations:

• I assume that you mean qrX^-1 everywhere...

• I doubt that: qrAll^-1 = qrA^-1 * qrB^-1 * qrC^-1

I would try: pt3 = qrAll * pt0 * qrAll^-1

Cheers!
/ Daniel

[mmeijer]

Thanks Daniel

• I assume that you mean qrX^-1 everywhere...

Of course! Thanks for reading what I meant.

• I doubt that: qrAll^-1 = qrA^-1 * qrB^-1 * qrC^-1

I would try: pt3 = qrAll * pt0 * qrAll^-1

Okay, I tried.. no luck.
It's probably due to quaternions not being commutative.
I've been trying to collapse this..
pt3 = qrC * qrB * qrA * pt0 * qrA^-1 * qrB^-1 * qrC^-1

forcing evaluation with brackets..
qrAll = (qrC * (qrB * qrA))
qrAll^-1 = ((qrA^-1 * qrB^-1) * qrC^-1)

Now I'm considering doing the rotations as matrices.

[mmeijer]

I found a fix.

Instead of multiplying with the quaternion AND it's inverse, I just use the quaternion.

I was doing too much math. I had to update my quaternion calculations since I was doing each rotation twice. So, the problem WAS due to quaternion multiplication being non-commutative, but in my case only because I was doing twice as many rotations.

Now my quaternion multiplications look like..
pt1 = qrA * pt0
pt2 = qrB * pt1
pt3 = qrC * pt2

which collapses to
pt3 = qrC * qrB * qrA * pt0

and then
qrAll = qrC * qrB * qrA
pt3 = qrAll * pt0