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Multiplying two quaternions gives you a quaternion equivalent to performing the two rotations they represent in sequence.
q3 = q1 * q2
q3 * object = q1 * (q2 * object)
// "Perform rotation q2 with respect to the world axes, then q1"
// Or equivalently: "Perform rotation q1 about your local axes, then q2"
q4 = q2 * q1
q4 * object = q2 * (...
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Is it possible to apply something to qx or qy to get the original q directly?
Yes it is! The transformation you're looking for is \$qy^{-1} * qx * qy\$
(My reasoning is like looking at a unit vector starting in the x direction, which if I rotate 45 degrees in the y axis would give me a vector pointing in the z=x direction, but this is clearly naive as it ...
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