I have a basic (maybe stupid) question which I would like to be 100% sure about.
I already searched online but could not find a precise answer about it.
How many elements of a quaternion do you need to uniquely define a rotation?
My answer would be 3 since the fourth can be found knowing that the quaternion must be a unit norm vector. For sure 2 elements are not enough.
Of course, even with 3 or 4 elements of a quaternion you would have the quaternion ambiguity. I.e. a certain rotation can be expressed by the quaternion $ (q_1, q_2, q_3, q_4) $ or by $ (-q_1, -q_2, -q_3, -q_4) $
Please tell me if I am forgetting anything.