I'm confused of the symbol, does "qxq"(the rotation expression) mean the production of q-,x and q? How to deduce that?
I am confused too... How do we interpret the expression of qxq?
I believe the interpretation is as follows. If q is the quaternion representing some rotation, then the expression for computing the rotated x is q_bar * x * q. q_bar is the conjugate of q, and each term is being multiplied.
How do we derive this expression q_bar * x * q?
Comparing to using matrix, quaternion is faster to compute and requires less memory in graphics.
I think q(bar) x q means the production discipline in quaternion coordinate. We use it to calculate rotations following other quaternion calculation disciplines like kj = j and ii = -1.
We can make an analogy to calculation on complex coordinate, where we also need to rotate a vector using production, and the same thing happened only on two axes.