- \(+q\) and \(-q\) correspond to the same rotation (\(n\to-n\), \(\theta\to 2\pi-\theta)\)
-
- Warning \(-q\) does not corresponds to the rotation matrix \(-R\).
- But to a different path when interpolated in the 4D quaternion space.
- \(\Rightarrow\) path \(q_1 \to -q_2\) is shorter than \(q_1 \to q_2\) when \(q_1\cdot q_2<0\).
- In practice we check for the shorter path before applying SLERP.
- Algorithm
if( dot(q1,q2)<0 ) q2 = -q2 q(t) = SLERP(q1,q2,t)