I'm here to ask for a simple question about unit quaternions. I have a quaternion, say $q_1$. Now, I would like to choose between $q_2$ and $-q_2$ (that represent the same rotation), by choosing the one that has the "smallest distance" to $q_1$. I can give an example of my question, then it is clearer to everyone. Actually, $q_1$ and $q_2$ is the same quaternion in two time instants. Since in my computations I have functions of the single elements of $q_2$, it is important the sign of those elements. Then, I would like the quaternion that is "more similar to" $q_2$. Roughly speaking, if my quaternion is [1 0 0 0] and then I have [0.99 0 0 0.1411] and [-0.99 0 0 -0.1411], I would like to choose the first one.
I have search in the web without a clear answer to this question, even because there can be cases in which the difference is not so evident as in the example that I provided above. Many thanks in advance for your reply.