I am trying to figure out how excatly the exponential/log map with quaternion works. I was reading this: http://alumni.media.mit.edu/~aries/papers/johnson_phd.pdf
Half way at page 70 it says: "Computationally, the most robust way..." but I don't really understand 2 things: 1- how does he get to that equation? 2- how does it prove that the logarithm map is linear?
I read somewhere else a proof for complex number that showed how log map is linear by deriving the exp and log functions and then the log derivative was a constant and therefore not curved. I think I would like to find an analogous proof for quaternions, can anyone help with it?
Cheers,