I would like to know if my understanding about quaternions is correct please:
lets say you have a vector in 3d space. You could rotate the x,y and-z frame on a fixed point so that it is parallel with this vector (source first sentences: http://www.u.arizona.edu/~pen/ame553/Notes/Lesson%2009.pdf).
Once this is done you know how much you rotated (theta) the vector and theta represents the eules axis. Quaternions give a simple way to encode this axis–angle representation in four numbers.
And this is what the quaternion of a vector is.
Is this correct?