Rotating Quaternion - Coordinate Free
We study all rotations of the unit sphere moving the starting point S with coordinates (1,0,0) to the point P. The axes of all such rotations happen to falls into the plane defined by the orange circle, bisecting SP.
Two of these rotations, the axes of which are shown by the red vectors , are easy to see. Can you determine their angles of rotation?
Each rotation can be described by a quaternion. This applet defines in a purely geometric coordinate free way. There is a similar applet, where are calculated coordinate-wise and which gives an error if the x-coordinate of P is -1. That doesn't happen here.
Why doe the coordinates of the two quaternions look so similar?