It’s hard enough to visualize a quaternion, geometrically speaking. A complex number is simple: it’s a point in a plane.
Suppose we had a number like this:
a + bi + cj
I supose you can visualize this as a point in a 3-dimensional space, where 1 of the dimensions is real, and two of them are imaginary.
Quaternions, on the other hand, have 4 dimensions, 1 real and 3 imaginary dimensions. So they are points in a very non-intuitive space. And unit quaternions are points on the “surface” of a hypersphere (whatever such mythical beast calls it its surface). How can I visualize linearly interpolating 2 such things as quaternions? I understand you often use something different for quaternion interpolation, called spheric interpolation. But before I try to understand the spheric interpolation, I would like to be able to root my knowledge on the familiar notion of linear interpolation.
And, if it's not to much to ask, how would I write the interpolation equation?