Rotating Objects Using Quaternions (Bobick, Gamasutra)

This paper provides a practical explanation of quaternions, how they
can be useful in representing rotations, and the mathematics behind
quaternions. This paper also provides example source code for
performing the described operations.
Key Ideas:

1. Quaternions can be used to provide smooth camera motion when moving
in a 3-D interactive world.

2. Quaternions provide a compact way of storing orientations as well
as an efficient way of composing rotations.

Questions:

Quaternions seem incredibly useful, but incredibly difficult to
visualize. It is very difficult to look at a quaternion and understand
the orientation it represents. As a consequence, it's very difficult
to use quaternions directly. It would seem the easiest way would be to
think of an orientation in terms of Euler angles or angle-axis and
convert it to a quaternion for use in the computer. I would be
interested in investigating quaternions further to find out if there
is any way to get an intuitive sense of what a particular quaternion
means.