
764 Chapter 17 Rotations
17.2 Quaternions
If you have already explored the concept of quaternions, you will have discovered a
number of ways to motivate how they are defined. Our interest, of course, is how
they are related to rotations. Some of the definitions for quaternions do not make
it immediately clear what this relationship is. This section motivates quaternions by
looking at 2D rotations but in the space of 4-tuples (x, y , z, w).
Equation (17.2) is a natural extension of the concept of rotation in the 2D xy-
plane, defined in Equation (17.1), to the concept of rotation in the xy-plane that lives
in a 3D space. The extension to a rotation in