Abstract
Chapter 7 is the focal point of the book and shows how quaternions are used to rotate vectors about an arbitrary 3D axis. The chapter begins by reviewing some of the history associated with quaternions, in particular, the role of Benjamin Olinde Rodrigues, who discovered the importance of half-angles in rotation transforms. Quaternion products are described and how they are employed to rotate points. Further sections explain how to compute eigenvalues and eigenvectors of a quaternion. Finally, the chapter contains details on frames of reference, interpolating quaternions, matrix to quaternion conversion, and Euler angles to quaternion conversion. The chapter summarises key formulae and contains some useful worked examples.