Appendix C. 3D Quaternion Frames
We next outline the basic features for 3D orientation and quaternion frames, following the pattern now established in Appendix B for 2D orientation and complex numbers. A quaternion frame is a unit four-vector q = (q0, q1, q2, q3) = (q0, q) with the following features.
If we define the inner product of two quaternions as
the components of a quaternion frame obey the constraint
and therefore lie on S3, the three-sphere embedded in 4D Euclidean space .
The quaternion ...