Appendix F. Quaternion Methods
This appendix presents a family of miscellaneous algorithms and methods we have found useful from time to time.
Quaternion Logarithms and Exponentials
If we parameterize a quaternion in a simplified way (with 0 ≤ θ < 2π) to cover the entire S3 as 
), we can show using the quaternion algebra that this parameterization of S3 follows from the exponential series
The logarithm of a structure is the object that, when exponentiated, produces the generic structure. Hence, we must have
Raising a quaternion to a power is defined via ...
Get The Morgan Kaufmann Series in Interactive 3D Technology: Visualizing Quaternions now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
