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Visualizing Quaternions
book

Visualizing Quaternions

by Andrew J. Hanson
February 2006
Intermediate to advanced content levelIntermediate to advanced
600 pages
8h 57m
English
Elsevier Science
Content preview from Visualizing Quaternions

Chapter 29. The Relationship of 4D Rotations to Quaternions

What Happened in Three Dimensions

In three dimensions, there were many ways to deduce the quadratic mapping from quaternions to the 3 × 3 rotation matrix belonging to the group SO(3) and implementing a rotation on ordinary 3D frames. The one most directly derived from the quaternion algebra conjugates “pure” quaternion three-vectors vi = (0, Vi) and pulls out the elements of the rotation matrix in the following way:

What Happened in Three Dimensions

We easily find that the quadratic relationship between R3(q) and q = (q0, q1, q2, q3) is

Equation 29.1. 

Quaternions and Four Dimensions

In the 4D case, which we should really regard ...

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Publisher Resources

ISBN: 9780120884001