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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

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.

Unit Norm

If we define the inner product of two quaternions as

Equation C.1. 

the components of a quaternion frame obey the constraint

Equation C.2. 

and therefore lie on S3, the three-sphere embedded in 4D Euclidean space .

Multiplication Rule

The quaternion ...

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Publisher Resources

ISBN: 9780120884001