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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 06. Fundamentals of Rotations

Quaternions are related in a fundamental way to 3D rotations, which can represent orientation frames and can act to produce changes in orientation frames. In this chapter, we begin by presenting the relationships among 2D rotation operations, 2D rotation matrices, and complex numbers. We then move on to 3D rotation matrices, examine an interesting idea that looks like the square root of a rotation, and finally relate all of this to 3D rotations and quaternions.

2D Rotations

Rotations of 2D vectors are implemented by the action of 2D orthogonal matrices R2 with determinant one, and thus

Equation 6.1. 

The 2 × 2 matrix ...

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Publisher Resources

ISBN: 9780120884001