Rotation Transforms for Computer Graphics

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Springer Science & Business Media, Jan 4, 2011 - Computers - 232 pages
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Rotation transforms are used everywhere in computer graphics from rotating pictures in editing software, to providing an arbitrary view of a 3D virtual environment. Although the former is a trivial operation, the latter can be a challenging task.

Rotation Transforms for Computer Graphics covers a wide range of mathematical techniques used for rotating points and frames of reference in the plane and 3D space. It includes many worked examples and over 100 illustrations that make it essential reading for students, academics, researchers and professional practitioners.

The book includes introductory chapters on complex numbers, matrices, quaternions and geometric algebra, and further chapters on how these techniques are employed in 2D and 3D computer graphics. In particular, matrix and bivector transforms are developed and evaluated to rotate points in a fixed frame of reference, and vice versa.

 

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Contents

Introduction
2
Complex Numbers
5
Vectors
17
Matrices
33
Quaternions
59
Multivectors
66
Rotation Transforms in the Plane
85
Frames of Reference in the Plane
103
Quaternion Transforms in Space
155
Bivector Rotors
181
Conclusion
197
Appendix A Composite Point Rotation Sequences
198
Appendix B Composite Frame Rotation Sequences
213
Appendix C The Four nSquare Algebras
227
References
229
Index
230

Rotation Transforms in Space
115
Frames of Reference in Space
143

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