Rotation Transforms for Computer Graphics

This book provides a comprehensive description of mathematical techniques for rotating points and frames in 2D and 3D computer graphics. Such transforms are notoriously difficult to visualize, which is why the book includes a large number of illustrations.

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.

Introduction to all the mathematical techniques employed in the book

Clear and concise explanations of 2D and 3D rotation transforms

Large number of illustrations to clarify rotational movements

Includes supplementary material: sn.pub/extras

Contenu

Introduction.- Complex Numbers.- Vectors.- Matrices.-Quaternions.- Multivectors.- Rotation Transforms in the Plane.-Frames of Reference in the Plane.- Rotation Transforms in Space.- Frames of Reference in Space.- Quaternion Transforms in Space.- Bivector Rotors.- Conclusion.- Appendix A: Composite Point Rotation Sequences.- Appendix B: Composite Frame Rotation Sequences.- Appendix C: The Four n -Square Algebras.- Index.