Rotation Transforms for Computer Graphics

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Product Description

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.

Rotation Transforms for Computer Graphics Review

This is a very well written book on the topic. I've been working in computer graphics for 15 years, and I've been teaching it for 7. I still managed to learn a few things from this book. On top of that, the presentation is very clear. Most computer math books are either very technical and targeted at mathematicians, or they are cute and hand-wavy. This book is neither. John manages to derive many fundamental equations, usually multiple ways, without giving the reader math overload.

The coverage of rotating objects versus rotating frames of reference was especially good. The partitioning where one chapter presents a concept as rotating the object and the next presents the same concept as rotating the reference frame worked really well. Many books do not cover this topic thoroughly enough, and new graphics programmers either have difficulty grasping the concept or use the wrong tool at the wrong time.

I was a little disappointed that there was no coverage of working with vectors instead of points. I would very much has liked to see a chapter about rotating vertex normals (using the inverse transpose of the upper 3x3 portion of the 4x4 matrix used for points).

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