Geometric Algebra for Computer Science (Revised Edition): An Object-Oriented Approach to Geometry

by Leo Dorst, Stephen Mann, Daniel Fontijne

Geometric Algebra for Computer Science (Revised Edition) presents a compelling alternative to the limitations of linear algebra. Geometric algebra (GA) is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. This book explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. It systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. It covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Numerous drills and programming exercises are helpful for both students and practitioners. A companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book; and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter. The book will be of interest to professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. It is also be ideal for students in graduate or advanced undergraduate programs in computer science.

Genres: Mathematics, Computer Science, Technology, Programming, Textbooks

664 pages, Hardcover

First published April 1, 2007

Reviews

[Corbin Smith · Rating 5 out of 5]

Super great book. Professor Dorst manages to both nail the theoretical aspects down, and provide relevant applications to computer graphics. A very excellent and important book.

Also congratulations on the recent retirement Professor Dorst, you have given us so much.

[Ben · Rating 3 out of 5]

This book needs to come with a warning. Maths textbooks are often challenging or difficult reads, I know. But I've read a fair few, and IMO this one is particularly and unnecessarily difficult.

Geometric Algebra is one of the big advances in contemporary math. The topic is worthy and the authors have mastery of the material.

However, the authors don't communicate the material well. They assume a great deal of prior knowledge of maths, from the outset littering the text with specific mathematical jargon they don't explain or define. They delight in dizzying layers of abstraction, while concrete examples are either omitted entirely or glanced over.

It feels like the book was never tested on a cohort of students or used in an actual university course. The introduction suggests the book was written for "computer scientists" but the assumed math is more suited to post-graduate mathematicians.

For me, Norman Bigg's Discrete Mathematics shows whats possible in math communication. Unfortunately this book falls well short..

[Dan'l · Rating 5 out of 5]

The undergraduate expository evangelical introduction to the resurrection of a branch of mathematics (Grassmann algebra) that was nearly forgotten for 1½ centuries for modeling 3D geometry other than projective geometry.

[Gary · Rating 1 out of 5]

Outdated. Sloppy. Misleading. If you want to learn geometric algebra, do yourself a favor and avoid this book because it's pure dreck. This book is full of errors (just look at the long errata on the website), and many of the claims it makes about capabilities and performance have been debunked by the real experts in the field. It has also been shown that this book is simply wrong about several important fundamental aspects of geometric algebra, and the writers just didn't know what they were doing. If you already have a copy of this book, the only reason to keep it would be as a backup plan in case of another toilet paper shortage.

[Christian Kotz · Rating 4 out of 5]

Clear and easy to read, lots of examples. Have a look at the accompanied website for further material, code (e.g. a generator for algebra implementations) and a GA viewer application. It might be too verbose for readers with a mathematical background, as it primarily addresses computer scientists.

Be sure to get the revised edition. It has errors corrected and is also a bit cheaper!

[Arnoud Visser]

Prof. Penrose claims that string theory is a dead end. The way to go for physics is to use the conformal model to describe time and space. Here that same conformal model is described for people that actually calculate with space in real time (game designers and robotics).