Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry

by Leo Dorst, Stephen Mann, Daniel Fontijne

Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down.

Genres: Mathematics, Computer Science, Geometry, Computers, 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).