Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics) (Hardcover)

by Leo Dorst (Author), Daniel Fontijne (Author), Stephen Mann (Author)
Key Phrases: Hermann Grassmann, Screenshot of Example

Editorial Reviews

Book Description
The first book on a hot new technique in 3D graphics from leaders in the area!

Product Description
Within the last decade, Geometric Algebra (GA) has emerged as a powerful alternative to classical matrix algebra as a comprehensive conceptual language and computational system for computer science. This book will serve as a standard introduction and reference to the subject for students and experts alike. As a textbook, it provides a thorough grounding in the fundamentals of GA, with many illustrations, exercises and applications. Experts will delight in the refreshing perspective GA gives to every topic, large and small.
-David Hestenes, Distinguished research Professor, Department of Physics, Arizona State University

Geometric Algebra is becoming increasingly important in computer science. This book is a comprehensive introduction to Geometric Algebra with detailed descriptions of important applications. While requiring serious study, it has deep and powerful insights into GA's usage. It has excellent discussions of how to actually implement GA on the computer.
-Dr. Alyn Rockwood, CTO, FreeDesign, Inc. Longmont, Colorado

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.

Features

Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics.
Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA.
Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space.
Presents effective approaches to making GA an integral part of your programming.
Includes numerous drills and programming exercises helpful for both students and practitioners.
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.

About the Authors

Leo Dorst is Assistant Professor of Computer Science at the University of Amsterdam, where his research focuses on geometrical issues in robotics and computer vision. He earned M.Sc. and Ph.D. degrees from Delft University of Technology and received a NYIPLA Inventor of the Year award in 2005 for his work in robot path planning.

Daniel Fontijne holds a Master's degree in artificial Intelligence and is a Ph.D. candidate in Computer Science at the University of Amsterdam. His main professional interests are computer graphics, motion capture, and computer vision.

Stephen Mann is Associate Professor in the David R. Cheriton School of Computer Science at the University of Waterloo, where his research focuses on geometric modeling and computer graphics. He has a B.A. in Computer Science and Pure Mathematics from the University of California, Berkeley, and a Ph.D. in Computer Science and Engineering from the University of Washington.

* The first book on Geometric Algebra for programmers in computer graphics and entertainment computing

* Written by leaders in the field providing essential information on this new technique for 3D graphics

* This full colour book includes a website with GAViewer, a program to experiment with GA

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Product Details

• Hardcover: 664 pages
• Publisher: Morgan Kaufmann; 1 edition (May 3, 2007)
• Language: English
• ISBN-10: 0123694655
• ISBN-13: 978-0123694652
• Product Dimensions: 9.4 x 7.7 x 1.4 inches
• Shipping Weight: 3.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
• Amazon.com Sales Rank: #702,807 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

25 of 27 people found the following review helpful:

5.0 out of 5 stars A reader from Los Alamos, NM, August 17, 2007

By	J. Hanlon "JH" (USA) - See all my reviews (REAL NAME)

Geometric Algebra (GA) is a unifying mathematical language that should be taught instead of or at least in combination with traditional vector analysis. Most other books on GA are aimed at Physicists. This book is a better match for Engineers and Programmers. The authors are all active researchers in applications of GA. They have done a comprehensive and up to date job of collecting, organizing and presenting the material for both beginners and those who follow the development of GA on the web. The examples and problems use GAViewer, an easy to learn programming language with an Open GL view window that can be downloaded for free from the book website. Using GAViewer with the book is very good way to learn GA, especially the 5D Conformal model of 3D space. The authors hold nothing back. Between the book, the code and the website everything is there to make learning GA fun and useful. I highly recommend this book.