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Geometric Algebra for Computer Science (Revised Edition), (The Morgan Kaufmann Series in Computer Graphics) [Hardcover]

Leo Dorst

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Book Description

26 Mar 2009 0123749425 978-0123749420 2nd Revised edition
Until recently, 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. This title 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. It presents effective approaches to making GA an integral part of your programming. It 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.

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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

About the Author

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

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This book is about geometric algebra, a powerful computational system to describe and solve geometrical problems. Read the first page
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Amazon.com: 4.5 out of 5 stars  4 reviews
39 of 41 people found the following review helpful
5.0 out of 5 stars A reader from Los Alamos, NM 17 Aug 2007
By J. Hanlon - Published on Amazon.com
Format:Hardcover
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.
12 of 12 people found the following review helpful
5.0 out of 5 stars An excellent introduction to the subject. 5 Sep 2009
By Peeter Joot - Published on Amazon.com
Format:Hardcover
The book Geometric Algebra For Computer Science, by Dorst, Fontijne, and Mann has one of the best introductions to the subject that I have seen.

It contains particularly good introductions to the dot and wedge products and how they can be applied and what they can be used to model. After one gets comfortable with these ideas they introduce the subject axiomatically. Much of the pre-axiomatic introductory material is based on the use of the scalar product, defined as a determinant. You'll have to be patient to see where and why that comes from, but this choice allows the authors to defer some of the mathematical learning overhead until one is ready for the ideas a bit better.

Having started study of the subject with papers of Hestenes, Cambridge, and Baylis papers, I found the alternate notation for the generalized dot product (L and backwards L for contraction) distracting at first but adjusting to it does not end up being that hard.

This book has three sections, the first covering the basics, the second covering the conformal applications for graphics, and the last covering implementation. As one reads geometric algebra books it is natural to wonder about this, and the pros, cons and efficiencies of various implementation techniques are discussed.

There are other web resources available associated with this book that are quite good. The best of these is GAViewer, a graphical geometric calculator that was the product of some of the research that generated this book. Performing the GAViewer tutorial exercises is a great way to build some intuition to go along with the math, putting the geometric back in the algebra.

There are specific GAViewer exercises that you can do independent of the book, and there is also an excellent interactive tutorial available. Browse the book website, or Search for '2003 Game Developer Lecture, Interactive GA tutorial. UvA GA Website: Tutorials'. Even if one decided not to learn GA, using this to play with the graphical cross product manipulation, with the ability to rotate viewpoints, is quite neat and worthwhile.
3 of 4 people found the following review helpful
5.0 out of 5 stars very good text 10 May 2010
By T. Czyczko - Published on Amazon.com
Format:Hardcover
This is the text I would first recommend to anyone involved in geometrical programming who would like to learn geometrical algebra.
4 of 13 people found the following review helpful
3.0 out of 5 stars ok, but... 5 Oct 2010
By Fuga Federico - Published on Amazon.com
Format:Hardcover|Verified Purchase
It's a good book, but the mathematics is poorly treated, not enough rigorous as would be expected.
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