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Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry Hardcover – Apr 19 2007

4 out of 5 stars 2 customer reviews

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Hardcover, Apr 19 2007
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Product Details

  • Hardcover: 664 pages
  • Publisher: Morgan Kaufmann; 1 edition (April 19 2007)
  • Language: English
  • ISBN-10: 0123694655
  • ISBN-13: 978-0123694652
  • Product Dimensions: 23.8 x 19.5 x 3.5 cm
  • Shipping Weight: 1.6 Kg
  • Average Customer Review: 4.0 out of 5 stars 2 customer reviews
  • Amazon Bestsellers Rank: #2,357,852 in Books (See Top 100 in Books)
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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

--This text refers to an alternate Hardcover edition.

Book Description

The first book on a new technique in 3D graphics

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Top Customer Reviews

Format: Hardcover
The more familiar we are with a particular technique, the harder it is to see its limitations. For those who have taken the appropriate courses, the machinery of real and complex numbers, vectors, matrices, and so on, seem to be the inevitable "right" way of doing things. Yet there is another way, pioneered in the nineteenth century by Grassmann (1844) and Clifford (1878) and called (by Clifford) "geometric algebra" (GA). For over a century, GA was buried by the "standard" approach of Hamilton, Gibbs, et al., but it has recently been resurrected by a small but dedicated group of people, perhaps most notably by David Hestenes in "New Foundations for Classical Mechanics" (1999).

The subtitle is misleading, as the authors admit in the Preface. This is a book about expressing geometric concepts algebraically, not about programming. (Nevertheless, programming examples, using C++, OpenGL, and the authors' libraries, appear throughout.) Part I (pp. 23-244) develops the main ideas of GA, including vector spaces, the geometric product, transformations, and differentiation. Part II (pp. 245-502) presents models of geometries, including vector space, homogeneous, conformal representations. Part III (pp. 503-584) discusses the software implementation of GA. The big problem is that a naive approach would be extremely inefficient, and so clever optimizations are needed. The authors' approach is to use generative programming: the user feeds parameters of the GA (dimension, metric, etc.) into a code generator, which then generates an optimized library (in C++) for that algebra.

This is a challenging book. It contains a large amount of detailed material and assumes fluency in mathematics, programming, and graphics.
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Format: Hardcover Verified Purchase
As a C++ software engineer in video game industry with mathematical physics background, I thought this book was well suited for me. However, even though I respect its authors, I must admit it is not very appropriate for what I was looking for (neither as a Library nor as a reference book). I must admit though that this book is very nice to get some illustrations of some properties of multivectors, which may be nice on its own! It is also got a nice brief discussion about affine (homogeneous) and conformal spaces in addition to traditionnal linear space.

I would suggest any interested readers either one (or both) of David Estenes books on geometric algebra or Doran and Lasenby's Geometric Algebra for Physicists. The later is a very good introduction to the subject and goes in some great détails. Interested readers will then want to have a look at Estenes' books.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: HASH(0xa634e8e8) out of 5 stars 5 reviews
42 of 44 people found the following review helpful
HASH(0xa6800480) out of 5 stars A reader from Los Alamos, NM Aug. 17 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.
14 of 14 people found the following review helpful
HASH(0xa6800888) out of 5 stars An excellent introduction to the subject. Sept. 5 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
HASH(0xa6800900) out of 5 stars very good text May 10 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.
HASH(0xa6800c90) out of 5 stars Very clear and careful exposition July 9 2015
By Bret Mulvey - Published on Amazon.com
Format: Hardcover
Most clear and careful explanation I've seen of GA. If you're a programmer trying to figure this stuff out from online sources, you've undoubtedly run into inconsistencies, incomplete explanations, circular definitions, and outright blunders. Do yourself a favor and read this book.
5 of 15 people found the following review helpful
HASH(0xa6800dc8) out of 5 stars ok, but... Oct. 5 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.