Geometric Algebra for Computer Science (Revised Edition): An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics) 1st Edition by Leo Dorst (PDF)

Description

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. 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐After the first year of GA studies this book is a must to read. When you arrive to a deadlock in your GA efforts this book supports you always as a compass of how to continue. It is not an application oriented classic but it is the missing part of the GA books forming the ring of the accepted core materials. Even more it is radiating a kind of balanced harmony between the secondary mismatchings of the divergent parts of the full Grassmann-Clifford-Hestenes arsenal. In itself the book does fill uniquely the gap between the GA and OO Computer Sciences & Programming and to utilize the GA it gives a good starting point toward the sophisticated geometrical examples of the past history.

⭐A lot of math textbooks will often follow the format of Definition -> Theorem -> Proof ad nauseum so it becomes easy to talk about how beautiful something is with no regards to reality. It’s also possible for proofs to be wrong and be totally undetectable.This book takes a different approach and introduces the primitives of geometric algebra and uses them to construct various kinds of interesting geometric transformations like projections, reflections etc.. If you’ve ever read a graphics book, linear algebra book or topological robotics book then you’re bound to find something you’ll find interesting.The authors also produced a free online tool which you can use to write your own geometric scripts and test your intuition.I’m by no means an expert on geometric algebra but I’m really appreciating the methodology of this book and wish I could find a similar book for generic abstract algebra

⭐I bought this for my son-in-law who is a computer science prof at a college. He spend a lot of time reading and rereading parts of it during their stay at Christmastime. He was greatly enjoying learning concepts and ideas from the book. It had been on his wish list since the book was published.

⭐happy I bought the book

⭐It’s a good book, but the mathematics is poorly treated, not enough rigorous as would be expected.

⭐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.

⭐Despite all mishaps (on my side mostly), the item got delivered ahead of time – everybody is happy.

⭐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.

⭐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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