- Contents
- Clifford Algebra: A visual introduction () | Hacker News
- Geometric Algebra for Computer Science (Revised Edition) (eBook, PDF)
- Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
- Applications of Geometric Algebra in Computer Science and Engineering

This book presents new results on applications of geometric algebra. Algebra in Computer Science and Engineering” (AGACSE) in order to promote the. DOWNLOAD PDF. Geometric Algebra for Computer Science This Page Intentionally Left Blank Geometric Algebra for Computer Science An Object- oriented. xxvi. LIST OF PROGRAMMING EXAMPLES xxviii. PREFACE xxxi. CHAPTER 1. WHYGEOMETRICALGEBRA? 1. An Example in Geometric Algebra. 1.

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CHAPTER 1. WHY GEOMETRIC ALGEBRA? An Example in Geometric Algebra How It Works and How It's Different Vector Spaces as Modeling Tools. Geometric Algebra for Computer Science (Revised Edition) | 𝗥𝗲𝗾𝘂𝗲𝘀𝘁 𝗣𝗗𝗙 on ResearchGate | Geometric Algebra for Computer Science (Revised Edition). PDF | Leo Dorst and others published Applications of geometric algebra in computer science and engineering. Papers from the conference, AGACSE , .

Geometric algebra is a powerful and practical framework for the representation and solution of geometrical problems. We believe it to be eminently suitable to those subfields of computer science in which such issues occur: computer graphics, robotics, and computer vision. We wrote this book to explain the basic structure of geometric algebra, and to help the reader become a practical user. We employ various tools to get there: Explanations that are not more mathematical than we deem necessary, connecting algebra and geometry at every step A large number of interactive illustrations to get the object-oriented feeling of constructions that are dependent only on the geometric elements in them rather than on coordinates Drills and structural exercises for almost every chapter Detailed programming examples on elements of practical applications An extensive section on the implementational aspects of geometric algebra Part III of this book This is the first book on geometric algebra that has been written especially for the computer science audience. When reading it, you should remember that geometric algebra is fundamentally simple, and fundamentally simplifying. That simplicity will not always be clear; precisely because it is so fundamental, it does basic things in a slightly different way and in a different notation. This requires your full attention, notably in the beginning, when we only seem to go over familiar things in a perhaps irritatingly different manner. The patterns we uncover, and the coordinate-free way in which we encode them, will all pay off in the end in generally applicable quantitative geometrical operators and constructions. We emphasize that this is not primarily a book on programming, and that the subtitle An Object-oriented Approach to Geometry should not be interpreted too literally. It is intended to convey that we finally achieve clean computational objects in the sense of object-oriented programming to correspond to the oriented elements and operators of geometry by identifying them with oriented objects of the algebra. Why Geometric Algebra?

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.

Professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. Students in graduate or advanced undergraduate programs in computer science.

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. This book is a comprehensive introduction to Geometric Algebra with detailed descriptions of important applications.

It has excellent discussions of how to actually implement GA on the computer. Longmont, Colorado.

His main professional interests are computer graphics, motion capture, and computer vision. We are always looking for ways to improve customer experience on Elsevier.

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Skip to content. Search for books, journals or webpages All Webpages Books Journals. View on ScienceDirect. Hardcover ISBN: Morgan Kaufmann. Published Date: Page Count: View all volumes in this series: Sorry, this product is currently out of stock. Flexible - Read on multiple operating systems and devices. By its very nature, geometric algebra collates many partial results in a single framework, and the original sources become hard to trace in their original context.

It is part of the pleasure of geometric algebra that it empowers the user; by mastering just a few techniques, you can usually easily rediscover the result you need.

Once you grasp its essence, geometric algebra will become so natural that you will wonder why we have not done geometry this way all along. The reason is a history of geometric mis representation, for almost all elements of geometric algebra are not new—in hindsight.

This gave us the mixed blessing of coordinates, and the tiresome custom of specifying geometry at the coordinate level whereas coordinates should be relegated to the lowest implementational level, reserved for the actual computations. To have a more direct means of expression, Hermann Grassmann — developed a theory of extended quantities, allowing geometry to be based on more than points and vectors.

Unfortunately, his ideas were ahead of their time, and his very compact notation made his work more obscure than it should have been. All these individual contributions pointed toward a geometric algebra, and at the end of the 19th century, there were various potentially useful systems to represent aspects of geometry. Gibbs — made a special selection of useful techniques for the 3D geometry of engineering, and this limited framework is basically what we have been using ever since in the geometrical applications of linear algebra.

Linear algebra and matrices, with their coordinate representations, became the mainstay of doing geometry, both in practice and in mathematical development. He rescued the half-forgotten geometric algebra by now called Clifford algebra and developed in nongeometric directions , developed it into an alternative to the classical linear algebra—based representations, and started advocating its universal use.

In the s, his voice was heard, and with the implementation of geometric algebra into interactive computer programs its practical applicability is becoming more apparent.

Gibbs was wrong in assuming that computing with the geometry of 3D space requires only representations of 3D points, although he did give us a powerful system to compute with those. This book will demonstrate that allowing more extended quantities in higher-dimensional representational spaces provides a more convenient executable language for geometry.

Maybe we could have had this all along; but perhaps we indeed needed to wait for the arrival of computers to appreciate the effectiveness of this approach. It was originally developed as a teaching tool, and a web tutorial is available, using GAViewer to explain the basics of geometric algebra. You can use GAViewer when reading the book to type in algebraic formulas and have them act on geometrical elements interactively.

This interaction should aid your understanding of the correspondence between geometry and algebra considerably. The GA sandbox source code package used for the programming examples and exercises in this book is built on top of Gaigen 2.

To compile and run the programming examples in Part I and Part II, you only have to download the sandbox package from the web site.

It is written in Java and intended to show only the essential structure; we do not deem it usable for anything that is computationally intensive, since it can easily be 10 to times slower than Gaigen 2. PREFACE xxxv If you are serious about implementing further applications, you can start with the GA sandbox package, or other available implementations of geometric algebra, or even write your own package.

We are grateful to Joan Lasenby of Cambridge University for her detailed comments on the early chapters, and for providing some of the applied examples.

We are also indebted to Timaeus Bouma for his keen insights that allowed our software to be well-founded in mathematical fact. Daniel Fontijne owes many thanks to Yvonne for providing the fun and artistic reasons to study geometric algebra, and to Femke and Tijmen for the many refreshing breaks while working at home.