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Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
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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
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.
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