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.
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.
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