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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
Includes numerous drills and programming exercises helpful for both students
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.