Geometric Algebra for Computer Science. Morgan Kaufmann

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. This title presents a compelling alternative to the limitations of linear algebra.

In fields such as robotics, computer graphics, and computer games, it is necessary to compute complex interactions of objects in virtual 3D worlds. In a virtual world, there may be thousands of these objects interacting with each other in real-time. Linear algebra (vector math) is traditionally used to perform these calculations, but linear algebra requires long and complex computer programs to implement and can create very difficult programming challenges. Developers of real-time applications spend a lot of time trying to squeeze the last ounce of performance out of them. Geometric algebra (GA) is a new and compact way of representing the geometry of these objects that makes the computation and the programming of them much easier. Once only the domain of academic researchers, this book introduces GA to programmers, shows how it extends from linear algebra, and describes how to model geometries using GA. The last part of the book describes techniques for creating applications. A companion website link is included with GaViewer, a program written in C that allows programming experiments with GA. Geometric Algebra for Computer Science describes what many feel will be the future of geometrical computation.
The first book on Geometric Algebra for programmers in computer graphics and entertainment computing
Written by leaders in the field providing essential information on this new technique for 3D graphics
This full color book includes a website with GAViewer, a program to experiment with GA

CHAPTER 1. WHY GEOMETRIC ALGEBRA?
PART I GEOMETRIC ALGEBRA
CHAPTER 2. SPANNING ORIENTED SUBSPACES
CHAPTER 3. METRIC PRODUCTS OF SUBSPACES
CHAPTER 4. LINEAR TRANSFORMATIONS OF
SUBSPACES
CHAPTER 5. INTERSECTION AND UNION OF
SUBSPACES
CHAPTER 6. THE FUNDAMENTAL PRODUCT OF
GEOMETRIC ALGEBRA
CHAPTER 7. ORTHOGONAL TRANSFORMATIONS AS
VERSORS
CHAPTER 8. GEOMETRIC DIFFERENTIATION
PART II MODELS OF GEOMETRIES
CHAPTER 9. MODELING GEOMETRIES
CHAPTER 10. THE VECTOR SPACE MODEL: THE
ALGEBRA OF DIRECTIONS
CHAPTER 11. THE HOMOGENEOUS MODEL
CHAPTER 12. APPLICATIONS OF THE
HOMOGENEOUS MODEL
CHAPTER 13. THE CONFORMAL MODEL:
OPERATIONAL EUCLIDEAN GEOMETRY
CHAPTER 14. NEW PRIMITIVES FOR EUCLIDEAN
GEOMETRY
CHAPTER 15. CONSTRUCTIONS IN EUCLIDEAN
GEOMETRY
CHAPTER 16. CONFORMAL OPERATORS
CHAPTER 17. OPERATIONAL MODELS FOR
GEOMETRIES
PART III IMPLEMENTING GEOMETRIC ALGEBRA
CHAPTER 18. IMPLEMENTATION ISSUES
CHAPTER 19. BASIS BLADES AND OPERATIONS
CHAPTER 20. THE LINEAR PRODUCTS AND
OPERATIONS
CHAPTER 21. FUNDAMENTAL ALGORITHMS FOR
NONLINEAR PRODUCTS
CHAPTER 22. SPECIALIZING THE STRUCTURE FOR
EFFICIENCY
CHAPTER 23. USING THE GEOMETRY IN A RAY-
TRACING APPLICATION
PART IV APPENDICES
A METRICS AND NULL VECTORS
B CONTRACTIONS AND OTHER INNER PRODUCTS
C SUBSPACE PRODUCTS RETRIEVED
D COMMON EQUATIONS
BIBLIOGRAPHY
INDEX