Geometric Algebra for Computer Science

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

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Description

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.
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Product details

  • Hardback | 664 pages
  • 196 x 238 x 36mm | 1,601.17g
  • Morgan Kaufmann Publishers In
  • San Francisco, United States
  • English
  • Approx. 190 illustrations (200 in full color); Illustrations, unspecified
  • 0123694655
  • 9780123694652
  • 1,107,040

Table of contents

CONTENTS
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
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About Stephen Mann

Daniel Fontijne holds a Master's degree in artificial Intelligence and a Ph.D. in Computer Science, both from the University of Amsterdam. His main professional interests are computer graphics, motion capture, and computer vision.
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3.88 out of 5 stars
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3 32% (8)
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