Geometric Algebra for Computer Science (Revised Edition): An Object-Oriented Approach to Geometry / Edition 2by Leo Dorst, Stephen Mann, Daniel Fontijne
Pub. Date: 03/23/2009
Publisher: Elsevier Science
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 complexoften a lot of effort is required to bring about even modest performance enhancements.… See more details below
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 complexoften 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.
- Elsevier Science
- Publication date:
- Morgan Kaufmann Series in Computer Graphics Series
- Edition description:
- Product dimensions:
- 7.80(w) x 9.40(h) x 1.60(d)
Table of 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
CHAPTER 5. INTERSECTION AND UNION OF
CHAPTER 6. THE FUNDAMENTAL PRODUCT OF
CHAPTER 7. ORTHOGONAL TRANSFORMATIONS AS
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
CHAPTER 13. THE CONFORMAL MODEL:
OPERATIONAL EUCLIDEAN GEOMETRY
CHAPTER 14. NEW PRIMITIVES FOR EUCLIDEAN
CHAPTER 15. CONSTRUCTIONS IN EUCLIDEAN
CHAPTER 16. CONFORMAL OPERATORS
CHAPTER 17. OPERATIONAL MODELS FOR
PART III IMPLEMENTING GEOMETRIC ALGEBRA
CHAPTER 18. IMPLEMENTATION ISSUES
CHAPTER 19. BASIS BLADES AND OPERATIONS
CHAPTER 20. THE LINEAR PRODUCTS AND
CHAPTER 21. FUNDAMENTAL ALGORITHMS FOR
CHAPTER 22. SPECIALIZING THE STRUCTURE FOR
CHAPTER 23. USING THE GEOMETRY IN A RAY-
PART IV APPENDICES
A METRICS AND NULL VECTORS
B CONTRACTIONS AND OTHER INNER PRODUCTS
C SUBSPACE PRODUCTS RETRIEVED
D COMMON EQUATIONS
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