Geometric Algebra for Computer Science
An Object-Oriented Approach to Geometry
Published on 26. April 2007
Book
Hardback
664 pages
978-0-12-369465-2 (ISBN)
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.
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.
More details
Series
Language
English
Place of publication
San Francisco
United States
Publishing group
Elsevier Science & Technology
Target group
College/higher education
Professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. Students in graduate or advanced undergraduate programs in computer science.
Illustrations
Approx. 190 illustrations (200 in full color); Illustrations
Dimensions
Height: 235 mm
Width: 191 mm
Weight
1600 gr
ISBN-13
978-0-12-369465-2 (9780123694652)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Leo Dorst | Daniel Fontijne | Stephen Mann
Geometric Algebra for Computer Science (Revised Edition)
An Object-Oriented Approach to Geometry
Book
03/2009
Morgan Kaufmann
€92.50
Shipment within 15-20 days
Additional editions
Leo Dorst | Daniel Fontijne | Stephen Mann
Geometric Algebra for Computer Science
An Object-Oriented Approach to Geometry
E-Book
07/2010
Morgan Kaufmann
€56.95
Available for download
Persons
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.
Content
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
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