Del i serien The Morgan Kaufmann Series in Computer Graphics

Geometric Algebra for Computer Science (Revised Edition)

An Object-Oriented Approach to Geometry

Inbunden, Engelska, 2009

AvLeo Dorst,Daniel Fontijne,Stephen Mann

1 179 kr

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Geometric Algebra for Computer Science (Revised Edition) presents a compelling alternative to the limitations of linear algebra.

Geometric algebra (GA) is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. This book explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. It systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. It covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Numerous drills and programming exercises are helpful for both students and practitioners. A 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.

The book will be of interest to professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. It is also be ideal for students in graduate or advanced undergraduate programs in computer science.

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.

Produktinformation

Utgivningsdatum2009-03-26
Mått196 x 239 x 41 mm
Vikt1 771 g
FormatInbunden
SpråkEngelska
SerieThe Morgan Kaufmann Series in Computer Graphics
Antal sidor664
FörlagElsevier Science
ISBN9780123749420

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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

"Within the last decade, Geometric Algebra (GA) has emerged as a powerful alternative to classical matrix algebra as a comprehensive conceptual language and computational system for computer science. This book will serve as a standard introduction and reference to the subject for students and experts alike. As a textbook, it provides a thorough grounding in the fundamentals of GA, with many illustrations, exercises and applications. Experts will delight in the refreshing perspective GA gives to every topic, large and small." --David Hestenes, Distinguished research Professor, Department of Physics, Arizona State University "Geometric Algebra is becoming increasingly important in computer science. This book is a comprehensive introduction to Geometric Algebra with detailed descriptions of important applications. While requiring serious study, it has deep and powerful insights into GA’s usage. It has excellent discussions of how to actually implement GA on the computer." --Dr. Alyn Rockwood, CTO, FreeDesign, Inc. Longmont, Colorado