Geometric Algebra for Computer Science (Revised Edition)

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.

"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

• 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