Geometric Algebra for Computer Science (Revised Edition). An Object-Oriented Approach to Geometry

✍ Scribed by Leo Dorst, Daniel Fontijne and Stephen Mann (Auth.)

• Publisher: Morgan Kaufmann
• Year: 2009
• Tongue: English
• Leaves: 621
• Category: Library

✦ Synopsis

• 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

  
  

✦ Table of Contents

Content:
Copyright, Page iv
List of Figures, Pages xx-xxv
List of Tables, Pages xxvi-xxvii
List of Programming Examples, Pages xxviii-xxix
Preface, Pages xxxi-xxxv
Chapter 1 - Why Geometric Algebra?, Pages 1-19
Chapter 2 - Spanning Oriented Subspaces, Pages 23-64
Chapter 3 - Metric Products of Subspaces, Pages 65-98
Chapter 4 - Linear Transformations of Subspaces, Pages 99-123
Chapter 5 - Intersection and Union of Subspaces, Pages 125-140
Chapter 6 - The Fundamental Product of Geometric Algebra, Pages 141-165
Chapter 7 - Orthogonal Transformations as Versors, Pages 167-212
Chapter 8 - Geometric Differentiation, Pages 213-241
Chapter 9 - Modeling Geometries, Pages 245-246
Chapter 10 - The Vector Space Model: The Algebra of Directions, Pages 247-270
Chapter 11 - The Homogeneous Model, Pages 271-326
Chapter 12 - Applications of the Homogeneous Model, Pages 327-354
Chapter 13 - The Conformal Model: Operational Euclidean Geometry, Pages 355-396
Chapter 14 - New Primitives for Euclidean Geometry, Pages 397-436
Chapter 15 - Constructions in Euclidean Geometry, Pages 437-464
Chapter 16 - Conformal Operators, Pages 465-495
Chapter 17 - Operational Models for Geometries, Pages 497-499
Chapter 18 - Implementation Issues, Pages 503-509
Chapter 19 - Basis Blades and Operations, Pages 511-519
Chapter 20 - The Linear Products and Operations, Pages 521-527
Chapter 21 - Fundamental Algorithms for Nonlinear Products, Pages 529-540
Chapter 22 - Specializing the Structure for Efficiency, Pages 541-556
Chapter 23 - Using the Geometry in a Ray-Tracing Application, Pages 557-581
A - Metrics and Null Vectors, Pages 585-587
B - Contractions and Other Inner Products, Pages 589-596
C - Subspace Products Retrieved, Pages 597-601
D - Common Equations, Pages 603-607
Bibliography, Pages 609-612
Index, Pages 613-626