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Geometric algebra for computer science : an object-oriented approach to geometry /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Francisco, CA :
Morgan Kaufmann,
[2007]
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| Colección: | Morgan Kaufmann series in computer graphics.
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| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Front Cover; Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry; Copyright Page; Contents; LIST OF FIGURES; LIST OF TABLES; LIST OF PROGRAMMING EXAMPLES; PREFACE; CHAPTER 1. WHY GEOMETRIC ALGEBRA?; 1.1 An Example in Geometric Algebra; 1.2 How It Works and How It's Different; 1.3 Programming Geometry; 1.4 The Structure of This Book; 1.5 The Structure of the Chapters; PART I: GEOMETRIC ALGEBRA; CHAPTER 2. SPANNING ORIENTED SUBSPACES; 2.1 Vector Spaces; 2.2 Oriented Line Elements; 2.3 Oriented Area Elements; 2.4 Oriented Volume Elements
- 2.5 Quadvectors in 3-D Are Zero2.6 Scalars Interpreted Geometrically; 2.7 Applications; 2.8 Homogeneous Subspace Representation; 2.9 The Graded Algebra of Subspaces; 2.10 Summary of Outer Product Properties; 2.11 Further Reading; 2.12 Exercises; 2.13 Programming Examples and Exercises; CHAPTER 3. METRIC PRODUCTS OF SUBSPACES; 3.1 Sizing Up Subspaces; 3.2 From Scalar Product to Contraction; 3.3 Geometric Interpretation of the Contraction; 3.4 The Other Contraction; 3.5 Orthogonality and Duality; 3.6 Orthogonal Projection of Subspaces; 3.7 The 3-D Cross Product
- 3.8 Application: Reciprocal Frames3.9 Further Reading; 3.10 Exercises; 3.11 Programming Examples and Exercises; CHAPTER 4. LINEAR TRANSFORMATIONS OF SUBSPACES; 4.1 Linear Transformations of Vectors; 4.2 Outermorphisms: Linear Transformations of Blades; 4.3 Linear Transformation of the Metric Products; 4.4 Inverses of Outermorphisms; 4.5 Matrix Representations; 4.6 Summary; 4.7 Suggestions for Further Reading; 4.8 Structural Exercises; 4.9 Programming Examples and Exercises; CHAPTER 5. INTERSECTION AND UNION OF SUBSPACES; 5.1 The Phenomenology of Intersection
- 5.2 Intersection through Outer Factorization5.3 Relationships Between Meet and Join; 5.4 Using Meet and Join; 5.5 Join and Meet are Mostly Linear; 5.6 Quantitative Properties of the Meet; 5.7 Linear Transformation of Meet and Join; 5.8 Offset Subspaces; 5.9 Further Reading; 5.10 Exercises; 5.11 Programming Examples and Exercises; CHAPTER 6. THE FUNDAMENTAL PRODUCT OF GEOMETRIC ALGEBRA; 6.1 The Geometric Product for Vectors; 6.2 The Geometric Product of Multivectors; 6.3 The Subspace Products Retrieved; 6.4 Geometric Division; 6.5 Further Reading; 6.6 Exercises
- 6.7 Programming Examples and ExercisesCHAPTER 7. ORTHOGONAL TRANSFORMATIONS AS VERSORS; 7.1 Reflections of Subspaces; 7.2 Rotations of Subspaces; 7.3 Composition of Rotations; 7.4 The Exponential Representation of Rotors; 7.5 Subspaces as Operators; 7.6 Versors Generate Orthogonal Transformations; 7.7 The Product Structure of Geometric Algebra; 7.8 Further Reading; 7.9 Exercises; 7.10 Programming Examples and Exercises; CHAPTER 8. GEOMETRIC DIFFERENTIATION; 8.1 Geometrical Changes by Orthogonal Transformations; 8.2 Transformational Changes; 8.3 Parametric Differentiation