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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 |
|---|---|
| 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) |
MARC
| LEADER | 00000cam a2200000Ia 4500 | ||
|---|---|---|---|
| 001 | OR_ocn822335969 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr unu|||||||| | ||
| 008 | 121220s2007 caua ob 001 0 eng d | ||
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| 019 | |a 988445551 | ||
| 020 | |a 9780080553108 | ||
| 020 | |a 0080553109 | ||
| 020 | |a 0123694655 | ||
| 020 | |a 9780123694652 | ||
| 020 | |z 9780123694652 | ||
| 029 | 1 | |a DEBBG |b BV040903282 | |
| 029 | 1 | |a DEBSZ |b 381393437 | |
| 029 | 1 | |a GBVCP |b 785364730 | |
| 029 | 1 | |a AU@ |b 000069033008 | |
| 035 | |a (OCoLC)822335969 |z (OCoLC)988445551 | ||
| 037 | |a CL0500000177 |b Safari Books Online | ||
| 050 | 4 | |a QA199 |b .D678 2007 | |
| 082 | 0 | 4 | |a 006.60151257 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Dorst, Leo, |d 1958- | |
| 245 | 1 | 0 | |a Geometric algebra for computer science : |b an object-oriented approach to geometry / |c Leo Dorst, Daniel Fotijne, Stephen Mann. |
| 260 | |a San Francisco, CA : |b Morgan Kaufmann, |c [2007] | ||
| 300 | |a 1 online resource (1 volume) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a The Morgan Kaufmann series in computer graphics | |
| 588 | 0 | |a Online resource; title from PDF title page (Safari, viewed Nov. 16, 2012). | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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 Phy. | ||
| 590 | |a O'Reilly |b O'Reilly Online Learning: Academic/Public Library Edition | ||
| 650 | 0 | |a Clifford algebras. | |
| 650 | 0 | |a Computer graphics |x Mathematics. | |
| 650 | 0 | |a Object-oriented methods (Computer science) | |
| 650 | 6 | |a Algèbres de Clifford. | |
| 650 | 6 | |a Infographie |x Mathématiques. | |
| 650 | 6 | |a Conception orientée objet (Informatique) | |
| 650 | 7 | |a Clifford algebras. |2 fast |0 (OCoLC)fst00864221 | |
| 650 | 7 | |a Computer graphics |x Mathematics. |2 fast |0 (OCoLC)fst00872135 | |
| 650 | 7 | |a Object-oriented methods (Computer science) |2 fast |0 (OCoLC)fst01042803 | |
| 700 | 1 | |a Fontijne, Daniel. | |
| 700 | 1 | |a Mann, Stephen, |d 1963- | |
| 830 | 0 | |a Morgan Kaufmann series in computer graphics. | |
| 856 | 4 | 0 | |u https://learning.oreilly.com/library/view/~/9780123694652/?ar |z Texto completo (Requiere registro previo con correo institucional) |
| 994 | |a 92 |b IZTAP | ||