Geometric algebra for computer science [electronic resource] : an object-oriented approach to geometry / Leo Dorst, Daniel Fontijne, Stephen Mann.

By: Dorst, Leo, 1958-Contributor(s): Fontijne, Daniel | Mann, Stephen, 1963-Material type: TextTextSeries: Morgan Kaufmann series in computer graphics: Publisher: Amsterdam ; Boston : Elsevier/Morgan Kaufmann, c2007Description: 1 online resource (xxxv, 626 p.) : ill. (some col.)ISBN: 9780080958798 (electronic bk.); 0080958796 (electronic bk.)Subject(s): Geometry, Algebraic | Computer science -- Mathematics | Object-oriented methods (Computer science) | G�eom�etrie alg�ebrique | Informatique -- Math�ematiques | Approche orient�ee objet (Informatique) | COMPUTERS -- Image Processing | PHOTOGRAPHY -- Techniques -- Digital | TECHNOLOGY & ENGINEERING -- Imaging Systems | COMPUTERS -- Digital Media -- Graphics Applications | Geometrische algebraGenre/Form: Electronic books.Additional physical formats: Print version:: Geometric algebra for computer science.DDC classification: 006.601/51257 LOC classification: QA564 | .D67 2007ebOnline resources: ScienceDirect
Contents:
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.
Summary: In fields such as robotics, computer graphics, and computer games, it is necessary to compute complex interactions of objects in virtual 3D worlds. In a virtual world, there may be thousands of these objects interacting with each other in real-time. Linear algebra (vector math) is traditionally used to perform these calculations, but linear algebra requires long and complex computer programs to implement and can create very difficult programming challenges. Developers of real-time applications spend a lot of time trying to squeeze the last ounce of performance out of them. Geometric algebra (GA) is a new and compact way of representing the geometry of these objects that makes the computation and the programming of them much easier. Once only the domain of academic researchers, this book introduces GA to programmers, shows how it extends from linear algebra, and describes how to model geometries using GA. The last part of the book describes techniques for creating applications. A companion website link is included with GaViewer, a program written in C that allows programming experiments with GA. Geometric Algebra for Computer Science describes what many feel will be the future of geometrical computation. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full color book includes a website with GAViewer, a program to experiment with GA.
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In fields such as robotics, computer graphics, and computer games, it is necessary to compute complex interactions of objects in virtual 3D worlds. In a virtual world, there may be thousands of these objects interacting with each other in real-time. Linear algebra (vector math) is traditionally used to perform these calculations, but linear algebra requires long and complex computer programs to implement and can create very difficult programming challenges. Developers of real-time applications spend a lot of time trying to squeeze the last ounce of performance out of them. Geometric algebra (GA) is a new and compact way of representing the geometry of these objects that makes the computation and the programming of them much easier. Once only the domain of academic researchers, this book introduces GA to programmers, shows how it extends from linear algebra, and describes how to model geometries using GA. The last part of the book describes techniques for creating applications. A companion website link is included with GaViewer, a program written in C that allows programming experiments with GA. Geometric Algebra for Computer Science describes what many feel will be the future of geometrical computation. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full color book includes a website with GAViewer, a program to experiment with GA.

Includes bibliographical references (p. 609-612) and index.

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.

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