Geometric Algebra for Computer Science

von Leo Dorst , Daniel Fontijne , Stephen Mann

73,50
inkl. gesetzl. MwSt.
In den Warenkorb
Geometric Algebra for Computer Science - Leo Dorst, Daniel Fontijne, Stephen Mann

Inhaltsverzeichnis

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 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