Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010205704 | QA564 D67 2007 | Open Access Book | Book | Searching... |
Searching... | 30000003482985 | QA 564 D67 2007 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming.
Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down.
Author Notes
Daniel Fontijne holds a Master's degree in artificial Intelligence and a Ph.D. in Computer Science, both from the University of Amsterdam. His main professional interests are computer graphics, motion capture, and computer vision.
Table of 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 |