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Geometric algebra for computer science : an object-oriented approach to geometry

Author: Leo Dorst; Daniel Fontijne; Stephen Mann
Publisher: Amsterdam : Elsevier ; San Francisco : Morgan Kaufmann, 2007.
Series: Morgan Kaufman series in computer graphics and geometric modeling.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Geometric Algebra for Computer Science presents an 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  Read more...
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Genre/Form: Einführung
Document Type: Book
All Authors / Contributors: Leo Dorst; Daniel Fontijne; Stephen Mann
ISBN: 0123694655 9780123694652 9780123749420 0123749425
OCLC Number: 132691969
Description: xxxv, 626 p. : ill. (some col.) ; 24 cm.
Contents: Why geometric algebra? --
Spanning oriented subspaces --
Metric products of subspaces --
Linear transformations of subspaces --
Intersection and union of subspaces --
The fundamental product of geometric algebra --
Orthogonal transformations as versors --
Geometric differentiation --
Modeling geometries --
The vector space model : the algebra of directions --
The homogeneous model --
Applications of the homogeneous model --
The conformal model : operational Euclidean geometry --
New primitives for Euclidean geometry --
Constructions in Euclidean geometry --
Conformal operations --
Operational models for geometries --
Implementation issues --
Basis blades and operations --
The linear products and operations --
Fundamental algorithms for nonlinear products --
Specializing the structure for efficiency --
Using the geometry in a ray-tracing application --
Metrics and null vectors --
Contractions and other inner products --
Subspace products retrieved --
Common equations.
Series Title: Morgan Kaufman series in computer graphics and geometric modeling.
Responsibility: Leo Dorst, Daniel Fontijne, Stephen Mann.
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Abstract:

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  Read more...

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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. Read more...

 
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schema:reviewBody""Geometric Algebra for Computer Science presents an 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."--BOOK JACKET."
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