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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:   Print 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 pages : illustrations (some color) ; 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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