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Geometric Algebra for Computer Graphics

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Synopses & Reviews

Publisher Comments:

Since its invention, geometric algebra has been applied to various branches of physics such as cosmology and electrodynamics, and is now being embraced by the computer graphics community where it is providing new ways of solving geometric problems. It took over two thousand years to discover this algebra, which uses a simple and consistent notation to describe vectors and their products. John Vince (best-selling author of a number of books including 'Geometry for Computer Graphics' and 'Vector Analysis for Computer Graphics') tackles this new subject in his usual inimitable style, and provides an accessible and very readable introduction. The first five chapters review the algebras of real numbers, complex numbers, vectors, and quaternions and their associated axioms, together with the geometric conventions employed in analytical geometry. As well as putting geometric algebra into its historical context, John Vince provides chapters on Grassmann's outer product and Clifford's geometric product, followed by the application of geometric algebra to reflections, rotations, lines, planes and their intersection. The conformal model is also covered, where a 5D Minkowski space provides an unusual platform for unifying the transforms associated with 3D Euclidean space. Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to geometric algebra for computer graphics.

Synopsis:

The author tackles this complex subject of Geometric algebra (a Clifford Algebra) with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated.

Synopsis:

Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.

Synopsis:

Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems.

John Vince (author of numerous books including 'Geometry for Computer Graphics' and 'Vector Analysis for Computer Graphics') has tackled this complex subject in his usual inimitable style, and provided an accessible and very readable introduction.

As well as putting geometric algebra into its historical context, John tackles complex numbers and quaternions; the nature of wedge product and geometric product; reflections and rotations (showing how geometric algebra can offer a powerful way of describing orientations of objects and virtual cameras); and how to implement lines, planes, volumes and intersections. Introductory chapters also look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.

Table of Contents

Introduction.- Elementary Algebra.- Complex Algebra.- Vector Algebra.- Quaternion Algebra.- Geometric Conventions.- History of Geometric Algebra.- The Geometric Product.- Reflections and Rotations.- Geometric Algebra and Geometry.- Conformal Geometry.- Applications of Geometric Algebra in Computer Graphics.- Programming Tools for Geometric Algebra.- Conclusion.- References.

Product Details

ISBN:
9781846289965
Author:
Vince, John A.
Publisher:
Springer
Author:
Vince, John
Location:
London
Subject:
Computer Graphics - General
Subject:
Mathematics
Subject:
Computer graphics
Subject:
Algebra
Subject:
Clifford-Algebra
Subject:
geometric algebra
Subject:
Algebraic Geometry
Subject:
Math Applications in Computer Science
Subject:
Geometry
Subject:
Graphics-General
Subject:
Computer Science
Subject:
B
Subject:
Geometry - Algebraic
Copyright:
Edition Description:
2008
Publication Date:
20080414
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
272
Dimensions:
235 x 178 mm

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Geometric Algebra for Computer Graphics New Hardcover
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Product details 272 pages Springer - English 9781846289965 Reviews:
"Synopsis" by , The author tackles this complex subject of Geometric algebra (a Clifford Algebra) with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated.
"Synopsis" by , Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.
"Synopsis" by , Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems.

John Vince (author of numerous books including 'Geometry for Computer Graphics' and 'Vector Analysis for Computer Graphics') has tackled this complex subject in his usual inimitable style, and provided an accessible and very readable introduction.

As well as putting geometric algebra into its historical context, John tackles complex numbers and quaternions; the nature of wedge product and geometric product; reflections and rotations (showing how geometric algebra can offer a powerful way of describing orientations of objects and virtual cameras); and how to implement lines, planes, volumes and intersections. Introductory chapters also look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.

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