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Geometric Algebra for Computer Graphics [electronic resource] /by John Vince.

by Vince, John [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: London : Springer London, 2008.Description: online resource.ISBN: 9781846289972.Subject(s): Computer science | Computer graphics | Geometry, algebraic | Geometry | Computer Science | Computer Graphics | Algebraic Geometry | Math Applications in Computer Science | GeometryDDC classification: 006.6 Online resources: Click here to access online
Contents:
Elementary Algebra -- Complex Algebra -- Vector Algebra -- Quaternion Algebra -- Geometric Conventions -- Geometric Algebra -- The Geometric Product -- Reflections and Rotations -- Geometric Algebra and Geometry -- Conformal Geometry -- Applications of Geometric Algebra -- Programming Tools for Geometric Algebra -- Conclusion.
In: Springer eBooksSummary: 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.
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Elementary Algebra -- Complex Algebra -- Vector Algebra -- Quaternion Algebra -- Geometric Conventions -- Geometric Algebra -- The Geometric Product -- Reflections and Rotations -- Geometric Algebra and Geometry -- Conformal Geometry -- Applications of Geometric Algebra -- Programming Tools for Geometric Algebra -- Conclusion.

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.

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