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Applications of geometric algebra in computer science and engineering
AGACSE 2001 (2001 : Newnham College, Cambridge)
1 online resource (xxiv, 478 pages) : illustrations
Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
I. Algebra and Geometry. 1. Point Groups and Space Groups in Geometric Algebra / David Hestenes. 2. The Inner Products of Geometric Algebra / Leo Dorst. 3. Unification of Grassmann's Progressive and Regressive Products using the Principle of Duality / Stephen Blake. 4. From Unoriented Subspaces to Blade Operators / Timaeus A. Bouma. 5. Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra / Hongbo Li. 6. Rotations in n Dimensions as Spherical Vectors / W.E. Baylis and S. Hadi. 7. Geometric and Algebraic Canonical Forms / Neil Gordon. 8. Functions of Clifford Numbers of Square Matrices / John Snygg.
Leo Dorst, Chris Doran, Joan Lasenby, editors.
Proceedings of AGACSE 2001, held July 9-13,2001, in Newnham College, Cambridge.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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