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Applications of Geometric Algebra in Computer Science and Engineering - Leo Dorst

Applications of Geometric Algebra in Computer Science and Engineering

By: Leo Dorst (Editor), Chris Doran (Editor), Joan Lasenby (Editor)

Hardcover Published: 8th March 2002
ISBN: 9780817642679
Number Of Pages: 478

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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.

Industry Reviews

"This book contains papers presented at the conference "Applied Geometric Algebra in Computer Science and Engineering" (AGACSE 2001).... The goal was to demonstrate how the framework of geometric algebra (Clifford algebra) could unify and illuminate diverse fields of science and engineering.

The articles reveal [a] range [of] fields: from quantum physics to robotics, from crystallographic groups to image understanding, from relativistic mechanics to signal processing. Despite this diversity, the combination of these subjects was not felt to be artificial.

This book should be...useful to mathematicians...physicists, [and] to mechanical and computer engineers."

--Iasi Polytechnic Magazine

"The conference 'Applied Geometric Algebras in Computer Science and Engineering' (AGACSE 2001) was held... July 9-13, 2001. The present book contains the papers of this scientific meeting and reflects the constantly growing interest in searching the applications of geometric algebra (or Clifford algebra) in various fields of science.

Geometric algebra includes a lot of techniques from several mathematical theories (linear algebra, vector calculus, projective geometry, complex analysis) and offers new directions in some unexpected domains like quantum physics, robotics, crystallographic groups, image understanding, relativistic mechanics, signal processing.

The volume begins with a preface written by the Editors and a useful list with contributors.... There are four sections: Algebra and Geometry..., Applications to Physics..., Computer Vision and Robotics..., Signal Processing and Other Applications....

In conclusion, a very useful book both for beginners and specialists!"

--Memoriile Sectiilor Stiintifice

Preface
Contributors
Algebra and Geometry Point Groups and Space Groups in Geometric Algebra
The Inner Products of Geometric Algebra
Unification of Grassmann's Progressive and Regressive Products using the Principle of Duality
From Unoriented Subspaces to Blade Operators
Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra
Rotations in n Dimensions as Spherical Vectors
Geometric and Algebraic Canonical Forms
Functions of Clifford Numbers or Square Matrices
Compound Matrices and Pfaffians: A Representation of Geometric Algebra
Analysis Using Abstract Vector Variables
A Multivector Data Structure for Differential Forms and Equations
Jet Bundles and the Formal Theory of Partial Differential Equations
Imaginary Eigenvalues and Complex Eigenvectors Explained by Real Geometry
Symbolic Processing of Clifford Numbers in C++
Clifford Numbers and their Inverses Calculated using the Matrix Representation
A Toy Vector Field Based on Geometric Algebra
Quadratic Transformations in the Projective Plane
Annihilators of Principal Ideals in the Grassmann Algebra
Applications to Physics Homogeneous Rigid Body Mechanics with Elastic Coupling
Analysis of One and Two Particle Quantum Systems using Geometric Algebra
Interaction and Entanglement in the Multiparticle Spacetime Algebra
Laws of Reflection from Two or More Plane Mirrors in Succession
Exact Kinetic Energy Operators for Polyatomic Molecules
Geometry of Quantum Computing by Hamiltonian Dynamics of Spin Ensembles
Is the Brain a 'Clifford Algebra Quantum Computer'?
A Hestenes Spacetime Algebra Approach to Light Polarization
Quaternions, Clifford Algebra and Symmetry Groups
Computer Vision and Robotics A Generic Framework for Image Geometry
Color Edge Detection Using Rotors
Numerical Evaluation of Versors with Clifford Algebra
The Role of Clifford Algebra in Structure-Preserving Transformations for Second-Order Systems
Applications of Algebra of Incidence in Visually Guided Robotics
Monocular Pose Estimation of Kinematic Chains
Stabilization of 3D Pose Estimation
Inferring Dynamical Information from 3D Position Data using Geometric Algebra
Clifford Algebra Space Singularities of Inline Planar Platforms
Signal Processing and Other Applications Fast Quantum Fourier--Heisenberg--Weyl Transforms
The Structure Multivector
The Application of Clifford Algebra to Calculations of Multicomponent Chemical Composition
An Algorithm to Solve the Inverse IFS-Problem
Fast Quantum n-D Fourier and Radon Transforms
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780817642679
ISBN-10: 0817642676
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 478
Published: 8th March 2002
Publisher: BIRKHAUSER BOSTON INC
Country of Publication: US
Dimensions (cm): 24.0 x 16.18  x 3.38
Weight (kg): 0.85

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