Applications of Geometric Algebra in Computer Science and Engineering / Edition 1

Applications of Geometric Algebra in Computer Science and Engineering / Edition 1

by Leo Dorst
     
 

ISBN-10: 0817642676

ISBN-13: 9780817642679

Pub. Date: 03/01/2002

Publisher: Birkhauser Verlag

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…  See more details below

Overview

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.

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Product Details

ISBN-13:
9780817642679
Publisher:
Birkhauser Verlag
Publication date:
03/01/2002
Edition description:
2002
Pages:
478
Product dimensions:
6.26(w) x 9.48(h) x 1.02(d)

Table of Contents

Preface
Contributors
IAlgebra and Geometry1
1Point Groups and Space Groups in Geometric Algebra3
2The Inner Products of Geometric Algebra35
3Unification of Grassmann's Progressive and Regressive Products using the Principle of Duality47
4From Unoriented Subspaces to Blade Operators59
5Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra69
6Rotations in n Dimensions as Spherical Vectors79
7Geometric and Algebraic Canonical Forms91
8Functions of Clifford Numbers of Square Matrices99
9Compound Matrices and Pfaffians: A Representation of Geometric Algebra109
10Analysis Using Abstract Vector Variables119
11A Multivector Data Structure for Differential Forms and Equations129
12Jet Bundles and the Formal Theory of Partial Differential Equations133
13Imaginary Eigenvalues and Complex Eigenvectors Explained by Real Geometry145
14Symbolic Processing of Clifford Numbers in C++157
15Clifford Numbers and their Inverses Calculated using the Matrix Representation169
16A Toy Vector Field Based on Geometric Algebra179
17Quadratic Transformations in the Projective Plane187
18Annihilators of Principal Ideals in the Grassmann Algebra193
IIApplications to Physics195
19Homogeneous Rigid Body Mechanics with Elastic Coupling197
20Analysis of One and Two Particle Quantum Systems using Geometric Algebra213
21Interaction and Entanglement in the Multiparticle Spacetime Algebra227
22Laws of Reflection from Two or More Plane Mirrors in Succession249
23Exact Kinetic Energy Operators for Polyatomic Molecules261
24Geometry of Quantum Computing by Hamiltonian Dynamics of Spin Ensembles271
25Is the Brain a 'Clifford Algebra Quantum Computer'?285
26A Hestenes Spacetime Algebra Approach to Light Polarization297
27Quaternions, Clifford Algebra and Symmetry Groups307
IIIComputer Vision and Robotics317
28A Generic Framework for Image Geometry319
29Color Edge Detection Using Rotors333
30Numerical Evaluation of Versors with Clifford Algebra341
31The Role of Clifford Algebra in Structure-Preserving Transformations for Second-Order Systems351
32Applications of Algebra of Incidence in Visually Guided Robotics361
33Monocular Pose Estimation of Kinematic Chains373
34Stabilization of 3D Pose Estimation385
35Inferring Dynamical Information from 3D Position Data using Geometric Algebra395
36Clifford Algebra Space Singularities of Inline Planar Platforms407
IVSignal Processing and Other Applications423
37Fast Quantum Fourier-Heisenberg-Weyl Transforms425
38The Structure Multivector437
39The Application of Clifford Algebra to Calculations of Multicomponent Chemical Composition449
40An Algorithm to Solve the Inverse IFS-Problem459
41Fast Quantum n-D Fourier and Radon Transforms469

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