Applications of Geometric Algebra in Computer Science and Engineering / edited by Leo Dorst, Chris Doran, Joan Lasenby
| データ種別 | 電子ブック |
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| 出版情報 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser , 2002 |
| 本文言語 | 英語 |
| 大きさ | XXV, 478 p : online resource |
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| 内容注記 | 1 Point Groups and Space Groups in Geometric Algebra 2 The Inner Products of Geometric Algebra 3 Unification of Grassmann’s Progressive and Regressive Products using the Principle of Duality 4 From Unoriented Subspaces to Blade Operators 5 Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra 6 Rotations in n Dimensions as Spherical Vectors 7 Geometric and Algebraic Canonical Forms 8 Functions of Clifford Numbers or Square Matrices 9 Compound Matrices and PfafRans: A Representation of Geometric Algebra 10 Analysis Using Abstract Vector Variables 11 A Multivector Data Structure for Differential Forms and Equations 12 Jet Bundles and the Formal Theory of Partial Differential Equations 13 Imaginary Eigenvalues and Complex Eigenvectors Explained by Real Geometry 14 Symbolic Processing of Clifford Numbers in C++ 15 Clifford Numbers and their Inverses Calculated using the Matrix Representation 16 A Toy Vector Field Based on Geometric Algebra 17 Quadratic Transformations in the Projective Plane 18 Annihilators of Principal Ideals in the Grassmann Algebra 19 Homogeneous Rigid Body Mechanics with Elastic Coupling 20 Analysis of One and Two Particle Quantum Systems using Geometric Algebra 21 Interaction and Entanglement in the Multiparticle Spacetime Algebra 22 Laws of Reflection from Two or More Plane Mirrors in Succession 23 Exact Kinetic Energy Operators for Polyatomic Molecules 24 Geometry of Quantum Computing by Hamiltonian Dynamics of Spin Ensembles 25 Is the Brain a ‘Clifford Algebra Quantum Computer’? 26 A Hestenes Spacetime Algebra Approach to Light Polarization 27 Quaternions, Clifford Algebra and Symmetry Groups 28 A Generic Framework for Image Geometry 29 Color Edge Detection Using Rotors 30 Numerical Evaluation of Versors with Clifford Algebra 31 The Role of Clifford Algebra in Structure-Preserving Transformations for Second-Order Systems 32 Applications of Algebra of Incidence in Visually Guided Robotics 33 Monocular Pose Estimation of Kinematic Chains 34 Stabilization of 3D Pose Estimation 35 Inferring Dynamical Information from 3D Position Data using Geometric Algebra 36 Clifford Algebra Space Singularities of Inline Planar Platforms 37 Fast Quantum Fourier—Heisenberg—Weyl Transforms 38 The Structure Multivector 39 The Application of Clifford Algebra to Calculations of Multicomponent Chemical Composition 40 An Algorithm to Solve the Inverse IFS-Problem 41 Fast Quantum n-D Fourier and Radon Transforms |
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| 一般注記 | 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 |
| 著者標目 | Dorst, Leo editor Doran, Chris editor Lasenby, Joan editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Computer-aided engineering LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Physics FREE:Mathematics FREE:Applications of Mathematics FREE:Computer-Aided Engineering (CAD, CAE) and Design FREE:Mathematical Methods in Physics FREE:Appl.Mathematics/Computational Methods of Engineering |
| 分 類 | DC23:519 |
| 巻冊次 | ISBN:9781461200895 
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| ISBN | 9781461200895 |
| URL | http://dx.doi.org/10.1007/978-1-4612-0089-5 |
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