Applications of Geometric Algebra in Computer Science and Engineering

Front Matter....Pages i-xxv
Front Matter....Pages 1-1
Point Groups and Space Groups in Geometric Algebra....Pages 3-34
The Inner Products of Geometric Algebra....Pages 35-46
Unification of Grassmann’s Progressive and Regressive Products using the Principle of Duality....Pages 47-57
From Unoriented Subspaces to Blade Operators....Pages 59-67
Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra....Pages 69-78
Rotations in n Dimensions as Spherical Vectors....Pages 79-90
Geometric and Algebraic Canonical Forms....Pages 91-98
Functions of Clifford Numbers or Square Matrices....Pages 99-107
Compound Matrices and Pfaffians: A Representation of Geometric Algebra....Pages 109-118
Analysis Using Abstract Vector Variables....Pages 119-128
A Multivector Data Structure for Differential Forms and Equations....Pages 129-131
Jet Bundles and the Formal Theory of Partial Differential Equations....Pages 133-143
Imaginary Eigenvalues and Complex Eigenvectors Explained by Real Geometry....Pages 145-155
Symbolic Processing of Clifford Numbers in C++....Pages 157-167
Clifford Numbers and their Inverses Calculated using the Matrix Representation....Pages 169-178
A Toy Vector Field Based on Geometric Algebra....Pages 179-185
Quadratic Transformations in the Projective Plane....Pages 187-191
Annihilators of Principal Ideals in the Grassmann Algebra....Pages 193-194
Front Matter....Pages 195-195
Homogeneous Rigid Body Mechanics with Elastic Coupling....Pages 197-212
Analysis of One and Two Particle Quantum Systems using Geometric Algebra....Pages 213-226
Front Matter....Pages 195-195
Interaction and Entanglement in the Multiparticle Spacetime Algebra....Pages 227-247
Laws of Reflection from Two or More Plane Mirrors in Succession....Pages 249-259
Exact Kinetic Energy Operators for Polyatomic Molecules....Pages 261-270
Geometry of Quantum Computing by Hamiltonian Dynamics of Spin Ensembles....Pages 271-283
Is the Brain a ‘Clifford Algebra Quantum Computer’?....Pages 285-295
A Hestenes Spacetime Algebra Approach to Light Polarization....Pages 297-306
Quaternions, Clifford Algebra and Symmetry Groups....Pages 307-315
Front Matter....Pages 317-317
A Generic Framework for Image Geometry....Pages 319-332
Color Edge Detection Using Rotors....Pages 333-339
Numerical Evaluation of Versors with Clifford Algebra....Pages 341-350
The Role of Clifford Algebra in Structure-Preserving Transformations for Second-Order Systems....Pages 351-359
Applications of Algebra of Incidence in Visually Guided Robotics....Pages 361-372
Monocular Pose Estimation of Kinematic Chains....Pages 373-383
Stabilization of 3D Pose Estimation....Pages 385-394
Inferring Dynamical Information from 3D Position Data using Geometric Algebra....Pages 395-406
Clifford Algebra Space Singularities of Inline Planar Platforms....Pages 407-421
Front Matter....Pages 423-423
Fast Quantum Fourier-Heisenberg-Weyl Transforms....Pages 425-435
The Structure Multivector....Pages 437-448
The Application of Clifford Algebra to Calculations of Multicomponent Chemical Composition....Pages 449-458
An Algorithm to Solve the Inverse IFS-Problem....Pages 459-467
Front Matter....Pages 423-423
Fast Quantum n -D Fourier and Radon Transforms....Pages 469-478