Geometric Algebra Computing in Engineering and Computer Science : [pioneer groups started the conference series entitled"Applications of Geometric Algebra in Computer Science and Engineeringʺ (AGACSE). The third conference, AGACSE'2008, took place in Augu

Geometric algebra provides a rich and general mathematical framework for the development of solutions, concepts and computer algorithms without losing geometric insight into the problem in question. Many current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra, such as multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras, and conformal geometry. __Geometric Algebra Computing in Engineering and Computer Science__ presents contributions from an international selection of experts in the field. This useful text/reference offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. The book also provides an introduction to advanced screw theory and conformal geometry. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. **Topics and features:** * Provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework * Introduces nonspecialists to screw theory in the geometric algebra framework, offering a tutorial on conformal geometric algebra and an overview of recent applications of geometric algebra * Explores new developments in the domain of Clifford Fourier Transforms and Clifford Wavelet Transform, including novel applications of Clifford Fourier transforms for 3D visualization and colour image spectral analysis * Presents a detailed study of fluid flow problems with quaternionic analysis * Examines new algorithms for geometric neural computing and cognitive systems * Analyzes computer software packages for extensive calculations in geometric algebra, investigating the algorithmic complexity of key geometric operations and how the program code can be optimized for real-time computations The book is an essential resource for computer scientists, applied physicists, AI researchers and mechanical and electrical engineers. It will also be of value to graduate students and researchers interested in a modern language for geometric computing. **Prof. Dr. Eng. Eduardo Bayro-Corrochano** is a Full Professor of Geometric Computing at Cinvestav, Mexico. He is the author of the Springer titles __Geometric Computing for Perception Action Systems__, __Handbook of Geometric Computing__, and __Geometric Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action__. **Prof. Dr. Gerik Scheuermann** is a Full Professor at the University of Leipzig, Germany. He is the author of the Springer title __Topology-Based Methods in Visualization II__. Geometric algebra provides a rich and general mathematical framework for the development of solutions, concepts and computer algorithms without losing geometric insight into the problem in question. Many current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra, such as multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras, and conformal geometry. Geometric Algebra Computing in Engineering and Computer Science presents contributions from an international selection of experts in the field. This useful text/reference offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. The book also provides an introduction to advanced screw theory and conformal geometry. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Topics and features: Provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework Introduces nonspecialists to screw theory in the geometric algebra framework, offering a tutorial on conformal geometric algebra and an overview of recent applications of geometric algebra Explores new developments in the domain of Clifford Fourier Transforms and Clifford Wavelet Transform, including novel applications of Clifford Fourier transforms for 3D visualization and colour image spectral analysis Presents a detailed study of fluid flow problems with quaternionic analysis Examines new algorithms for geometric neural computing and cognitive systems Analyzes computer software packages for extensive calculations in geometric algebra, investigating the algorithmic complexity of key geometric operations and how the program code can be optimized for real-time computations The book is an essential resource for computer scientists, applied physicists, AI researchers and mechanical and electrical engineers. It will also be of value to graduate students and researchers interested in a modern language for geometric computing. Prof. Dr. Eng. Eduardo Bayro-Corrochano is a Full Professor of Geometric Computing at Cinvestav, Mexico. He is the author of the Springer titles Geometric Computing for Perception Action Systems , Handbook of Geometric Computing , and Geometric Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action . Prof. Dr. Gerik Scheuermann is a Full Professor at the University of Leipzig, Germany. He is the author of the Springer title Topology-Based Methods in Visualization II . Front Matter....Pages I-XXII Front Matter....Pages 1-1 New Tools for Computational Geometry and Rejuvenation of Screw Theory....Pages 3-33 Tutorial: Structure-Preserving Representation of Euclidean Motions Through Conformal Geometric Algebra....Pages 35-52 Engineering Graphics in Geometric Algebra....Pages 53-69 Parameterization of 3D Conformal Transformations in Conformal Geometric Algebra....Pages 71-90 Front Matter....Pages 91-91 Two-Dimensional Clifford Windowed Fourier Transform....Pages 93-106 The Cylindrical Fourier Transform....Pages 107-119 Analyzing Real Vector Fields with Clifford Convolution and Clifford–Fourier Transform....Pages 121-133 Clifford–Fourier Transform for Color Image Processing....Pages 135-162 Hilbert Transforms in Clifford Analysis....Pages 163-187 Front Matter....Pages 189-189 Geometric Neural Computing for 2D Contour and 3D Surface Reconstruction....Pages 191-209 Geometric Associative Memories and Their Applications to Pattern Classification....Pages 211-230 Classification and Clustering of Spatial Patterns with Geometric Algebra....Pages 231-247 QWT: Retrospective and New Applications....Pages 249-273 Front Matter....Pages 275-275 Image Sensor Model Using Geometric Algebra: From Calibration to Motion Estimation....Pages 277-297 Model-Based Visual Self-localization Using Gaussian Spheres....Pages 299-324 Front Matter....Pages 325-325 Geometric Characterization of -Conformal Mappings....Pages 327-343 Fluid Flow Problems with Quaternionic Analysis—An Alternative Conception....Pages 345-381 Front Matter....Pages 383-383 Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra....Pages 385-400 Geometric Algebra Model of Distributed Representations....Pages 401-430 Computational Complexity Reductions Using Clifford Algebras....Pages 431-453 Front Matter....Pages 455-455 Efficient Algorithms for Factorization and Join of Blades....Pages 457-476 Gaalop—High Performance Parallel Computing Based on Conformal Geometric Algebra....Pages 477-494 Some Applications of Gröbner Bases in Robotics and Engineering....Pages 495-517 Back Matter....Pages 519-526 This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; introduces nonspecialists to screw theory in the geometric algebra framework; explores new developments in the domain of Clifford Fourier Transforms and Clifford Wavelet Transform; presents a detailed study of fluid flow problems with quaternionic analysis; examines new algorithms for geometric neural computing and cognitive systems; analyzes computer software packages for extensive calculations in geometric algebra Pt.1. Geometric Algebra Pt.2. Clifford Fourier Transform Pt.3. Image Processing, Wavelets and Neurocomputing Pt.4. Computer Vision Pt.5. Conformal Mapping and Fluid Analysis Pt.6. Crystallography, Holography and Complexity Pt.7. Efficient Computing with Clifford (Geometric) Algebra.