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Part I: Geometric AlgebraNew Tools for Computational Geometry and Rejuvenation of Screw TheoryDavid HestenesTutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric AlgebraLeo DorstEngineering Graphics in Geometric AlgebraAlyn Rockwood and Dietmar HildenbrandParametrization of 3D Conformal Transformations in Conformal Geometric AlgebraHongbo LiPart II: Clifford Fourier TransformTwo-Dimensional Clifford Windowed Fourier TransformMawardi Bahri, Eckhard M. S. Hitzer and Sriwulan AdjiThe Cylindrical Fourier TransformFred Brackx, Nele De Schepper, and Frank SommenAnalyzing Real Vector Fields with Clifford Convolution and Clifford Fourier TransformWieland Reich and Gerik ScheuermannClifford Fourier Transform for Color Image ProcessingThomas Batard, Michel Berthier and Christophe Saint-JeanHilbert Transforms in Clifford AnalysisFred Brackx, Bram De Knock and Hennie De SchepperPart III: Image Processing, Wavelets and NeurocomputingGeometric Neural Computing for 2D Contour and 3D Surface ReconstructionJorge Rivera-Rovelo, Eduardo Bayro-Corrochano and Ruediger DillmannGeometric Associative Memories and their Applications to Pattern ClassificationBenjamin Cruz, Ricardo Barron, Humberto SossaClassification and Clustering of Spatial Patterns with Geometric AlgebraMinh Tuan Pham, Kanta Tachibana, Eckhard M. S. Hitzer, Tomohiro Yoshikawa, and Takeshi FuruhashiQWT: Retrospective and New ApplicationsYi Xu, Xiaokang Yang, Li Song, Leonardo Traversoni and Wei LuPart IV: Computer VisionImage Sensor Model using Geometric Algebra: from Calibration to Motion EstimationThibaud Debaecker, Ryad Benosman and Sio H. IengModel-Based Visual Self-Localization Using Gaussian SpheresD. Gonzalez-Aguirre, T. Asfour, E. Bayro-Corrochano and R. DillmannPart V: Conformal Mapping and Fluid AnalysisGeometric Characterization of M-conformal MappingsK. Gürlebeck and J. MoraisFluid Flow Problems with Quaternionic Analysis: An Alternative ConceptionK. Gürlebeck and W. SprössigPart VI: Cristalography, Holography and ComplexityInteractive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric AlgebraEckhard Hitzer, Christian Perwass and Daisuke IchikawaGeometric Algebra Model of Distributed RepresentationsAgnieszka PatykComputational Complexity Reductions using Clifford AlgebrasRené Schott and G. Stacey StaplesPart VII: Efficient Computing with Clifford (Geometric) AlgebraEfficient Algorithms for Factorization and Join of BladesDaniel Fontijne, Leo DorstGaalop - High Performance Parallel Computing based on Conformal Geometric AlgebraDietmar Hildenbrand, Joachim Pitt, Andreas KochSome Applications of Gröbner Bases in Robotics and EngineeringRafal Ablamowicz
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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.
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Geometric Algebra Computing : in Engineering and Computer Science
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 frameworkIntroduces nonspecialists to screw theory in the geometric algebra framework, offering a tutorial on conformal geometric algebra and an overview of recent applications of geometric algebraExplores 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 analysisPresents a detailed study of fluid flow problems with quaternionic analysisExamines new algorithms for geometric neuralcomputing and cognitive systemsAnalyzes 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 computationsThe 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 FullProfessor at the University of Leipzig, Germany. He is the author of the Springer title Topology-Based Methods in Visualization II. Artikel-Nr. 9781447157687
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