Geometric Algebra Computing
in Engineering and Computer Science
(Sprache: Englisch)
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. Its accessible style is enhanced by examples, figures and experimental analysis.
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Produktinformationen zu „Geometric Algebra Computing “
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. Its accessible style is enhanced by examples, figures and experimental analysis.
Klappentext zu „Geometric Algebra Computing “
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:
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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 FullProfessor at the University of Leipzig, Germany. He is the author of the Springer title Topology-Based Methods in Visualization II.
- 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 neuralcomputing 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 FullProfessor at the University of Leipzig, Germany. He is the author of the Springer title Topology-Based Methods in Visualization II.
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Inhaltsverzeichnis zu „Geometric Algebra Computing “
Part I: Geometric AlgebraNew Tools for Computational Geometry and Rejuvenation of Screw Theory
David Hestenes
Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra
Leo Dorst
Engineering Graphics in Geometric Algebra
Alyn Rockwood and Dietmar Hildenbrand
Parametrization of 3D Conformal Transformations in Conformal Geometric Algebra
Hongbo Li
Part II: Clifford Fourier Transform
Two-Dimensional Clifford Windowed Fourier Transform
Mawardi Bahri, Eckhard M. S. Hitzer and Sriwulan Adji
The Cylindrical Fourier Transform
Fred Brackx, Nele De Schepper, and Frank Sommen
Analyzing Real Vector Fields with Clifford Convolution and Clifford Fourier Transform
Wieland Reich and Gerik Scheuermann
Clifford Fourier Transform for Color Image Processing
Thomas Batard, Michel Berthier and Christophe Saint-Jean
Hilbert Transforms in Clifford Analysis
Fred Brackx, Bram De Knock and Hennie De Schepper
Part III: Image Processing, Wavelets and Neurocomputing
Geometric Neural Computing for 2D Contour and 3D Surface Reconstruction
Jorge Rivera-Rovelo, Eduardo Bayro-Corrochano and Ruediger Dillmann
Geometric Associative Memories and their Applications to Pattern Classification
Benjamin Cruz, Ricardo Barron, Humberto Sossa
Classification and Clustering of Spatial Patterns with Geometric Algebra
Minh Tuan Pham, Kanta Tachibana, Eckhard M. S. Hitzer, Tomohiro Yoshikawa, and Takeshi Furuhashi
QWT: Retrospective and New Applications
Yi Xu, Xiaokang Yang, Li Song, Leonardo Traversoni and Wei Lu
Part IV: Computer Vision
Image Sensor Model using Geometric Algebra: from Calibration to Motion Estimation
Thibaud Debaecker, Ryad Benosman and Sio H. Ieng
Model-Based Visual Self-Localization Using Gaussian Spheres
D. Gonzalez-Aguirre, T. Asfour, E. Bayro-Corrochano and R. Dillmann
Part V: Conformal Mapping and Fluid Analysis
Geometric Characterization of M-conformal Mappings
K. Gürlebeck and
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J. Morais
Fluid Flow Problems with Quaternionic Analysis: An Alternative Conception
K. Gürlebeck and W. Sprössig
Part VI: Cristalography, Holography and Complexity
Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra
Eckhard Hitzer, Christian Perwass and Daisuke Ichikawa
Geometric Algebra Model of Distributed Representations
Agnieszka Patyk
Computational Complexity Reductions using Clifford Algebras
René Schott and G. Stacey Staples
Part VII: Efficient Computing with Clifford (Geometric) Algebra
Efficient Algorithms for Factorization and Join of Blades
Daniel Fontijne, Leo Dorst
Gaalop - High Performance Parallel Computing based on Conformal Geometric Algebra
Dietmar Hildenbrand, Joachim Pitt, Andreas Koch
Some Applications of Gröbner Bases in Robotics and Engineering
Rafal Ablamowicz
Fluid Flow Problems with Quaternionic Analysis: An Alternative Conception
K. Gürlebeck and W. Sprössig
Part VI: Cristalography, Holography and Complexity
Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra
Eckhard Hitzer, Christian Perwass and Daisuke Ichikawa
Geometric Algebra Model of Distributed Representations
Agnieszka Patyk
Computational Complexity Reductions using Clifford Algebras
René Schott and G. Stacey Staples
Part VII: Efficient Computing with Clifford (Geometric) Algebra
Efficient Algorithms for Factorization and Join of Blades
Daniel Fontijne, Leo Dorst
Gaalop - High Performance Parallel Computing based on Conformal Geometric Algebra
Dietmar Hildenbrand, Joachim Pitt, Andreas Koch
Some Applications of Gröbner Bases in Robotics and Engineering
Rafal Ablamowicz
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Bibliographische Angaben
- 2014, 2010, XXII, 526 Seiten, Masse: 15,4 x 23,6 cm, Kartoniert (TB), Englisch
- Herausgegeben: Eduardo Bayro-Corrochano, Gerik Scheuermann
- Verlag: Springer, Berlin
- ISBN-10: 1447157680
- ISBN-13: 9781447157687
Sprache:
Englisch
Pressezitat
From the reviews:"This book is a result of the edited proceedings of the 2008 conference. It contains many advanced ideas from mathematics, physics, and computer science, and ... serve as a reference book on geometric algebra and its applications. ... includes numerous color illustrations, and the chapters end with references to the literature. ... This book should be treasured for presenting various geometric algebra applications in several areas ... . It will be useful to physicists, computer scientists, and engineers. ... this is a very useful book." (S. V. Nagaraj, ACM Computing Reviews, February, 2012)
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