Applications Of Geometric Algebra In Computer Science And Engineering
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Applications Of Geometric Algebra In Computer Science And Engineering
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Author : Leo Dorst
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Geometric Algebra In Computer Science And Engineering written by Leo Dorst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Applications Of Geometric Algebra In Computer Science And Engineering
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Author : Leo Dorst
language : en
Publisher: Birkhauser
Release Date : 2002
Applications Of Geometric Algebra In Computer Science And Engineering written by Leo Dorst and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computer science categories.
Geometric Algebra With Applications In Engineering
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Author : Christian Perwass
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Geometric Algebra With Applications In Engineering written by Christian Perwass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Computers categories.
The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation. Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.
Geometric Algebra Computing
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Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-19
Geometric Algebra Computing written by Eduardo Bayro-Corrochano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-19 with Computers categories.
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.
Geometric Algebra With Applications In Science And Engineering
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Author : Eduardo Bayro Corrochano
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Geometric Algebra With Applications In Science And Engineering written by Eduardo Bayro Corrochano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.
Geometric Algebra Applications Vol I
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Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer
Release Date : 2018-07-05
Geometric Algebra Applications Vol I written by Eduardo Bayro-Corrochano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Computers categories.
The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: 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. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.
Guide To Geometric Algebra In Practice
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Author : Leo Dorst
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-28
Guide To Geometric Algebra In Practice written by Leo Dorst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-28 with Computers categories.
This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
Foundations Of Geometric Algebra Computing
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Author : Dietmar Hildenbrand
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-31
Foundations Of Geometric Algebra Computing written by Dietmar Hildenbrand and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Computers categories.
The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.
Geometric Computing With Clifford Algebras
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Author : Gerald Sommer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Geometric Computing With Clifford Algebras written by Gerald Sommer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.
This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.
Computer Algebra And Geometric Algebra With Applications
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Author : Hongbo Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-21
Computer Algebra And Geometric Algebra With Applications written by Hongbo Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Computers categories.
This book constitutes the thoroughly refereed joint post-proceedings of the 6th International Workshop on Mathematics Mechanization, IWMM 2004, held in Shanghai, China in May 2004 and the International Workshop on Geometric Invariance and Applications in Engineering, GIAE 2004, held in Xian, China in May 2004. The 30 revised full papers presented were rigorously reviewed and selected from 65 presentations given at the two workshops. The papers are devoted to topics such as applications of computer algebra in celestial and engineering multibody systems, differential equations, computer vision, computer graphics, and the theory and applications of geometric algebra in geometric reasoning, robot vision, and computer graphics.