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Geometric Computing with Clifford Algebras

2001-05-22 Computers
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Release : 2001-05-22
Genre : Computers
Kind : eBook
Book Rating : 987/5 ( reviews)

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Book Synopsis Geometric Computing with Clifford Algebras by : Gerald Sommer

Download or read book Geometric Computing with Clifford Algebras written by Gerald Sommer. This book was released on 2001-05-22. Available in PDF, EPUB and Kindle. Book excerpt: Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. 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 outlines that Clifford algebra provides a universal and powerfull algebraic framework for an elegant and coherent representation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism.

Geometric Computing with Clifford Algebras

2012-12-22 Computers
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Release : 2012-12-22
Genre : Computers
Kind : eBook
Book Rating : 227/5 ( reviews)

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Book Synopsis Geometric Computing with Clifford Algebras by : Gerald Sommer

Download or read book Geometric Computing with Clifford Algebras written by Gerald Sommer. This book was released on 2012-12-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Algebra Computing

2010-05-19 Computers
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Release : 2010-05-19
Genre : Computers
Kind : eBook
Book Rating : 085/5 ( reviews)

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Book Synopsis Geometric Algebra Computing by : Eduardo Bayro-Corrochano

Download or read book Geometric Algebra Computing written by Eduardo Bayro-Corrochano. This book was released on 2010-05-19. Available in PDF, EPUB and Kindle. Book excerpt: 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 Computing

2010-04-01 Computers
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Release : 2010-04-01
Genre : Computers
Kind : eBook
Book Rating : 282/5 ( reviews)

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Book Synopsis Geometric Computing by : Eduardo Bayro Corrochano

Download or read book Geometric Computing written by Eduardo Bayro Corrochano. This book was released on 2010-04-01. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a gentle introduction to Clifford geometric algebra, an advanced mathematical framework, for applications in perception action systems. Part I, is written in an accessible way allowing readers to easily grasp the mathematical system of Clifford algebra. Part II presents related topics. While Part 3 features practical applications for Computer Vision, Robotics, Image Processing and Neural Computing. Topics and Features include: theory and application of the quaternion Fourier and wavelet transforms, thorough discussion on geometric computing under uncertainty, an entire chapter devoted to the useful conformal geometric algebra, presents examples and hints for the use of public domain computer programs for geometric algebra. The modern framework for geometric computing highlighted will be of great use for communities working on image processing, computer vision, artificial intelligence, neural networks, neuroscience, robotics, control engineering, human and robot interfaces, haptics and humanoids.

Foundations of Geometric Algebra Computing

2012-12-31 Computers
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Release : 2012-12-31
Genre : Computers
Kind : eBook
Book Rating : 944/5 ( reviews)

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Book Synopsis Foundations of Geometric Algebra Computing by : Dietmar Hildenbrand

Download or read book Foundations of Geometric Algebra Computing written by Dietmar Hildenbrand. This book was released on 2012-12-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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