Geometric Algebra For Computer Science

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Geometric Algebra for Computer Science

Leo Dorst,Daniel Fontijne,Stephen Mann
Geometric Algebra for Computer Science Book PDF

Author : Leo Dorst,Daniel Fontijne,Stephen Mann
Publisher : Elsevier
Page : 664 pages
File Size : 48,7 Mb
Release : 2010-07-26
Category : Juvenile Nonfiction
ISBN : 9780080553108

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Geometric Algebra for Computer Science by Leo Dorst,Daniel Fontijne,Stephen Mann Pdf

Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA

Applications of Geometric Algebra in Computer Science and Engineering

Leo Dorst,Chris Doran,Joan Lasenby
Applications of Geometric Algebra in Computer Science and Engineering Book PDF

Author : Leo Dorst,Chris Doran,Joan Lasenby
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200895

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Applications of Geometric Algebra in Computer Science and Engineering by Leo Dorst,Chris Doran,Joan Lasenby Pdf

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.

Geometric Algebra Computing

Eduardo Bayro-Corrochano,Gerik Scheuermann
Geometric Algebra Computing Book PDF

Author : Eduardo Bayro-Corrochano,Gerik Scheuermann
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 54,7 Mb
Release : 2010-05-19
Category : Computers
ISBN : 9781849961080

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Geometric Algebra Computing by Eduardo Bayro-Corrochano,Gerik Scheuermann Pdf

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 for Computer Graphics

John Vince
Geometric Algebra for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 45,7 Mb
Release : 2008-04-21
Category : Computers
ISBN : 9781846289965

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Geometric Algebra for Computer Graphics by John Vince Pdf

Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.

Geometric Algebra Applications Vol. I

Eduardo Bayro-Corrochano
Geometric Algebra Applications Vol I Book PDF

Author : Eduardo Bayro-Corrochano
Publisher : Springer
Page : 742 pages
File Size : 43,7 Mb
Release : 2018-06-20
Category : Technology & Engineering
ISBN : 9783319748306

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Geometric Algebra Applications Vol. I by Eduardo Bayro-Corrochano Pdf

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.

Geometric Algebra with Applications in Science and Engineering

Eduardo Bayro Corrochano,Garret Sobczyk
Geometric Algebra with Applications in Science and Engineering Book PDF

Author : Eduardo Bayro Corrochano,Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 632 pages
File Size : 47,7 Mb
Release : 2001-04-20
Category : Mathematics
ISBN : 0817641998

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Geometric Algebra with Applications in Science and Engineering by Eduardo Bayro Corrochano,Garret Sobczyk Pdf

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.

Foundations of Geometric Algebra Computing

Dietmar Hildenbrand
Foundations of Geometric Algebra Computing Book PDF

Author : Dietmar Hildenbrand
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 49,9 Mb
Release : 2012-12-31
Category : Computers
ISBN : 9783642317941

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Foundations of Geometric Algebra Computing by Dietmar Hildenbrand Pdf

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 Algebra: An Algebraic System for Computer Games and Animation

John A. Vince
Geometric Algebra An Algebraic System for Computer Games and Animation Book PDF

Author : John A. Vince
Publisher : Springer Science & Business Media
Page : 195 pages
File Size : 42,8 Mb
Release : 2009-05-20
Category : Computers
ISBN : 9781848823792

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Geometric Algebra: An Algebraic System for Computer Games and Animation by John A. Vince Pdf

Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design. Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs. The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.

Understanding Geometric Algebra

Kenichi Kanatani
Understanding Geometric Algebra Book PDF

Author : Kenichi Kanatani
Publisher : CRC Press
Page : 207 pages
File Size : 43,6 Mb
Release : 2015-04-06
Category : Computers
ISBN : 9781482259513

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Understanding Geometric Algebra by Kenichi Kanatani Pdf

Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics introduces geometric algebra with an emphasis on the background mathematics of Hamilton, Grassmann, and Clifford. It shows how to describe and compute geometry for 3D modeling applications in computer graphics and computer vision.Unlike similar texts

The Power of Geometric Algebra Computing

Dietmar Hildenbrand
The Power of Geometric Algebra Computing Book PDF

Author : Dietmar Hildenbrand
Publisher : CRC Press
Page : 202 pages
File Size : 43,6 Mb
Release : 2021-09-30
Category : Computers
ISBN : 9781000461169

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The Power of Geometric Algebra Computing by Dietmar Hildenbrand Pdf

Geometric Algebra is a very powerful mathematical system for an easy and intuitive treatment of geometry, but the community working with it is still very small. The main goal of this book is to close this gap from a computing perspective in presenting the power of Geometric Algebra Computing for engineering applications and quantum computing. The Power of Geometric Algebra Computing is based on GAALOPWeb, a new user-friendly, web-based tool for the generation of optimized code for different programming languages as well as for the visualization of Geometric Algebra algorithms for a wide range of engineering applications. Key Features: Introduces a new web-based optimizer for Geometric Algebra algorithms Supports many programming languages as well as hardware Covers the advantages of high-dimensional algebras Includes geometrically intuitive support of quantum computing This book includes applications from the fields of computer graphics, robotics and quantum computing and will help students, engineers and researchers interested in really computing with Geometric Algebra.

Geometric Computing with Clifford Algebras

Gerald Sommer
Geometric Computing with Clifford Algebras Book PDF

Author : Gerald Sommer
Publisher : Springer Science & Business Media
Page : 559 pages
File Size : 54,7 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9783662046210

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Geometric Computing with Clifford Algebras by Gerald Sommer Pdf

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 Methods and Applications

Jean Gallier
Geometric Methods and Applications Book PDF

Author : Jean Gallier
Publisher : Springer Science & Business Media
Page : 584 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301370

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Geometric Methods and Applications by Jean Gallier Pdf

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

Guide to Geometric Algebra in Practice

Leo Dorst,Joan Lasenby
Guide to Geometric Algebra in Practice Book PDF

Author : Leo Dorst,Joan Lasenby
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 51,5 Mb
Release : 2011-08-28
Category : Computers
ISBN : 0857298119

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Guide to Geometric Algebra in Practice by Leo Dorst,Joan Lasenby Pdf

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.

Geometric Algebra Applications Vol. II

Eduardo Bayro-Corrochano
Geometric Algebra Applications Vol II Book PDF

Author : Eduardo Bayro-Corrochano
Publisher : Springer Nature
Page : 609 pages
File Size : 42,5 Mb
Release : 2020-06-19
Category : Mathematics
ISBN : 9783030349783

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Geometric Algebra Applications Vol. II by Eduardo Bayro-Corrochano Pdf

This book presents a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford or geometric alge- bra. By addressing a wide spectrum of problems in a common language, it offers both fresh insights and new solutions that are useful to scientists and engineers working in areas related with robotics. It introduces non-specialists to Clifford and geometric algebra, and provides ex- amples to help readers learn how to compute using geometric entities and geomet- ric formulations. It also includes an in-depth study of applications of Lie group theory, Lie algebra, spinors and versors and the algebra of incidence using the universal geometric algebra generated by reciprocal null cones. Featuring a detailed study of kinematics, differential kinematics and dynamics using geometric algebra, the book also develops Euler Lagrange and Hamiltoni- ans equations for dynamics using conformal geometric algebra, and the recursive Newton-Euler using screw theory in the motor algebra framework. Further, it comprehensively explores robot modeling and nonlinear controllers, and discusses several applications in computer vision, graphics, neurocomputing, quantum com- puting, robotics and control engineering using the geometric algebra framework. The book also includes over 200 exercises and tips for the development of future computer software packages for extensive calculations in geometric algebra, and a entire section focusing on how to write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Lastly, it shows how program code can be optimized for real-time computations. An essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, the book clarifies and demon- strates the importance of geometric computing for building autonomous systems to advance cognitive systems research.

Geometric Algebra with Applications in Engineering

Christian Perwass
Geometric Algebra with Applications in Engineering Book PDF

Author : Christian Perwass
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 40,7 Mb
Release : 2009-02-11
Category : Computers
ISBN : 9783540890683

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Geometric Algebra with Applications in Engineering by Christian Perwass Pdf

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.