Geometric Algebra For Computer Science
DOWNLOAD
Download Geometric Algebra For Computer Science PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Geometric Algebra For Computer Science book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Geometric Algebra For Computer Science
DOWNLOAD
Author : Leo Dorst
language : en
Publisher: Elsevier
Release Date : 2010-07-26
Geometric Algebra For Computer Science written by Leo Dorst and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-26 with Computers categories.
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
DOWNLOAD
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.
Geometric Algebra For Computer Graphics
DOWNLOAD
Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-21
Geometric Algebra For Computer Graphics written by John Vince 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 2008-04-21 with Computers categories.
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.
Na
DOWNLOAD
Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-20
Na 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 2010-11-20 with Computers categories.
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.
Applications Of Geometric Algebra In Computer Science And Engineering
DOWNLOAD
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 Applications Vol I
DOWNLOAD
Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer
Release Date : 2018-06-20
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 2018-06-20 with Technology & Engineering 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.
Foundations Of Geometric Algebra Computing
DOWNLOAD
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 Algebra Computing
DOWNLOAD
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 Engineering
DOWNLOAD
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 For Computer Graphics
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2008
Geometric Algebra For Computer Graphics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Clifford algebras categories.