Introduction To Geometric Computing
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Introduction To Geometric Computing
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Author : Sherif Ghali
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-05
Introduction To Geometric Computing written by Sherif Ghali 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 2008-07-05 with Computers categories.
Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.
Geometric Computing
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Author : Eduardo Bayro Corrochano
language : en
Publisher: Springer
Release Date : 2010-04-01
Geometric Computing 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 2010-04-01 with Computers categories.
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.
Geometric Computing Science
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Author : Robert Hermann
language : en
Publisher:
Release Date : 1991
Geometric Computing Science written by Robert Hermann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Computational Geometry
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Author : Franco P. Preparata
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Geometry written by Franco P. Preparata 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.
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
Handbook Of Geometric Computing
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Author : Eduardo Bayro Corrochano
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-06
Handbook Of Geometric 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 2005-12-06 with Computers categories.
Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner. This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.
Introduction To Geometric Algebra Computing
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Author : Dietmar Hildenbrand
language : en
Publisher: CRC Press
Release Date : 2020-12-29
Introduction To Geometric Algebra Computing written by Dietmar Hildenbrand and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-29 with Computers categories.
From the Foreword: "Dietmar Hildenbrand's new book, Introduction to Geometric Algebra Computing, in my view, fills an important gap in Clifford's geometric algebra literature...I can only congratulate the author for the daring simplicity of his novel educational approach taken in this book, consequently combined with hands on computer based exploration. Without noticing, the active reader will thus educate himself in elementary geometric algebra algorithm development, geometrically intuitive, highly comprehensible, and fully optimized." --Eckhard Hitzer, International Christian University, Tokyo, Japan 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 with an introduction to Geometric Algebra from an engineering/computing perspective. This book is intended to give a rapid introduction to computing with Geometric Algebra and its power for geometric modeling. From the geometric objects point of view, it focuses on the most basic ones, namely points, lines and circles. This algebra is called Compass Ruler Algebra, since it is comparable to working with a compass and ruler. The book explores how to compute with these geometric objects, and their geometric operations and transformations, in a very intuitive way. The book follows a top-down approach, and while it focuses on 2D, it is also easily expandable to 3D computations. Algebra in engineering applications such as computer graphics, computer vision and robotics are also covered.
Geometric Computing For Perception Action Systems
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Author : Eduardo Bayro Corrochano
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
Geometric Computing For Perception Action Systems 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 2011-06-27 with Computers categories.
All the efforts to build an intelligent machine have not yet produced a satisfactory autonomous system despite the great progress that has been made in developing computer hardware over the last three decades. The complexity of the tasks that a cognitive system must perform is still not understood well enough. Let us call the endeavor of building intelligent systems as the construction of Perception Action Cycles (PAC). The key idea is to incorporate representation and learning in a flexible geometric system. Until now this issue has always been a matter of neurocomputing. The most frequently used algebraic system for neurocomputation is matrix algebra. However, calculations in geometric algebra often reveal a geometric structure which remains obscure in the equivalent matrix computations. The development of PAC in a unified comprehensive mathematical system is urgently needed to bring unity and coherance to the problems of artificial intelligence. Accordingly, we are motivated by the challenge of applying geometric algebra to the development of PAC systems. Geometric algebra provides the general mathematical framework for the development of the ideas of multi-linear algebra, multi-variable analysis, and the representation of LIE groups and LIE algebras. There is strong evidence that geobetric albegra can be used to carry out efficient computations at all levels in the cognitive system. Geometric algebra reduces the complexity of algebraic expressions and as a result, it improves algorithms both in speed and accuracy. Thus, our goal is to construct PAC systems solely in the geometric algebra language. The preliminary chapters of this book introduce the reader to geometric algebra and the necessary mathematical concepts that will be needed. The latter chapters deal with a variety of applications in the field of cognitive systems in
Na
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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.
Introduction To Computing With Geometry
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Author : Adrian Bowyer
language : en
Publisher:
Release Date : 1993-01-01
Introduction To Computing With Geometry written by Adrian Bowyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Computer graphics categories.
An Introduction To Computational Geometry For Curves And Surfaces
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Author : Alan J. Davies
language : en
Publisher: Oxford University Press, USA
Release Date : 1996
An Introduction To Computational Geometry For Curves And Surfaces written by Alan J. Davies and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This is an introductory textbook for undergraduates studying mathematics, engineering, or computer science, and explains how differential and computational geometry are used to explain the mathematics of curves and surfaces. It assumes only a basic knowledge of vector and matrix algebra, andis filled with numerous exercises, solutions, and worked examples. Ideal for those interested in computer graphics or computer-aided design, this book will be invaluable for those needing to understand the complex mathematics which lies behind these important areas of application.