Introduction To Geometric Computing

Introduction to Geometric Computing PDF
Author: Sherif Ghali
Publisher: Springer Science & Business Media
ISBN: 1848001150
Size: 61.89 MB
Format: PDF, Docs
Category : Computers
Languages : en
Pages : 340
View: 1506

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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.

Introduction To Geometric Algebra Computing

Introduction to Geometric Algebra Computing PDF
Author: Dietmar Hildenbrand
Publisher: CRC Press
ISBN: 1351648217
Size: 31.46 MB
Format: PDF, ePub, Mobi
Category : Computers
Languages : en
Pages : 194
View: 4544

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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 Science

Geometric Computing Science PDF
Author: Robert Hermann
Publisher: Math Science Press
ISBN: 9780915692415
Size: 20.31 MB
Format: PDF, Kindle
Category : Computers
Languages : en
Pages : 400
View: 660

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Computational Geometry

Computational Geometry PDF
Author: de Berg (M.T.)
Publisher: Springer Science & Business Media
ISBN: 9783540656203
Size: 12.83 MB
Format: PDF, Kindle
Category : Computers
Languages : en
Pages : 367
View: 3889

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For students this motivation will be especially welcome.

Perceptrons

Perceptrons PDF
Author: Marvin Minsky
Publisher: MIT Press
ISBN: 0262534770
Size: 71.45 MB
Format: PDF, Kindle
Category : Computers
Languages : en
Pages : 316
View: 3395

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Reissue of the 1988 Expanded Edition with a new foreword by Léon Bottou In 1969, ten years after the discovery of the perceptron -- which showed that a machine could be taught to perform certain tasks using examples -- Marvin Minsky and Seymour Papert published Perceptrons, their analysis of the computational capabilities of perceptrons for specific tasks. As Léon Bottou writes in his foreword to this edition, "Their rigorous work and brilliant technique does not make the perceptron look very good." Perhaps as a result, research turned away from the perceptron. Then the pendulum swung back, and machine learning became the fastest-growing field in computer science. Minsky and Papert's insistence on its theoretical foundations is newly relevant. Perceptrons -- the first systematic study of parallelism in computation -- marked a historic turn in artificial intelligence, returning to the idea that intelligence might emerge from the activity of networks of neuron-like entities. Minsky and Papert provided mathematical analysis that showed the limitations of a class of computing machines that could be considered as models of the brain. Minsky and Papert added a new chapter in 1987 in which they discuss the state of parallel computers, and note a central theoretical challenge: reaching a deeper understanding of how "objects" or "agents" with individuality can emerge in a network. Progress in this area would link connectionism with what the authors have called "society theories of mind."

Geometric Computing With Clifford Algebras

Geometric Computing with Clifford Algebras PDF
Author: Gerald Sommer
Publisher: Springer Science & Business Media
ISBN: 3662046210
Size: 28.81 MB
Format: PDF, Mobi
Category : Computers
Languages : en
Pages : 551
View: 1862

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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.

Introduction To Geometric Probability

Introduction to Geometric Probability PDF
Author: Daniel A. Klain
Publisher: Cambridge University Press
ISBN: 9780521596541
Size: 74.43 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 178
View: 1084

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The basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited.

Geometric Programming For Computer Aided Design

Geometric Programming for Computer Aided Design PDF
Author: Alberto Paoluzzi
Publisher: Wiley
ISBN: 9780471899426
Size: 52.23 MB
Format: PDF, ePub, Docs
Category : Computers
Languages : en
Pages : 800
View: 6293

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Geometric Programming is currently of interest in CAD (Computer Aided Design) and related areas such as computer graphics, modeling and animation, scientific simulation and robotics. A growing interest towards gemotric programming is forecast in the next few years with respect to market specific CAD applications (e.g. for architecture and mechanical CAD) and web-based collaborative design environments. PLaSM is a general purpose functional language to compute with geometry which the authors use throughout their text. The PLaSM language output produces VRML (Virtual Reality Modelling Language) files which are used to create virtual worlds. PLaSM blends the powerful algebraic approach to programming developed at IBM research, with a dimension-independent approach to geometric data structures and algorithms, This book shows that such geometric code can be surprisingly compact and easy to write. It begins by introducing the basic programming with PLaSM and algebraic and geometric foundations of shape modeling, the foundations of computer graphics, solid modeling and geometric modeling of manifolds follows and finally discusses the application of geometric programming. For each topic, the mathematics is given, together with the PLaSM implementation (usually with a few lines of readable code) and some worked examples. * Combines excellent coverage of the theory with well-developed examples * Numerous applications eg. scientific stimulation, robotics, CAD, Virtual Reality * Worked exercises for each topic * Uses PLaSM language (supplied) throughout to illustrate techniques * Supported with web presence Written for Industrial Practioners developing CAD software, mechanical engineers in Graphics, CAD and CAM, undergraduate and postgraduate courses in Computer Science and Mechanical Engineering,as well as programmers involved with developing visualization software.

Introduction To Visual Computing

Introduction to Visual Computing PDF
Author: Aditi Majumder
Publisher: CRC Press
ISBN: 1315355523
Size: 33.77 MB
Format: PDF, Mobi
Category : Computers
Languages : en
Pages : 376
View: 2935

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Introduction to Visual Computing: Core Concepts in Computer Vision, Graphics, and Image Processing covers the fundamental concepts of visual computing. Whereas past books have treated these concepts within the context of specific fields such as computer graphics, computer vision or image processing, this book offers a unified view of these core concepts, thereby providing a unified treatment of computational and mathematical methods for creating, capturing, analyzing and manipulating visual data (e.g. 2D images, 3D models). Fundamentals covered in the book include convolution, Fourier transform, filters, geometric transformations, epipolar geometry, 3D reconstruction, color and the image synthesis pipeline. The book is organized in four parts. The first part provides an exposure to different kinds of visual data (e.g. 2D images, videos and 3D geometry) and the core mathematical techniques that are required for their processing (e.g. interpolation and linear regression.) The second part of the book on Image Based Visual Computing deals with several fundamental techniques to process 2D images (e.g. convolution, spectral analysis and feature detection) and corresponds to the low level retinal image processing that happens in the eye in the human visual system pathway. The next part of the book on Geometric Visual Computing deals with the fundamental techniques used to combine the geometric information from multiple eyes creating a 3D interpretation of the object and world around us (e.g. transformations, projective and epipolar geometry, and 3D reconstruction). This corresponds to the higher level processing that happens in the brain combining information from both the eyes thereby helping us to navigate through the 3D world around us. The last two parts of the book cover Radiometric Visual Computing and Visual Content Synthesis. These parts focus on the fundamental techniques for processing information arising from the interaction of light with objects around us, as well as the fundamentals of creating virtual computer generated worlds that mimic all the processing presented in the prior sections. The book is written for a 16 week long semester course and can be used for both undergraduate and graduate teaching, as well as a reference for professionals.

Handbook Of Computational Geometry

Handbook of Computational Geometry PDF
Author: J.R. Sack
Publisher: Elsevier
ISBN: 9780080529684
Size: 66.15 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 1075
View: 3381

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Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

Ideals Varieties And Algorithms

Ideals  Varieties  and Algorithms PDF
Author: David A. Cox
Publisher: Springer
ISBN: 3319167219
Size: 40.63 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 646
View: 5528

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This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of MapleTM, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. From the reviews of previous editions: “...The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.” —Peter Schenzel, zbMATH, 2007 “I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.” —The American Mathematical Monthly

Geometric Algebra For Computer Science

Geometric Algebra for Computer Science PDF
Author: Leo Dorst
Publisher: Elsevier
ISBN: 0080553109
Size: 33.54 MB
Format: PDF, ePub
Category : Computers
Languages : en
Pages : 664
View: 2650

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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

Introduction To Computer Security

Introduction to Computer Security PDF
Author: Michael T. Goodrich
Publisher: Pearson Education
ISBN: 9780321702012
Size: 48.81 MB
Format: PDF, Kindle
Category : Computer security
Languages : en
Pages : 541
View: 2349

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This books is an introduction to general principles of computer security and its applications. Subjects a.o.: cyberattacks, worms, password crackers, keystroke loggers, DoS attacks, DNS cache poisoning, port scanning, spoofing and phishing. The reader is assumed to have knowledge of high-level programming languages such as C, C++, Python or Java. Help with exercises are available via http://securitybook.net.