Projective Geometry and Its Applications to Computer Graphics PDF Download
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Author: Michael A. Penna
Publisher: Prentice Hall
ISBN:
Category : Computers
Languages : en
Pages : 426
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Book Description
Author: Michael A. Penna
Publisher: Prentice Hall
ISBN:
Category : Computers
Languages : en
Pages : 426
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Book Description
Author: Ivan Herman
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 166
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Book Description
Author: Jean Gallier
Publisher: Springer Science & Business Media
ISBN: 1461301378
Category : Mathematics
Languages : en
Pages : 584
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Book Description
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.
Author: Albrecht Beutelspacher
Publisher: Cambridge University Press
ISBN: 9780521483643
Category : Mathematics
Languages : en
Pages : 272
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Book Description
Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Author: Annalisa Crannell
Publisher: Princeton University Press
ISBN: 0691197385
Category : Mathematics
Languages : en
Pages : 291
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Book Description
Through a unique approach combining art and mathematics, Perspective and Projective Geometry introduces students to the ways that projective geometry applies to perspective art. Geometry, like mathematics as a whole, offers a useful and meaningful lens for understanding the visual world. Exploring pencil-and-paper drawings, photographs, Renaissance paintings, and GeoGebra constructions, this textbook equips students with the geometric tools for projecting a three-dimensional scene onto two dimensions. Organized as a series of exercise modules, this book teaches students through hands-on inquiry and participation. Each lesson begins with a visual puzzle that can be investigated through geometry, followed by exercises that reinforce new concepts and hone students’ analytical abilities. An electronic instructor’s manual available to teachers contains sample syllabi and advice, including suggestions for pacing and grading rubrics for art projects. Drawing vital interdisciplinary connections between art and mathematics, Perspective and Projective Geometry is ideally suited for undergraduate students interested in mathematics or computer graphics, as well as for mathematically inclined students of architecture or art. · Features computer-based GeoGebra modules and hands-on exercises · Contains ample visual examples, math and art puzzles, and proofs with real-world applications · Suitable for college students majoring in mathematics, computer science, and art · Electronic instructor’s manual (available only to teachers)
Author: Richard Hartley
Publisher: Cambridge University Press
ISBN: 1139449141
Category : Computers
Languages : en
Pages : 676
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Book Description
A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.
Author: Jorge Stolfi
Publisher: Academic Press
ISBN: 1483265196
Category : Mathematics
Languages : en
Pages : 246
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Book Description
Oriented Projective Geometry: A Framework for Geometric Computations proposes that oriented projective geometry is a better framework for geometric computations than classical projective geometry. The aim of the book is to stress the value of oriented projective geometry for practical computing and develop it as a rich, consistent, and effective tool for computer programmers. The monograph is comprised of 20 chapters. Chapter 1 gives a quick overview of classical and oriented projective geometry on the plane, and discusses their advantages and disadvantages as computational models. Chapters 2 through 7 define the canonical oriented projective spaces of arbitrary dimension, the operations of join and meet, and the concept of relative orientation. Chapter 8 defines projective maps, the space transformations that preserve incidence and orientation; these maps are used in chapter 9 to define abstract oriented projective spaces. Chapter 10 introduces the notion of projective duality. Chapters 11, 12, and 13 deal with projective functions, projective frames, relative coordinates, and cross-ratio. Chapter 14 tells about convexity in oriented projective spaces. Chapters 15, 16, and 17 show how the affine, Euclidean, and linear vector spaces can be emulated with the oriented projective space. Finally, chapters 18 through 20 discuss the computer representation and manipulation of lines, planes, and other subspaces. Computer scientists and programmers will find this text invaluable.
Author: Duncan Marsh
Publisher: Springer
ISBN: 1846281091
Category : Computers
Languages : en
Pages : 361
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Book Description
Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and useful links.
Author: Leo Dorst
Publisher: Elsevier
ISBN: 0080553109
Category : Juvenile Nonfiction
Languages : en
Pages : 664
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Book Description
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
Author: Samuel R. Buss
Publisher: Cambridge University Press
ISBN: 1139440381
Category : Computers
Languages : en
Pages : 397
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Book Description
This textbook, first published in 2003, emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, Bézier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site.
