The Use of Projective Geometry in Computer Graphics PDF Download
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Author: Ivan Herman
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 166
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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: Michael A. Penna
Publisher: Prentice Hall
ISBN:
Category : Computers
Languages : en
Pages : 426
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Book Description
Author: Annalisa Crannell
Publisher: Princeton University Press
ISBN: 0691197385
Category : Mathematics
Languages : en
Pages : 240
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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: Gerald Farin
Publisher: CRC Press
ISBN: 1439863903
Category : Computers
Languages : en
Pages : 282
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Book Description
Non-Uniform Rational B-Splines have become the de facto standard in CAD/CAM and computer graphics. This well-known book covers NURBS from their geometric beginnings to their industrial applications. The second edition incorporates new results and a chapter on Pythagorean curves, a development that shows promise in applications such as NC machining
Author: Bianca Falcidieno
Publisher: Springer Science & Business Media
ISBN: 3642775861
Category : Computers
Languages : en
Pages : 317
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Book Description
Since its very existence as a separate field within computer science, computer graphics had to make extensive use of non-trivial mathematics, for example, projective geometry, solid modelling, and approximation theory. This interplay of mathematics and computer science is exciting, but also makes it difficult for students and researchers to assimilate or maintain a view of the necessary mathematics. The possibilities offered by an interdisciplinary approach are still not fully utilized. This book gives a selection of contributions to a workshop held near Genoa, Italy, in October 1991, where a group of mathematicians and computer scientists gathered to explore ways of extending the cooperation between mathematics and computer graphics.
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: 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: 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: Sherif Ghali
Publisher: Springer Science & Business Media
ISBN: 1848001150
Category : Computers
Languages : en
Pages : 338
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Book Description
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.
Author: W.T. Hewitt
Publisher: Springer Science & Business Media
ISBN: 3642840604
Category : Computers
Languages : en
Pages : 265
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Book Description
This fourth volume of Advances in Computer Graphics gathers together a selection of the tutorials presented at the EUROGRAPHICS annual conference in Nice, France, Septem ber 1988. The six contributions cover various disciplines in Computer Graphics, giving either an in-depth view of a specific topic or an updated overview of a large area. Chapter 1, Object-oriented Computer Graphics, introduces the concepts of object ori ented programming and shows how they can be applied in different fields of Computer Graphics, such as modelling, animation and user interface design. Finally, it provides an extensive bibliography for those who want to know more about this fast growing subject. Chapter 2, Projective Geometry and Computer Graphics, is a detailed presentation of the mathematics of projective geometry, which serves as the mathematical background for all graphic packages, including GKS, GKS-3D and PRIGS. This useful paper gives in a single document information formerly scattered throughout the literature and can be used as a reference for those who have to implement graphics and CAD systems. Chapter 3, GKS-3D and PHIGS: Theory and Practice, describes both standards for 3D graphics, and shows how each of them is better adapted in different typical applications. It provides answers to those who have to choose a basic 3D graphics library for their developments, or to people who have to define their future policy for graphics.
