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Introduction to the Mathematics of Computer Graphics

Author : Nathan Carter

Publisher : American Mathematical Soc.

Page : 483 pages

File Size : 45,51 MB

Release : 2016-12-31

Category : Mathematics

ISBN : 1614441227

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Book Description

This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.



3D Computer Graphics

Author : Samuel R. Buss

Publisher : Cambridge University Press

Page : 397 pages

File Size : 33,7 MB

Release : 2003-05-19

Category : Computers

ISBN : 1139440381

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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.



Mathematics for Computer Graphics

Author : John Vince

Publisher : Springer Science & Business Media

Page : 268 pages

File Size : 11,88 MB

Release : 2005-11-09

Category : Computers

ISBN : 9781846280344

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Book Description

This is a concise and informal introductory book on the mathematical concepts that underpin computer graphics. The author, John Vince, makes the concepts easy to understand, enabling non-experts to come to terms with computer animation work. The book complements the author's other works and is written in the same accessible and easy-to-read style. It is also a useful reference book for programmers working in the field of computer graphics, virtual reality, computer animation, as well as students on digital media courses, and even mathematics courses.





3D Math Primer for Graphics and Game Development, 2nd Edition

Author : Fletcher Dunn

Publisher : CRC Press

Page : 848 pages

File Size : 44,10 MB

Release : 2011-11-02

Category : Computers

ISBN : 1568817231

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Book Description

This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.



Mathematical Elements for Computer Graphics

Author : David F. Rogers

Publisher : McGraw-Hill Science, Engineering & Mathematics

Page : 648 pages

File Size : 10,2 MB

Release : 1990

Category : Computers

ISBN :

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Book Description

This text is ideal for junior-, senior-, and graduate-level courses in computer graphics and computer-aided design taught in departments of mechanical and aeronautical engineering and computer science. It presents in a unified manner an introduction to the mathematical theory underlying computer graphic applications. It covers topics of keen interest to students in engineering and computer science: transformations, projections, 2-D and 3-D curve definition schemes, and surface definitions. It also includes techniques, such as B-splines, which are incorporated as part of the software in advanced engineering workstations. A basic knowledge of vector and matrix algebra and calculus is required.



Linear Geometry with Computer Graphics

Author : John Loustau

Publisher : CRC Press

Page : 466 pages

File Size : 44,44 MB

Release : 1992-12-16

Category : Mathematics

ISBN : 9780824788988

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Book Description

Stressing the interplay between theory and its practice, this text presents the construction of linear models that satisfy geometric postulate systems and develops geometric topics in computer graphics. It includes a computer graphics utility library of specialized subroutines on a 3.5 disk, designed for use with Turbo PASCAL 4.0 (or later version) - an effective means of computer-aided instruction for writing graphics problems.;Providing instructors with maximum flexibility that allows for the mathematics or computer graphics sections to be taught independently, this book: reviews linear algebra and notation, focusing on ideas of geometric significance that are often omitted in general purpose linear algebra courses; develops symmetric bilinear forms through classical results, including the inertia theorem, Witt's cancellation theorem and the unitary diagonalization of symmetric matrices; examines the Klein Erlanger programm, constructing models of geometries, and studying associated transformation groups; clarifies how to construct geometries from groups, encompassing topological notions; and introduces topics in computer graphics, including geometric modeling, surface rendering and transformation groups.



Applied Geometry for Computer Graphics and CAD

Author : Duncan Marsh

Publisher : Springer

Page : 361 pages

File Size : 25,6 MB

Release : 2006-03-30

Category : Computers

ISBN : 1846281091

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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.



Computer Graphics through Key Mathematics

Author : Huw Jones

Publisher : Springer Science & Business Media

Page : 358 pages

File Size : 50,26 MB

Release : 2012-12-06

Category : Computers

ISBN : 1447102975

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Book Description

This book introduces the mathematical concepts that underpin computer graphics. It is written in an approachable way, without burdening readers with the skills of ow to do'things. The author discusses those aspects of mathematics that relate to the computer synthesis of images, and so gives users a better understanding of the limitations of computer graphics systems. Users of computer graphics who have no formal training and wish to understand the essential foundations of computer graphics systems will find this book very useful, as will mathematicians who want to understand how their subject is used in computer image synthesis. '



Mathematics for Computer Graphics Applications

Author : Michael E. Mortenson

Publisher : Industrial Press Inc.

Page : 372 pages

File Size : 31,79 MB

Release : 1999

Category : Computers

ISBN : 9780831131111

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Book Description

"Mathematics for Computer Graphics Applications is written for several audiences: for college students majoring in computer science, engineering, or applied mathematics and science, whose special interests are in computer graphics, CAD/CAM, geometric modeling, visualization, or related subjects; for industry and government on-the-job training of employees whose skills can be profitably expanded into these areas; and for the professional working in these fields in need of a comprehensive reference and skills refresher."--BOOK JACKET.