3D - Computer Graphics P1

A Mathematical Introduction with OpenGLThis book is an introduction to 3-D computer graphics with particular emphasis on fundamentals and the mathematics underlying computer graphics. It includes descriptions of how to use the cross-platform OpenGL programming environment. It also includes source code for a ray tracing software package. (Accompanying software is available freely from the book’s Web site.) Topics include a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, B´ zier curves and B-splines, ray e tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and color theory....
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3D - Computer Graphics P1This page intentionally left blank Team LRN3-D Computer GraphicsA Mathematical Introduction with OpenGLThis book is an introduction to 3-D computer graphics with particular emphasison fundamentals and the mathematics underlying computer graphics. It includesdescriptions of how to use the cross-platform OpenGL programming environment.It also includes source code for a ray tracing software package. (Accompanyingsoftware is available freely from the book’s Web site.) Topics include a thorough treatment of transformations and viewing, lightingand shading models, interpolation and averaging, B´ zier curves and B-splines, ray etracing and radiosity, and intersection testing with rays. Additional topics, coveredin less depth, include texture mapping and color theory. The book also covers someaspects of animation, including quaternions, orientation, and inverse kinematics.Mathematical background on vectors and matrices is reviewed in an appendix. This book is aimed at the advanced undergraduate level or introductory graduatelevel and can also be used for self-study. Prerequisites include basic knowledge ofcalculus and vectors. The OpenGL programming portions require knowledge ofprogramming in C or C++. The more important features of OpenGL are coveredin the book, but it is intended to be used in conjunction with another OpenGLprogramming book.Samuel R. Buss is Professor of Mathematics and Computer Science at the Univer-sity of California, San Diego. With both academic and industrial expertise, Busshas more than 60 publications in the fields of computer science and mathematicallogic. He is the editor of several journals and the author of a book on boundedarithmetic. Buss has years of experience in programming and game developmentand has acted as consultant for SAIC and Angel Studios. Team LRNTeam LRN3-D Computer GraphicsA Mathematical Introduction with OpenGLSAMUEL R. BUSSUniversity of California, San Diego Team LRN  Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São PauloCambridge University PressThe Edinburgh Building, Cambridge  , United KingdomPublished in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orgInformation on this title: www.cambridge.org/9780521821032© Samuel R. Buss 2003This book is in copyright. Subject to statutory exception and to the provision ofrelevant collective licensing agreements, no reproduction of any part may take placewithout the written permission of Cambridge University Press.First published in print format 2003- ---- eBook (NetLibrary)- --- eBook (NetLibrary)- ---- hardback- --- hardbackCambridge University Press has no responsibility for the persistence or accuracy ofs for external or third-party internet websites referred to in this book, and does notguarantee that any content on such websites is, or will remain, accurate or appropriate. Team LRNTo my family Teresa, Stephanie, and Ian Team LRNContentsPreface page xiI Introduction 1 I.1 Display Models 1 I.2 Coordinates, Points, Lines, and Polygons 4 I.3 Double Buffering for Animation 15II Transformations and Viewing 17 II.1 Transformations in 2-Space 18 II.2 Transformations in 3-Space 34 II.3 Viewing Transformations and Perspective 46 II.4 Mapping to Pixels 58III Lighting, Illumination, and Shading 67 III.1 The Phong Lighting Model 68 III.2 The Cook–Torrance Lighting Model 87IV Averaging and Interpolation 99 IV.1 Linear Interpolation 99 IV.2 Bilinear and Trilinear Interpolation 107 IV.3 Convex Sets and Weighted Averages 117 IV.4 Interpolation and Homogeneous Coordinates 119 IV.5 Hyperbolic Interpolation 121 IV.6 Spherical Linear Interpolation 122V Texture Mapping 126 V.1 Texture Mapping an Image 126 V.2 Bump Mapping 135 V.3 Environment Mapping 137 V.4 Texture Mapping in OpenGL ...