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Fundamentals of Computer Graphics F O U R T H E D I T I O N

Fundamentals of Computer Graphics F O U R T H E D I T I O N Steve Marschner Cornell University Peter Shirley Purity, LLC with Michael Ashikhmin Michael Gleicher Naty Hoffman Garrett Johnson Tamara Munzner Erik Reinhard William B. Thompson Peter Willemsen Brian Wyvill

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20151012 International Standard Book Number-13: 978-1-4822-2941-7 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Contents Preface 1 Introduction . . . . 1.1 Graphics Areas . . . . . . . 1.2 Major Applications . . . . . Graphics APIs 1.3 . . . . . . . 1.4 Graphics Pipeline . . . . . . Numerical Issues . . 1.5 Efﬁciency . . . 1.6 . . . . . . . Designing and Coding Graphics Programs . 1.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 2 3 4 4 5 7 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Miscellaneous Math Sets and Mappings . . . . . Solving Quadratic Equations . . . . . . . . . . . . . . . Trigonometry . . . . . . . . . Vectors . . . . . . . . . . . Curves and Surfaces . . . . Linear Interpolation . . . . . . . . . . . . . . . . Triangles . . . 2.1 2.2 2.3 2.4 2.5 2.6 2.7 . . . 3 Raster Images 3.1 3.2 3.3 3.4 . . . . . . . . Raster Devices . . . Images, Pixels, and Geometry . . . . . . . RGB Color . . . . . Alpha Compositing . . . . . . . . . . . . . 4 Ray Tracing 4.1 4.2 4.3 4.4 4.5 . . . The Basic Ray-Tracing Algorithm . . . . . Perspective . . . . . . Computing Viewing Rays . . . . . . . . . Ray-Object Intersection . . Shading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 . . . . 13 . . . . 17 . . . . 18 . . . . 21 . . . . 30 . . . . 44 . . . . 44 53 . . . . 54 . . . . 59 . . . . 64 . . . . 65 69 . . . . 70 . . . . 71 . . . . 73 . . . . 76 . . . . 81 v

vi 4.6 4.7 4.8 4.9 A Ray-Tracing Program . . Shadows . . . . Ideal Specular Reﬂection . . . . . . Historical Notes . . . . . . . . Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 . . . . 86 . . . . 87 . . . . 87 5 Linear Algebra Determinants . . . . . . . . 5.1 5.2 Matrices . . . 5.3 5.4 . . . . . . . . Computing with Matrices and Determinants . . . Eigenvalues and Matrix Diagonalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Transformation Matrices 2D Linear Transformations . . . . 3D Linear Transformations . . . . Translation and Afﬁne Transformations . Inverses of Transformation Matrices . . . Coordinate Transformations . . . . . . . 6.1 6.2 6.3 6.4 6.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Viewing 7.1 7.2 7.3 7.4 7.5 . . . . Viewing Transformations . . . . . . Projective Transformations . Perspective Projection . . . . . . . Some Properties of the Perspective Transform . . Field-of-View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 The Graphics Pipeline 8.1 8.2 8.3 8.4 . . . . . . . . Rasterization . . . . . . . . Operations Before and After Rasterization . . . . . . . . Simple Antialiasing . . . . . Culling Primitives for Efﬁciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Signal Processing 9.1 9.2 9.3 9.4 9.5 Digital Audio: Sampling in 1D . . . . . . . Convolution . . . . . Convolution Filters . . . . . Signal Processing for Images . . . . Sampling Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 . . . . 89 . . . . 91 . . . . 96 . . . . 101 109 . . . . 109 . . . . 123 . . . . 128 . . . . 132 . . . . 133 139 . . . . 140 . . . . 146 . . . . 149 . . . . 153 . . . . 154 159 . . . . 160 . . . . 171 . . . . 177 . . . . 179 183 . . . . 184 . . . . 187 . . . . 201 . . . . 208 . . . . 217

Contents 10 Surface Shading 10.1 Diffuse Shading . . 10.2 Phong Shading . . . 10.3 Artistic Shading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Texture Mapping . . . . 11.1 Looking Up Texture Values . . . 11.2 Texture Coordinate Functions 11.3 Antialiasing Texture Lookups . . . 11.4 Applications of Texture Mapping . . . . . 11.5 Procedural 3D Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Data Structures for Graphics . . . . . . . . . . . . . 12.1 Triangle Meshes . . . . 12.2 Scene Graphs . . . . . . . . . 12.3 Spatial Data Structures . . . 12.4 BSP Trees for Visibility . . . . . . 12.5 Tiling Multidimensional Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 More Ray Tracing 13.1 Transparency and Refraction . . . . 13.2 Instancing . . . . . . . 13.3 Constructive Solid Geometry . . . . 13.4 Distribution Ray Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Sampling . . . 14.1 Integration . . . . . . 14.2 Continuous Probability . . . 14.3 Monte Carlo Integration . . 14.4 Choosing Random Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Curves . . . . . . . . . . . 15.1 Curves . . . . 15.2 Curve Properties . . 15.3 Polynomial Pieces . . . . . 15.4 Putting Pieces Together . . . 15.5 Cubics . . . . 15.6 Approximating Curves . . . 15.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 233 . . . . 233 . . . . 236 . . . . 239 243 . . . . 244 . . . . 246 . . . . 260 . . . . 267 . . . . 273 281 . . . . 282 . . . . 295 . . . . 297 . . . . 309 . . . . 317 323 . . . . 324 . . . . 327 . . . . 328 . . . . 329 337 . . . . 337 . . . . 342 . . . . 346 . . . . 349 359 . . . . 359 . . . . 365 . . . . 368 . . . . 375 . . . . 378 . . . . 385 . . . . 402

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Fundamentals of Computer Graphics, Fourth Edition, 4th Edition.pdf

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