principles of digital image synthesis
TRANSCRIPT
Principles of Digital Image SynthesisPrinciples of Digital Image Synthesis
This book is provided in digital form with the permission of the rights holder as part of a
Google project to make the world's books discoverable online:
http://books.google.com
License
This book is licensed under a Creative Commons license. By using a Creative Commons
license, the rights holder chose to give you more freedom to share or re-use the book than
would otherwise be possible under copyright law.
This license allows distribution of this book and derivative works provided there is
attribution in each case, but prohibits commercial use. Terms available here:
http://creativecommons.org/licenses/by-nc/3.0/
Credits
The release of this book in its current form has been made possible by the collaborative effort
of a number of people:
Andrew Glassner (glassner.com)
authorized the free release of the e-book and provided the errata
Eric Haines (erichaines.com)
Iliyan Georgiev (iliyan.com)
assembled all digitized pages into one volume, ran OCR on the text, created a PDF
table of contents, folded in the errata
Notes on the Electronic Version
The PDF version of the book has been enhanced in a number of ways:
Table of Contents
A PDF bookmark content tree has been added for easy navigation. It can be revealed
by opening the Bookmarks pane in Adobe Reader. Additionally, hyperlinks to the
corresponding pages have been added to the chapter titles in the Contents section of
the book.
Errata
The errata have been applied to the text using the annotation feature of the PDF
format 1 , which is most useful for reading on a computer. Annotation indicators appear
as wavy red lines or red arrows. Clicking them or hovering them with the mouse
reveals the annotations. Annotations can be browsed in the Comments pane in Adobe
Reader. For printing, there is a separate errata listing at the end of the file, as only the
annotation indicators can be printed with Adobe Reader (which can be controlled in
the print dialog).
Attachments
The sources of the license page, this (credits & notes) page and the errata pages are
attached to the PDF file. Use the Attachments panel in Adobe Reader to extract them.
1 At the time of this writing (January 2011), Preview (the Mac OS built-in PDF viewer) does not automatically
display PDF annotations – please use Adobe Reader for that purpose.
............. ,, .... A. .. nky
Radiosity & Global Illumination Fran\ois X. Sillion and Claude Puech
Knotty: A B-Spline Visualization Program Jonathan Yen
User Interface Management Systems: Models and Algorithms Dan R. Olsen, Jr.
Making Them Move: Mechanics, Control, and Animation of Articulated Figures Edited by Norman I. Badler, Brian A. Barsky, and David Zeltzer
Geometric and Solid Modeling: An Introduction Christoph M. Hoffmann
An Introduction to Splines for Use in Computer Graphics and Geometric Modeling Richard H. Bartels, John C. Beatty, and Brian A. Barsky
VOLUMI ONI
SYNTHESIS
M 0 R G AN KAUFMANN P U ILl SHE R S, I N C. SAN FR A N C I S C 0, CALl F 0 R N I A
Sponsoring Editor Michael B. Morgan Production Manager Yonie Overton Assistant Editor Douglas Sery Assistant Production Editor Julie Pabst Composition Ed Sznyter, Babel Press Illustration Tech-Graphics Cover, Text, and Color Insert Design Carron Design Copyeditor Gary Morris Indexer Steve Rath Proofreaders Bill Cassell, Ken DellaPenta, and Mary Gillam Color Separation Color Tech Printer Quebecor Printing
Morgan Kaufmann Publishers, Inc. Editorial and Sales Office 340 Pine Street, Sixth Floor San Francisco, CA 94104-3205 USA Telephone 415/392-2665 Facsimile 415/982-2665 Internet [email protected]
@1995 by Morgan Kaufmann Publishers, Inc. All rights reserved Printed in the United States of America
08 07 06 05 04 5 4 3 2
No part of this publication may be reproduced, stored in a retrieval system, or transmit ted in any form or by any means-electronic, mechanical, photocopying, recording, or otherwise-without the prior written permission of the publisher.
Library of Congress Cataloging-in-Publication Data Glassner, Andrew S.
Principles of digital image synthesis I Andrew S. Glassner. p. em.
Includes bibliographical references and index. ISBN 1-55860-276-3 (v. 1: hardcover) 1. Computer graphics. 2. Image processing-Digital techniques.
I. Title. T385.G585 1995 006.6-<lc20 94-36565
Andrew Glassner
Update
All contents are copyright (c) 2010 by Andrew Glassner. This book is not in the public domain, but it has been made available by the author under the terms of the Creative Commons Attribution-NonCommercial 3.0 Unported License. Contact information for the author is available at www.glassner.com
To the inspiration of Leonardo da Vinci: artist, musician, writer, and bold explorer of the imagination
Those who fall in love with practice without science are like a sailor who enters a ship without a helm or a compass, and who never can be certain whither he is going.
Leonardo da Vmci
Digitized by le
Color Plates
THI HUMAN VISUAL IYITIM AND
1 The Human Visual System 1.1 Introduction 1.2 Structure and Optics of the Human Eye 1.3 Spectral and Temporal Aspects of the HVS 1.4 Visual Phenomena
1.4.1 Contrast Sensitivity 1.4.2 Noise 1.4.3 Mach Bands 1.4.4 Lightness Contrast and Constancy
1.5 Depth Perception 1.5.1 Oculomotor Depth 1.5.2 Binocular Depth 1.5.3 Monocular Depth 1.5.4 Motion Parallax
1.6 Color Opponency 1.7 Perceptual Color Matching: CIE XYZ Space
CONTENTS
XXI
XXIX
5 5 6
14 23 23 28 29 31 33 34 35 37 41 42 44
viii
2 Color Spaces
51 55 55
2.1 Perceptually Uniform Color Spaces: L"'u•v• and L •a•b• 59 59 66 68 68
2.2 Other Color Systems 2.3 Further Reading 2.4 Exercises
3 Displays 3.1 Introduction 3.2 CRT Displays 3.3 Display Spot Interaction
3.3.1 Display Spot Profile 3.3.2 Two-Spot Interaction 3.3.3 Display Measurement 3.3.4 Pattern Description 3.3.5 The Uniform Black Field (T = 0) 3.3.6 Clusters of Four (T = .25) 3.3.7 Clusters of Two (T = .5) 3.3.8 The Uniform White Field (T = 1) 3.3.9 Spot Interaction Discussion
3.4 Monitors 3.5 RGB Color Space
3.5.1 Converting XYZ to Spectra 3.6 Gamut Mapping 3. 7 Further Reading 3.8 Exercises
II SIGNAL PROCIIIING
4 Signals and Systems 4.1 Introduction 4.2 Types of Signals and Systems
4.2.1 Continuous-Time (Cf) Signals 4.2.2 Discrete-Time (DT) Signals 4.2.3 Periodic Signals 4.2.4 Linear Time-Invariant Systems
4.3 Notation 4.3.1 The Real Numbers 4.3.2 The Integers 4.3.3 Intervals 4.3.4 Product Spaces
71 71 71 76 76 78 79 82 85 85 89 94 97 97
100 104 106 111 112
1 1 s 127 127 127 128 129 130 132 135 135 136 136 137
CONTENTS ix
4.3.5 The Complex Numbers 138 4.3.6 Assignment and Equality 139 4.3.7 Summation and Integration 140 4.3.8 The Complex Exponentials 140 4.3.9 Braker Notation 143 4.3.10 Spaces 146
4.4 Some Useful Signals 148 4.4.1 The Impulse Signal 148 4.4.2 The Box Signal 153 4.4.3 The Impulse Train 154 4.4.4 The Sine Signal 155
4.5 Convolution 155 4.5.1 A Physical Example of Convolution 160 4.5.2 The Response of Composite Systems 161 4.5.3 Eigenfunctions and Frequency Response of LTI Systems 163 4.5.4 Discrete-Time Convolution 164
4.6 Two-Dimensional Signals and Systems 165 4.6.1 Linear Systems 165 4.6.2 Two-Dimensional Brakets 166 4.6.3 Convolution 167 4.6.4 Two-Dimensional Impulse Response 168 4.6.5 Eigenfunctions and Frequency Response 168
4.7 Further Reading 169 4.8 Exercises 170
5 Fourier Transforms 5.1 Introduction 5.2 Basis Functions
5.2.1 Projections of Points in Space 5.2.2 Projection of Functions 5.2.3 Orthogonal Families of Functions 5.2.4 The Dual Basis 5.2.5 The Complex Exponential Basis
5.3 Representation in Bases of Lower Dimension 5.4 Continuous-Time Fourier Representations 5.5 The Fourier Series
5.5.1 Convergence 5.6 The Continuous-Time Fourier Transform
5.6.1 Fourier Transform of Periodic Signals 5.6.2 Parseval's Theorem
5.7 Examples 5.7.1 The Box Signal
173 173 175 175 176 179 182 184 186 191 192 194 197 201 203 203 203
X CONTENTS
5.7.2 The Box Spectrum 206 5.7.3 The Gaussian 208 5.7.4 The Impulse Signal 210 5.7.5 The Impulse Train 211
5.8 Duality 213 5.9 Filtering and Convolution 214
5.9.1 Some Common Filters 219 5.10 The Fourier Transform Table 221 5.11 Discrete-Time Fourier Representations 222
5.11.1 The Discrete-Time Fourier Series 222 5.11.2 The Discrete-Time Fourier Transform 225
5.12 Fourier Series and Transforms Summary 229 5.13 Convolution Revisited 231 5.14 Two-Dimensional Fourier Transforms 234
5.14.1 Continuous-Time 2D Fourier Transforms 234 5.14.2 Discrete-Time 2D Fourier Transforms 238
5.15 Higher-Order Transforms 239 5.16 The Fast Fourier Transform 240 5.17 Further Reading 240 5.18 Exercises 240
6 Wavelet Transforms 243 6.1 Introduction 243 6.2 Short-Time Fourier Transform 246 6.3 Scale and Resolution 252 6.4 The Dilation Equation and the Haar Transform 252 6.5 Decomposition and Reconstruction 263
6.5.1 Building the Operators 267 6.6 Compression 274 6.7 Coefficient Conditions 277 6.8 Multiresolution Analysis 282 6.9 Wavelets in the Fourier Domain 285 6.10 Two-Dimensional Wavelets 291
6.10.1 The Rectangular Wavelet Decomposition 291 6.10.2 The Square Wavelet Decomposition 293
6.11 Further Reading 297 6.12 Exercises 297
7 Monte Carlo Integration 299 7.1 Introduction 299 7.2 Basic Monte Carlo Ideas 300 7.3 Confidence 305 7.4 Blind Monte Carlo 307
CONTENTS xi
7.4 .1 Crude Monte Carlo 7.4.2 Rejection Monte Carlo 7.4.3 Blind Stratified Sampling 7.4.4 Quasi Monte Carlo 7.4.5 Weighted Monte Carlo 7.4.6 Multidimensional Weighted Monte Carlo Informed Monte Carlo 7.5.1 Informed Stratified Sampling 7.5.2 Importance Sampling 7.5.3 Control Variates 7.5.4 Antithetic Variates Adaptive Sampling Other Approaches Summary Further Reading Exercises
307 308 309 310 312 315 319 319 320 325 326 327 327 327 329 329
8 Uniform Sampling and Reconstruction 331 8.1 Introduction 331
8.1.1 Sampling: Anti-Aliasing in a Pixel 332 8.1.2 Reconstruction: Evaluating Incident Light at a Point 334 8.1.3 Outline of this Chapter 336 8.1.4 Uniform Sampling and Reconstruction of a 10
Continuous Signal 336 8.1.5 What Signals Are Bandlimited? 340
8.2 Reconstruction 341 8.2.1 Zero-Order Hold Reconstruction 344
8.3 Sampling in Two Dimensions 347 8.4 Two-Dimensional Reconstruction 352 8.5 Reconstruction in Image Space 354
8.5.1 The Box Reconstruction Filter 354 8.5.2 Other Reconstruction Filters 358
8.6 Supersampling 359 8. 7 Further Reading 365 8.8 Exercises 366
9 Nonuniform Sampling and Reconstruction 369 9.1 Introduction 369
9.1.1 Variable Sampling Density 369 9.1.2 Trading Aliasing for Noise 371 9.1.3 Summary 375
9.2 Nonuniform Sampling 375 9.2.1 Adaptive Sampling 376
.x II
9.3 Informed Sampling 9.4 Stratified Sampling
9.4.1 Importance Sampling 9.4.2 Importance and Stratified Sampling
9.5 Interlude: The Duality of Aliasing and Noise 9.6 Nonuniform Reconstruction 9. 7 Further Reading 9.8 Exercises
10 Sampling and Reconstruction Techniques 1 0.1 Introduction 10.2 General Outline of Signal Estimation 10.3 Initial Sampling Patterns 10.4 Uniform and Nonuniform Sampling 10.5 Initial Sampling
10.5.1 Uniform Sampling 10.5.2 Rectangular Lattice 10.5.3 Hexagonal Lattice 10.5.4 Triangular Lattice 10.5.5 Diamond Lattice 10.5.6 Comparison of Subdivided Hexagonal
and Square Lattices 10.5.7 Nonuniform Sampling 10.5.8 Poisson Sampling 10.5.9 N-Rooks Sampling 10.5.10 Jitter Distribution 10.5.11 Poisson-Disk Pattern 10.5.12 Precomputed Poisson-Disk Patterns 10.5.13 Multiple-Scale Poisson-Disk Patterns 10.5.14 Sampling Tiles 10.5.15 Dynamic Poisson-Disk Patterns 10.5.16 Importance Sampling 10.5.17 Multidimensional Patterns 10.5.18 Discussion
10.6 Refinement 10.6.1 Sample Intensity
10.7 Refinement Tests 10.7.1 Intensity Comparison Refinement Test 10.7.2 Contrast Refinement Test 10.7.3 Object-Based Refinement Test
CONTENTS
381 386 388 388 392 395 398 404 404 404
407 407 409 409 411 415 415 417 417 420 420
420 424 424 424 426 427 427 430 437 440 443 448 455 463 464 465 465 467 468
CONTENTS
10.8 Refinement Sample Geometry 10.9 Refinement Geometry
10.9.1 Linear Bisection 10.9.2 Area Bisection 10.9.3 Nonuniform Geometry 10.9.4 Multiple-Level Sampling 10.9.5 Tree-Based Sampling 10.9.6 Multiple-Scale Template Refinement
10.10 Interpolation and Reconstruction 10.10.1 Functional Techniques 10.10.2 Warping 10.10.3 Iteration 10.10.4 Piecewise-Continuous Reconstruction 10.10.5 Local Filtering 10.10.6 Yen's Method 10.1 0. 7 Multistep Reconstruction
10.11 Further Reading 10.12 Exercises
Bibliography
Index
Color Plates
11 Light 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8
11.9
Introduction The Double-Slit Experiment The Wave Nature of Light Polarization The Photoelectric Effect Particle-Wave Duality Reflection and Transmission Index of Refraction 11.8.1 Sellmeier's Formula 11.8.2 Cauchy's Formula Computing Specular Vectors 11.9.1 The Reflected Vector
xili
472 473 480 481 481 485 490 490 492 497 497 499 499 503 507 517 522 531 537 538
B-1
1-1
541
545 545 545 549 554 560 563 563 567 569 570 572 573
xiv CONTENTS
11.10 Further Reading 578 11.11 Exercises 579
12 Energy Transport 581 12.1 Introduction 581 12.2 The Rod Model 582 12.3 Particle Density and Flux 583 12.4 Scattering 584
12.4.1 Counting New Particles 585 12.5 The Scattering-Only Particle Distribution Equations 587 12.6 A More Complete Medium 591
12.6.1 Explicit Flux 593 12.6.2 Implicit Flux 595
12.7 Particle Transport in 3D 596 12.7.1 Points 596 12.7.2 Projected Areas 597 12.7.3 Directions 598 12.7.4 Solid Angles 599 12.7.5 Integrating over Solid Angles 605 12.7.6 Direction Sets 606 12.7.7 Particles 613 12.7.8 Flux 614
12.8 Scattering in 3D 619 12.9 Components of 3D Transport 621
12.9.1 Streaming 622 12.9.2 Emission 623 12.9.3 Absorption 623 12.9.4 Outscattering 624 12.9.5 Inscattering 625 12.9.6 A Complete Transport Model 626 12.9.7 Isotropic Materials 629
12.10 Boundary Conditions 630 12.11 The Integral Form 635
12.11.1 An Example 636 12.11.2 The Integral Form of the Transport Equation 637
12.12 The Light Transport Equation 643 12.13 Further Reading 644 12.14 Exercises 644
13 Radiometry 647 13.1 Introduction 647
Digitized by Goog le
CONTENTS XV
13.2 Radiometric Conventions 648 13.3 Notation 648 13.4 Spherical Patches 649 13.5 Radiometric Terms 651 13.6 Radiometric Relations 653
13.6.1 Discussion of Radiance 656 13.6.2 Spectral Radiometry 659 13.6.3 Photometry 660
13.7 Reflectance 661 13.7.1 The BRDF (,. 663 13.7.2 Reflectance p 667 13.7.3 Reflectance Factor R 670
13.8 Examples 672 13.8.1 Perfect Diffuse 672 13.8.2 Perfect Specular 673
13.9 Spherical Harmonics 675 13.10 Further Reading 678 13.11 Exercises 678
14 Materials 681 14.1 Introduction 681 14.2 Atomic Structure 682 14.3 Particle Statistics 690
14.3.1 Fermi-Dirac Statistics 691 14.4 Molecular Structure 694
14.4.1 Ionic Bonds 695 14.4.2 Molecular-Orbital Bonds 696
14.5 Radiation 704 14.6 Blackbodies 705
14.6.1 Bose-Einstein Statistics 705 14.7 Blackbody Energy Distribution 708
14.7.1 Constant Index of Refraction 713 14.7.2 Linear Index of Refraction 714 14.7.3 Radiators 715
14.8 Phosphors 715 14.9 Further Reading 718 14.10 Exercises 718
15 Shading 721 15.1 Introduction 721 15.2 Lambert, Phong, and Blinn-Phong Shading Models 726
15.2.1 Diffuse Plus Specular 728 15.3 Cook-Torrance Shading Model 731
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15.3.1 Torrance-Sparrow Microfacets 732 15.3.2 Fresnel's Formulas 732 15.3.3 Roughness 737 15.3.4 The Cook-Torrance Model 738 15.3.5 Polarization 739
15.4 Anisotropy 740 15.4.1 The Kajiya Model 741 15.4.2 The Poulin-Fournier Model 742
15.5 The HTSG Model 744 15.6 Empirical Models 747
15.6.1 The Strauss Model 747 15.6.2 The Ward Model 750 15.6.3 The Programmable Model 752
15.7 Precomputed BRDF 753 15.7.1 Sampled Hemispheres 753 15.7.2 Spherical Harmonics 756
15.8 Volume Shading 757 15.8.1 Phase Functions 758 15.8.2 Atmospheric Modeling 764 15.8.3 The Earth's Ocean 769 15.8.4 The Kubelka-Munk Pigment Model 770 15.8.5 The Hanrahan-Krueger Multiple-Layer Model 778
15.9 Texture 780 15.10 Hierarchies of Scale 781 15.11 Color 786 15.12 Further Reading 789 15.13 Exercises 789
16 Integral Equations 791 16.1 Introduction 791 16.2 Types of Integral Equations 792 16.3 Operators 795
16.3.1 Operator Norms 798 16.4 Solution Techniques 798
16.4.1 Residual Minimization 800 16.5 Degenerate Kernels 801 16.6 Symbolic Methods 804
16.6.1 The Fubini Theorem 804 16.6.2 Successive Substitution 805 16.6.3 Neumann Series 806
16.7 Numerical Approximations 808 16.7.1 Numerical Integration (Quadrature) 809
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16.7.2 Method of Undetermined Coefficients 810 16.7.3 Quadrature on Expanded Functions 812 16.7.4 Nystrom Method 814 16.7.5 Monte Carlo Quadrature 817
16.8 Projection Methods 817 16.8.1 Projection 819 16.8.2 Pictures of the Function Space 819 16.8.3 Polynomial Collocation 825 16.8.4 T chebyshev Approximation 830 16.8.5 Least Squares 831 16.8.6 Galer kin 833 16.8.7 Wavelets 837 16.8.8 Discussion 839
16.9 Monte Carlo Estimation 840 16.9.1 Random Walks 842 16.9.2 Path Tracing 844 16.9.3 The Importance Function 848
16.10 Singularities 864 16.10.1 Removal 866 16.10.2 Factorization 867 16.10.3 Divide and Conquer 868 16.10.4 Coexistence 868
16.11 Further Reading 868 16.12 Exercises 869
17 The Radiance Equation 871 17.1 Introduction 871 17.2 Forming the Radiance Equation 872
17.2.1 BDF 872 17.2.2 Phosphorescence 873 17.2.3 Fluorescence 874 17.2.4 FRE 875
17.3 TIGRE 877 17.4 VTIGRE 878 17.5 Solving for L 880 17.6 Further Reading 882 17.7 Exercises 882
IV RINDIRING 883
18 Radiosity 887 18.1 Introduction 887 18.2 Classical Radiosity 888
Digitized by Goog le
18.3 Solving the Matrix Equation 18.3.1 Jacobi Iteration 18.3.2 Gauss-Seidel Iteration 18.3.3 Southwell Iteration 18.3.4 Overrelaxation
18.4 Solving Radiosity Matrices 18.4.1 Jacobi Iteration 18.4.2 Gauss-Seidel Iteration 18.4.3 Southwell Iteration 18.4.4 Progressive Refinement 18.4.5 Overrelaxation 18.4.6 Comparison
18.5 Form Factors 18.5.1 Analytic Methods 18.5.2 Contour Integration 18.5.3 Physical Devices 18.5.4 Projection 18.5.5 Discussion
18.6 Hierarchical Radiosity 18.6.1 One Step of HR 18.6.2 Adaptive HR 18.6.3 Importance HR 18.6.4 Discussion
18.7 Meshing 18.8 Shooting Power 18.9 Extensions to Classical Radiosity 18.10 Further Reading 18.11 Exercises
19 Ray Tracing 19.1 Introduction 19.2 Photon and Visibility Tracing 19.3 Visibility Tracing
19.3.1 Strata Sets 19.3.2 Applying Resolved Strata 19.3.3 Direct and Indirect Illumination 19.3.4 Discussion
19.4 Photon Tracing
CONTENTS
891 892 893 899 900 903 903 904 905 906 907 907 909 911 913 914 916 916 919 921 925 937 937 954 961 964 974 974 976 979 982 984
987 987 988 990 993 999
1002 1035 1037
19.5 Bidirectional Ray-Tracing Methods 1039 19.6 Hybrid Algorithms 1044 19.7 Ray-Tracing Volumes 1049 19.8 Further Reading 1050 19.9 Exercises 1050
20 Rendering and Images 1053 20.1 Introduction 1053 20.2 Postprocessing 1054
20.2.1 A Nonlinear Observer Model 1057 20.2.2 Image-Based Processing 1061 20.2.3 Linear Processing 1063
20.3 Feedback Rendering 1064 20.3.1 Illumination Painting 1066 20.3.2 Subjective Constraints 1067 20.3.3 Device-Directed Rendering 1069
20.4 Further Reading 1072 20.5 Exercise 1072
21 The Future 1073 21.1 Technical Progress 1073
21.1.1 Physical Optics 1074 21.1.2 Volume Rendering 1074 21.1.3 Information Theory 1075 21.1.4 Beyond Photo-Realism: Subjective Rendering 1076
21.2 Other Directions 1077 21.3 Summary 1080
v APPINDICII 1083
A Linear Algebra 1085 A.1 General Notation 1085 A.2 Linear Spaces 1085
A.2.1 Norms 1086 A.2.2 Inf and Sup 1087 A.2.3 Metrics 1087 A.2.4 Completeness 1088 A.2.5 Inner Products 1088
A.3 Function Spaces 1090 A.4 Further Reading 1091
B Probability 1093 B.1 Events and Probability 1093 B.2 Total Probability 1095
Digitized by Goog le
XX CONTENTS
B.3 Repeated Trials 1097 B.4 Random Variables 1098 B.5 Measures 1101 B.6 Distributions 1102 B.7 Geometric Series 1103 B.8 Further Reading 1103
c Historical Notes 1105 C.1 Specular Reflection and Transmission 1105
C.1.1 Specular Reflection 1109 C.1.2 Specular Transmission 1110
D Analytic Form Factors 1113 D.1 Differential and Finite Surfaces 1113
D.1.1 Differential to Differential 1113 D.1.2 Differential to Finite 1114 0.1.3 Finite to Finite 1122
0.2 Two Polygons 1132
E Constants and Units 1135
F Luminaire Standards 1139 F.1 Terminology 1139 F.2 Notation 1143 F.3 The IES Standard 1143
F.3.1 The Big Picture 1145 F.3.2 The Tilt Block 1145 F.3.3 The Photometry Block 1149
F.4 The CIE Standard 1152 F.4.1 The Main Block 1154 F.4.2 The Measurement Block 1155 F.4.3 The Photometry Block 1159
G Reference Data 1163 G.1 Material Data 1164 G.2 Human Data 1169 G.3 Light Sources 1172 G.4 Phosphors 1177 G.5 Macbeth ColorChecker 1179 G.6 Real Objects 1191
Bibliography B-1
Index 1-1
PREFACE
I nspiration begins with imagination and the spirit to create. Then comes the need to communicate, to share an idea or thought. Grab a pencil and you can make it
real: a picture, abstraction made concrete, ideas preserved in time. Our hearts and minds are moved to tell stories, to teach what we think and feel to others and learn the same from them.
Of all the visual media, computer graphics is one of the newest. The computer is a powerful amplifier-it can take terse descriptions of the world and create pictures of that world, using any rules you choose. If we choose the classical rules of light, then we can make pictures that can pass for photographs; other rules explore other ways of seeing.
The field of image synthesis, also called rendering,…
This book is provided in digital form with the permission of the rights holder as part of a
Google project to make the world's books discoverable online:
http://books.google.com
License
This book is licensed under a Creative Commons license. By using a Creative Commons
license, the rights holder chose to give you more freedom to share or re-use the book than
would otherwise be possible under copyright law.
This license allows distribution of this book and derivative works provided there is
attribution in each case, but prohibits commercial use. Terms available here:
http://creativecommons.org/licenses/by-nc/3.0/
Credits
The release of this book in its current form has been made possible by the collaborative effort
of a number of people:
Andrew Glassner (glassner.com)
authorized the free release of the e-book and provided the errata
Eric Haines (erichaines.com)
Iliyan Georgiev (iliyan.com)
assembled all digitized pages into one volume, ran OCR on the text, created a PDF
table of contents, folded in the errata
Notes on the Electronic Version
The PDF version of the book has been enhanced in a number of ways:
Table of Contents
A PDF bookmark content tree has been added for easy navigation. It can be revealed
by opening the Bookmarks pane in Adobe Reader. Additionally, hyperlinks to the
corresponding pages have been added to the chapter titles in the Contents section of
the book.
Errata
The errata have been applied to the text using the annotation feature of the PDF
format 1 , which is most useful for reading on a computer. Annotation indicators appear
as wavy red lines or red arrows. Clicking them or hovering them with the mouse
reveals the annotations. Annotations can be browsed in the Comments pane in Adobe
Reader. For printing, there is a separate errata listing at the end of the file, as only the
annotation indicators can be printed with Adobe Reader (which can be controlled in
the print dialog).
Attachments
The sources of the license page, this (credits & notes) page and the errata pages are
attached to the PDF file. Use the Attachments panel in Adobe Reader to extract them.
1 At the time of this writing (January 2011), Preview (the Mac OS built-in PDF viewer) does not automatically
display PDF annotations – please use Adobe Reader for that purpose.
............. ,, .... A. .. nky
Radiosity & Global Illumination Fran\ois X. Sillion and Claude Puech
Knotty: A B-Spline Visualization Program Jonathan Yen
User Interface Management Systems: Models and Algorithms Dan R. Olsen, Jr.
Making Them Move: Mechanics, Control, and Animation of Articulated Figures Edited by Norman I. Badler, Brian A. Barsky, and David Zeltzer
Geometric and Solid Modeling: An Introduction Christoph M. Hoffmann
An Introduction to Splines for Use in Computer Graphics and Geometric Modeling Richard H. Bartels, John C. Beatty, and Brian A. Barsky
VOLUMI ONI
SYNTHESIS
M 0 R G AN KAUFMANN P U ILl SHE R S, I N C. SAN FR A N C I S C 0, CALl F 0 R N I A
Sponsoring Editor Michael B. Morgan Production Manager Yonie Overton Assistant Editor Douglas Sery Assistant Production Editor Julie Pabst Composition Ed Sznyter, Babel Press Illustration Tech-Graphics Cover, Text, and Color Insert Design Carron Design Copyeditor Gary Morris Indexer Steve Rath Proofreaders Bill Cassell, Ken DellaPenta, and Mary Gillam Color Separation Color Tech Printer Quebecor Printing
Morgan Kaufmann Publishers, Inc. Editorial and Sales Office 340 Pine Street, Sixth Floor San Francisco, CA 94104-3205 USA Telephone 415/392-2665 Facsimile 415/982-2665 Internet [email protected]
@1995 by Morgan Kaufmann Publishers, Inc. All rights reserved Printed in the United States of America
08 07 06 05 04 5 4 3 2
No part of this publication may be reproduced, stored in a retrieval system, or transmit ted in any form or by any means-electronic, mechanical, photocopying, recording, or otherwise-without the prior written permission of the publisher.
Library of Congress Cataloging-in-Publication Data Glassner, Andrew S.
Principles of digital image synthesis I Andrew S. Glassner. p. em.
Includes bibliographical references and index. ISBN 1-55860-276-3 (v. 1: hardcover) 1. Computer graphics. 2. Image processing-Digital techniques.
I. Title. T385.G585 1995 006.6-<lc20 94-36565
Andrew Glassner
Update
All contents are copyright (c) 2010 by Andrew Glassner. This book is not in the public domain, but it has been made available by the author under the terms of the Creative Commons Attribution-NonCommercial 3.0 Unported License. Contact information for the author is available at www.glassner.com
To the inspiration of Leonardo da Vinci: artist, musician, writer, and bold explorer of the imagination
Those who fall in love with practice without science are like a sailor who enters a ship without a helm or a compass, and who never can be certain whither he is going.
Leonardo da Vmci
Digitized by le
Color Plates
THI HUMAN VISUAL IYITIM AND
1 The Human Visual System 1.1 Introduction 1.2 Structure and Optics of the Human Eye 1.3 Spectral and Temporal Aspects of the HVS 1.4 Visual Phenomena
1.4.1 Contrast Sensitivity 1.4.2 Noise 1.4.3 Mach Bands 1.4.4 Lightness Contrast and Constancy
1.5 Depth Perception 1.5.1 Oculomotor Depth 1.5.2 Binocular Depth 1.5.3 Monocular Depth 1.5.4 Motion Parallax
1.6 Color Opponency 1.7 Perceptual Color Matching: CIE XYZ Space
CONTENTS
XXI
XXIX
5 5 6
14 23 23 28 29 31 33 34 35 37 41 42 44
viii
2 Color Spaces
51 55 55
2.1 Perceptually Uniform Color Spaces: L"'u•v• and L •a•b• 59 59 66 68 68
2.2 Other Color Systems 2.3 Further Reading 2.4 Exercises
3 Displays 3.1 Introduction 3.2 CRT Displays 3.3 Display Spot Interaction
3.3.1 Display Spot Profile 3.3.2 Two-Spot Interaction 3.3.3 Display Measurement 3.3.4 Pattern Description 3.3.5 The Uniform Black Field (T = 0) 3.3.6 Clusters of Four (T = .25) 3.3.7 Clusters of Two (T = .5) 3.3.8 The Uniform White Field (T = 1) 3.3.9 Spot Interaction Discussion
3.4 Monitors 3.5 RGB Color Space
3.5.1 Converting XYZ to Spectra 3.6 Gamut Mapping 3. 7 Further Reading 3.8 Exercises
II SIGNAL PROCIIIING
4 Signals and Systems 4.1 Introduction 4.2 Types of Signals and Systems
4.2.1 Continuous-Time (Cf) Signals 4.2.2 Discrete-Time (DT) Signals 4.2.3 Periodic Signals 4.2.4 Linear Time-Invariant Systems
4.3 Notation 4.3.1 The Real Numbers 4.3.2 The Integers 4.3.3 Intervals 4.3.4 Product Spaces
71 71 71 76 76 78 79 82 85 85 89 94 97 97
100 104 106 111 112
1 1 s 127 127 127 128 129 130 132 135 135 136 136 137
CONTENTS ix
4.3.5 The Complex Numbers 138 4.3.6 Assignment and Equality 139 4.3.7 Summation and Integration 140 4.3.8 The Complex Exponentials 140 4.3.9 Braker Notation 143 4.3.10 Spaces 146
4.4 Some Useful Signals 148 4.4.1 The Impulse Signal 148 4.4.2 The Box Signal 153 4.4.3 The Impulse Train 154 4.4.4 The Sine Signal 155
4.5 Convolution 155 4.5.1 A Physical Example of Convolution 160 4.5.2 The Response of Composite Systems 161 4.5.3 Eigenfunctions and Frequency Response of LTI Systems 163 4.5.4 Discrete-Time Convolution 164
4.6 Two-Dimensional Signals and Systems 165 4.6.1 Linear Systems 165 4.6.2 Two-Dimensional Brakets 166 4.6.3 Convolution 167 4.6.4 Two-Dimensional Impulse Response 168 4.6.5 Eigenfunctions and Frequency Response 168
4.7 Further Reading 169 4.8 Exercises 170
5 Fourier Transforms 5.1 Introduction 5.2 Basis Functions
5.2.1 Projections of Points in Space 5.2.2 Projection of Functions 5.2.3 Orthogonal Families of Functions 5.2.4 The Dual Basis 5.2.5 The Complex Exponential Basis
5.3 Representation in Bases of Lower Dimension 5.4 Continuous-Time Fourier Representations 5.5 The Fourier Series
5.5.1 Convergence 5.6 The Continuous-Time Fourier Transform
5.6.1 Fourier Transform of Periodic Signals 5.6.2 Parseval's Theorem
5.7 Examples 5.7.1 The Box Signal
173 173 175 175 176 179 182 184 186 191 192 194 197 201 203 203 203
X CONTENTS
5.7.2 The Box Spectrum 206 5.7.3 The Gaussian 208 5.7.4 The Impulse Signal 210 5.7.5 The Impulse Train 211
5.8 Duality 213 5.9 Filtering and Convolution 214
5.9.1 Some Common Filters 219 5.10 The Fourier Transform Table 221 5.11 Discrete-Time Fourier Representations 222
5.11.1 The Discrete-Time Fourier Series 222 5.11.2 The Discrete-Time Fourier Transform 225
5.12 Fourier Series and Transforms Summary 229 5.13 Convolution Revisited 231 5.14 Two-Dimensional Fourier Transforms 234
5.14.1 Continuous-Time 2D Fourier Transforms 234 5.14.2 Discrete-Time 2D Fourier Transforms 238
5.15 Higher-Order Transforms 239 5.16 The Fast Fourier Transform 240 5.17 Further Reading 240 5.18 Exercises 240
6 Wavelet Transforms 243 6.1 Introduction 243 6.2 Short-Time Fourier Transform 246 6.3 Scale and Resolution 252 6.4 The Dilation Equation and the Haar Transform 252 6.5 Decomposition and Reconstruction 263
6.5.1 Building the Operators 267 6.6 Compression 274 6.7 Coefficient Conditions 277 6.8 Multiresolution Analysis 282 6.9 Wavelets in the Fourier Domain 285 6.10 Two-Dimensional Wavelets 291
6.10.1 The Rectangular Wavelet Decomposition 291 6.10.2 The Square Wavelet Decomposition 293
6.11 Further Reading 297 6.12 Exercises 297
7 Monte Carlo Integration 299 7.1 Introduction 299 7.2 Basic Monte Carlo Ideas 300 7.3 Confidence 305 7.4 Blind Monte Carlo 307
CONTENTS xi
7.4 .1 Crude Monte Carlo 7.4.2 Rejection Monte Carlo 7.4.3 Blind Stratified Sampling 7.4.4 Quasi Monte Carlo 7.4.5 Weighted Monte Carlo 7.4.6 Multidimensional Weighted Monte Carlo Informed Monte Carlo 7.5.1 Informed Stratified Sampling 7.5.2 Importance Sampling 7.5.3 Control Variates 7.5.4 Antithetic Variates Adaptive Sampling Other Approaches Summary Further Reading Exercises
307 308 309 310 312 315 319 319 320 325 326 327 327 327 329 329
8 Uniform Sampling and Reconstruction 331 8.1 Introduction 331
8.1.1 Sampling: Anti-Aliasing in a Pixel 332 8.1.2 Reconstruction: Evaluating Incident Light at a Point 334 8.1.3 Outline of this Chapter 336 8.1.4 Uniform Sampling and Reconstruction of a 10
Continuous Signal 336 8.1.5 What Signals Are Bandlimited? 340
8.2 Reconstruction 341 8.2.1 Zero-Order Hold Reconstruction 344
8.3 Sampling in Two Dimensions 347 8.4 Two-Dimensional Reconstruction 352 8.5 Reconstruction in Image Space 354
8.5.1 The Box Reconstruction Filter 354 8.5.2 Other Reconstruction Filters 358
8.6 Supersampling 359 8. 7 Further Reading 365 8.8 Exercises 366
9 Nonuniform Sampling and Reconstruction 369 9.1 Introduction 369
9.1.1 Variable Sampling Density 369 9.1.2 Trading Aliasing for Noise 371 9.1.3 Summary 375
9.2 Nonuniform Sampling 375 9.2.1 Adaptive Sampling 376
.x II
9.3 Informed Sampling 9.4 Stratified Sampling
9.4.1 Importance Sampling 9.4.2 Importance and Stratified Sampling
9.5 Interlude: The Duality of Aliasing and Noise 9.6 Nonuniform Reconstruction 9. 7 Further Reading 9.8 Exercises
10 Sampling and Reconstruction Techniques 1 0.1 Introduction 10.2 General Outline of Signal Estimation 10.3 Initial Sampling Patterns 10.4 Uniform and Nonuniform Sampling 10.5 Initial Sampling
10.5.1 Uniform Sampling 10.5.2 Rectangular Lattice 10.5.3 Hexagonal Lattice 10.5.4 Triangular Lattice 10.5.5 Diamond Lattice 10.5.6 Comparison of Subdivided Hexagonal
and Square Lattices 10.5.7 Nonuniform Sampling 10.5.8 Poisson Sampling 10.5.9 N-Rooks Sampling 10.5.10 Jitter Distribution 10.5.11 Poisson-Disk Pattern 10.5.12 Precomputed Poisson-Disk Patterns 10.5.13 Multiple-Scale Poisson-Disk Patterns 10.5.14 Sampling Tiles 10.5.15 Dynamic Poisson-Disk Patterns 10.5.16 Importance Sampling 10.5.17 Multidimensional Patterns 10.5.18 Discussion
10.6 Refinement 10.6.1 Sample Intensity
10.7 Refinement Tests 10.7.1 Intensity Comparison Refinement Test 10.7.2 Contrast Refinement Test 10.7.3 Object-Based Refinement Test
CONTENTS
381 386 388 388 392 395 398 404 404 404
407 407 409 409 411 415 415 417 417 420 420
420 424 424 424 426 427 427 430 437 440 443 448 455 463 464 465 465 467 468
CONTENTS
10.8 Refinement Sample Geometry 10.9 Refinement Geometry
10.9.1 Linear Bisection 10.9.2 Area Bisection 10.9.3 Nonuniform Geometry 10.9.4 Multiple-Level Sampling 10.9.5 Tree-Based Sampling 10.9.6 Multiple-Scale Template Refinement
10.10 Interpolation and Reconstruction 10.10.1 Functional Techniques 10.10.2 Warping 10.10.3 Iteration 10.10.4 Piecewise-Continuous Reconstruction 10.10.5 Local Filtering 10.10.6 Yen's Method 10.1 0. 7 Multistep Reconstruction
10.11 Further Reading 10.12 Exercises
Bibliography
Index
Color Plates
11 Light 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8
11.9
Introduction The Double-Slit Experiment The Wave Nature of Light Polarization The Photoelectric Effect Particle-Wave Duality Reflection and Transmission Index of Refraction 11.8.1 Sellmeier's Formula 11.8.2 Cauchy's Formula Computing Specular Vectors 11.9.1 The Reflected Vector
xili
472 473 480 481 481 485 490 490 492 497 497 499 499 503 507 517 522 531 537 538
B-1
1-1
541
545 545 545 549 554 560 563 563 567 569 570 572 573
xiv CONTENTS
11.10 Further Reading 578 11.11 Exercises 579
12 Energy Transport 581 12.1 Introduction 581 12.2 The Rod Model 582 12.3 Particle Density and Flux 583 12.4 Scattering 584
12.4.1 Counting New Particles 585 12.5 The Scattering-Only Particle Distribution Equations 587 12.6 A More Complete Medium 591
12.6.1 Explicit Flux 593 12.6.2 Implicit Flux 595
12.7 Particle Transport in 3D 596 12.7.1 Points 596 12.7.2 Projected Areas 597 12.7.3 Directions 598 12.7.4 Solid Angles 599 12.7.5 Integrating over Solid Angles 605 12.7.6 Direction Sets 606 12.7.7 Particles 613 12.7.8 Flux 614
12.8 Scattering in 3D 619 12.9 Components of 3D Transport 621
12.9.1 Streaming 622 12.9.2 Emission 623 12.9.3 Absorption 623 12.9.4 Outscattering 624 12.9.5 Inscattering 625 12.9.6 A Complete Transport Model 626 12.9.7 Isotropic Materials 629
12.10 Boundary Conditions 630 12.11 The Integral Form 635
12.11.1 An Example 636 12.11.2 The Integral Form of the Transport Equation 637
12.12 The Light Transport Equation 643 12.13 Further Reading 644 12.14 Exercises 644
13 Radiometry 647 13.1 Introduction 647
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CONTENTS XV
13.2 Radiometric Conventions 648 13.3 Notation 648 13.4 Spherical Patches 649 13.5 Radiometric Terms 651 13.6 Radiometric Relations 653
13.6.1 Discussion of Radiance 656 13.6.2 Spectral Radiometry 659 13.6.3 Photometry 660
13.7 Reflectance 661 13.7.1 The BRDF (,. 663 13.7.2 Reflectance p 667 13.7.3 Reflectance Factor R 670
13.8 Examples 672 13.8.1 Perfect Diffuse 672 13.8.2 Perfect Specular 673
13.9 Spherical Harmonics 675 13.10 Further Reading 678 13.11 Exercises 678
14 Materials 681 14.1 Introduction 681 14.2 Atomic Structure 682 14.3 Particle Statistics 690
14.3.1 Fermi-Dirac Statistics 691 14.4 Molecular Structure 694
14.4.1 Ionic Bonds 695 14.4.2 Molecular-Orbital Bonds 696
14.5 Radiation 704 14.6 Blackbodies 705
14.6.1 Bose-Einstein Statistics 705 14.7 Blackbody Energy Distribution 708
14.7.1 Constant Index of Refraction 713 14.7.2 Linear Index of Refraction 714 14.7.3 Radiators 715
14.8 Phosphors 715 14.9 Further Reading 718 14.10 Exercises 718
15 Shading 721 15.1 Introduction 721 15.2 Lambert, Phong, and Blinn-Phong Shading Models 726
15.2.1 Diffuse Plus Specular 728 15.3 Cook-Torrance Shading Model 731
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15.3.1 Torrance-Sparrow Microfacets 732 15.3.2 Fresnel's Formulas 732 15.3.3 Roughness 737 15.3.4 The Cook-Torrance Model 738 15.3.5 Polarization 739
15.4 Anisotropy 740 15.4.1 The Kajiya Model 741 15.4.2 The Poulin-Fournier Model 742
15.5 The HTSG Model 744 15.6 Empirical Models 747
15.6.1 The Strauss Model 747 15.6.2 The Ward Model 750 15.6.3 The Programmable Model 752
15.7 Precomputed BRDF 753 15.7.1 Sampled Hemispheres 753 15.7.2 Spherical Harmonics 756
15.8 Volume Shading 757 15.8.1 Phase Functions 758 15.8.2 Atmospheric Modeling 764 15.8.3 The Earth's Ocean 769 15.8.4 The Kubelka-Munk Pigment Model 770 15.8.5 The Hanrahan-Krueger Multiple-Layer Model 778
15.9 Texture 780 15.10 Hierarchies of Scale 781 15.11 Color 786 15.12 Further Reading 789 15.13 Exercises 789
16 Integral Equations 791 16.1 Introduction 791 16.2 Types of Integral Equations 792 16.3 Operators 795
16.3.1 Operator Norms 798 16.4 Solution Techniques 798
16.4.1 Residual Minimization 800 16.5 Degenerate Kernels 801 16.6 Symbolic Methods 804
16.6.1 The Fubini Theorem 804 16.6.2 Successive Substitution 805 16.6.3 Neumann Series 806
16.7 Numerical Approximations 808 16.7.1 Numerical Integration (Quadrature) 809
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16.7.2 Method of Undetermined Coefficients 810 16.7.3 Quadrature on Expanded Functions 812 16.7.4 Nystrom Method 814 16.7.5 Monte Carlo Quadrature 817
16.8 Projection Methods 817 16.8.1 Projection 819 16.8.2 Pictures of the Function Space 819 16.8.3 Polynomial Collocation 825 16.8.4 T chebyshev Approximation 830 16.8.5 Least Squares 831 16.8.6 Galer kin 833 16.8.7 Wavelets 837 16.8.8 Discussion 839
16.9 Monte Carlo Estimation 840 16.9.1 Random Walks 842 16.9.2 Path Tracing 844 16.9.3 The Importance Function 848
16.10 Singularities 864 16.10.1 Removal 866 16.10.2 Factorization 867 16.10.3 Divide and Conquer 868 16.10.4 Coexistence 868
16.11 Further Reading 868 16.12 Exercises 869
17 The Radiance Equation 871 17.1 Introduction 871 17.2 Forming the Radiance Equation 872
17.2.1 BDF 872 17.2.2 Phosphorescence 873 17.2.3 Fluorescence 874 17.2.4 FRE 875
17.3 TIGRE 877 17.4 VTIGRE 878 17.5 Solving for L 880 17.6 Further Reading 882 17.7 Exercises 882
IV RINDIRING 883
18 Radiosity 887 18.1 Introduction 887 18.2 Classical Radiosity 888
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18.3 Solving the Matrix Equation 18.3.1 Jacobi Iteration 18.3.2 Gauss-Seidel Iteration 18.3.3 Southwell Iteration 18.3.4 Overrelaxation
18.4 Solving Radiosity Matrices 18.4.1 Jacobi Iteration 18.4.2 Gauss-Seidel Iteration 18.4.3 Southwell Iteration 18.4.4 Progressive Refinement 18.4.5 Overrelaxation 18.4.6 Comparison
18.5 Form Factors 18.5.1 Analytic Methods 18.5.2 Contour Integration 18.5.3 Physical Devices 18.5.4 Projection 18.5.5 Discussion
18.6 Hierarchical Radiosity 18.6.1 One Step of HR 18.6.2 Adaptive HR 18.6.3 Importance HR 18.6.4 Discussion
18.7 Meshing 18.8 Shooting Power 18.9 Extensions to Classical Radiosity 18.10 Further Reading 18.11 Exercises
19 Ray Tracing 19.1 Introduction 19.2 Photon and Visibility Tracing 19.3 Visibility Tracing
19.3.1 Strata Sets 19.3.2 Applying Resolved Strata 19.3.3 Direct and Indirect Illumination 19.3.4 Discussion
19.4 Photon Tracing
CONTENTS
891 892 893 899 900 903 903 904 905 906 907 907 909 911 913 914 916 916 919 921 925 937 937 954 961 964 974 974 976 979 982 984
987 987 988 990 993 999
1002 1035 1037
19.5 Bidirectional Ray-Tracing Methods 1039 19.6 Hybrid Algorithms 1044 19.7 Ray-Tracing Volumes 1049 19.8 Further Reading 1050 19.9 Exercises 1050
20 Rendering and Images 1053 20.1 Introduction 1053 20.2 Postprocessing 1054
20.2.1 A Nonlinear Observer Model 1057 20.2.2 Image-Based Processing 1061 20.2.3 Linear Processing 1063
20.3 Feedback Rendering 1064 20.3.1 Illumination Painting 1066 20.3.2 Subjective Constraints 1067 20.3.3 Device-Directed Rendering 1069
20.4 Further Reading 1072 20.5 Exercise 1072
21 The Future 1073 21.1 Technical Progress 1073
21.1.1 Physical Optics 1074 21.1.2 Volume Rendering 1074 21.1.3 Information Theory 1075 21.1.4 Beyond Photo-Realism: Subjective Rendering 1076
21.2 Other Directions 1077 21.3 Summary 1080
v APPINDICII 1083
A Linear Algebra 1085 A.1 General Notation 1085 A.2 Linear Spaces 1085
A.2.1 Norms 1086 A.2.2 Inf and Sup 1087 A.2.3 Metrics 1087 A.2.4 Completeness 1088 A.2.5 Inner Products 1088
A.3 Function Spaces 1090 A.4 Further Reading 1091
B Probability 1093 B.1 Events and Probability 1093 B.2 Total Probability 1095
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XX CONTENTS
B.3 Repeated Trials 1097 B.4 Random Variables 1098 B.5 Measures 1101 B.6 Distributions 1102 B.7 Geometric Series 1103 B.8 Further Reading 1103
c Historical Notes 1105 C.1 Specular Reflection and Transmission 1105
C.1.1 Specular Reflection 1109 C.1.2 Specular Transmission 1110
D Analytic Form Factors 1113 D.1 Differential and Finite Surfaces 1113
D.1.1 Differential to Differential 1113 D.1.2 Differential to Finite 1114 0.1.3 Finite to Finite 1122
0.2 Two Polygons 1132
E Constants and Units 1135
F Luminaire Standards 1139 F.1 Terminology 1139 F.2 Notation 1143 F.3 The IES Standard 1143
F.3.1 The Big Picture 1145 F.3.2 The Tilt Block 1145 F.3.3 The Photometry Block 1149
F.4 The CIE Standard 1152 F.4.1 The Main Block 1154 F.4.2 The Measurement Block 1155 F.4.3 The Photometry Block 1159
G Reference Data 1163 G.1 Material Data 1164 G.2 Human Data 1169 G.3 Light Sources 1172 G.4 Phosphors 1177 G.5 Macbeth ColorChecker 1179 G.6 Real Objects 1191
Bibliography B-1
Index 1-1
PREFACE
I nspiration begins with imagination and the spirit to create. Then comes the need to communicate, to share an idea or thought. Grab a pencil and you can make it
real: a picture, abstraction made concrete, ideas preserved in time. Our hearts and minds are moved to tell stories, to teach what we think and feel to others and learn the same from them.
Of all the visual media, computer graphics is one of the newest. The computer is a powerful amplifier-it can take terse descriptions of the world and create pictures of that world, using any rules you choose. If we choose the classical rules of light, then we can make pictures that can pass for photographs; other rules explore other ways of seeing.
The field of image synthesis, also called rendering,…