Table Of ContentImage Synthesis
Image Synthesis
by
Michel Bret
Springer Science+Business Media, B.V.
Library of Congress Cataloging-in-Publication Data
Bret, Michel.
(Images de synthese. Englishl
Image synthesls I by Michel Bret.
p. cm.
Translation of: Les images de synthese.
Includes index,
ISBN 978-94-010-5133-0 ISBN 978-94-011-2568-0 (eBook)
DOI 10.1007/978-94-011-2568-0
1. Image processlng--Digital technloues. 2. Computer graprolcs.
3. Digital computer simulation. I. Tltle.
TA1632.B7313 1991
S21.3S'7--dc20 91-33018
ISBN 978-94-010-5133-0
Printed on acid-free paper
All Rights Reserved
1992 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1992
Softcover reprint ofthe hardcover 1st edition 1992
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
remevai SYSlem, WiÜJOUl wriuen pennission irom me copyrighll ,wner.
Table of contents
Preface xiii
1. Images
1.1. Images and communication
1.1.1. Speaking 1
1.1.2. Writing 1
1.1.3. Images 1
1.1.4. Discourse.image. andcomputer 2
1.2. Visual perception
1.2.1. Thoughtand vision 3
1.2.2. Themechanismsofphotoreception 4
1.2.3. Theopticalpaths 4
1.2.4. Thetreatmentofvisualinformation 5
1.2.5. Multiplexingofsensorialmessages 5
1.3. Different aspects ofimages
1.3.1. Attempttodermetheconceptofanimage 7
1.3.2. Physicalimages 8
1.3.3. Psychicimages 8
1.3.4. Theparticularstatusofnumericalimages 8
2. Numerical images
2.1. Image and computer
2.1.1. Imagesasmemory 11
2.1.1.1. Psychicimagesand memory 11
2.1.1.2. Encodinganddecodingofimages 11
2.1.2. Representations 12
2.1.2.1. Analoguerepresentation 12
2.1.2.2. Numericalrepresentation 13
2.1.3. Numerical(digital)images 13
2.1.3.1. Screen memory 13
2.1.3.2. Vectormemory 13
2.2. The graphical peripherals
2.2.1. Centralunitandperipherals 14
2.2.2. Graphicaloutputperipherals 15
2.2.2.1. History 15
2.2.2.2. Printers,tape andcard punchers 15
2.2.2.3. Plotters 16
vi
2.2.2.4. Cathoderay tubes 18
2.2.2.5. COMs 19
2.2.2.6. Flatscreens 19
2.2.2.7. Lasertechniques 19
2.2.3. Peripheralsofgraphicsprocessing 19
2.2.3.1. Theopticalpen 19
2.2.3.2. Datatablet 21
2.2.3.3. Mouse 24
2.2.3.4. Digitizersofimages 24
2.2.3.5. Others 25
2.2.4. Interaction 26
2.3. Cathode ray tubes
2.3.1. History 26
2.3.2. Principlesoffunctioning 26
2.3.3. Scanningmodes 27
2.3.4. Graphics processor 29
2.3.5. Tubeswithfree scanning 30
2.3.6. Tubeswithmemory(orwithimagepreservation) 31
2.3.7. Tubeswithrecurrentscanning 32
2.3.8. Colorscreens 33
2.3.9. Linearizationoftheintensitylevels 34
2.3.10. Lookup tables 35
2.3.10.1. Principle 35
2.3.10.2. Applications 35
2.3.10.3. Digitizersofimages 37
2.4. Flat screens 39
2.5. The programming ofgraphics processors 40
3. Modelling problems
3.1. Image and formalism
3.1.1. Imageandmodel 43
3.1.2. Thecomputerasatoolofcreation 43
3.1.3. Thedifferentlevelsofdescription 44
3.2. The modelling ofimages
3.2.1. Processingofanumericalimage 45
3.2.2. Synthesis 46
3.2.3. Abstractplaneimages 47
3.2.4. Figurativeplaneimages 47
3.2.5. Three-dimensionalimages 48
3.2.6. Realisticimages 49
3.3. Constructive geometry
vii
3.3.1. Modularstructures 51
3.3.2. Euleroperators 52
3.3.3. Applications 53
3.4. Polyhedral models
3.4.1. Polyhedralapproximationofacurvedsurface 54
3.4.1.1. Modellingbymeansoffacets 54
3.4.1.2. Triangulationmethods 55
3.4.2. Datastructuresassociatedwithpolyhedraldescriptions 57
3.4.3. Domainsofapplications 57
3.5. Curves and surfaces
3.5.1. Graphicalprimitives 58
3.5.2. Generatingplanecurves 59
3.5.2.1. Polygonalapproximations 59
3.5.2.2. Reductionofnumericalplanecurves 60
3.5.3. Parameticcurvesandsurfaces 63
3.5.3.1. Cubics 63
3.5.3.2. Coons' surfaces 68
3.5.3.3. Beziercurvesandsurfaces 69
3.5.3.4. B-splinecurvesandsurfaces 73
3.5.3.5. Beta-splines 76
3.5.4. Thevisualizationofcurvesandsurfaces 78
3.6. Fractal objects
3.6.1. FractalobjectsaccordingtoBenoitMandelbrot 78
3.6.1.1. Continuityand reality 79
3.6.1.2. Theconceptofdimension 79
3.6.1.3. Measure 80
3.6.1.4. Theconceptofaninternalhomothety 81
3.6.1.5. Homothetydimension 82
3.6.1.6. Stochasticmodels 83
3.6.1.7. Terrain models 85
3.6.2. Algorithmsforthegenerationofthree-dimensionalfractalobjects 85
3.6.2.1. Numericalimagesandfractaldimension 85
3.6.2.2. Iterationoffunctions 86
3.6.2.3. Stochasticmodels 88
3.6.2.4. Stochasticprimitives 90
3.6.2.5. Stochasticmovement 95
3.7. Systems ofparticles
3.7.1. Themodelingofunsharpobjects 96
3.7.2. Systemsofparticles 97
3.7.3. Applicationtothemodellingoffireandexplosions 97
3.8. Modelling waves
3.8.1. Explanationoftheproblem 98
viii
3.8.2. Peachey'smodel 99
3.8.3. ThemodelofFournierandReeves 103
3.9. The synthesis offabrics
3.9.1. Explanationoftheproblem 107
3.9.2. Weil's model 107
3.9.2.1. Theconditions 107
3.9.2.2. Approximationofthesurface 107
3.9.2.3. Iterativeapproximation 108
3.10. The modelling ofshells and plants
3.10.1.Explanationoftheproblem 109
3.10.2.Kawaguchiandthesea 110
3.10.3.Plantsandformallanguages 111
3.10.4.Tree-likemodelsofplants 114
3.10.5. AMAP 114
4. Problems of visualization
4.1. The visualization ofnumerical images
4.1.1. Numericalimages 115
4.1.2. Codingnumericalimages 116
4.1.2.1. Run-length coding 116
4.1.2.2. CodingaccordingtoFreeman 116
4.1.2.3. Codingbymeansofquaternarytrees 116
4.2. 2D-images
4.2.1. Graphicalprimitives 117
4.2.1.1. Points 117
4.2.1.2. Segments 118
4.2.1.3. Simple figures 124
4.2.2. 2Dclipping 125
4.2.2.1. Explanationoftheproblem 125
4.2.2.2. Clippingofasegmentbyarectangularwindow 126
4.2.2.3. Clippingbyan arbitrarywindow 128
4.2.2.4. Theclippingofpolygons 131
4.2.2.5. Concave windows 134
4.2.3. Colouringsurfaces 136
4.2.3.1. Explanationoftheproblem 136
4.2.3.2. Algorithmswhichworkontheimagememory 136
4.2.3.3. Algorithmswhichuseassociateddatastructures 145
4.2.4. Theuse ofsmoothings 149
4.2.4.1. Principles 149
4.2.4.2. Smoothingsdefinedonthebasisofpoles 150
4.2.4.3. Methodsofcolourpoints 152
ix
4.3. Perspective projections
4.3.1. 3D-Images 153
4.3.1.1. Objectspaceandimagespace 153
4.3.1.2. Theperceptionofspace 154
4.3.1.3. Perspectiveprojection 155
4.3.1.4. Theproblemofenteringthedata 156
4.3.2. Homogeneouscoordinates 158
4.3.3. Thematrixassociatedto alineartransfonnation 161
4.3.3.1. Matrixofalineartransfonnation 161
4.3.3.2. Productoflineartransfonnations 162
4.3.3.3. Examples 162
4.3.4. Perspectivetransfonnations 164
4.3.5. Clipping 167
4.3.6. Coordinatesystemofthescreenandperspectiveprojection 168
4.4. Aliasing
4.4.1. Explanationoftheproblem 171
4.4.2. Filteringanumericalimage 172
4.4.3. Increasingtheresolution 174
4.4.4. Randomsampling 174
4.4.5. Themethodofdividingpixels 175
4.5. Motifs, mappings
4.5.1. Explanationoftheproblem 176
4.5.2. Motifs 176
4.5.3. Maps 177
4.6. Textures
4.6.1. Defmitionoftheconceptoftexture 180
4.6.2. Analysisandsynthesisoftextures 180
4.6.3. Blinn's method 181
4.6.4. 3D-textures 182
5. The elimination of hidden parts
5.1. The problem ofhidden parts
5.1.1. Explanationoftheproblem 185
5.1.2. Principles 185
5.2. Elements ofgeometry
5.2.1. Boxtests 186
5.2.2. Belongingtotheinteriorofapolygon 187
5.2.3. Equationsofplanes 188
5.2.4. Sortingproblems 189
5.2.5. Coherence 189
5.3. Classification ofalgorithms 189
x
5.4. The algorithm with a mobile horizon
5.4.1. Principles 191
5.4.2. Thealgorithm 191
5.4.3. Implementation 191
5.5. Roberts' algorithm
5.5.1. Principles 193
5.5.2. Eliminationofbackfacets 194
5.5.3. Eliminationoftheremainingedges 195
5.6. Schumacker's algorithm 196
5.7. The algorithm ofNewell-Newell-Sancha
5.7.1. Principles 197
5.7.2. Newell'salgorithm 198
5.8. Warnock's algorithm
5.8.1. Principles 199
5.8.2. Optimization 201
5.9. Scan-line algorithms 201
5.10. Application of automatic programming: Goad's algorithm 202
5.11. Using coherence 203
5.12. The z-buffer algorithm
5.12.1. Principles 204
5.12.2. Implementation 204
5.12.3. Limitationsofthemethod 204
5.12.4. Scan-lineand z-buffer 205
5.13. The ray-tracing algorithm
5.13.1. Principles 205
5.13.2. Implementation 205
5.13.3. Calculatingintersections 206
5.13.4. Arrangingtheobjectsinahierarchy 207
6. Illumination models
6.1. Illumination ofa scene 209
6.2. The models ofPhong and ofBlinn
6.2.1. Diffuseillumination(orambientlighting) 210
6.2.2. Lambert'slaw 210
6.2.3. Specularreflection 211
6.2.4. Multiplesources 212
6.3. Cook's model
6.3.1. The model 213
6.3.2. Bidirectionaldistribution ofreflectedlight 215
6.3.3. Spectraldistributionofreflectedlight 216
6.4. Transparency 217
6.5. Smoothing methods
xi
6.5.1. Thesmoothingproblem 218
6.5.2. Gouraudsmoothing 220
6.5.3. Phong smoothing 222
6.5.4. Comparisonofthetwo methods 222
6.6. Shadows
6.6.1. Explanationoftheproblem 223
6.6.2. Projectionmethod 224
6.6.3. z-buffermethod 225
6.6.4. Ray-tracingmethod 225
6.7. Radiosity
6.7.1. Theilluminationproblem 228
6.7.2. Theradiosityprinciple 228
6.7.3. Calculationoftheformcoefficients 229
6.7.4. Cohen'shemi-cube 231
6.8. Ray-tracing
6.8.1. Principles 233
6.8.2. Whitted'smodel 233
6.8.3. Calculatingsecondaryrays 235
6.8.4. Anti-aliasing 236
6.8.5. Optimization
6.8.5.1. Box tests 238
6.8.5.2. Optimizationaccordingtothetypeofprimitives 241
6.8.6. Bundletracing
6.8.6.1. Ray and bundle 247
6.8.6.2. Representationofarayinabundle 248
6.8.6.3. Matricesassociatedtoopticalsystems 249
6.8.6.4. Evaluationofthedeviation 250
6.9. Simulation ofclouds and fluffy surfaces
6.9.1. Dispersionmodelsinacloud 253
6.9.2. Phase functions 258
6.10. Simulation ofatmospheric dispersion
6.10.1. Explanationoftheproblem 260
6.10.2. Nishita's model 260
Bibliography 265
Glossary 281
Index 287
