| Foreword |
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xiii | |
| About the Cover |
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xv | |
| Preface |
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xix | |
| 1 Introduction |
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1 | (18) |
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1.1 Data, Images, and Computer Graphics |
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1 | (3) |
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1.2 Applications of Computer Graphics |
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4 | (2) |
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1.3 The Four-Universe Paradigm |
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6 | (2) |
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1.4 Example Models: Terrains and 2D Images |
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8 | (2) |
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10 | (1) |
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11 | (1) |
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1.7 Image Making: The Physical and Mathematical Universes |
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12 | (2) |
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1.8 Comments and References |
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14 | (5) |
| 2 Geometry |
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19 | (34) |
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19 | (3) |
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2.2 Transformations and Computer Graphics |
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22 | (1) |
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22 | (4) |
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26 | (6) |
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2.5 The. Geometry of Computer Graphics |
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32 | (1) |
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33 | (2) |
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2.7 Projective Transformations |
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35 | (5) |
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2.8 The Fundamental Theorem of Projective Geometry |
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40 | (4) |
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2.9 Projections and. Projective Geometry |
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44 | (2) |
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2.10 Comments and References |
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46 | (7) |
| 3 Coordinates |
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53 | (22) |
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3.1 Affine Transformations and Coordinate Changes |
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53 | (8) |
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3.2 Local and Global Transformations |
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61 | (2) |
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63 | (5) |
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3.4 Curvilinear Coordinates |
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68 | (1) |
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3.5 Comments and References |
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69 | (6) |
| 4 The Space of Rotations |
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75 | (34) |
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76 | (1) |
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4.2 Introduction to Rotations in Space |
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77 | (2) |
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4.3 Axis and Angle of Rotation |
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79 | (1) |
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4.4 Parameterizations by Three Rotation Angles |
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80 | (5) |
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4.5 Interpolation of Rotations |
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85 | (2) |
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87 | (1) |
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88 | (12) |
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4.8 Converting between Representations |
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100 | (3) |
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4.9 Comments and References |
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103 | (6) |
| 5 Color |
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109 | (28) |
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5.1 Color in the Physical Universe |
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109 | (2) |
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111 | (1) |
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5.3 Color Representation and Reconstruction |
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112 | (3) |
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5.4 Physical Color Systems |
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115 | (1) |
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5.5 Tristimulus Values and Metameric Reconstruction |
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116 | (3) |
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5.6 The Standard CIE-RGB System |
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119 | (1) |
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5.7 The Geometry of Color Space |
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120 | (5) |
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5.8 The CIE-XYZ Color System |
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125 | (1) |
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5.9 Dominant Wavelength and Complementary Colors |
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126 | (1) |
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5.10 Color Systems and Computer Graphics |
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127 | (5) |
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5.11 Comments and References |
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132 | (5) |
| 6 Image |
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137 | (40) |
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6.1 Image Abstraction Paradigms |
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137 | (1) |
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138 | (3) |
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6.3 Matrix Representation and Reconstruction |
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141 | (6) |
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6.4 Elements of a Digital Image |
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147 | (1) |
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6.5 Color and Image Quantization |
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148 | (4) |
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6.6 Quantization and Cell Geometry |
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152 | (2) |
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6.7 Adaptive Quantization Methods |
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154 | (3) |
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6.8 Optimization and Quantization |
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157 | (4) |
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161 | (6) |
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6.10 Dithering Algorithms |
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167 | (5) |
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6.11 Quantization and Dithering |
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172 | (1) |
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173 | (1) |
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6.13 Comments and References |
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174 | (3) |
| 7 Planar Graphics Objects |
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177 | (34) |
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177 | (1) |
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7.2 Planar Graphics Objects |
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178 | (8) |
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7.3 Polygonal Curves and Triangulation |
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186 | (1) |
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7.4 Representation of Curves and Regions |
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187 | (6) |
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193 | (7) |
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7.6 Representation, Sampling, and Interpolation |
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200 | (1) |
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7.7 Viewing Planar Graphic Objects |
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201 | (3) |
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204 | (2) |
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206 | (1) |
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7.10 Comments and References |
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207 | (4) |
| 8 Spatial Graphics Objects |
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211 | (36) |
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8.1 Digital Geometry Processing |
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211 | (1) |
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212 | (1) |
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213 | (4) |
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217 | (3) |
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8.5 Triangulations and Polyhedral Surfaces |
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220 | (6) |
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8.6 Representation of Parametric Surfaces |
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226 | (7) |
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8.7 Representation of Implicit Surfaces |
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233 | (5) |
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8.8 Representation of Volumetric Objects |
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238 | (4) |
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8.9 Comments and References |
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242 | (5) |
| 9 Hierarchies |
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247 | (30) |
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9.1 Objects with Hierarchy |
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247 | (2) |
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9.2 Hierarchy of Articulated Objects |
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249 | (6) |
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9.3 Hierarchy of the Human Body |
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255 | (7) |
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9.4 Current Transformation and Data Structure |
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262 | (3) |
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9.5 Hierarchies of Composed Objects |
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265 | (3) |
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9.6 Partitioning Trees (BSP-Trees) |
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268 | (3) |
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9.7 Classification and Search using BSP-Trees |
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271 | (2) |
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9.8 Comments and References |
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273 | (4) |
| 10 Geometric Modeling |
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277 | (24) |
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10.1 Modeling and Representation |
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277 | (5) |
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282 | (4) |
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10.3 Conversion between Representations |
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286 | (2) |
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288 | (5) |
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293 | (2) |
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10.6 Operations with Models |
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295 | (1) |
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10.7 Comments and References |
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296 | (5) |
| 11 Virtual Camera |
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301 | (26) |
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301 | (1) |
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11.2 Viewing Coordinate Systems |
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302 | (5) |
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11.3 Virtual Camera Parameters |
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307 | (2) |
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309 | (10) |
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319 | (1) |
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11.6 Camera Specification |
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320 | (3) |
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11.7 Comments and References |
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323 | (4) |
| 12 Clipping |
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327 | (26) |
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12.1 Classification, Partitioning, and Clipping |
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327 | (2) |
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12.2 Clipping Applications |
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329 | (2) |
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12.3 Clipping Acceleration |
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331 | (2) |
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12.4 Clipping Methodology |
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333 | (2) |
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335 | (3) |
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12.6 Clipping a Segment against the Virtual Screen |
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338 | (4) |
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342 | (3) |
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345 | (1) |
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12.9 Clipping and Viewing |
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346 | (2) |
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12.10 Comments and References |
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348 | (5) |
| 13 Visibility |
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353 | (14) |
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13.1 Visibility Foundations |
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353 | (3) |
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13.2 (YXZ) Algorithms: Visibility with Rasterization |
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356 | (1) |
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13.3 (XY)Z Algorithms: Visibility after Rasterization |
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356 | (4) |
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13.4 Z(XY) Algorithms: Visibility before Rasterization |
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360 | (5) |
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13.5 Comments and References |
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365 | (2) |
| 14 Illumination |
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367 | (32) |
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367 | (1) |
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368 | (7) |
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14.3 A Simple Illumination Model |
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375 | (5) |
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14.4 Illumination Calculation |
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380 | (3) |
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383 | (5) |
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14.6 Ray Tracing Acceleration |
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388 | (5) |
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14.7 Sampling and Ray Tracing |
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393 | (3) |
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14.8 Comments and References |
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396 | (3) |
| 15 Rasterization |
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399 | (10) |
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399 | (1) |
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399 | (2) |
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401 | (7) |
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15.4 Comments and References |
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408 | (1) |
| 16 Mappings |
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409 | (44) |
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16.1 Mapping Graphics Objects |
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409 | (4) |
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413 | (3) |
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16.3 Calculating the 2D Mapping |
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416 | (6) |
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16.4 Some 2D Mapping Applications |
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422 | (7) |
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429 | (5) |
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434 | (4) |
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438 | (9) |
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16.8 Comments and References |
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447 | (6) |
| 17 Composition |
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453 | (16) |
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453 | (2) |
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17.2 Composition and Pixel Geometry |
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455 | (4) |
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459 | (7) |
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17.4 Composition of Images and Visibility |
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466 | (2) |
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17.5 Comments and References |
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468 | (1) |
| 18 Radiometry and Photometry |
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469 | (20) |
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18.1 Radiometry and Illumination |
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469 | (10) |
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479 | (3) |
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482 | (6) |
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488 | (1) |
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18.5 Comments and References |
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488 | (1) |
| 19 The Illumination Equation |
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489 | (18) |
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489 | (5) |
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494 | (4) |
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498 | (7) |
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19.4 Comments and References |
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505 | (2) |
| Bibliography |
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507 | |