Computer graphics: theory and practice/ Jonas Gomes, Luis Velho, Mario Costa Sousa

Includes bibliographical references (p. 507-515) and index.

Introduction
1.1 Data, Images, and Computer Graphics 1
1.2 Applications of Computer Graphics 4
1.3 The Four-Universe Paradigm
1.4 Example Models: Terrains and 2D Images 8
1.5 Reconstruction
1.6 A Practical Problem
1.7 Image Making: The Physical and Mathematical Universes
1.8 Comments and References
19 Geometry
2.1 What Is Geometry?
2.2 Transformations and Computer Graphics 22
2.3 Euclidean Geometry 22
2.4 Affine Geometry 26
2.5 The Geometry of Computer Graphics 32
2.6 Projective Space ^2
2.7 Projective Transformations 35
2.8 The Fundamental Theorem of Projective Geometry 40
2.9 Projections and Projective Geometry 44
2.10 Comments and References 46
Coordinates 53
3.1 Affine Transformations and Coordinate Changes 53
3.2 Local and Global Transformations 61
3.3 Coordinates in Space 63
3.4 Curvilinear Coordinates 68
3.5 Comments and References 69
The Space of Rotations 75
4.1 Plane Rotations 76
4.2 Introduction to Rotations in Space 77
4.3 Axis and Angle of Rotation 79
4.4 Parameterizations by Three Rotation Angles 80
4.5 Interpolation of Rotations 85
4.6 Commercial Break 87
4.7 Quaternions
4.8 Converting between Representations 100
4.9 Comments and References 103
Color
5.1 Color in the Physical Universe 109
5.2 Spectral Color Space Ill
5.3 Color Representation and Reconstruction 112
5.4 Physical Color Systems 115
5.5 Tristimulus Values and Metameric Reconstruction 116
5.6 The Standard CIE-RGB System 119
5.7 The Geometry of Color Space 120
5.8 The CIE-XYZ Color System 125
5.9 Dominant Wavelength and Complementary Colors 126
5.10 Color Systems and Computer Graphics • 127
5.11 Comments and References ^^2
Image ' ^7
6.1 Image Abstraction Paradigms 127
6.2 Image Representation 128
6.3 Matrix Representation and Reconstruction 141
6.4 Elements of a Digital Image 147
6.5 Color and Image Quantization 148
6.6 Quantization and Cell Geometry 152
6.7 Adaptive Quantization Methods 154
6.8 Optimization and Quantization 157
6.9 Dithering 1^1
6.10 Dithering Algorithms 167
6.11 Quantization and Dithering 172
6.12 Image Coding
6.13 Comments and References
7 Planar Graphics Objects
7.1 Graphics Objects yj
7.2 Planar Graphics Objects
7.3 Polygonal Curves and Triangulation 186
7.4 Representation of Curves and Regions 187
7.5 Rasterization
7.6 Representation, Sampling, and Interpolation 200
7.7 Viewing Planar Graphic Objects 201
7.8 2D cupping
7.9 Viewing Operations
7.10 Comments and References
8 Spatial Graphics Objects J
8.1 Digital Geometry Processing 211
8.2 Spatial Curves
8.3 Surfaces
8.4 Volumetric Objects
8.5 Triangulations and Polyhedral Surfaces 220
8.6 Representation of Parametric Surfaces 226
8.7 Representation of Implicit Surfaces 233
8.8 Representation of Volumetric Objects 238
8.9 Comments and References 242
9 Hierarchies
9.1 Objects with Hierarchy
9.2 Hierarchy of Articulated Objects 249
9.3 Hierarchy of the Human Body 255
9.4 Current Transformation and Data Structure 262
9.5 Hierarchies of Composed Objects 265
9.6 Partitioning Trees (BSP-Trees) 268
9.7 Classification and Search using BSP-Trees 271
9.8 Comments and References 273
10 Geometric Modeling
10.1 Modeling and Representation 277
10.2 CSG Representation 282
10.3 Conversion between Representations 286
10.4 Generative Modeling ^
10.5 Modeling Systems
10.6 Operations with Models
10.7 Comments and References
I I Virtual Camera
11.1 A Basic Model
11.2 Viewing Coordinate Systems
11.3 Virtual Camera Parameters
11.4 Viewing Operations
11.5 Other Camera Models
11.6 Camera Specification
11.7 Comments and References 323
'2 Clipping
12.1 Classification, Partitioning, and Clipping
12.2 Clipping Applications 329
12.3 Clipping Acceleration 331
12.4 Clipping Methodology
12.5 2D Clipping
12 6 Clipping a Segment against the Virtual Screen 338
12.7 Polygon clipping
12.8 3D Clipping
12.9 Clipping and Viewing
12.10 Comments and References 348
13 Visibility
13.1 Visibility Foundations ^
13.2 (YXZ) Algorithms: Visibility with Rasterization 356
13.3 (XY)Z Algorithms: Visibility after Rasterization 356
13.4 Z(XY) Algorithms: Visibility before Rasterization 360
13.5 Comments and References 365
14 Illumination
14.1 Foundations
14.2 The Nature of Light
14.3 A Simple Illumination Model
14.4 Illumination Calculation 380
14.5 Ray Tracing
14.6 Ray Tracing Acceleration
14.7 Sampling and Ray Tracing 393
14.8 Comments and References
15 Rasterization
15.1 Sampling
15.2 Point Sampling
15.3 Area Sampling
15.4 Comments and References
16 Mappings 409
16.1 Mapping Graphics Objects 409
16.2 2D Mapping Methods 413
16.3 Calculating the 2D Mapping 416
16.4 Some 2D Mapping Applications 422
16.5 Noise Function 429
16.6 Scalar Noise 434
16.7 Gradient Noise 438
16.8 Comments and References 447
17 Composition 453
17.1 The Alpha Channel 453
17.2 Composition and Pixel Geometry 455
17.3 Composition Algebra 459
17.4 Composition of Images and Visibility 466
17.5 Comments and References 468
18 Radiometry and Photometry 469
18.1 Radiometry and Illumination 469
18.2 BRDF 479
18.3 Photometry 482
18.4 Summary 488
18.5 Comments and References 488
19 The Illumination Equation 489
19.1 Illumination Model 489
19.2 Ray Tracing Method 494
19.3 Radiosity Method 498
19.4 Comments and References 505