TY - BOOK AU - Gomes,Jonas AU - Velho, Luiz. AU - Costa Sousa, Mario. TI - Computer graphics: theory and practice SN - 9781568815800 U1 - 006.6 PY - 2012/// CY - Boca Raton PB - AK Peters/Taylor & Francis KW - Computer graphics KW - Microcomputers--Programming KW - C (Computer program language) KW - Image processing--Mathematics KW - Computer graphics--Mathematical models N1 - 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 ER -