List of Figures
List of Tables
Preface
Ch. 1 Introduction 1
Ch. 2 Geometrical Methods 7
2.1 Transformations 8
2.2 Coordinate Systems 10
2.3 Quaternions 11
2.4 Euler Angles 18
2.5 Standard 3D Objects 26
2.6 Distance Methods 38
Ch. 3 The Graphics Pipeline 79
3.1 Model and World Coordinates 80
3.2 Perspective Projection 80
3.3 Camera Models 84
3.4 Culling and Clipping 91
3.5 Surface and Vertex Attributes 99
3.6 Rasterizing 113
3.7 An Efficient Clipping and Lighting Pipeline 132
3.8 Issues of Software, Hardware, and APIS 138
Ch. 4 Hierarchical Scene Representations 141
4.1 Tree-Based Representation 143
4.2 Updating a Scene Graph 147
4.3 Rendering a Scene Graph 157
Ch. 5 Picking 169
5.1 Intersection of a Linear Component and a Sphere 171
5.2 Intersection of a Linear Component and a Box 172
5.3 Intersection of a Linear Component and a Capsule 179
5.4 Intersection of a Linear Component and a Lozenge 180
5.5 Intersection of a Linear Component and a Cylinder 181
5.6 Intersection of a Linear Component and an Ellipsoid 182
5.7 Intersection of a Linear Component and a Triangle 182
Ch. 6 Collision Detection 185
6.1 Design Issues 186
6.2 Intersection of Dynamic Objects and Lines 188
6.3 Intersection of Dynamic Objects and Planes 193
6.4 Static Object-Object Intersection 203
6.5 Dynamic Object-Object Intersection 214
6.6 Oriented Bounding Box Trees 244
6.7 Processing of Rotating and Moving Objects 245
Ch. 7 Curves 257
7.1 Definitions 258
7.2 Reparameterization by Arc Length 260
7.3 Special Curves 261
7.4 Subdivision 276
7.5 Orientation of Objects on Curved Paths 285
Ch. 8 Surfaces 287
8.1 Definitions 288
8.2 Curvature 289
8.3 Special Surfaces 293
8.4 Subdivision 306
Ch. 9 Animation of Characters 341
9.1 Key Frame Animation 342
9.2 Inverse Kinematics 348
9.3 Skinning 356
Ch. 10 Geometric Level of Detail 359
10.1 Sprites and Billboards 360
10.2 Discrete Level of Detail 361
10.3 Continuous Level of Detail 362
Ch. 11 Terrain 369
11.1 Terrain Topology 370
11.2 Vertex Based Simplification 373
11.3 Block-Based Simplification 375
11.4 Vertex Dependencies 381
11.5 Block Rendering 383
11.6 The Full Algorithm 385
11.7 Other Issues 392
11.8 Height Fields from Point Sets or Triangle Meshes 398
Ch. 12 Spatial Sorting 411
12.1 Quadtrees and Octrees 412
12.2 Portals 413
12.3 Binary Space Partitioning 417
Ch. 13 Special Effects 427
13.1 Lens Flare 427
13.2 Environment Mapping 428
13.3 Bump Mapping 429
13.4 Volumetric Fogging 430
13.5 Projected Lights 430
13.6 Projected Shadows 431
13.7 Particle Systems 432
13.8 Morphing 433
App. A Object-Oriented Infrastructure 435
App. B Numerical Methods 469
Glossary 509
Bibliography 521
Index 527
About the Author 557
About the CD-ROM 559
Trademarks 561



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