3D COMPUTER GRAPHICS THIRD EDITION2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1 Mathematical fundamentals of computer graphics1

1.1 Manipulating three-dimensional structures1

1.1.1 Three-dimensional geometry in computer graphics - affine transformations2

1.1.2 Transformations for changing coordinate systems8

1.2 Structure-deforming transformations9

1.3 Vectors and computer graphics11

1.3.1 Addition of vectors12

1.3.2 Length of vectors12

1.3.3 Normal vectors and cross products12

1.3.4 Normal vectors and dot products14

1.3.5 Vectors associated with the normal vector reflection15

1.4 Rays and computer graphics17

1.4.1 Ray geometry - intersections17

1.4.2 Intersections - ray-sphere18

1.4.3 Intersections - ray-convex polygon19

1.4.4 Intersections - ray-box21

1.4.5 Intersections - ray-quadric23

1.4.6 Ray tracing geometry - reflection and refraction23

1.5 Interpolating properties in the image plane25

2 Representation and modelling of three-dimensional objects （1）27

Introduction27

2.1 Polygonal representation of three-dimensional objects33

2.1.1 Creating polygonal objects37

2.1.2 Manual modelling of polygonal objects38

2.1.3 Automatic generation of polygonal objects38

2.1.4 Mathematical generation of polygonal objects39

2.1.5 Procedural polygon mesh objects - fractal objects44

2.2 Constructive solid geometry （CSG） representation of objects46

2.3 Space subdivision techniques for object representation51

2.3.1 Octrees and polygons53

2.3.2 BSP trees55

2.3.3 Creating voxel objects56

2.4 Representing objects with implicit functions56

2.5 Scene management and object representation58

2.5.1 Polygon mesh optimization59

2.6 Summary64

3 Representation and modelling of three-dimensional objects （2）66

Introduction66

3.1 Bézier curves69

3.1.1 joining Bézier curve segments75

3.1.2 Summary of Bézier curve properties77

3.2 B-spline representation78

3.2.1 B-spline curves78

3.2.2 Uniform B-splines80

3.2.3 Non-uniform B-splines84

3.2.4 Summary of B-spline curve properties90

3.3 Rational curves90

3.3.1 Rational Bézier curves91

3.3.2 NURBS93

3.4 From curves to surfaces94

3.4.1 Continuity and Bézier patches98

3.4.2 A Bézier patch object - the Utah teapot100

3.5 B-spline surface patches101

3.6 Modelling or creating patch surfaces106

3.6.1 Cross-sectional or linear axis design example107

3.6.2 Control polyhedron design - basic technique110

3.6.3 Creating patch objects by surface fitting115

3.7 From patches to objects121

4 Representation and rendering123

Introduction123

4.1 Rendering polygon meshes - a brief overview124

4.2 Rendering parametric surfaces125

4.2.1 Rendering directly from the patch descriptions125

4.2.2 Patch to polygon conversion128

4.2.3 Object space subdivision128

4.2.4 Image space subdivision135

4.3 Rendering a CSG description138

4.4 Rendering a voxel description140

4.5 Rendering implicit functions141

5 The graphics pipeline （1）: geometric operations142

Introduction142

5.1 Coordinate spaces in the graphics pipeline143

5.1.1 Local or modelling coordinate systems143

5.1.2 World coordinate systems143

5.1.3 Camera or eye or view coordinate system143

5.2 Operations carried out in view space147

5.2.1 Culling or back-face elimination147

5.2.2 The view volume147

5.2.3 Three-dimensional screen space149

5.2.4 View volume and depth152

5.3 Advanced viewing systems （PHIGS and GKS）156

5.3.1 Overview of the PHIGS viewing system157

5.3.2 The view orientation parameters159

5.3.3 The view mapping parameters159

5.3.4 The view plane in more detail162

5.3.5 Implementing a PHIGS-type viewing system164

6 The graphics pipeline （2）: rendering or algorithmic processes167

Introduction167

6.1 Clipping polygons against the view volume168

6.2 Shading pixels171

6.2.1 Local reflection models173

6.2.2 Local reflection models - practical points177

6.2.3 Local reflection models - light source considerations179

6.3 Interpolative shading techniques179

6.3.1 Interpolative shading techniques - Gouraud shading180

6.3.2 Interpolative shading techniques - Phong shading181

6.3.3 Renderer shading options182

6.3.4 Comparison of Gouraud and Phong shading183

6.4 Rasterization183

6.4.1 Rasterizing edges183

6.4.2 Rasterizing polygons185

6.5 Order of rendering187

6.6 Hidden surface removal189

6.6.1 The Z-buffer algorithm189

6.6.2 Z-buffer and CSG representation190

6.6.3 Z-buffer and compositing191

6.6.4 Z-buffer and rendering192

6.6.5 Scan line Z-buffer193

6.6.6 Spanning hidden surface removal193

6.6.7 A spanning scan line algorithm194

6.6.8 Z-buffer and complex scenes196

6.6.9 Z-buffer summary198

6.6.10 BSP trees and hidden surface removal199

6.7 Multi-pass rendering and accumulation buffers202

7 Simulating light-object interaction: local reflection models205

Introduction205

7.1 Reflection from a perfect surface206

7.2 Reflection from an imperfect surface207

7.3 The bi-directional reflectance distribution function208

7.4 Diffuse and specular components211

7.5 Perfect diffuse - empirically spread specular reflection212

7.6 Physically based specular reflection213

7.6.1 Modelling the micro-geometry of the surface214

7.6.2 Shadowing and masking effects214

7.6.3 Viewing geometry216

7.6.4 The Fresnel term216

7.7 Pre-computing BRDFs219

7.8 Physically based diffuse component221

8 Mapping techniques223

Introduction223

8.1 Two-dimensional texture maps to polygon mesh objects228

8.1.1 Inverse mapping by bilinear interpolation229

8.1.2 Inverse mapping by using an intermediate surface230

8.2 Two-dimensional texture domain to bi-cubic parametric patch objects234

8.3 Billboards235

8.4 Bump mapping236

8.4.1 A multi-pass technique for bump mapping238

8.4.2 A pre-calculation technique for bump mapping239

8.5 Light maps240

8.6 Environment or reflection mapping243

8.6.1 Cubic mapping245

8.6.2 Sphere mapping247

8.6.3 Environment mapping: comparative points248

8.6.4 Surface properties and environment mapping249

8.7 Three-dimensional texture domain techniques251

8.7.1 Three-dimensional noise251

8.7.2 Simulating turbulence252

8.7.3 Three-dimensional texture and animation254

8.7.4 Three-dimensional light maps256

8.8 Anti-aliasing and texture mapping256

8.9 Interactive techniques in texture mapping260

9 Geometric shadows263

Introduction263

9.1 Properties of shadows used in computer graphics265

9.2 Simple shadows on a ground plane265

9.3 Shadow algorithms267

9.3.1 Shadow algorithms: projecting polygons/scan line267

9.3.2 Shadow algorithms: shadow volumes268

9.3.3 Shadow algorithms: derivation of shadow polygons from light source transformations271

9.3.4 Shadow algorithms: shadow Z-buffer271

10 Global illumination275

Introduction275

10.1 Global illumination models276

10.1.1 The rendering equation277

10.1.2 Radiance, irradiance and the radiance equation278

10.1.3 Path notation281

10.2 The evolution of global illumination algorithms283

10.3 Established algorithms - ray tracing and radiosity284

10.3.1 Whitted ray tracing284

10.3.2 Radiosity286

10.4 Monte Carlo techniques in global illumination288

10.5 Path tracing292

10.6 Distributed ray tracing294

10.7 Two-pass ray tracing297

10.8 View dependence/independence and multi-pass methods300

10.9 Caching illumination301

10.10 Light volumes303

10.11 Particle tracing and density estimation304

11 The radiosity method306

Introduction306

11.1 Radiosity theory308

11.2 Form factor determination310

11.3 The Gauss-Seidel method314

11.4 Seeing a partial solution - progressive refinement315

11.5 Problems with the radiosity method318

11.6 Artefacts in radiosity images319

11.6.1 Hemicube artefacts319

11.6.2 Reconstruction artefacts321

11.6.3 Meshing artefacts323

11.7 Meshing strategies325

11.7.1 Adaptive or a posteriori meshing325

11.7.2 A priori meshing332

12 Ray tracing strategies342

Introduction - Whitted ray tracing342

12.1 The basic algorithm343

12.1.1 Tracing rays - initial considerations343

12.1.2 Lighting model components344

12.1.3 Shadows345

12.1.4 Hidden surface removal346

12.2 Using recursion to implement ray tracing347

12.3 The adventures of seven rays - a ray tracing study350

12.4 Ray tracing polygon objects - interpolation of a normal at an intersection point in a polygon352

12.5 Efficiency measures in ray tracing354

12.5.1 Adaptive depth control354

12.5.2 First hit speed up355

12.5.3 Bounding objects with simple shapes355

12.5.4 Secondary data structures357

12.5.5 Ray space subdivision363

12.6 The use of ray coherence364

12.7 A historical digression - the optics of the rainbow367

13 Volume rendering370

Introduction370

13.1 Volume rendering and the visualization of volume data373

13.2 ′Semi-transparent gel′ option377

13.2.1 Voxel classification378

13.2.2 Transforming into the viewing direction379

13.2.3 Compositing pixels along a ray379

13.3 Semi-transparent gel plus surfaces380

13.3.1 Explicit extraction of isosurfaces382

13.4 Structural considerations in volume rendering algorithms384

13.4.1 Ray casting （untransformed data）385

13.4.2 Ray casting （transformed data）387

13.4.3 Voxel projection method388

13.5 Perspective projection in volume rendering390

13.6 Three-dimensional texture and volume rendering391

14 Anti-aliasing theory and practice392

Introduction392

14.1 Aliases and sampling393

14.2 Jagged edges397

14.3 Sampling in computer graphics compared with sampling reality398

14.4 Sampling and reconstruction400

14.5 A simple comparison401

14.6 Pre-filtering methods402

14.7 Supersampling or post-filtering404

14.8 Non-uniform sampling - some theoretical concepts406

14.9 The Fourier transform of images411

15 Colour and computer graphics418

Introduction418

15.1 Colour sets in computer imagery419

15.2 Colour and three-dimensional space420

15.2.1 RGB space423

15.2.2 The HSV single hexcone model424

15.2.3 YIQ space427

15.3 Colour, information and perceptual spaces427

15.3.1 CIE XYZ space429

15.3.2 CIE xyY space433

15.4 Rendering and colour spaces435

15.5 Monitor considerations436

15.5.1 RGB monitor space and other monitor considerations436

15.5.2 Monitor considerations - different monitors and the same colour437

15.5.3 Monitor considerations - colour gamut mapping439

15.5.4 Monitor considerations - gamma correction440

16 Image-based rendering and photo-modelling443

Introduction443

16.1 Reuse of previously rendered imagery - two-dimensional techniques444

16.1.1 Planar impostors or sprites445

16.1.2 Calculating the validity of planar impostors445

16.2 Varying rendering resources447

16.2.1 Priority rendering447

16.2.2 Image layering448

16.3 Using depth information452

16.3.1 Three-dimensional warping452

16.3.2 Layered depth images （LDIs）456

16.4 View interpolation458

16.4.1 View morphing460

16.5 Four-dimensional techniques - the Lumigraph or light field rendering approach463

16.6 Photo-modelling and IBR465

16.6.1 Image-based rendering using photographic panoramas469

16.6.2 Compositing panoramas469

16.6.3 Photo-modelling for image-based rendering470

17 Computer animation473

Introduction473

17.1 A categorization and description of computer animation techniques476

17.2 Rigid body animation477

17.2.1 Interpolation or keyframing477

17.2.2 Explicit scripting479

17.2.3 Interpolation of rotation483

17.2.4 Using quaternions to represent rotation484

17.2.5 Interpolating quaternions488

17.2.6 The camera as an animated object492

17.3 Linked structures and hierarchical motion493

17.3.1 Solving the inverse kinematics problem500

17.4 Dynamics in computer animation504

17.4.1 Basic theory for a rigid body - particles505

17.4.2 The nature of forces506

17.4.3 Rigid bodies - extended masses507

17.4.4 Using dynamics in computer animation510

17.4.5 Simulating the dynamics of a lumped mass511

17.4.6 Space-time constraints515

17.5 Collision detection517

17.5.1 Broad phase/narrow phase algorithms518

17.5.2 Broad phase collision detection with OBBs519

17.5.3 Narrow phase: pairs of convex polyhedra - exact collision detection522

17.5.4 Single phase algorithms - object hierarchies524

17.6 Collision response526

17.7 Particle animation529

17.8 Behavioural animation531

17.9 Summary534

18 Comparative Image study536

Introduction536

18.1 Local reflection models537

18.2 Texture and shadow mapping538

18.3 Whitted ray tracing539

18.4 Radiosity541

18.5 RADIANCE543

18.6 Summary543

References544

Index553