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1 Introducing: Computer Graphics1

1.1 A Few Uses of Computer Graphics1

1.2 A Brief History of Computer Graphics6

1.2.1 Output Technology8

1.2.2 Input Technology11

1.2.3 Software Portability and Graphics Standards12

1.3 The Advantages of Interactive Graphics14

1.4 Conceptual Framework for Interactive Graphics15

1.4.1 Application Modeling16

1.4.2 Display of the Model16

1.4.3 Interaction Handling17

SUMMARY18

Exercises19

2 Programming in the Simple Raster Graphics Package （SRGP）21

2.1 Drawing with SRGP22

2.1.1 Specification of Graphics Primitives22

2.1.2 Attributes27

2.1.3 Filled Primitives and Their Attributes29

2.1.4 Saving and Restoring Attributes33

2.1.5 Text33

2.2 Basic Interaction Handling36

2.2.1 Human Factors36

2.2.2 Logical Input Devices37

2.2.3 Sampling Versus Event-Driven Processing38

2.2.4 Sample Mode40

2.2.5 Event Mode41

2.2.6 Pick Correlation for Interaction Handling45

2.2.7 Setting Device Measure and Attributes47

2.3 Raster Graphics Features49

2.3.1 Canvases49

2.3.2 Clipping Rectangles52

2.3.3 The SRGP copyPixel Operation52

2.3.4 Write Mode or RasterOp54

2.4 Limitations of SRGP58

2.4.1 Application Coordinate Systems58

2.4.2 Storage of Primitives for Respecification59

SUMMARY61

Exercises62

Programming Projects63

3 Basic Raster Graphics Algorithms for Drawing 2D Primitives65

3.1 Overview66

3.1.1 Implications of Display-System Architecture66

3.1.2 The Output Pipeline in Software69

3.2 Scan Converting Lines70

3.2.1 The Basic Incremental Algorithm71

3.2.2 Midpoint Line Algorithm73

3.2.3 Additional Issues77

3.3 Scan Converting Circles80

3.3.1 Eight-Way Symmetry80

3.3.2 Midpoint Circle Algorithm81

3.4 Filling Rectangles85

3.5 Filling Polygons87

3.5.1 Horizontal Edges89

3.5.2 Slivers90

3.5.3 Edge Coherence and the Scan-Line Algorithm90

3.6 Pattern Filling94

3.6.1 Pattern Filling Using Scan Conversion94

3.6.2 Pattern Filling Without Repeated Scan Conversion95

3.7 Thick Primitives97

3.7.1 Replicating Pixels98

3.7.2 The Moving Pen99

3.8 Clipping in a Raster World100

3.9 Clipping Lines101

3.9.1 Clipping Endpoints102

3.9.2 Clipping Lines by Solving Simultaneous Equations102

3.9.3 The Cohen-Sutherland Line-Clipping Algorithm103

3.9.4 A Parametric Line-Clipping Algorithm107

3.10 Clipping Circles111

3.11 Clipping Polygons112

3.11.1 The Sutherland-Hodgman Polygon-Clipping Algorithm112

3.12 Generating Characters116

3.12.1 Defining and Clipping Characters116

3.12.2 Implementing a Text Output Primitive117

3.13 SRGP copyPixel119

3.14 Antialiasing119

3.14.1 Increasing Resolution119

3.14.2 Unweighted Area Sampling120

3.14.3 Weighted Area Sampling122

3.15 Advanced Topics125

SUMMARY126

Exercises126

4 Graphics Hardware129

4.1 Hardcopy Technologies130

4.2 Display Technologies135

4.3 Raster-scan Display Systems141

4.3.1 Simple Raster Display System142

4.3.2 Raster Display System with Peripheral Display Processor145

4.3.3 Additional Display-Processor Functionality148

4.3.4 Raster Display System with Integrated Display Processor150

4.4 The Video Controller151

4.4.1 Video Mixing152

4.5 Input Devices for Operator Interaction153

4.5.1 Locator Devices153

4.5.2 Keyboard Devices156

4.5.3 Valuator Devices156

4.5.4 Choice Devices157

4.6 Image Scanners157

Exercises158

5 Geometrical Transformations161

5.1 Mathematical Preliminaries161

5.1.1 Vectors and Their Properties162

5.1.2 The Vector Dot Product164

5.1.3 Properties of the Dot Product164

5.1.4 Matrices165

5.1.5 Matrix Multiplication165

5.1.6 Determinants166

5.1.7 Matrix Transpose166

5.1.8 Matrix Inverse167

5.2 2D Transformations168

5.3 Homogeneous Coordinates and Matrix Representation of 2D Transformations170

5.4 Composition of 2D Transformations175

5.5 The Window-to-Viewport Transformation177

5.6 Efficiency179

5.7 Matrix Representation of 3D Transformations180

5.8 Composition of 3D Transformations183

5.9 Transformations as a Change in Coordinate System187

Exercises191

6 Viewing in 3D193

6.1 The Synthetic Camera and Steps In 3D Viewing193

6.2 Projections195

6.2.1 Perspective Projections197

6.2.2 Parallel Projections198

6.3 Specification of an Arbitrary 3D View201

6.4 Examples of 3D Viewing206

6.4.1 Perspective Projections207

6.4.2 Parallel Projections211

6.4.3 Finite View Volumes212

6.5 The Mathematics of Planar Geometric Projections213

6.6 Implementation of Planar Geometric Projections216

6.6.1 The Parallel Projection Case217

6.6.2 The Perspective Projection Case222

6.6.3 Clipping Against a Canonical View Volume in 3D227

6.6.4 Clipping in Homogeneous Coordinates229

6.6.5 Mapping into a Viewport231

6.6.6 Implementation Summary233

6.7 Coordinate Systems234

Exercises235

7 Object Hierarchy and Simple PHIGS （SPHIGS）239

7.1 Geometric Modeling240

7.1.1 Geometric Models242

7.1.2 Hierarchy in Geometric Models243

7.1.3 Relationship Among Model, Application Program, and Graphics System245

7.2 Characteristics of Retained-Mode Graphics Packages247

7.2.1 Central Structure Storage and Its Advantages247

7.2.2 Limitations of Retained-Mode Packages248

7.3 Defining and Displaying Structures249

7.3.1 Opening and Closing Structures249

7.3.2 Specifying Output Primitives and Their Attributes250

7.3.3 Posting Structures for Display Traversal253

7.3.4 Viewing253

7.3.5 Graphics Applications Sharing a Screen via Window Management256

7.4 Modeling Transformations257

7.5 Hierarchical Structure Networks262

7.5.1 Two-Level Hierarchy262

7.5.2 Simple Three-Level Hierarchy263

7.5.3 Bottom-Up Construction of the Robot265

7.5.4 Interactive Modeling Programs268

7.6 Matrix Composition in Display Traversal269

7.7 Appearance-Attribute Handling in Hierarchy273

7.7.1 Inheritance Rules273

7.7.2 SPHIGS Attributes and Text Unaffected by Transformations275

7.8 Screen Updating and Rendering Modes276

7.9 Structure Network Editing for Dynamic Effects277

7.9.1 Accessing Elements with Indices and Labels278

7.9.2 Intrastructure Editing Operations278

7.9.3 Instance Blocks for Editing Convenience279

7.9.4 Controlling Automatic Regeneration of the Screen Image281

7.10 Interaction282

7.10.1 Locator282

7.10.2 Pick Correlation282

7.11 Advanced Issues289

7.11.1 Additional Output Features289

7.11.2 Implementation Issues290

7.11.3 Optimizing Display of Hierarchical Models292

7.11.4 Limitations of Hierarchical Modeling in PHIGS292

7.11.5 Alternative Forms of Hierarchical Modeling293

7.11.6 Other （Industry） Standards293

SUMMARY294

Exercises295

8 Input Devices, Interaction Techniques, and Interaction Tasks297

8.1 Interaction Hardware298

8.1.1 Locator Devices299

8.1.2 Keyboard Devices300

8.1.3 Valuator Devices300

8.1.4 Choice Devices301

8.1.5 Other Devices301

8.1.6 3D Interaction Devices301

8.2 Basic Interaction Tasks304

8.2.1 The Position Interaction Task304

8.2.2 The Select Interaction Task—Variable-Sized Set of Choices305

8.2.3 The Select Interaction Task—Relatively Fixed-Sized Choice Set308

8.2.4 The Text Interaction Task311

8.2.5 The Quantify Interaction Task311

8.2.6 3D Interaction Tasks312

8.3 Composite Interaction Tasks314

8.3.1 Dialogue Boxes315

8.3.2 Construction Techniques315

8.3.3 Dynamic Manipulation316

8.4 Interaction-Technique Toolkits318

SUMMARY319

Exercises319

9 Representation of Curves and Surfaces321

9.1 Polygon Meshes323

9.1.1 Representing Polygon Meshes323

9.1.2 Plane Equations325

9.2 Parametric Cubic Curves328

9.2.1 Basic Characteristics329

9.2.2 Hermite Curves332

9.2.3 Bézier Curves336

9.2.4 Uniform Nonrational B-Splines342

9.2.5 Nonuniform, Nonrational B-Splines345

9.2.6 Nonuniform, Rational Cubic Polynomial Curve Segments348

9.2.7 Fitting Curves to Digitized Points348

9.2.8 Comparison of the Cubic Curves349

9.3 Parametric Bicubic Surfaces351

9.3.1 Hermite Surfaces351

9.3.2 Bézier Surfaces353

9.3.3 B-Spline Surfaces354

9.3.4 Normals to Surfaces354

9.3.5 Displaying Bicubic Surfaces355

9.4 Quadric Surfaces357

9.5 Specialized Modeling Techniques358

9.5.1 Fractal Models358

9.5.2 Grammar-Based Models363

SUMMARY366

Exercises367

10 Solid Modeling369

10.1 Representing Solids370

10.2 Regularized Boolean Set Operations371

10.3 Primitive Instancing375

10.4 Sweep Representations376

10.5 Boundary Representations377

10.5.1 Polyhedra and Euler’s Formula378

10.5.2 Boolean Set Operations380

10.6 Spatial-Partitioning Representations381

10.6.1 Cell Decomposition381

10.6.2 Spatial-Occupancy Enumeration382

10.6.3 Octrees383

10.6.4 Binary Space-Partitioning Trees386

10.7 Constructive Solid Geometry388

10.8 Comparison of Representations390

10.9 User Interfaces for Solid Modeling392

SUMMARY392

Exercises393

11 Achromatic and Colored Light395

11.1 Achromatic Light395

11.1.1 Selection of Intensities396

11.1.2 Halftone Approximation399

11.2 Chromatic Color402

11.2.1 Psychophysics403

11.2.2 The CIE Chromaticity Diagram406

11.3 Color Models for Raster Graphics410

11.3.1 The RGB Color Model410

11.3.2 The CMY Color Model411

11.3.3 The YIQ Color Model412

11.3.4 The HSV Color Model413

11.3.5 Interactive Specification of Color417

11.3.6 Interpolation in Color Space418

11.4 Use of Color in Computer Graphics418

SUMMARY421

Exercises421

12 The Quest for Visual Realism423

12.1 Why Realism?424

12.2 Fundamental Difficulties425

12.3 Rendering Techniques for Line Drawings427

12.3.1 Multiple Orthographic Views427

12.3.2 Perspective Projections428

12.3.3 Depth Cueing428

12.3.4 Depth Clipping429

12.3.5 Texture429

12.3.6 Color429

12.3.7 Visible-Line Determination429

12.4 Rendering Techniques for Shaded Images430

12.4.1 Visible-Surface Determination430

12.4.2 Illumination and Shading430

12.4.3 Interpolated Shading431

12.4.4 Material Properties431

12.4.5 Modeling Curved Surfaces432

12.4.6 Improved Illumination and Shading432

12.4.7 Texture432

12.4.8 Shadows432

12.4.9 Transparency and Reflection432

12.4.10 Improved Camera Models433

12.5 Improved Object Models433

12.6 Dynamics and Animation434

12.6.1 The Value of Motion434

12.6.2 Animation434

12.7 Stereopsis437

12.8 Improved Displays438

12.9 Interacting with Our Other Senses438

SUMMARY439

Exercises440

13 Visible-Surface Determination441

13.1 Techniques for Efficient Visible-Surface Algorithms443

13.1.1 Coherence443

13.1.2 The Perspective Transformation444

13.1.3 Extents and Bounding Volumes446

13.1.4 Back-Face Culling448

13.1.5 Spatial Partitioning449

13.1.6 Hierarchy450

13.2 The z-Buffer Algorithm451

13.3 Scan-Line Algorithms454

13.4 Visible-Surface Ray Tracing459

13.4.1 Computing Intersections460

13.4.2 Efficiency Considerations for Visible-Surface Ray Tracing462

13.5 Other Approaches465

13.5.1 List-Priority Algorithms465

13.5.2 Area-Subdivision Algorithms468

13.5.3 Algorithms for Curved Surfaces471

SUMMARY473

Exercises474

14 Illumination and Shading477

14.1 Illumination Models478

14.1.1 Ambient Light478

14.1.2 Diffuse Reflection479

14.1.3 Atmospheric Attenuation483

14.1.4 Specular Reflection484

14.1.5 Improving the Point-Light-Source Model487

14.1.6 Multiple Light Sources488

14.1.7 Physically Based illumination Models489

14.2 Shading Models for Polygons491

14.2.1 Constant Shading492

14.2.2 Interpolated Shading492

14.2.3 Polygon Mesh Shading493

14.2.4 Gouraud Shading494

14.2.5 Phong Shading495

14.2.6 Problems with Interpolated Shading496

14.3 Surface Detail498

14.3.1 Surface-Detail Polygons498

14.3.2 Texture Mapping498

14.3.3 Bump Mapping500

14.3.4 Other Approaches501

14.4 Shadows501

14.4.1 Scan-Line Generation of Shadows502

14.4.2 Shadow Volumes503

14.5 Transparency505

14.5.1 Non refractive Transparency505

14.5.2 Refractive Transparency507

14.6 Global Illumination Algorithms509

14.7 Recursive Ray Tracing510

14.8 Radiosity Methods514

14.8.1 The Radiosity Equation515

14.8.2 Computing Form Factors517

14.8.3 Progressive Refinement519

14.9 The Rendering Pipeline521

14.9.1 Local Illumination Pipelines521

14.9.2 Global Illumination Pipelines523

14.9.3 Progressive Refinement524

SUMMARY525

Exercises525

Bibliography527

Index545