Real-Time Rendering. Tomas Möller Eric Haines. A K Peters Natick, Massachusetts

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1 Real-Time Rendering Tomas Möller Eric Haines n A K Peters Natick, Massachusetts

2 Contents Preface 1 Introduction Contents Overview Notation and Definitions Mathematical Notation Geometrical Definitions 5 2 The Graphics Rendenng Pipeline Architecture The Application Stage The Geometry Stage Model and View Transform Lighting and Shading Projection Clipping Screen Mapping The Rasterizer Stage Through the Pipeline 20 3 Transforms Basic Transforms Translation Matrix Rotation Maurices Scaling Matrix Shearing Matrices Concatenation of Transforms The Rigid-Body Transform Normal Transform Computation of Inverses Special Matrix Transforms and Operations The Euler Transform 36 xiü vii

3 viii Contents Extracting Parameters from the Euler Transform Matrix Decomposition Rotation About an Arbitrary Axis Quaternions Mathematical Background Quaternion Transforms Interpolation Protections Orthographie Projection Perspective Projection 60 4 Visual Appearance Light Sources Material Lighting and Shading Diffuse Component Specular Component Ambient Component Lighting Equation Aliasing and Antialiasing Transparency, Alpha, and Compositing Fog Gamma Correction 93 5 Texturing Generalized Texturing Image Texturing ' Magnification Minification Texture Caching and Compression Multipass Rendering Multitexturing ' Texture Animation Texturing Methods Alpha Mapping Light Mapping Gloss Mapping Environment Mapping Bump Mapping Other Texturing Techniques 143

4 Contents ix 6 Special Effects The Rendenng Spectram Image-Based Rendenng Lens Flare and Bloom Billboarding Full-Screen Billboarding Particle Systems Fixed-View Effects Motion Blur Depth of Field Reflections Planar Reflections Glossy Effects Reflections from Curved Reflectors Shadows Planar Shadows Shadows on Curved Surfaces Lines Edge Highlighting Polygon Edge Rendering Hidden-Line Rendering Haloing Height-Field and Volume Rendering Speed-Up Techniques Culling Techniques Backface and Clustered Culling Hierarchical View-Frastum Culling Portal Culling Detail Culling Occlusion Culling Impostors Nailboards Hierarchical Image Caching Related Work Levels of Detail Discrete Geometry LODs Alpha LODs Geomorph LODs LOD Management Triangle Strips, Fans, and Meshes 231

5 x Contents Strips,,;, Fans Creating Strips Polygon Meshes Pipeline Optimization Locating the Bottleneck Testing the Application Stage Testing the Geometry Stage Testing the Rasterizer Stage Optimization Application Stage Geometry Stage Rasterizer Stage Overall Optimization Balancing the Graphics Pipeline Host and Accelerator Multiprocessing Multiprocessor Pipelining Parallel Processing Polygonal Techniques Sources of Three-Dimensional Data Tessellation Shading Problems., Edge Cracking and T-Vertices Consolidation Simplification Intersection Test Methods Defmitions Rules of Thumb Ray/Sphere Intersection Mathematical Solution Optimized Solution Ray/Box Intersection Slabs Method Woo's Method Ray/Triangle Intersection Intersection Algorithm Implementation 305

6 Contents xi 10.6 Ray/Polygon Intersection The Crossings Test Plane/Box Intersection Detection AABB OBB Triangle/Triangle Intersection Interval Overlap Method ERIT's Method Performance Comparison / Cube/Polygon Intersection General Algorithm BV/BV Intersection Tests Sphere/Box Intersection AABB/AABB Intersection fc-DOP/fc-DOPIntersection OBB/OBB Intersection View Frustrum Intersection Frustum/Sphere Intersection Frustum/Box Intersection Line/Line Intersection Tests Two Dimensions Three Dimensions Intersection Between Three Planes CoUision Detection CoUision Detection with Rays General Hierarchical CoUision Detection Hierarchy Building CoUision Testing between Hierarchies Cost Function OBBTree fc-doptree A Multiple Objects CD System The First-Level CD Summary Graphics Hardware Buffers and Buffering A Simple Display System The Color Buffer Z-buffering and W-buffering 368

7 XII Contents Single, Double, and Triple Buffering Stereo Buffers Stencil and Accumulation Buffering Memory Architecture General Case Study: Neon Case Study: VISUALIZE fx..., Case Study: InfiniteReality Other Architectures The Fnture Everything Else You 391 A Some Linear Algebra 395 A.l The Euclidean Space 396 A.2 Geometrical Interpretation 398 A.3 Matrices 403 A.3.1 Definitions and Operations 403 A.3.2 Change of Base 410 A.4 Homogeneous Notation 411 A.5 Geometry 412 A.5.1 Lines 412 A.5.2 Planes. 414 A.5.3 Convex Hüll 415 A.5.4 Miscellaneous 416 B Trigonometry 419 B.l Definitions 419 B.2 Trigonometrie Laws and Formulae 421 References 427 Index 463

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