5 Linear Algebra Determinants Matrices...121

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1 Preface xi 1 Introduction Graphics Areas MajorApplications Graphics APIs D Geometric Models Graphics Pipeline NumericalIssues Efficiency Software Engineering Miscellaneous Math Sets and Mappings Solving Quadratic Equations Trigonometry Vectors DImplicitCurves DParametricCurves D Implicit Surfaces DParametricCurves v

2 vi 2.9 3D Parametric Surfaces Linear Interpolation Triangles Raster Algorithms RasterDisplays Monitor Intensities and Gamma RGBColor The Alpha Channel LineDrawing Triangle Rasterization SimpleAntialiasing ImageCaptureandStorage Signal Processing DigitalAudio:Samplingin1D Convolution Convolution Filters Signal Processing for Images Sampling Theory Linear Algebra Determinants Matrices Transformation Matrices Basic2DTransforms Basic3DTransforms Translation InversesofTransformationMatrices CoordinateTransformations Viewing Drawing the Canonical View Volume Orthographic Projection Perspective Projection Some Properties of the Perspective Transform Field-of-View...173

3 vii 8 Hidden Surface Elimination BSPTree Z-Buffer Surface Shading Diffuse Shading Phong Shading Artistic Shading Ray Tracing TheBasicRay-TracingAlgorithm ComputingViewingRays Ray-ObjectIntersection ARay-TracingProgram Shadows Specular Reflection Refraction Instancing Sub-Linear Ray-Object Intersection ConstructiveSolidGeometry DistributionRayTracing Texture Mapping D Texture Mapping D Texture Mapping Tessellated Models Texture Mapping for Rasterized Triangles BumpTextures Displacement Mapping EnvironmentMaps Shadow Maps A Full Graphics Pipeline Clipping LocationofClippingSegmentofthePipeline An Expanded Graphics Pipeline Backface Elimination Triangle Strips and Fans PreservedState A Full Graphics Pipeline...267

4 viii 13 Data Structures for Graphics Triangle Meshes Winged-Edge Data Structure Scene Graphs Tiling Multidimensional Arrays Sampling Integration Continuous Probability MonteCarloIntegration Choosing Random Points Curves Curves Curve Properties Polynomial Pieces Putting Pieces Together Cubics ApproximatingCurves Summary Computer Animation PrinciplesofAnimation Keyframing Deformations CharacterAnimation Physics-BasedAnimation Procedural Techniques Groups of Objects Notes Using Graphics Hardware What is Graphics Hardware DescribingGeometryfortheHardware ProcessingGeometryintoPixels Building Interactive Graphics Applications The Ball Shooting Program Programming Models The Modelview-Controller Architecture

5 ix 18.4 ExampleImplementations ApplyingOurResults Notes Exercises Light Radiometry TransportEquation Photometry Color LightandLightDetectors Tristimulus Color Theory CIETristimulusValues Chromaticity Scotopic Luminance RGBMonitors ApproximateColorManipulation Opponent Color Spaces Visual Perception Vision Science Visual Sensitivity SpatialVision Objects,Locations,andEvents PicturePerception Tone Reproduction Classification Dynamic Range Color ImageFormation Frequency-Based Operators Gradient-DomainOperators SpatialOperators Division Sigmoids Other Approaches Night Tonemapping Discussion...544

6 x 23 Global Illumination Particle Tracing for Lambertian Scenes PathTracing Accurate Direct Lighting Reflection Models Real-WorldMaterials Implementing Reflection Models Specular Reflection Models Smooth Layered Model Rough Layered Model Image-Based Rendering TheLightField Creating a Novel Image from a Set of Images Visualization D Scalar Fields D Scalar Fields References 595 Index 613