book

Fundamentals of Computer Graphics, 4th Edition

by Steve Marschner, Peter Shirley

October 2018

Beginner

734 pages

22h 15m

English

A K Peters/CRC Press

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Preliminaries
Preface
About the CoverOnline ResourcesAcknowledgments
Chapter 1 Introduction
1.1 Graphics Areas1.2 Major Applications1.3 Graphics APIs1.4 Graphics Pipeline1.5 Numerical Issues1.6 Efficiency1.7 Designing and Coding Graphics Programs1.7.1 Class Design1.7.2 Float vs. Double1.7.3 Debugging Graphics ProgramsThe Scientific MethodImages as Coded Debugging OutputUsing a DebuggerData Visualization for DebuggingNotes
Chapter 2 Miscellaneous Math
2.1 Sets and Mappings2.1.1 Inverse Mappings2.1.2 Intervals2.1.3 Logarithms2.2 Solving Quadratic Equations2.3 Trigonometry2.3.1 Angles2.3.2 Trigonometric Functions2.3.3 Useful Identities2.4 Vectors2.4.1 Vector Operations2.4.2 Cartesian Coordinates of a Vector2.4.3 Dot Product2.4.4 Cross Product2.4.5 Orthonormal Bases and Coordinate Frames2.4.6 Constructing a Basis from a Single Vector2.4.7 Constructing a Basis from Two Vectors2.4.8 Squaring Up a Basis2.5 Curves and Surfaces2.5.1 2D Implicit Curves2.5.2 The 2D GradientImplicit 2D LinesImplicit Quadric Curves2.5.3 3D Implicit Surfaces2.5.4 Surface Normal to an Implicit Surface2.5.5 Implicit Planes3D Quadric Surfaces3D Curves from Implicit Surfaces2.5.6 2D Parametric Curves2D Parametric Lines2D Parametric Circles2.5.7 3D Parametric Curves3D Parametric Lines2.5.8 3D Parametric Surfaces2.5.9 Summary of Curves and Surfaces2.6 Linear Interpolation2.7 Triangles2.7.1 2D Triangles2.7.2 3D TrianglesFrequently Asked QuestionsNotesExercisesFigure 2.1Figure 2.2Figure 2.3Figure 2.4Figure 2.5Figure 2.6Figure 2.7Figure 2.8Figure 2.9Figure 2.10Figure 2.11Figure 2.12Figure 2.13Figure 2.14Figure 2.15Figure 2.16Figure 2.17Figure 2.18Figure 2.19Figure 2.20Figure 2.21Figure 2.22Figure 2.23Figure 2.24Figure 2.25Figure 2.26Figure 2.27Figure 2.28Figure 2.29Figure 2.30Figure 2.31Figure 2.32Figure 2.33Figure 2.34Figure 2.35Figure 2.36Figure 2.37Figure 2.38Figure 2.39Figure 2.40
Chapter 3 Raster Images
3.1 Raster Devices3.1.1 Displays3.1.2 Hardcopy Devices3.1.3 Input Devices3.2 Images, Pixels, and Geometry3.2.1 Pixel Values3.2.2 Monitor Intensities and Gamma3.3 RGB Color3.4 Alpha Compositing3.4.1 Image StorageFrequently Asked QuestionsExerciseFigure 3.1Figure 3.2Figure 3.3Figure 3.4Figure 3.5Figure 3.6Figure 3.7Figure 3.8Figure 3.9Figure 3.10Figure 3.11Figure 3.12Figure 3.13Figure 3.14
Chapter 4 Ray Tracing
4.1 The Basic Ray-Tracing Algorithm4.2 Perspective4.3 Computing Viewing Rays4.3.1 Orthographic Views4.3.2 Perspective Views4.4 Ray-Object Intersection4.4.1 Ray-Sphere Intersection4.4.2 Ray-Triangle Intersection4.4.3 Ray-Polygon Intersection4.4.4 Intersecting a Group of Objects4.5 Shading4.5.1 Lambertian Shading4.5.2 Blinn-Phong Shading4.5.3 Ambient Shading4.5.4 Multiple Point Lights4.6 A Ray-Tracing Program4.6.1 Object-Oriented Design for a Ray-Tracing Program4.7 Shadows4.8 Ideal Specular Reflection4.9 Historical NotesFrequently Asked QuestionsExercisesFigure 4.1Figure 4.2Figure 4.3Figure 4.4Figure 4.5Figure 4.6Figure 4.7Figure 4.8Figure 4.9Figure 4.10Figure 4.11Figure 4.12Figure 4.13Figure 4.14Figure 4.15Figure 4.16Figure 4.17Figure 4.18Figure 4.19Figure 4.20
Chapter 5 Linear Algebra
5.1 Determinants5.2 Matrices5.2.1 Matrix Arithmetic5.2.2 Operations on Matrices5.2.3 Vector Operations in Matrix Form5.2.4 Special Types of Matrices5.3 Computing with Matrices and Determinants5.3.1 Computing Inverses5.3.2 Linear Systems5.4 Eigenvalues and Matrix Diagonalization5.4.1 Singular Value DecompositionFrequently Asked QuestionsNotesExercisesFigure 5.1Figure 5.2Figure 5.3Figure 5.4Figure 5.5Figure 5.6Figure 5.7Figure 5.8
Chapter 6 Transformation Matrices
6.1 2D Linear Transformations6.1.1 Scaling6.1.2 Shearing6.1.3 Rotation6.1.4 Reflection6.1.5 Composition and Decomposition of Transformations6.1.6 Decomposition of TransformationsSymmetric Eigenvalue DecompositionSingular Value DecompositionPaeth Decomposition of Rotations6.2 3D Linear Transformations6.2.1 Arbitrary 3D Rotations6.2.2 Transforming Normal Vectors6.3 Translation and Affine Transformations6.4 Inverses of Transformation Matrices6.5 Coordinate TransformationsFrequently Asked QuestionsNotesExercisesFigure 6.1Figure 6.2Figure 6.3Figure 6.4Figure 6.5Figure 6.6Figure 6.7Figure 6.8Figure 6.9Figure 6.10Figure 6.11Figure 6.13Figure 6.14Figure 6.15Figure 6.12Figure 6.16Figure 6.17Figure 6.18Figure 6.19Figure 6.20
Chapter 7 Viewing
7.1 Viewing Transformations7.1.1 The Viewport Transformation7.1.2 The Orthographic Projection Transformation7.1.3 The Camera Transformation7.2 Projective Transformations7.3 Perspective Projection7.4 Some Properties of the Perspective Transform7.5 Field-of-ViewFrequently Asked QuestionsNotesExercisesFigure 7.1Figure 7.2Figure 7.3Figure 7.4Figure 7.5Figure 7.6Figure 7.7Figure 7.8Figure 7.9Figure 7.10Figure 7.11Figure 7.12Figure 7.13Figure 7.14
Chapter 8 The Graphics Pipeline
8.1 Rasterization8.1.1 Line DrawingLine Drawing Using Implicit Line Equations8.1.2 Triangle RasterizationDealing with Pixels on Triangle Edges8.1.3 Clipping8.1.4 Clipping Before the Transform (Option 1)8.1.5 Clipping in Homogeneous Coordinates (Option 2)8.1.6 Clipping against a Plane8.2 Operations Before and After Rasterization8.2.1 Simple 2D Drawing8.2.2 A Minimal 3D Pipeline8.2.3 Using a z-Buffer for Hidden SurfacesPrecision Issues8.2.4 Per-vertex Shading8.2.5 Per-fragment Shading8.2.6 Texture Mapping8.2.7 Shading Frequency8.3 Simple Antialiasing8.4 Culling Primitives for Efficiency8.4.1 View Volume Culling8.4.2 Backface CullingFrequently Asked QuestionsNotesExercisesFigure 8.1Figure 8.2Figure 8.3Figure 8.4Figure 8.5Figure 8.6Figure 8.7Figure 8.8Figure 8.9Figure 8.10Figure 8.11Figure 8.12Figure 8.13Figure 8.14Figure 8.15

Chapter 9 Signal Processing
9.1 Digital Audio: Sampling in 1D9.1.1 Sampling Artifacts and Aliasing9.2 Convolution9.2.1 Moving Averages9.2.2 Discrete ConvolutionConvolution FiltersProperties of Convolution9.2.3 Convolution as a Sum of Shifted Filters9.2.4 Convolution with Continuous FunctionsThe Dirac Delta Function9.2.5 Discrete-Continuous Convolution9.2.6 Convolution in More Than One Dimension9.3 Convolution Filters9.3.1 A Gallery of Convolution FiltersThe Box FilterThe Tent FilterThe Gaussian FilterThe B-Spline Cubic FilterThe Catmull-Rom Cubic FilterThe Mitchell-Netravali Cubic Filter9.3.2 Properties of FiltersSeparable Filters9.4 Signal Processing for Images9.4.1 Image Filtering Using Discrete Filters9.4.2 Antialiasing in Image Sampling9.4.3 Reconstruction and Resampling9.5 Sampling Theory9.5.1 The Fourier Transform9.5.2 Convolution and the Fourier Transform9.5.3 A Gallery of Fourier Transforms9.5.4 Dirac Impulses in Sampling Theory9.5.5 Sampling and AliasingPreventing Aliasing in SamplingPreventing Aliasing in ReconstructionPreventing Aliasing in Resampling9.5.6 Ideal Filters vs. Useful FiltersExercisesFigure 9.1Figure 9.2Figure 9.3Figure 9.4Figure 9.5Figure 9.6Figure 9.7Figure 9.8Figure 9.9Figure 9.10Figure 9.11Figure 9.12Figure 9.13Figure 9.14Figure 9.15Figure 9.16Figure 9.17Figure 9.18Figure 9.19Figure 9.20Figure 9.21Figure 9.22Figure 9.23Figure 9.24Figure 9.25Figure 9.26Figure 9.27Figure 9.28Figure 9.29Figure 9.30Figure 9.31Figure 9.32Figure 9.33Figure 9.34Figure 9.35Figure 9.36Figure 9.37Figure 9.38Figure 9.39Figure 9.40Figure 9.41Figure 9.42Figure 9.43Figure 9.44Figure 9.45Figure 9.46Figure 9.47Figure 9.48Figure 9.49Figure 9.50Figure 9.51Figure 9.52Figure 9.53
Chapter 10 Surface Shading
10.1 Diffuse Shading10.1.1 Lambertian Shading Model10.1.2 Ambient Shading10.1.3 Vertex-Based Diffuse Shading10.2 Phong Shading10.2.1 Phong Lighting Model10.2.2 Surface Normal Vector Interpolation10.3 Artistic Shading10.3.1 Line Drawing10.3.2 Cool-to-Warm ShadingFrequently Asked QuestionsExercisesFigure 10.1Figure 10.2Figure 10.3Figure 10.4Figure 10.5Figure 10.6Figure 10.7Figure 10.8Figure 10.9
Chapter 11 Texture Mapping
11.1 Looking Up Texture Values11.2 Texture Coordinate Functions11.2.1 Geometrically Determined CoordinatesPlanar ProjectionSpherical CoordinatesCylindrical CoordinatesCubemaps11.2.2 Interpolated Texture Coordinates11.2.3 Tiling, Wrapping Modes, and Texture Transformations11.2.4 Perspective Correct Interpolation11.2.5 Continuity and Seams11.3 Antialiasing Texture Lookups11.3.1 The Footprint of a Pixel11.3.2 Reconstruction11.3.3 Mipmapping11.3.4 Basic Texture Filtering with Mipmaps11.3.5 Anisotropic Filtering11.4 Applications of Texture Mapping11.4.1 Controlling Shading Parameters11.4.2 Normal Maps and Bump Maps11.4.3 Displacement Maps11.4.4 Shadow Maps11.4.5 Environment Maps11.5 Procedural 3D Textures11.5.1 3D Stripe Textures11.5.2 Solid Noise11.5.3 TurbulenceFrequently Asked QuestionsNotesExercisesFigure 11.1Figure 11.2Figure 11.3Figure 11.4Figure 11.5Figure 11.6Figure 11.7Figure 11.8Figure 11.9Figure 11.10Figure 11.11Figure 11.12Figure 11.13Figure 11.14Figure 11.15Figure 11.16Figure 11.17Figure 11.18Figure 11.19Figure 11.20Figure 11.21Figure 11.22Figure 11.23Figure 11.24Figure 11.25Figure 11.26Figure 11.27Figure 11.28Figure 11.29Figure 11.30
Chapter 12 Data Structures for Graphics
12.1 Triangle Meshes12.1.1 Mesh Topology12.1.2 Indexed Mesh Storage12.1.3 Triangle Strips and Fans12.1.4 Data Structures for Mesh ConnectivityThe Triangle-Neighbor StructureThe Winged-Edge StructureThe Half-Edge Structure12.2 Scene Graphs12.3 Spatial Data Structures12.3.1 Bounding Boxes12.3.2 Hierarchical Bounding Boxes12.3.3 Uniform Spatial Subdivision12.3.4 Axis-Aligned Binary Space Partitioning12.4 BSP Trees for Visibility12.4.1 Overview of BSP Tree Algorithm12.4.2 Building the Tree12.4.3 Cutting Triangles12.4.4 Optimizing the Tree12.5 Tiling Multidimensional Arrays12.5.1 One-Level Tiling for 2D Arrays12.5.2 Example: Two-Level Tiling for 3D ArraysFrequently Asked QuestionsNotesExercisesFigure 12.1Figure 12.2Figure 12.3Figure 12.4Figure 12.5Figure 12.6Figure 12.7Figure 12.8Figure 12.9Figure 12.10Figure 12.11Figure 12.12Figure 12.13Figure 12.14Figure 12.15Figure 12.16Figure 12.17Figure 12.18Figure 12.19Figure 12.20Figure 12.21Figure 12.22Figure 12.23Figure 12.24Figure 12.25Figure 12.26Figure 12.27Figure 12.28Figure 12.29Figure 12.30Figure 12.31Figure 12.32Figure 12.33Figure 12.34Figure 12.35Figure 12.36Figure 12.37Figure 12.38Figure 12.39Figure 12.40Figure 12.41Figure 12.42
Chapter 13 More Ray Tracing
13.1 Transparency and Refraction13.2 Instancing13.3 Constructive Solid Geometry13.4 Distribution Ray Tracing13.4.1 Antialiasing13.4.2 Soft Shadows13.4.3 Depth of Field13.4.4 Glossy Reflection13.4.5 Motion BlurNotesFrequently Asked QuestionsFigure 13.1Figure 13.2Figure 13.3Figure 13.4Figure 13.5Figure 13.6Figure 13.7Figure 13.8Figure 13.9Figure 13.10Figure 13.11Figure 13.12Figure 13.13Figure 13.14Figure 13.15Figure 13.16Figure 13.17Figure 13.18Figure 13.19
Chapter 14 Sampling
14.1 Integration14.1.1 Measures and Averages14.1.2 Example: Measures on the Lines in the 2D Plane14.1.3 Example: Measure of Lines in 3D14.2 Continuous Probability14.2.1 One-Dimensional Continuous Probability Density Functions14.2.2 One-Dimensional Expected Value14.2.3 Multidimensional Random Variables14.2.4 Variance14.2.5 Estimated Means14.3 Monte Carlo Integration14.3.1 Quasi—Monte Carlo Integration14.4 Choosing Random Points14.4.1 Function Inversion14.4.2 Rejection14.4.3 Metropolis14.4.4 Example: Choosing Random Lines in the SquareFrequently Asked QuestionsNotesExercisesFigure 14.1Figure 14.2Figure 14.3Figure 14.4Figure 14.5Figure 14.6Figure 14.7Figure 14.8Figure 14.9Figure 14.10Table 14.1
Chapter 15 Curves
15.1 Curves15.1.1 Parameterizations and Reparameterizations15.1.2 Piecewise Parametric Representations15.1.3 Splines15.2 Curve Properties15.2.1 Continuity15.3 Polynomial Pieces15.3.1 Polynomial Notation15.3.2 A Line SegmentMatrix Form for Polynomials15.3.3 Beyond Line Segments15.3.4 Basis Matrices for Cubics15.3.5 Blending Functions15.3.6 Interpolating Polynomials15.4 Putting Pieces Together15.4.1 Knots15.4.2 Using Independent Pieces15.4.3 Putting Segments Together15.5 Cubics15.5.1 Natural Cubics15.5.2 Hermite Cubics15.5.3 Cardinal Cubics15.6 Approximating Curves15.6.1 Bézier CurvesGeometric Intuition for Bézier CurvesThe de Casteljau Algorithm15.6.2 B-SplinesUniform Linear B-SplinesUniform Quadratic B-SplinesUniform Cubic B-Splines15.6.3 Nonuniform B-SplinesRepeated Knots and B-Spline Interpolation15.6.4 NURBS15.7 SummaryNotes15.7.1 ExercisesFigure 15.1Figure 15.2Figure 15.3Figure 15.4Figure 15.5Figure 15.6Figure 15.7Figure 15.8Figure 15.9Figure 15.10Figure 15.11Figure 15.12Figure 15.13Figure 15.14Figure 15.15Figure 15.16Figure 15.17Figure 15.18Figure 15.19Figure 15.20Figure 15.21Figure 15.22Figure 15.23Figure 15.24Figure 15.25
Chapter 16 Computer Animation
16.1 Principles of Animation16.1.1 Timing16.1.2 Action Layout16.1.3 Animation Techniques16.1.4 Animator Control vs. Automatic Methods16.2 Keyframing16.2.1. Motion Controls16.2.2 Interpolating Rotation16.3 Deformations16.4 Character Animation16.4.1 Facial Animation16.4.2 Motion Capture16.5 Physics-Based Animation16.6 Procedural Techniques16.7 Groups of ObjectsNotesFigure 16.1Figure 16.2Figure 16.3Figure 16.4Figure 16.5Figure 16.6Figure 16.7Figure 16.8Figure 16.9Figure 16.10Figure 16.11Figure 16.12Figure 16.13Figure 16.14Figure 16.15Figure 16.16Figure 16.17Figure 16.18Figure 16.19Figure 16.20Figure 16.21Figure 16.22Figure 16.23Figure 16.24Figure 16.25Figure 16.26Figure 16.27Figure 16.28Figure 16.29
Chapter 17 Using Graphics Hardware
17.1 Hardware Overview17.2 What Is Graphics Hardware17.3 Heterogeneous Multiprocessing17.3.1 Programming with OpenGL17.4 Graphics Hardware Programming: Buffers, State, and Shaders17.4.1 Buffers17.4.2 Display Buffer17.4.3 Cycle of Refresh17.5 State Machine17.6 Basic OpenGL Application Layout17.7 Geometry17.7.1 Describing Geometry for the Hardware17.8 A First Look at Shaders17.8.1 Vertex Shader Example17.8.2 Fragment Shader Example17.8.3 Loading, Compiling, and Using Shaders17.9 Vertex Buffer Objects17.10 Vertex Array Objects17.11 Transformation Matrices17.11.1 GLM17.11.2 Using an Orthographic Projection17.12 Shading with Per-Vertex Attributes17.12.1 Structs of Vertex Data17.13 Shading in the Fragment Processor17.13.1 Blinn-Phong Shader Program: Vertex Shader17.13.2 Blinn-Phong Shader Program: Fragment Shader17.13.3 A Normal Shader17.14 Meshes and Instancing17.14.1 Instancing Models17.15 Texture Objects17.15.1 Texture Lookup in Shaders17.16 Object-Oriented Design for Graphics Hardware Programming17.17 Continued LearningFrequently Asked QuestionsNotesExercisesFigure 17.1Figure 17.2Figure 17.3Figure 17.4Figure 17.5Figure 17.6Figure 17.7Figure 17.8Figure 17.9Figure 17.10Figure 17.11Figure 17.12Figure 17.13Figure 17.14
Chapter 18 Light
18.1 Radiometry18.1.1 Photons18.1.2 Spectral Energy18.1.3 Power18.1.4 Irradiance18.1.5 RadianceRadiance and Other Radiometric Quantities18.1.6 BRDFDirectional Hemispherical ReflectanceIdeal Diffuse BRDF18.2 Transport Equation18.3 PhotometryFrequently Asked QuestionsNotesExercisesFigure 18.1Figure 18.2Figure 18.3Figure 18.4Figure 18.5Figure 18.6Figure 18.7Figure 18.8
Chapter 19 Color
19.1 Colorimetry19.1.1 Grassmann’s Laws19.1.2 Cone Responses19.1.3 Color Matching Experiments19.1.4 Standard Observers19.1.5 Chromaticity Coordinates19.2 Color Spaces19.2.1 Constructing a Matrix Transform19.2.2 Device-Dependent RGB Spaces19.2.3 LMS Cone Space19.2.4 CIE 1976 L*a*b*19.3 Chromatic Adaptation19.4 Color AppearanceNotesFigure 19.1Figure 19.2Figure 19.3Figure 19.4Figure 19.5Figure 19.6Figure 19.7Figure 19.8Figure 19.9Figure 19.10Table 19.1Table 19.2
Chapter 20 Visual Perception
20.1 Vision Science20.2 Visual Sensitivity20.2.1 Brightness and Contrast20.2.2 Color20.2.3 Dynamic Range20.2.4 Field-of-View and Acuity20.2.5 Motion20.3 Spatial Vision20.3.1 Frames of Reference and Measurement Scales20.3.2 Ocularmotor Cues20.3.3 Binocular Disparity20.3.4 Motion Cues20.3.5 Pictorial Cues20.4 Objects, Locations, and Events20.4.1 Object Recognition20.4.2 Size and Distance20.4.3 Events20.5 Picture PerceptionFigure 20.1Figure 20.2Figure 20.3Figure 20.4Figure 20.5Figure 20.6Figure 20.7Figure 20.8Figure 20.9Figure 20.10Figure 20.11Figure 20.12Figure 20.13Figure 20.14Figure 20.15Figure 20.16Figure 20.17Figure 20.18Figure 20.19Figure 20.20Figure 20.21Figure 20.22Figure 20.23Figure 20.24Figure 20.25Figure 20.26Figure 20.27Figure 20.28Figure 20.29Figure 20.30Figure 20.31Figure 20.32Figure 20.33Figure 20.34Figure 20.35Figure 20.36Figure 20.37Figure 20.38Figure 20.39Figure 20.40Figure 20.41Figure 20.42Figure 20.43Figure 20.44Figure 20.45Figure 20.46Table 20.1
Chapter 21 Tone Reproduction
21.1 Classification21.2 Dynamic Range21.3 Color21.4 Image Formation21.5 Frequency-Based Operators21.6 Gradient-Domain Operators21.7 Spatial Operators21.8 Division21.9 Sigmoids21.10 Other Approaches21.11 Night Tonemapping21.12 DiscussionFigure 21.1Figure 21.2Figure 21.3Figure 21.4Figure 21.5Figure 21.6Figure 21.7Figure 21.8Figure 21.9Figure 21.10Figure 21.11Figure 21.12Figure 21.13Figure 21.14Figure 21.15Figure 21.16Figure 21.17Figure 21.18Figure 21.19Figure 21.20Figure 21.21Figure 21.22Figure 21.23Figure 21.24Figure 21.25Figure 21.26Figure 21.27Figure 21.28Figure 21.29Figure 21.30Figure 21.31
Chapter 22 Implicit Modeling
22.1 Implicit Functions, Skeletal Primitives, and Summation Blending22.1.1 C1 Continuity and the Gradient22.1.2 Distance Fields, R-Functions, and F-Reps22.1.3 Level Sets22.1.4 Variational Implicit Surfaces22.1.5 Convolution Surfaces22.1.6 Defining Skeletal Primitives22.2 Rendering22.3 Space Partitioning22.3.1 Exhaustive Search22.3.2 Algorithm DescriptionData Structures22.3.3 Polygonization AlgorithmFinding Cube-Surface Intersections22.3.4 Sampling ProblemsSubdividing a Cube22.3.5 Cell Polygonization22.4 More on Blending22.5 Constructive Solid Geometry22.6 Warping22.6.1 Twist22.6.2 Taper22.6.3 Bend22.7 Precise Contact Modeling22.8 The BlobTree22.8.1 Traversing the BlobTree22.9 Interactive Implicit Modeling SystemsExercisesFigure 22.1Figure 22.2Figure 22.3Figure 22.4Figure 22.5Figure 22.6Figure 22.7Figure 22.8Figure 22.9Figure 22.10Figure 22.11Figure 22.12Figure 22.13Figure 22.14Figure 22.15Figure 22.16Figure 22.17Figure 22.18Figure 22.19Figure 22.20Figure 22.21Figure 22.22Figure 22.23Figure 22.24Figure 22.25Figure 22.26Figure 22.27Figure 22.28Figure 22.29Figure 22.30Figure 22.31
Chapter 23 Global Illumination
23.1 Particle Tracing for Lambertian Scenes23.2 Path Tracing23.3 Accurate Direct Lighting23.3.1 Mathematical Framework23.3.2 Sampling a Spherical Luminaire23.3.3 Nondiffuse LuminariesFrequently Asked QuestionsNotesExercisesFigure 23.1Figure 23.2Figure 23.3Figure 23.4Figure 23.5Figure 23.6Figure 23.7Figure 23.8Figure 23.9
Chapter 24 Reflection Models
24.1 Real-World Materials24.1.1 smooth Dielectrics and Metals24.1.2 Rough Surfaces24.1.3 Diffuse Materials24.1.4 Translucent Materials24.1.5 Layered Materials24.2 Implementing Reflection Models24.3 Specular Reflection Models24.4 smooth-Layered Model24.5 Rough-Layered Model24.5.1 Anisotropic Specular BRDF24.5.2 Diffuse Term for the Anisotropic Phong Model24.5.3 Implementing the ModelFrequently Asked QuestionsNotesExercisesFigure 24.1Figure 24.2Figure 24.3Figure 24.4Figure 24.5Figure 24.6Figure 24.7Figure 24.8
Chapter 25 Computer Graphics in Games
25.1 Platforms25.2 Limited Resources25.2.1 Processing Time25.2.2 Storage25.2.3 Development Resources25.3 Optimization Techniques25.4 Game Types25.5 The Game Production Process25.5.1 Asset CreationInitial ModelingTexturingShadingLightingAnimationNotesExercisesFigure 25.1Figure 25.2Figure 25.3Figure 25.4Figure 25.5Figure 25.6Figure 25.7Figure 25.8Figure 25.9Figure 25.10Figure 25.11Figure 25.12Figure 25.13Figure 25.14Figure 25.15
Chapter 26 Visualization
26.1 Background26.1.1 History26.1.2 Resource Limitations26.2 Data Types26.2.1 Dimension and Item Count26.2.2 Data Transformation and Derived Dimensions26.3 Human-Centered Design Process26.3.1 Task Characterization26.3.2 Abstraction26.3.3 Technique and Algorithm Design26.3.4 Validation26.4 Visual Encoding Principles26.4.1 Visual Channel Characteristics26.4.2 Color26.4.3 2D vs. 3D Spatial Layouts26.4.4 Text Labels26.5 Interaction Principles26.5.1 Overview First, Zoom and Filter, Details on Demand26.5.2 Interactivity Costs26.5.3 Animation26.6 Composite and Adjacent Views26.6.1 Single Drawing26.6.2 Superimposing and Layering26.6.3 Glyphs26.6.4 Multiple Views26.7 Data Reduction26.7.1 Overviews and Aggregation26.7.2 Filtering and Navigation26.7.3 Focus+Context26.7.4 Dimensionality Reduction26.8 Examples26.8.1 Tables26.8.2 Graphs26.8.3 Trees26.8.4 Geographic26.8.5 Spatial FieldsFrequently Asked QuestionsFigure 26.1Figure 26.2Figure 26.3Figure 26.4Figure 26.5Figure 26.6Figure 26.7Figure 26.8Figure 26.9Figure 26.10Figure 26.11Figure 26.12Figure 26.13Figure 26.14Figure 26.15Figure 26.16Figure 26.17Figure 26.18Figure 26.19Figure 26.20Figure 26.21Figure 26.22Figure 26.23Figure 26.24Figure 26.25Figure 26.26
References

Content preview from Fundamentals of Computer Graphics, 4th Edition

Chapter 6

Transformation Matrices

The machinery of linear algebra can be used to express many of the operations required to arrange objects in a 3D scene, view them with cameras, and get them onto the screen. Geometric transformations like rotation, translation, scaling, and projection can be accomplished with matrix multiplication, and the transformation matrices used to do this are the subject of this chapter.

We will show how a set of points transforms if the points are represented as offset vectors from the origin, and we will use the clock shown in Figure 6.1 as an example of a point set. So think of the clock as a bunch of points that are the ends of vectors whose tails are at the origin. We also discuss how these transforms operate differently ...

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Fundamentals of Computer Graphics, 3rd Edition

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Fundamentals of Computer Graphics, 4th Edition

by Steve Marschner, Peter Shirley

Transformation Matrices

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