• Graphics Areas
• Major Applications
• Graphics APIs
• Graphics Pipeline
• Numerical Issues
• Efficiency
• Designing and Coding Graphics

Math

• Sets and Mappings
• Solving Quadratic Equations
• Trigonometry
• Vectors
• Curves and Surfaces
• Linear Interpolation
• Triangles

Raster Images

• Raster Devices
• Images, Pixels, and Geometry
• RGB Color
• Alpha Compositing

Ray Tracing

• Basic Ray-Tracing Algorithm
• Perspective
• Computing Viewing Rays
• Ray-Object Intersection
• Shading
• A Ray-Tracing Program
• Shadows
• Ideal Specular Reflection

Transformation Matrices

• 2D Linear Transformations
• 3D Linear Transformations
• Translation and Affine Transformations
• Inverses of Transformation Matrices
• Coordinate Transformations

Viewing

• Viewing Transformations
• Projective Transformations
• Perspective Projection
• Some Properties of the Perspective Transform
• Field-of-View

The Graphics Pipeline

• Rasterization
• Operations Before and After Rasterization
• Simple Antialiasing
• Culling Primitives for Efficiency

Signal Processing

• Digital Audio: Sampling in 1D
• Convolution
• Convolution Filters
• Signal Processing for Images
• Sampling Theory

Surface Shading

• Diffuse Shading
• Phong Shading
• Artistic Shading

Texture Mapping

• Looking Up Texture Values
• Texture Coordinate Functions
• Antialiasing Texture Lookups
• Applications of Texture Mapping
• Procedural 3D Textures

Data Structures for Graphics

• Triangle Meshes
• Scene Graphs
• Spatial Data Structures
• BSP Trees for Visibility
• Tiling Multidimensional Arrays

More Ray Tracing

• Transparency and Refraction
• Instancing
• Constructive Solid Geometry
• Distribution Ray Tracing

Sampling

• Integration
• Continuous Probability
• Monte Carlo Integration
• Choosing Random Points

• Curve Properties
• Polynomial Pieces
• Putting Pieces Together
• Cubics
• Approximating Curves

Computer Animation

• Principles of Animation
• Keyframing
• Deformations
• Character Animation
• Physics-Based Animation
• Procedural Techniques
• Groups of Objects

Using Graphics Hardware

• What Is Graphics Hardware
• Heterogeneous Multiprocessing
• Graphics Hardware Programming
• State Machine
• Basic OpenGL Application Layout
• First Look at Shaders
• Vertex Buffer Objects
• Vertex Array Objects
• Transformation Matrices
• Shading with Per-Vertex Attributes
• Shading in the Fragment Processor
• Meshes and Instancing
• Texture Objects
• Object-Oriented Design

Light

• Radiometry
• Transport Equation
• Photometry

Color

• Colorimetry
• Color Spaces
• Chromatic Adaptation
• Color Appearance

Visual Perception

• Visual Sensitivity
• Spatial Vision
• Objects, Locations, and Events
• Picture Perception

Tone Reproduction

• Classification
• Dynamic Range
• Color
• Image Formation
• Frequency-Based Operators
• Gradient-Domain Operators
• Spatial Operators
• Division
• Sigmoids
• Night Tone mapping

Implicit Modeling

• Implicit Functions, Skeletal Primitives, and Summation Blending
• Rendering
• Space Partitioning
• More on Blending
• Constructive Solid Geometry
• Warping
• Precise Contact Modeling
• Interactive Implicit Modeling Systems

Global Illumination

• Particle Tracing for Lambertian Scenes
• Path Tracing
• Accurate Direct Lighting

Reflection Models

• Real-World Materials
• Implementing Reflection Models
• Specular Reflection Models
• Smooth-Layered Model
• Rough-Layered Model

Visualization

• Background
• Data Types
• Human-Centered Design Process
• Visual Encoding Principles
• Interaction Principles
• Composite and Adjacent Views
• Data Reduction