Fundamentals of Computer Graphics

Steve Marschner, Cornell University, Ithaca, New York, USA Peter Shirley, Purity LLC

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

Miscellaneous 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
The Basic Ray-Tracing Algorithm
Perspective
Computing Viewing Rays
Ray-Object Intersection
Shading
A Ray-Tracing Program
Shadows
Ideal Specular Reflection
Historical Notes

Linear Algebra
Determinants
Matrices
Computing with Matrices and Determinants
Eigenvalues and Matrix Diagonalization

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

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

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

Using Graphics Hardware
Hardware Overview
What Is Graphics Hardware
Heterogeneous Multiprocessing
Graphics Hardware Programming: Buffers, State, and Shaders
State Machine
Basic OpenGL Application Layout
Geometry
A 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 for Graphics Hardware Programming
Continued Learning

Light
Radiometry
Transport Equation
Photometry

Color
Colorimetry
Color Spaces
Chromatic Adaptation
Color Appearance

Visual Perception
Vision Science
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
Other Approaches
Night Tonemapping
Discussion

Implicit Modeling
Implicit Functions, Skeletal Primitives, and Summation Blending
Rendering
Space Partitioning
More on Blending
Constructive Solid Geometry
Warping
Precise Contact Modeling
The Blob Tree
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

Computer Graphics in Games
Platforms
Limited Resources
Optimization Techniques
Game Types
The Game Production Process

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