Foundations of 3D Computer Graphics

✍ Scribed by Steven J. Gortler

• Publisher: MIT
• Year: 2012
• Tongue: English
• Leaves: 284
• Category: Library

✦ Synopsis

Computer graphics technology is an amazing success story. Today, all of our PCs are capable of producing high-quality computer-generated images, mostly in the form of video games and virtual-life environments; every summer blockbuster movie includes jaw-dropping computer generated special effects. This book explains the fundamental concepts of 3D computer graphics. It introduces the basic algorithmic technology needed to produce 3D computer graphics

✦ Table of Contents

Preface
I Getting Started
1 Introduction
1.1 OpenGL
2 Linear
2.1 Geometric Data Types
2.2 Vectors, Coordinate Vectors, and Bases
2.3 Linear Transformations and 3 by 3 Matrices
2.4 Extra Structure
2.5 Rotations
2.6 Scales
3 Affine
3.1 Points and Frames
3.2 Affine transformations and Four by Four Matrices
3.3 Applying Linear Transformations to Points
3.4 Translations
3.5 Putting Them Together
3.6 Normals
4 Respect
4.1 The Frame Is Important
4.2 Multiple Transformations
5 Frames In Graphics
5.1 World, Object and Eye Frames
5.2 Moving Things Around
5.3 Scales
5.4 Hierarchy
6 Hello World 3D
6.1 Coordinates and Matrices
6.2 Drawing a Shape
6.3 The Vertex Shader
6.4 What Happens Next
6.5 Placing and Moving With Matrices
II Rotations and Interpolation
7 Quaternions (a bit technical)
7.1 Interpolation
7.2 The Representation
7.3 Operations
7.4 Power
7.5 Code
7.6 Putting Back the Translations
8 Balls: Track and Arc
8.1 The Interfaces
8.2 Properties
8.3 Implementation
9 Smooth Interpolation
9.1 Cubic Bezier Functions
9.2 Catmull-Rom Splines
9.3 Quaternion Splining
9.4 Other Splines
9.5 Curves in Space
III Cameras and Rasterization
10 Projection
10.1 Pinhole Camera
10.2 Basic Mathematical Model
10.3 Variations
10.4 Context
11 Depth
11.1 Visibility
11.2 Basic Mathematical Model
11.3 Near And Far
11.4 Code
12 From Vertex to Pixel
12.1 Clipping
12.2 Backface Culling
12.3 Viewport
12.4 Rasterization
13 Varying Variables (Tricky)
13.1 Motivating The Problem
13.2 Rational Linear Interpolation
IV Pixels and Such
14 Materials
14.1 Basic Assumptions
14.2 Diffuse
14.3 Shiny
14.4 Anisotropy
15 Texture Mapping
15.1 Basic Texturing
15.2 Normal Mapping
15.3 Environment Cube Maps
15.4 Projector Texture Mapping
15.5 Multipass
16 Sampling
16.1 Two Models
16.2 The Problem
16.3 The Solution
16.4 Alpha
17 Reconstruction
17.1 Constant
17.2 Bilinear
17.3 Basis functions
18 Resampling
18.1 Ideal Resampling
18.2 Blow up
18.3 Mip Map
V Advanced Topics
19 Color
19.1 Simple Bio-Physical Model
19.2 Mathematical Model
19.3 Color Matching
19.4 Bases
19.5 Reflection Modeling
19.6 Adaptation
19.7 Non Linear Color
20 What is Ray Tracing
20.1 Loop Ordering
20.2 Intersection
20.3 Secondary Rays
21 Light (technical)
21.1 Units
21.2 Reflection
21.3 Light Simulation
21.4 Sensors
21.5 Integration Algorithms
21.6 More General Effects
22 Geometric Modeling: Basic Intro
22.1 Triangle Soup
22.2 Meshes
22.3 Implicit Surfaces
22.4 Volume
22.5 Parametric Patches
22.6 Subdivision Surfaces
23 Animation: Not Even an Introduction
23.1 Interpolation
23.2 Simulation
23.3 Human Locomotion
A Hello World 2D
A.1 APIs
A.2 Main Program
A.3 Adding some Interaction
A.4 Adding a Texture
A.5 What’s Next
B Affine Functions
B.1 2D Affine
B.2 3D Affine
B.3 Going Up
B.4 Going Down
B.5 Going Sideways