3D Computer Graphics

Table of contents

1. Mathematical fundamentals of computer graphics
1.1 Manipulating three-dimensional structures

1.1.1 Three-dimensional geometry in computer graphics - affine transformations

1.1.2 Transformations for changing coordinate systems
1.2 Structure-deforming transformations
1.3 Vectors and computer graphics

1.3.1 Addition of vectors

1.3.2 Length of vectors

1.3.3 Normal vectors and cross products

1.3.4 Normal vectors and dot products

1.3.5 Vectors associated with the normal vector
1.4 Rays and computer graphics

1.4.1 Ray geometry - intersections

1.4.2 Intersections - ray-sphere

1.4.3 intersections - ray-convex polygon

1.4.4 Intersections - ray-box

1.4.5 Intersections - ray-quadric

1.4.6 Ray tracing geometry - reflections and refraction
1.5 Interpolating properties in the image plane

2. Representation and modelling of three-dimensional objects (1)

Introduction
2.1 Polygonal representation of three-dimensional objects

2.1.1 Creating polygonal objects

2.1.2 Manual modelling of polygonal objects

2.1.3 Automatic generation of polygonal objects

2.1.4 Mathematical generation of polygonal objects

2.1.5 Procedural polygon mesh objects - fractal objects
2.2 Constructive solid geometry (CSG) representation of objects
2.3 Space subdivision techniques for object representation

2.3.1 Octrees and rendering

2.3.2 BSP trees

2.3.3 Creating voxel objects
2.4 Representing objects with implicit functions
2.5 Scene management and object representation

2.5.1 Polygon mesh optimization
2.6 Summary

3. Representation and modelling of three-dimensional objects (2)

Introduction
3.1 Bezier curves

3.1.1 Joining Bezier curve segments

3.1.2 Summary of B-spline curve properties
3.2 B-spline representation

3.2.1 B-spline curves

3.2.2 Uniform B-splines

3.2.3 Non-uniform B-splines

3.2.4 Summary of B-spline curve properties
3.3 Rational curves

3.3.1 Rational Bezier curves

3.3.2 NURBS
3.4 From curves to surfaces

3.4.1 Continuity and Bezier patches

3.4.2 Bezier patch object - the Utah teapot
3.5 B-spline surface patches
3.6 Modelling or creating patch surfaces

3.6.1 Cross-sectional or linear axis design example

3.6.2 Control polyhedron design - basic technique

3.6.3 Creating patch objects by surface fitting
3.7 From patches to objects

4. Representation and rendering

Introduction
4.1 Rendering polygon meshes - a brief overview
4.2 Rendering parametric surfaces

4.2.1 Rendering directly from the patch descriptions

4.2.2 Patch to polygon conversion

4.2.3 Object space subdivision

4.2.4 Image space subdivision
4.3 Rendering a CSG description
4.4 Rendering a Yoxel description
4.5 Rendering implicit functions

5. The graphics pipeline 1: geometric operations

Introduction
5.1 Coordinate spaces in the graphics pipeline

5.1.1 Local or modelling coordinate systems

5.1.2 World coordinate systems

5.1.3 Camera or eye or view coordinate system
5.2 Operations carried out in view space

5.2.1 Culling or back-face elimination

5.2.2 The View volume

5.2.3 Three-dimensional screen space

5.2.4 View volume and depth
5.3 Advanced Viewing systems (PHIGS and CKS)

5.3.1 Overview of the PHIGS viewing system

5.3.2 The view orientation parameters

5.3.3 The View mapping parameters

5.3.4 The view plane in more detail

5.3.5 Implementing a PHIGS-type viewing system

6. The graphics pipeline 2: rendering or algorithmic processes

Introduction
6.1 Clipping polygons against the view volume
6.2 Shading pixels

6.2.1 Local reflection models

6.2.2 Local reflection models - practical points

6.2.3 Local reflection models - light source considerations
6.3 Interpolative shading techniques

6.3.1 Interpolative shading techniques - Gouraud shading

6.3.2 Interpolative shading techniques - Phong shading

6.3.3 Renderer shading options

6.3.4 Comparison of Gouraud and Phong shading
6.4 Rasterization

6.4.1 Rasterizing edges

6.4.2 Rasterizing polygons
6.5 Order of rendering
6.6 Hidden surface removal

6.6.1 The Z-buffer algorithm

6.6.2 Z-buffer and CSG representation

6.6.3 Z-buffer and compositing

6.6.4 Z-buffer and rendering

6.6.5 Scan line Z-buffer

6.6.6 Spanning hidden surface removal

6.6.7 A spanning scan line algorithm

6.6.8 Z-buffer and complex scenes

6.6.9 Z-buffer summary

6.6.10 BSP trees and hidden surface removal
6.7 Multi-pass rendering and accumulation buffers

7. Simulating light-object interaction: local reflection models

Introduction
7.1 Reflection from a perfect surface
7.2 Reflection from an imperfect surface
7.3 The bi-directional reflectance distribution function
7.4 Diffuse and specular components
7.5 Perfect diffuse - empirically spread specular reflection (Phong)
7.6 Physically based specular reflection

7.6.1 Modelling the micro-geometry of the surface

7.6.2 Shadowing and masking effects

7.6.3 Viewing geometry

7.6.4 The Fresnel term
7.7 Pre-computing BRDFs
7.8 Physically based diffuse component

8. Mapping techniques

Introduction
8.1 Two-dimensional texture maps to polygon mesh objects

8.1.1 Inverse mapping by bilinear interpolation

8.1.2 Inverse mapping by using an intermediate surface
8.2 Two-dimensional texture domain to bi-cubic parametric patch objects
8.3 Billboards
8.4 Bump mapping

8.4.1 A multi-pass technique for bump mapping

8.4.2 A pre-calculation technique for bump mapping
8.5 Light maps
8.6 Environment or reflection mapping

8.6.1 Cubic mapping

8.6.2 Sphere mapping

8.6.3 Environmental mapping: comparative points

8.6.4 Surface properties and environment mapping
8.7 Three-dimensional texture domain techniques

8.7.1 Three-dimensional noise

8.7.2 Simulating turbulence

8.7.3 Three-dimensional texture and animation

8.7.4 Three-dimensional light maps
8.8 Anti-aliasing and texture mapping
8.9 Interactive techniques in texture