List of Course Topics

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Introduction

January 6, 2025

• Textbook: Chapter 1
• Applications
• Brief history
• Research areas
• Class organization

Drawing and Animation

January 8, 2025

• Akenine-Möller et al.: Chapter 2, 4.7
• Drawing and graphics pipeline
• Modelling a tetrahedron
• Projections from 3D to 2D
• Rasterization
• Animations

Introduction to WebGL and Three.js

January 13, 2025

• Game or Rendering Engines, Graphics API, Low-level APIs
• Three.js, OpenGL (ES) and WebGL
• Programmable pipeline
• Drawing a triangle (yeah!)
• Akenine-Möller et al.: Chapter 2; WebGL Guide

Transformations in 2D

January 15, 2025

• Akenine-Möller et al.: Chapter 4.1
• Marschner and Shirley, Chapters 6.1, 5.2-5.3
• Why spatial transformations in computer graphics?
• Scaling, shearing and rotation
• Multiple transformations: Matrix composition and decomposition
• Self-Study: Basic linear algebra, Textbooks, on-line appendix

Transformations in 3D

January 20, 2025

• Akenine-Möller et al.: Chapter 4.1
• Marschner and Shirley: Chapters 6.2-6.3, 5.4
• Translations and homogeneous transforms
• 3D Transformation

Coordinate Transformations

January 22, 2025

• Textbook: Chapter 4.2
• Akenine-Möller et al., Chapter 4.2
• Marschner and Shirley, Chapters 7.2.2, 7.4-7.5
• Inverse transforms
• Coordinate transforms

Scenegraph and Viewing Transformations

January 27, 2025

• Akenine-Möller et al., Chapter 4.2
• Marschner and Shirley, Chapters 7.4, 7.5, 12.2, 8.1
• Scenegraph transforms
• Viewing and canonical viewing volume

Camera Modelling

January 29, 2025

• Akenine-Möller et al., Chapter 4.7
• Marschner and Shirley, Chapters 8.2-8.5
• 3D to 2D projection
• Projection matrix
• Camera modelling in WebGL

Curves and Surfaces

February 3, 2025

• Textbook: Chapter
• Akenine-Möller et al., Chapter 17.1-17.3
• Marschner and Shirley, Chapters 2.7, 2.8
• 2D implicit and parametric curves
• 3D implicit and parametric curves
• 3D parametric surfaces
• Linear interpolation

Triangle Rasterization and Line Drawing

February 5, 2025

• Akenine-Möller et al., Chapter 2
• Marschner and Shirley, Chapters 9.1-9.3
• Triangles and Rasterization
• Baricentric coordinates
• Triangle rasterization
• Simple Anti-Aliasing

Shading

February 10 & 24, 2025

• Akenine-Möller et al., Chapters 5.1-5.3, 9.3
• Marschner and Shirley, Chapter 5
• Tradition OpenGL Shading
• Diffuse Shading
• Phong Shading
• Light sources
• Point lights, spot lights and directional lights

Midterm

February 12, 2025

• Material covered in class

Reading Week

February 17-21, 2025

• No classes, no lab

Meshes and 2D Texture Mapping

February 26, 2025

• Akenine-Möller et al., Chapters 6.1, 6.2
• Marschner and Shirley, Chapters 11.2, 12.1
• Indexed meshes
• 2D texture mapping
• Sphere mapping

3D Texture and Noise

March 3, 2025

• Akenine-Möller et al., Chapter 6.3, 6.7
• Marschner and Shirley, Chapters 11.5
• 3D texture mapping
• Procedural textures
• Noise textures

More Texturing Techniques

March 5, 2025

• Akenine-Möller et al., Chapters 6.7, 10.4, 7.4
• Marschner and Shirley, Chapters 11.4, 11.5, 17.5
• Bump Mapping
• Displacement Mapping
• Environment Mapping
• Shadow Mapping

Ray Tracing

March 10, 2025

• Akenine-Möller et al., Chapters 11.2,19.1,22.7-22.9
• Marschner and Shirley, Chapters 4
• Basic algorithm
• Eye and shadow rays
• Acceleration data structures

Volume Rendering

March 12, 2025

• Akenine-Möller et al., Chapters 14.1-14.3
• Overview
• Particle-light interaction
• Volume rendering integral, ray casting and alpha blending
• Shear-Warp algorithm, 3D Textures, GPU approaches
• NeRF Rendering

Point-based Rendering or Splatting

March 17, 2025

• Akenine-Möller et al., Chapters 13.9
• Pure point respresentation and neighborhoods
• Surface splats
• PBR or rendering approaches
• 3D Gaussian Splatting

Bezier Curves

March 19, 2025

• Akenine-Möller et al., Chapter 17.1
• Marschner and Shirley, Chpt. 15.1-15.3
• Subdivision
• Bernstein-Bezier formula
• De Casteljau algorithm

Splines

March 24, 2019

• T. Akenine-Möller et al., Chapter 17.4
• Marschner and Shirley, Chpt. 15.5.2-15.6.2
• Canonical form, constraint and basis matrix
• Catmull-Rom splines
• B-splines

Spline Surfaces

March 26, 2025

• T. Akenine-Möller et al., Chapter 17.2, 17.4, 17.5
• Bi-linear patches
• Bezier surfaces
• Loop subdivision

Particle Systems

March 31, 2025

• T. Akenine-Möller et al., Chapter 13.8
• Motivation and goals
• Particle systems
• Time stepping and basic equations
• ODE solvers

Project Presentations

April 2, 2025