mshah.ioCourse ScheduleCourse Information
Introduction to Computer GraphicsGraphics Application, SDL Setup, and PPM ImagesBuilding Virtual Worlds, and GPU Graphics Pipeline IntroductionModern Graphics: Buffers, Shaders, and a first triangleAttributes and UniformsMeshes 01: Indexed MeshesMath 1 - Transformations: Numbers, Coordinate Systems, and VectorsMath 2 - Transformations: Matrices, Rotation, and CameraMath 3 - Transformations: CameraScenegraphs and the Visibility ProblemTextures, MipmappingGraphics Architecture and DebuggingTerrain Rendering and MultitexturingBasic LightingPoint Lights and Multiple LightsNo Class -- Exam OnlineNo ClassNo ClassNo ClassNo ClassAdvanced Lighting (Normal and Parallax), Cube and Environment MappingFramebuffer Objects (FBO): Color + Stencil + Depth and post-processingCube Maps and Shadow MapsAdvanced Graphics - Deferred RenderingGraphics Engine StudyAdvanced Graphics - More Shaders (Geometry, Tesselation, and Compute)Shading Models: PBR and Procedural TexturesInstructors Choice -- TBD (e.g. Water, animation, particles)Vulkan and future graphics APIs or Reserved for Tentative Industry Guest SpeakersCourse wrap up


Module 8 - Math 2 - Transformations: Matrices, Rotation, and Camera - 2025-Feb-04

Overview

In this module we learn about matrix transformations and viewing transformations!

  • Special 4x4 Transformation Matrices
  • Vertex Transformations
  • Scaling, Rotation, Translation, and Shear

Slides and Class Content

Please note: Your in-class activity is graded. Your first attempt will be graded. You can use your notes and slides if you like. You have 1 week from the date of this module opening to complete the in-class activity. In-class activities are completed individually.

Audio/Video Recording

Note: Audio/Video recordings are made in a best effort in case you have to miss class or you would otherwise like to re-watch a portion of lecture. Occassional recording errors (e.g. missing sound, corrupted video, etc.) may occur, and I apologize in advance if a recording is not able to be made available.

Readings

    Please use the following resources to supplement this lecture. You may choose to read 1 or more of these before/during/after the lecture to fully immerse into the material.

  1. Transformations
    • (Nice summary of graphics transformations)
  2. Tutorial on Matrices and Transformations
    • Nice OpenGL and 'glm' centric tutorial
  3. Why is w=1
    • (Reading)
  4. Matrices for Tech Artists Cheat sheet
    • More visual explanations
  5. Dear linear algebra students, This is what matrices really look like
    • Another nice visualization of matrices
  6. Math for Game Programmers: Understanding Homogeneous Coordinates
    • (Video - Squirrel Eiserlo gives wonderful talks!)
  7. Linear Maps
    • (More formal properties of linear maps)
  8. What are Affine Transformations
    • 5 minute explainer video
  9. Matrix Explorable
    • (Interactive reading with visualizations)
Please do not redistribute or host any materials without e-mailing me first. Thank you for your time!