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 7 - Math 1 - Transformations: Numbers, Coordinate Systems, and Vectors - 2025-Jan-30

Overview

In this module we discuss linear algebra starting with vectors

  • Numbers
  • Coordinate Systems
  • 3D Vectors (Length, Unit Vectors, Dot Product, Cross Product, Normals)

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. Essence of Linear Algebra
    • (Video - Videos 3-5)
  2. Immersive Math Book
    • (Use chapters 1,2,3,4,6 as reference for this course)
  3. Essential Mathematics For Aspiring Game Developers
    • (Video - Nice review of mathematics)
  4. Coordinate Systems
    • (learnopengl.com)
  5. Unite 2015 - A Little Math for Your Big Ideas
    • (Nice video on vectors (From Unity3D Game engine perspective)
  6. Dot product, and projections
    • Scalar dot product is length of vector, projection gives you the vector
  7. Notes on dot products and projections
    • (Helpful reading)
Please do not redistribute or host any materials without e-mailing me first. Thank you for your time!