This course will help you to understand the mathematics and algorithms necessary to perform real time 3D graphics using a modern 3D API like OpenGL, DirectX or Vulkan.

Requisites

• Linear algebra
• Calculus
• Data structure and algorithms
• C and C++
• Optimizing CPU programs

IMPORTANT

What this course is NOT about

• Specifics on how to use a 3D API like Direct3D, Vulkan or OpenGL
• Specifics on how to program in C or C++, or any other low level language, previous experience on any of those languages is mandatory

Syllabus Part 1

• Pipeline stages
• Matrices through the pipeline
• The rasterization algorithm
• Z-buffer

• Familiarize with the framework and solutions (Windows VS2019 community)
• Familiarize with a particular API and real time rendering

• Matrices for the camera
• Tansformations
• Perspective and orthogonal cameras
• Algorithms to build graphs
• Derive formulas for the camera

• Manipulate a crystal ball and/or fly camera
• Define and load scenes using general transformations

• Lambertian term
• Blinn-Phong model
• Texturing

• Apply the lighting model to a general scene

• Stages
• Intersection algorithms
• Shadows
• Reflection
• Shading
• Recursion

• Generate high quality images using ray tracing algorithms

• AABB
• Space traversal
• Multiple rays
• Multi-threading
• SIMD

• Get the most out of the CPU power using at least 3 or all the recommended optimizations

Part 2 of the course continues after the Ray Tracing assignment (Project 3). It is a mandatory to have completed with good scores all the previous projects (except otional sections).

Syllabus Part 2

• The rendering equation
• Area lights
• Analytic solution
• Monte Carlo stratify, random sampling

• Cornell box using Monte Carlo stratify area lights

Resources

• The OpenGL Programming Guide Ninth Edition (The Red Book) http://www.opengl-redbook.com/
• The OpenGL Shading Language: Third Edition (Orange Book) https://www.oreilly.com/library/view/opengl-shading-language/9780321669247/fm.html
• Computer Graphics: Principles and Practice (3rd Edition), John F. Hughes Andries van Dam Morgan McGuire David F. Sklar James D. Foley Steven K. Feiner Kurt Akeley https://www.pearson.com/uk/educators/higher-education-educators/program/Hughes-Computer-Graphics-Principles-and-Practice-3rd-Edition/PGM819382.html
• An introduction to ray tracing By Andrew Glassne https://www.realtimerendering.com/raytracing/An-Introduction-to-Ray-Tracing-The-Morgan-Kaufmann-Series-in-Computer-Graphics-.pdf
• Ray tracing in a weekend https://github.com/RayTracing/raytracing.github.io
• Physically Based Rendering: From theory to practice https://www.pbrt.org/
• Introduction to DirectX Ray Tracing https://intro-to-dxr.cwyman.org/
• Mitsuba https://github.com/mmp/pbrt-v4
• pbrt https://github.com/mmp/pbrt-v4
• Test scenes https://www.pbrt.org/scenes-v3