Computer Graphics & Vision
Making and understanding images.
The Graphics Pipeline & Rasterization
Transform a scene full of 3D triangles into pixels on a screen — understanding every mathematical step the GPU takes, from model coordinates to final color.
Transformations & Homogeneous Coordinates
Homogeneous coordinates are the algebraic sleight-of-hand that lets a single 4×4 matrix unify translation, rotation, scale, and perspective projection into one composable operation — the mathematical backbone of every 3D renderer ever built.
Lighting, Shading & Materials
From photons to pixels: master the physics of light transport, build Phong's elegant reflection model, and understand why shading algorithms are the soul of 3D rendering.
Ray Tracing & Global Illumination
Ray tracing simulates light transport physically, casting rays from the camera into a scene and recursively tracing reflections, refractions, and shadows to render photorealistic images from first principles.
Geometry: Curves, Surfaces & Meshes
From a triangle soup to smooth surfaces: master the mathematical machinery that lets computers model, deform, and render any shape in 3D.
Image Processing Fundamentals
Master the mathematics of pixels: learn how convolution, Fourier analysis, and filtering give computers the ability to see edges, blur noise, and understand images.
Computer Vision
Computer vision teaches machines to see: from handcrafted edge detectors and keypoint descriptors to deep networks that surpass human accuracy on recognition benchmarks.
Animation & Physical Simulation
From a single keyframe to a living world: the mathematics and algorithms that bring motion, flesh, and physics to digital life.