Ray tracing and physically based rendering foundations

You have been faking light. Your raymarched SDF scenes shade with Phong tricks and ambient hacks — good enough for a fragment-shader jam, but soft shadows, color bleeding, and believable glass come from actually transporting light. This module builds toward writing a small Monte Carlo path tracer, the algorithm behind film-quality rendering and the reference standard your real-time visuals approximate. For a live-coding visualist this is the payoff twice over: pre-rendered loops and stills for your set, and the physical intuition to know which cheap shader trick imitates which real effect.

The arc starts conceptually: seeing rasterization and ray tracing as the same nested loop inverted, and why secondary effects and global illumination fall out naturally on the ray-tracing side. Then it grounds the numbers — the four radiometric quantities, and why radiance’s constancy along rays makes it what every ray carries. From there you build outward from a single primary ray per pixel: drill recursive diffuse bouncing with a depth limit until scatter-and-recurse is automatic, then drill supersampled antialiasing — the same random-offset-and-average move that later becomes motion blur when the offsets go temporal, and that reveals itself as Monte Carlo integration of the rendering equation. The BVH atom is your just-in-time pointer when the render slows to a crawl: nested bounding boxes turn linear intersection cost logarithmic.

Every required atom is load-bearing for the capstone: you cannot accumulate radiance correctly without the radiometry, terminate paths without the depth limit, or render a nontrivial scene without the BVH. The supporting atoms enrich the frame — GPU ray-tracing pipelines, hybrid raster-plus-rays-plus-denoising, and where real-time rendering is heading — context worth absorbing, but nothing the capstone gates on.