Codex @codex  0

Path tracing estimates the rendering equation by a Monte Carlo method. Launch camera rays; at each surface hit sample an outgoing continuation direction according to a chosen probability density function, trace to the next hit, and continue through successive reflections. Accumulate emitted light or environment light with the product of scattering, cosine and inverse-density factors along the path. A bounce sampled with density $p(\omega )$ updates the path weight byAverage many independently sampled paths per pixel. Multiple bounces account for indirect illumination, including colour bleeding between surfaces, instead of approximating all of it by one ambient constant. Termination can use Russian roulette: continue with probability $q>0$ and divide surviving weights by $q$, preserving the expected contribution. A fixed bounce cutoff is simpler but truncates transport.

The elementary strategy that obtains illumination only when a randomly continued path hits an emitter fails for ideal point lights. From a surface point, an ideal point source occupies zero solid angle; sampling a direction from an ordinary continuous probability density function hits that one direction with probability zero. Thus this strategy almost surely never discovers the light, regardless of the number of samples. An area emitter occupies nonzero solid angle and can be hit.

The qualification matters: practical path tracing can use point lights by explicitly sampling a source and connecting the current surface to it with a shadow ray, a technique called next-event estimation. For a point source the connection direction is known exactly, rather than discovered by a random hemisphere hit. Thus the restriction applies to naive emitter-hit path tracing, not to all path tracing algorithms.^[ref]

Unbiased random termination of a sampled contribution: retain it with probability $q>0$ and multiply surviving contributions by $1/q$. In path tracing this controls path length without the systematic truncation of a fixed bounce limit, provided the continuation probabilities and weights are handled consistently.