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Rendering equation

Programming På svenska → Updated: 2026-10-25

The integral that all photorealistic rendering tries to solve: the light leaving a point equals what it emits plus all incoming light weighted by the surface's reflectance.

Stated by James Kajiya in 1986 — David Immel and colleagues arrived at the same result independently that year. It says the light leaving a surface in a given direction is what the surface emits plus an integral over every incoming direction: incoming radiance times the surface's BRDF times a cosine term for the angle of incidence.

The equation is recursive — the light arriving has bounced off other surfaces solving the same integral — and has no closed-form solution outside trivial cases. Every rendering method is an approximation of it: ray tracing, radiosity and Monte Carlo global illumination each solve it to a different depth. Writing it down gave the field a single target to measure itself against.

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