The Rendering Equation

Computer Graphics · Foundations · 1986 · rendering-equation.yaml

States outgoing radiance at a point as emission plus the integral of incoming radiance weighted by the BSDF. Unified the previously separate ray tracing and radiosity traditions as approximations of one integral.

• supersedescorrects · extends
• classifiesspecializes · part-of
• substitutes forapproximates · alternative-to
• depends onrequires · validates

Colour is the family; a dashed line is the second member of it.

This node

• part-ofis a subtopic of Light Transport
• requiresdoes not work without Radiancethe unknown it solves for is a radiance field

Referenced by

• approximatesAmbient Occlusion is a cheaper stand-in for thisone visibility scalar instead of an indirect bounce
• approximatesImage-Based Lighting is a cheaper stand-in for thisdistant incoming radiance baked into a single map
• approximatesInstant Radiosity is a cheaper stand-in for thiscollapses indirect bounces into a set of point lights
• specializesPath Tracing is a specific case of thisexpands the recursive integral into random walks
• extendsRadiative Transfer Equation adds capability to thistransport along a ray, not just across surfaces
• specializesRadiosity is a specific case of thissolves the diffuse-only case as a linear system
• specializesWhitted Ray Tracing is a specific case of thisonly mirror and refraction bounces, plus one shadow ray

References

• The Rendering Equation — Kajiya — 1986 · link
• Background — Rendering equation on Wikipedia