Global illumination refers to rendering methods that account for the full transport of light through a scene, including light that arrives at a surface only after bouncing off other surfaces. Direct, or local, illumination considers only light that travels straight from a source to a surface and then to the eye. Global illumination adds the indirect contribution: soft shadows, color bleeding where a red wall tints a nearby white floor, the diffuse glow that fills a room lit through a single window, and caustics focused by glass and water. These effects are what make rendered images read as physically real rather than merely shaded.
The problem was given a unifying mathematical statement in James Kajiya’s 1986 SIGGRAPH paper “The Rendering Equation.” Kajiya wrote down an integral equation expressing that the light leaving a surface point in a given direction equals the light emitted there plus the integral, over all incoming directions, of light arriving from the rest of the scene weighted by the surface’s reflectance. Because the incoming light is itself the outgoing light of other surfaces, the equation is recursive, and Kajiya showed that many earlier rendering algorithms are approximations that drop or simplify some of its terms. He also introduced path tracing, a Monte Carlo method that estimates the equation by randomly sampling light paths through the scene.
A different approach to indirect light had appeared two years earlier. The 1984 SIGGRAPH paper “Modeling the Interaction of Light Between Diffuse Surfaces” by Cindy Goral, Kenneth Torrance, Donald Greenberg, and Bennett Battaile brought the radiosity method from thermal engineering into graphics. Radiosity divides the scene into patches and solves a system of linear equations for the diffuse light exchanged between every pair of patches, capturing soft interreflection and color bleeding between matte surfaces. Unlike ray based methods it produces a view independent solution, but in its basic form it handles only diffuse surfaces and not mirror reflection or refraction.
Path tracing and radiosity sit at two ends of a spectrum. Path tracing is general, handling arbitrary materials and all light paths, but it is stochastic: it converges to the correct image only as the number of sampled paths grows, and undersampling shows up as noise. Radiosity is specialized to diffuse transport and produces smooth results without noise, but struggles with specular effects and with very complex geometry. Practical renderers have long combined ideas from both, and many modern systems use path tracing with importance sampling and denoising to reach clean images in feasible time.
Global illumination was for decades strictly an offline pursuit, but faster hardware and dedicated ray tracing units have brought approximate real-time global illumination into interactive applications. Whatever the method, the rendering equation remains the standard against which a global illumination technique is judged: a method is more physically accurate to the degree that it solves more of that equation. Kajiya’s 1986 paper and the Goral radiosity paper are the primary sources for the field.