radiosities

Radiosities, in the context of computer graphics, refer to the set of energy values that surfaces in a scene emit and reflect as part of a global illumination calculation. The radiosity method computes a steady-state distribution of light among diffuse surfaces by treating each surface patch as a separate light source that can both emit and receive light from other patches. The collection of radiosities for all patches is called radiosities (plural) of the scene.

The core idea is captured by the radiosity equation. For each patch i, the radiosity B_i is the sum of its emitted energy E_i and the energy it reflects from other patches, scaled by its reflectivity rho_i and the form factors F_ji that describe geometric relationships and visibility between patches. A common form is B_i = E_i + rho_i * sum_j F_ji B_j, where F_ji is the form factor from patch j to patch i. The equations for all patches form a linear system, often written as (I - R F) B = E, with R a diagonal matrix of reflectivities. Solving this system yields the radiosities, which determine the diffuse light leaving each patch.

Computation involves subdividing surfaces into patches, computing form factors (often using geometric and visibility considerations), and solving the resulting linear system. In practice, radiosity is commonly implemented with iterative or progressive refinement techniques to manage computational cost, and may employ hierarchical methods to handle large scenes.

Radiosity is best suited for diffuse interreflection and tends to underrepresent specular effects. It traditionally produced precomputed illumination for static scenes, making it influential in architectural visualization and early CGI. While newer rendering approaches (ray tracing, path tracing, and photon mapping) have supplanted many uses, radiosity remains foundational in the study of global illumination and energy-conserving rendering.