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Radiosity is a global illumination algorithm used in 3D computer graphics rendering. Radiosity is an application of the finite element method to solving the rendering equation for scenes with purely diffuse surfaces. Unlike Monte Carlo algorithms (such as path tracing) which handle all types of light paths, typical radiosity methods only account for paths of the form LD*E, i.e., paths which leave a light source and are reflected diffusely some number of times (possibly zero) before hitting the eye.

As a rendering method, radiosity was introduced in 1984 by researchers at Cornell University (C. Goral, K. E. Torrance, D. P. Greenberg and B. Battaile) in their paper "Modeling the interaction of light between diffuse surfaces". The theory had been in use in engineering to solve problems in radiative heat transfer since about 1950.

Notable commercial radiosity engines are Lightscape (now incorporated into the Autodesk 3D Studio Max internal render engine), Radiozity by Auto*Des*Sys, and ElAS (Electric Image Animation System). Radiance, an open source Synthetic Image System that seeks physically accurate lighting effects, also makes use of the radiosity method.

Difference between Standard Direct Illumination and Radiosity

The inclusion of radiosity calculations in the rendering process often lends an added element of realism to the finished scene, because of the way it mimics real-world phenomena. Consider a simple room scene.

The image on the left was rendered with a typical direct illumination renderer. There are three types of lighting in this scene, chosen and placed by the artist in attempt to create realistic lighting: Spot Lighting with Shadows (to create the light shining on the floor), Ambient Lighting (without which the rest of the room would be totally dark), and Omnidirectional lighting without shadows (to reduce the flatness of the ambient lighting).

The image on the right was rendered using a radiosity algorithm. There is only one source of light, an image of the sky placed outside the window. The difference is marked. The room positively glows with light. Soft shadows are visible on the floor, and subtle lighting effects are noticable around the room. Furthermore, the red color from the carpet has bled onto the grey walls, giving them a slightly warm appearance. None of these effects were specifically chosen or designed by the artist.

The surfaces of the scene to be rendered are each divided up into one or more smaller surfaces (patches) and the algorithm considers the problem from the perspective of each patch in turn. For each pass of the algorithm, the total amount of light arriving at each patch, from all other patches in the scene, is calculated. Some of this light is considered to be absorbed by the patch, and the rest will be reflected back into the scene in the next pass of the algorithm.

One common method for solving the radiosity equation is "shooting radiosity," which iteratively solves the radiosity equation by "shooting" light from the patch with the most error at each step. After the first pass, only those patches which are in direct line of sight of a light-emitting patch will be illuminated. After the second pass, more patches will become illuminated as the light begins to bounce around the scene. The scene continues to grow brighter and eventually reaches a steady state.

As the algorithm iterates, light can be seen to flow into the scene, as multiple bounces are computed. Individual patches are visible as squares on the walls and floor.

The basic radiosity method has its basis in the theory of thermal radiation, since radiosity relies on computing the amount of light energy transferred among surfaces. In order to simplify computations, the method assumes that all scattering is perfectly diffuse. Surfaces are typically discretized into quadrilateral or triangular elements over which a piecewise polynomial function is defined.

After this breakdown, the amount of light energy transfer can be computed by using the known reflectivity of the reflecting patch, combined with the form factor of the two patches. This dimensionless quantity is computed from the geometric orientation of two patches, and can be thought of as the fraction of the total possible emitting area of the first patch which is covered by the second patch.

More correctly radiosity is the energy leaving the patch surface per discrete time interval and is the combination of emitted and reflected energy:

where:

• B_i is the radiosity of patch i.
• E_i is emitted energy.
• R_i is the reflectivity of the patch, giving reflected energy by multiplying by the incident energy (the energy which arrives from other patches).
• All j () in the rendered environment are integrated for B_jF_ji dA_j, to determine the energy leaving each patch j that arrives at patch i.
• F_ji is a constant form factor for the geometric relation between patch i and each patch j.

The reciprocity:

gives:

For ease of use the integral is replaced and constant radiosity is assumed over the patch, creating the simpler:

This equation can then be applied to each patch. The equation is monochromatic, so color radiosity rendering requires calculation for each of the required colors.

The constant F_ji can be calculated in a number of ways. Early methods used a hemicube (an imaginary cube centered upon the first surface to which the second surface was projected, devised by Cohen and Greenberg in 1985) to approximate the form factor, which also solved the intervening patch problem. This is quite computationally expensive, because ideally form factors must be derived for every possible pair of patches, leading to a quadratic increase in computation with added geometry.

Although in its basic form, radiosity is assumed to have a quadratic increase in computation time with added geometry (surfaces and patches), this need not be the case. The radiosity problem can be rephrased as a problem of rendering a texture mapped scene. In this case, the computation time increases only linearly with the number of patches (ignoring complex issues like cache use). Using a Binary Space Partitioning Tree can massively reduce the amount of time spent determining which patches are completely hidden from others, in complex scenes.

Since radiosity can be computed using standard texture mapping algorithms, it lends itself to acceleration using standard graphics acceleration hardware, available for a standard PC.

One of the advantages of the Radiosity algorithm is that it is relatively simple to explain and implement. This makes it a useful algorithm for teaching students about global illumination algorithms. A typical direct illumination renderer already contains nearly all of the algorithms (perspective transformations, texture mapping, hidden surface removal) required to implement radiosity. A strong grasp of mathematics is not required to understand or implement this algorithm.

Typical radiosity methods only account for light paths of the form LD*E, i.e., paths which start at a light source and make multiple diffuse bounces before reaching the eye. Although there are several approaches to integrating other illumination effects such as specular[1] and glossy[2] reflections, radiosity-based methods are generally not used to solve the complete rendering equation.

Basic radiosity also has trouble resolving sudden changes in visibility (e.g., hard-edged shadows) because coarse, regular discretization into piecewise constant elements corresponds to a low-pass box filter of the spatial domain. Discontinuity meshing[3] uses knowledge of visibility events to generate a more intelligent discretization.

Radiosity was perhaps the first rendering algorithm in widespread use which accounted for diffuse indirect lighting. Earlier rendering algorithms, such as Whitted-style ray tracing were capable of computing effects such as reflections, refractions, and shadows, but despite being highly global phenomena these effects were not commonly referred to as "global illumination." As a consequence, the term "global illumination" became confused with "diffuse interreflection," and "Radiosity" became confused with "global illumination" in popular parlance. However, the three are distinct concepts.

Yet another source of confusion is the radiometric term "radiosity." In a radiometric context, "radiosity" is the power per unit area (W/m^2) leaving a surface. This term is uncommon outside of computer graphics, and is more typically called "radiant exitance."

• Radiosity Overview, from HyperGraph of SIGGRAPH (provides full matrix radiosity algorithm and progressive radiosity algorithm)
• Radiosity, by Hugo Elias (also provides a general overview of lighting algorithms, along with programming examples)
• Radiosity, by Allen Martin (a slightly more mathematical explanation of radiosity)
• RADical, by Parag Chaudhuri (an implementation of shooting & sorting variant of progressive radiosity algorithm with OpenGL acceleration, extending from GLUTRAD by Colbeck)
• ROVER, by Tralvex Yeap (Radiosity Abstracts & Bibliography Library)