A solution for Eqn. (9.5) is the radiosity method, in which all objects of the scene are divided into triangles and squares. Furthermore it is assumed that the objects consist of diffuse material only, which scatters the light evenly in all directions. The BRDF reduces itself in this case to a factor p, which is independent of the direction of the outgoing radiance. This combination, together with the application of a finite element method, makes it possible to convert Eqn. (9.5) into a large linear equation system in the following form:
Bi = Ei + pi Bj Gij. (9.6)
In the form of a matrix equation this can be expressed as:
E =(I — G) B. (9.7)
Final results are the radiosity values Bi (as vector B) of the triangles and squares, which are converted afterwards into a visible image. E is the emission of the surfaces, and Gij a discretized form of the geometry term, which
is also called the form factor, and is to be computed from the geometrical data beforehand. This finds its place together with the reflection pi in the matrix G. The term I describes the identity matrix (see also ).
Thus, for a scene with n triangles a set of equations develops with an n x n – matrix, which is to be solved by numeric methods. The computational cost as well as the difficulty of finding realistic working reflection values and appropriately parameterizing the procedure have so far prevented the broad use of radiosity methods. For special applications and for the precalculation of global lighting effects in the context of fast local rendering methods for computer games, they are however used.