The ``scattering equation'' 1 describes the transport of light and is derived in ,
where is the intensity of the light at the position in the direction , is the scattering (phase) function, is the absorption coefficient and is density of the material.
Previous attempts at approximating the solution of this equation have placed restrictions on the phase function , or the number of light paths between the light source and the observer, usually to one  or many single scattering events . However, as pointed out in  the single scattering approximation is not sufficient in the case of clouds due to excessive self shadowing. A recent unpublished paper  brought to the authors attention approaches the problem in similar fashion to this paper, from more of a radiosity point of view.
In  an appoximate solution for the scattering equation was derived by expressing the intensities on a 3D grid as the sum of spherical harmonics
then solving for the coefficients through a relaxation-like technique. Since Kajiya and Von Herzen  never implemented the technique, it remains to be seen how well it would perform.