The ``scattering equation'' 1 describes the transport of light and is derived in [7][3],

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
[13], or the number of light paths between the
light source and the observer, usually to one
[9][6][5][2] or many *single
scattering* events [8]. However, as pointed out in
[7] the single scattering approximation is not sufficient
in the case of clouds due to excessive self shadowing. A recent
unpublished paper [12] brought to the authors attention
approaches the problem in similar fashion to this paper, from more of
a radiosity point of view.

In [7] 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 [7] never implemented the technique, it remains to be seen how well it would perform.

Thu Nov 17 10:01:16 EST 1994