Scattering Equation

next up previous
Next: A Discrete Solution Up: A Discrete Solution of Previous: Introduction

Scattering Equation

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 A recent unpublished paper [12] brought to the authors attention approaches the problem in similar fashion to this paper, from more of a radiosity point of view.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.

Drew R. Whitehouse
Thu Nov 17 10:01:16 EST 1994