Fog with a Linear Density Function

Derivation Let the density function  ρ  be defined as    ρ a  F  (3.4) for some positive constant a, and let dg represent the contribution to the fog factor exponent along a differential length ds, given by the product  dg ρ ds  . (3.5) By integrating over the portion of the path that lies beneath the fog plane between the shaded point  and the camera position , we obtain a function  g  that can be substituted for the product ρd in Equation (3.2).