A real-time algorithm for rendering an inhomogeneous scattering medium such as fog is described. An input media animation is represented as a sequence of density fields, each of which is decomposed into a weighted sum of a set of radial basis functions (RBFs) such as Gaussians. The algorithm computes airlight and surface reflectance of the inhomogeneous scattering medium. Several approximations are taken which lead to analytical solutions of quantities such as an optical depth integrations and single scattering integrations, and a reduced number of integrations that need to be calculated. The resultant algorithm is able to render inhomogeneous media including their shadowing and scattering effects in real time. The algorithm may be adopted for a variety of light sources including point lights and environmental lights.