  We consider the scattering of light in participating media composed of
sparsely and randomly distributed discrete particles. The particle size is
expected to range from the scale of the wavelength to the scale several orders
of magnitude greater than the wavelength, and the appearance shows distinct
graininess as opposed to the smooth appearance of continuous media. One
fundamental issue in physically-based synthesizing this appearance is to
determine necessary optical properties in every local region. Since these
optical properties vary spatially, we resort to geometrical optics
approximation (GOA), a highly efficient alternative to rigorous Lorenz-Mie
theory, to quantitatively represent the scattering of a single particle. This
enables us to quickly compute bulk optical properties according to any particle
size distribution. Then, we propose a practical Monte Carlo rendering solution
to solve the transfer of energy in discrete participating media. Results show
that for the first time our proposed framework can simulate a wide range of
discrete participating media with different levels of graininess and converges
to continuous media as the particle concentration increases.
