Suppose we have a set of particles in 3-dimensional space, and we know differential cross-section of scattering of light by each particle (one single function for all particles). Now, as we increase the density of particles and decrease total scattering cross-section, we'll come to a limit of continuous foggy-like medium (inhomogeneous in general).

Now the question is: assuming purely geometric-optics approach to the calculation (i.e. ignoring any interference effects), how can one efficiently calculate light intensity at a given point, given a ray coming from some point $\vec P$ in direction $\vec D$?

My idea is to somehow calculate an integral over all possible paths of a (backwards-traced) ray, taking into account the angle it gets scattered at each point to attenuate it correspondingly. But this would require enormous amount of numerical calculations. Is there a much more efficient way to achieve this? Maybe I'm missing something obvious?


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