When describing neutrons interacting with homogeneous media, Monte Carlo can generate a sequence of energies and flight directions without locating the positions of the collisions that produced them. If the spatial distribution of one of these collisions is then described analytically, unbiased direct samples of the neutron density can conveniently be obtained at specified positions and energies and at discretely sampled angles. Previous applications for plane sources in infinite media with real cross sections are here generalized for plane sources in slabs and point sources within infinite half spaces. A modified treatment for heterogeneous media is also formulated. These extensions to other geometries can provide not only additional calculational standards, but also theoretical results that could disagree with experimental facts only because of the assumed nuclear data.