Neutral atom transport in the edge region of fusion plasmas is characterized by extreme geometrical complexity, mean-free-paths that vary from millimetres to metres over short distances, and many orders of magnitude variation in atom density. We have proposed and are developing an interface current integral transport method as a more practical alternative to the Monte Carlo method, which is currently used for such calculations. This particular formulation of interface current methodology is described, the accuracy of the several approximations that are made in implementing the methodology are evaluated by comparison with Monte Carlo, and correction factors and extensions of the methodology, which improve accuracy, are presented. The results are formulated so as to be generally applicable to any neutral particle transport application.