An efficient algorithm for choosing scattering directions in Monte Carlo work with arbitrary phase functions

Abstract

This paper describes an efficient Monte Carlo algorithm for choosing a new direction of a photon after a scattering interaction. The algorithm chooses a scattering angle by linear interpolation in a table of the inverse cumulative scattering probability. A Legendre expansion of the phase function makes it easy to apply Clenshaw's algorithm to build the interpolation table. The points in the table are close enough together that linear interpolation is accurate. With a table of 100,000 entries, we can keep the absolute and relative errors in matching the probability distribution below 10(exp -5).