The equations and computer algorithms are derived and developed to determine the limiting rotational and scattering angles for spherical, planar circular, and right circular cylindrical detectors. In addition, the computer algorithms developed provide most of what is required for implementing the expected value technique in analog Monte Carlo simulation. This includes providing a specific rotational angle, a specific cosine of the scattering angle, a weight factor for forcing within the limiting cosines of the scattering angle, and the direction cosines for the specific angles chosen.