A Monte Carlo method to calculate the average solid angle subtended by a detector to an ellipsoidal surface or solid source at any position and orientation

This note discusses and implements an algorithm for modelling a uniform distribution over a scalene ellipsoidal surface or in a solid so that a Monte Carlo method, suitable for a personal computer, can be used to calculate the average solid angle subtended by a right cylinder or rectangular cuboid detector to the ellipsoidal surface or solid at any position and orientation. The distributions over the surface include 2π and 4π surface sources. The algorithm is developed for truncated ellipsoidal solid and surface sources (where the planes of truncation are restricted to those normal to one of the semi-axes). Plane (window) detectors can be modelled by setting the detector height to zero. The discussion includes the estimation of confidence limits. The current performance of personal computers makes it realistic to achieve accuracies of typically better than 0.05%.