Volume of intersection of two cones

Radiation measurements utilising collimated source and detector systems inv ariably result in a target volume described by the overlap of their fields of view. When these collimators are cylindrical, this is derived from the v olume of intersection of two cones. In general, analysis of this volume doe s not lend itself to a direct analytical process. Here, numerical methods o f estimating the common volume of two intersecting right cones are presente d. These include methods which employ, (a) a sequential scanning of an elem ental volume with a predetermined size across a defined space containing th e volume of interest and (b) a Monte Carlo technique. The accuracy obtainab le and the execution time in the first type of algorithm depend on the size of the elemental volume (bin-size). On the other hand, these two parameter s are independent of the bin-size but dependent on the number of histories sampled, for the Monte Carlo technique. At 0 degrees angle of inclination, where an analytical estimation is easily obtained, the three algorithms con sidered here resulted in values with a precision better than 0.1% when comp ared to the analytically calculated one. (C) 2000 Elsevier Science Ltd. All rights reserved.