Balogun, Fatai A. and Brunetti, Antonio and Cesareo, Roberto (2000) Volume of intersection of two cones. Radiation Physics and Chemistry, Vol. 59 (1), p. 23-30. ISSN 0969-806X. Article.
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Radiation measurements utilising collimated source and detector systems invariably result in a target volume described by the overlap of their fields of view. When these collimators are cylindrical, this is derived from the volume of intersection of two cones. In general, analysis of this volume does not lend itself to a direct analytical process. Here, numerical methods of estimating the common volume of two intersecting right cones are presented. These include methods which employ, (a) a sequential scanning of an elemental volume with a predetermined size across a defined space containing the volume of interest and (b) a Monte Carlo technique. The accuracy obtainable 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 parameters are independent of the bin-size but dependent on the number of histories sampled, for the Monte Carlo technique. At 0° angle of inclination, where an analytical estimation is easily obtained, the three algorithms considered here resulted in values with a precision better than 0.1% when compared to the analytically calculated one.
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