# Evaluation of the volume of intersection of a sphere with a cylinder by elliptic integrals

## Description

Abstract We have developed an analytic expression for the volume of intersection of any cylinder with any sphere in the usual three-dimensional space. To our knowledge, it is the first time that an exact expression, valid in all cases, is presented for this volume. Here we derive this expression, show how it can be implemented numerically, and give examples of its usefulness for physics, as for example the fast evaluation of the number of participants in relativistic... Title of program: CYLSPHER Catalogue Id: ABRH_v1_0 Nature of problem A program for computing the volume of intersection of a cylinder with a sphere, useful in calculations of the number of participating nucleons in heavy-ion collisions, has been written. Using elliptic integrals, we achieve very good speed (hundreds of FLOPs) and precision. Versions of this program held in the CPC repository in Mendeley Data ABRH_v1_0; CYLSPHER; 10.1016/0010-4655(90)90184-3 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)