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

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)摘要：我们针对常规三维空间内任意圆柱与任意球体的相交体积推导出了解析表达式。据我们所知，这是首次提出适用于所有场景的该体积精确解析表达式。本文推导了该表达式，展示了其数值实现方法，并给出了其在物理学中的应用示例，例如快速计算相对论性参与粒子数…… 程序名称：CYLSPHER 目录编号：ABRH_v1_0 问题属性：本程序用于计算圆柱与球体的相交体积，可应用于重离子碰撞中的参与核子数计算。通过采用椭圆积分，本程序实现了极佳的运算速度（仅需数百次浮点运算（FLOPs））与精度。 本程序在Mendeley数据的CPC仓库中的版本信息为：ABRH_v1_0；CYLSPHER；10.1016/0010-4655(90)90184-3 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018年）。