A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics' theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well.

翻译：翻译后的摘要： 距离平均函数测量了空间中一组给定点的元素（焦点集合）到这些点的平均距离。距离平均函数的水平集称为广义圆锥体。在焦点点数无限的情况下，平均距离通常通过焦点集上的积分来计算。本文概述了出租车距离平均函数和广义圆锥体理论在几何层析成像中的应用：焦点集合等分和通过坐标 X 射线的重建问题。本文以 Maple 实现、方法和示例来说明理论结果。