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On Taxicab Distance Mean Functions and their Geometric Applications: Methods, Implementations and Examples

Vincze Csaba, Nagy Abris

Fundamenta Informaticae

2022

Vol. 189, nr 2

145--169

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.