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arXiv · 2304.08626

On taxicab distance mean functions and their geometric applications: methods, implementations and examples

Csaba Vincze·Ábris Nagy
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Abstract

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.

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Csaba Vincze, Ábris Nagy. 2023-04-17. On taxicab distance mean functions and their geometric applications: methods, implementations and examples. https://doi.org/10.46298/fi.11216

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