Csaba Vincze ; Ábris Nagy - On taxicab distance mean functions and their geometric applications: methods, implementations and examples

fi:11216 - Fundamenta Informaticae, September 21, 2023, Volume 189, Issue 2: Tomography and Applications 2022
On taxicab distance mean functions and their geometric applications: methods, implementations and examplesArticle

Authors: Csaba Vincze ; Ábris Nagy

    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.


    Volume: Volume 189, Issue 2: Tomography and Applications 2022
    Published on: September 21, 2023
    Accepted on: July 10, 2023
    Submitted on: April 19, 2023
    Keywords: Mathematics - Optimization and Control,Computer Science - Discrete Mathematics,G.2.3

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