{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:27:28Z","timestamp":1777645648432,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["FI"],"published-print":{"date-parts":[[2023,8,1]]},"abstract":"<jats:p>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\u2019 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.1<\/jats:p>","DOI":"10.3233\/fi-222156","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T10:46:18Z","timestamp":1690886778000},"page":"145-169","source":"Crossref","is-referenced-by-count":1,"title":["On Taxicab Distance Mean Functions and their Geometric Applications: Methods, Implementations and Examples"],"prefix":"10.1177","volume":"189","author":[{"given":"Csaba","family":"Vincze","sequence":"first","affiliation":[{"name":"Institute of Mathematics, University of Debrecen, P.O.Box 400, H-4002 Debrecen, Hungary, csvincze@science.unideb.hu"}]},{"given":"\u00c1bris","family":"Nagy","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Debrecen, Debrecen, Hungary, abris.nagy@science.unideb.hu"}]}],"member":"179","container-title":["Fundamenta Informaticae"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/FI-222156","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:51Z","timestamp":1777444371000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/FI-222156"}},"subtitle":[],"editor":[{"given":"Paolo","family":"Dulio","sequence":"additional","affiliation":[]},{"given":"Andrea","family":"Frosini","sequence":"additional","affiliation":[]},{"given":"Grzegorz","family":"Rozenberg","sequence":"additional","affiliation":[]},{"given":"Lama","family":"Tarsissi","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2023,8,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.3233\/fi-222156","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,1]]}}}