2026-07-22T11:58:54Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7190 2024-03-06T10:40:00Z ddc:004 open_access

High Dimensional Consistent Digital Segments Chiu, Man-Kwun Korman, Matias Consistent Digital Line Segments Digital Geometry Computer Vision We consider the problem of digitalizing Euclidean line segments from R^d to Z^d. Christ {et al.} (DCG, 2012) showed how to construct a set of {consistent digital segments} (CDS) for d=2: a collection of segments connecting any two points in Z^2 that satisfies the natural extension of the Euclidean axioms to Z^d. In this paper we study the construction of CDSs in higher dimensions. We show that any total order can be used to create a set of {consistent digital rays} CDR in Z^d (a set of rays emanating from a fixed point p that satisfies the extension of the Euclidean axioms). We fully characterize for which total orders the construction holds and study their Hausdorff distance, which in particular positively answers the question posed by Christ {et al.}. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Man-Kwun Chiu and Matias Korman 2017 Is Part Of LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2017.31 urn:nbn:de:0030-drops-71900 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.31 eng https://creativecommons.org/licenses/by/3.0/legalcode