{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T16:22:02Z","timestamp":1781108522420,"version":"3.54.1"},"reference-count":0,"publisher":"IGI Global Scientific Publishing","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,10,1]]},"abstract":"<p>This article introduces a novel approach to higher dimensional spatial database design. Instead of extending the canonical Solid\u2013Face\u2013Edge\u2013Vertex schema of topological data, these classes are replaced altogether by a common type SpatialEntity, and the individual \u201cbounded-by\u201d relations between two consecutive classes are replaced by one separate binary relation BoundedBy on SpatialEntity which defines a so-called Alexandrov topology on SpatialEntity and thus exposes mathematical principles of spatial data design. This has important consequences: First, a mathematical definition of topological \u201cdimension\u201d for spatial data can be given. Second, every topology for data of arbitrary dimension has such a simple representation. Also, version histories have a canonical Alexandrov topology, and generalizations can be consistently modeled by continuous foreign keys between LoDs. The result is a relational database schema for spatial data of dimension 6 and more which seamlessly integrates 4D space-time, levels of details and version history. Topological constructions enable queries across these different aspects.<\/p>","DOI":"10.4018\/ij3dim.2015100104","type":"journal-article","created":{"date-parts":[[2016,5,26]],"date-time":"2016-05-26T15:55:52Z","timestamp":1464278152000},"page":"64-85","source":"Crossref","is-referenced-by-count":1,"title":["Integrating Space, Time, Version, and Scale using Alexandrov Topologies"],"prefix":"10.4018","volume":"4","author":[{"given":"Norbert","family":"Paul","sequence":"first","affiliation":[{"name":"Geodetic Institute (GIK), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick E.","family":"Bradley","sequence":"additional","affiliation":[{"name":"Institute for Photogrammetry and Remote Sensing (IPF), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2432","container-title":["International Journal of 3-D Information Modeling"],"original-title":[],"language":"ng","link":[{"URL":"https:\/\/www.igi-global.com\/viewtitle.aspx?TitleId=154020","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T22:54:50Z","timestamp":1654124090000},"score":1,"resource":{"primary":{"URL":"https:\/\/services.igi-global.com\/resolvedoi\/resolve.aspx?doi=10.4018\/IJ3DIM.2015100104"}},"subtitle":[""],"short-title":[],"issued":{"date-parts":[[2015,10,1]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,10]]}},"URL":"https:\/\/doi.org\/10.4018\/ij3dim.2015100104","relation":{},"ISSN":["2156-1710","2156-1702"],"issn-type":[{"value":"2156-1710","type":"print"},{"value":"2156-1702","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,1]]}}}