{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T15:15:31Z","timestamp":1783782931808,"version":"3.55.0"},"reference-count":42,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["BR 3513\/12-1"],"award-info":[{"award-number":["BR 3513\/12-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Boundary representation models are data models that represent the topology of a building or city model. This leads to an issue in combination with geometry, as the geometric model necessarily has an underlying topology. In order to allow topological queries to rely on the incidence graph only, a new notion of topological consistency is introduced that captures possible topological differences between the incidence graph and the topology coming from geometry. Intersection matrices then describe possible types of topological consistency and inconsistency. As an application, it is examined which matrices can occur as intersection matrices, and how matrices from topologically consistent data look. The analysis of CityGML data sets stored in a spatial database system then shows that many real-world data sets contain many topologically inconsistent pairs of polygons. It was observed that even if data satisfy the val3dity test, they can still be topologically inconsistent. On the other hand, it is shown that the ISO 19107 standard is equivalent to our notion of topological consistency. In the case when the intersection is a point, topological inconsistency occurs because a vertex lies on a line segment. However, the most frequent topological inconsistencies seem to arise when the intersection of two polygons is a line segment. Consequently, topological queries in present CityGML data cannot rely on the incidence graph only, but must always make costly geometric computations if correct results are to be expected.<\/jats:p>","DOI":"10.3390\/ijgi8060278","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T11:19:58Z","timestamp":1560511198000},"page":"278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Evaluation of Topological Consistency in CityGML"],"prefix":"10.3390","volume":"8","author":[{"given":"Anna","family":"Giovanella","sequence":"first","affiliation":[{"name":"Institute of Photogrammetry and Remote Sensing, Karlsruhe Institute of Technology (KIT), Englerstr. 7, 76131 Karlsruhe, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5595-490X","authenticated-orcid":false,"given":"Patrick Erik","family":"Bradley","sequence":"additional","affiliation":[{"name":"Institute of Photogrammetry and Remote Sensing, Karlsruhe Institute of Technology (KIT), Englerstr. 7, 76131 Karlsruhe, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1734-6986","authenticated-orcid":false,"given":"Sven","family":"Wursthorn","sequence":"additional","affiliation":[{"name":"Institute of Photogrammetry and Remote Sensing, Karlsruhe Institute of Technology (KIT), Englerstr. 7, 76131 Karlsruhe, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"59","DOI":"10.5194\/isprs-annals-IV-4-59-2018","article-title":"Detection and evaluation of topological consistency in CityGML datasets","volume":"4","author":"Giovanella","year":"2018","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2842","DOI":"10.3390\/ijgi4042842","article-title":"Applications of 3D City Models: State of the Art Review","volume":"4","author":"Biljecki","year":"2015","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1093\/comjnl\/bxn054","article-title":"Using the relational model to capture topological information of spaces","volume":"53","author":"Bradley","year":"2010","journal-title":"Comput. J."},{"key":"ref_4","unstructured":"Paul, N. (2008). Topologische Datenbanken f\u00fcr Architektonische R\u00e4ume. [Ph.D. Thesis, Universit\u00e4t Karlsruhe]."},{"key":"ref_5","first-page":"77","article-title":"Elements of spatial data quality as information technology support for sustainable development planning","volume":"11","author":"Bajat","year":"2004","journal-title":"Spatium"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3151","DOI":"10.1007\/s10601-006-6847-9","article-title":"On topological consistency and realization","volume":"11","author":"Li","year":"2006","journal-title":"Constraints"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Akoka, J. (2005). Assessing topological consistency for collapse operation in generalization of spatial databases. Perspectives in Conceptual Modeling, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/11568346"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Rodriguez, M., Brisaboa, N., Meza, J., and Luaces, M. (2010, January 3\u20135). Measuring consistency with respect to topological dependency constraints. Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, San Jose, CA, USA.","DOI":"10.1145\/1869790.1869818"},{"key":"ref_9","first-page":"406","article-title":"Supporting Data Analytics for Smart Cities: An Overview of Data Models and Topology","volume":"Volume 9047","author":"Gammerman","year":"2015","journal-title":"Statistical Learning and Data Sciences SLDS 2015"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"65","DOI":"10.5194\/isprs-annals-IV-4-W5-65-2017","article-title":"Topologically consistent models for efficient big geo-spatio-temporal data distribution","volume":"IV-4\/W5","author":"Jahn","year":"2017","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_11","unstructured":"Isikdag, U. (2014). Towards Automatic Validation and Healing of CityGML Models for Geometric and Semantic Consistency. Innovations in 3D Geo\u2013Information Sciences, Springer International Publishing."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s10707-009-0091-6","article-title":"How to Achieve Consistency for 3D City Models","volume":"15","year":"2011","journal-title":"Geoinformatica"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1080\/13658811003623277","article-title":"Topologically consistent 3D city models obtained by extrusion","volume":"25","author":"Ledoux","year":"2011","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_14","unstructured":"Breunig, M., Al-Doori, M., Butwilowski, E., Kuper, P.V., Benner, J., and Haefele, K.H. (2015). Improving the Consistency of Multi-LOD CityGML Datasets by Removing Redundancy. 3D Geoinformation Science: The Selected Papers of the 3D GeoInfo 2014, Springer International Publishing. Lecture Notes in Geoinformation and Cartography."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bacao, F., Santos, M., and Painho, M. (2015). Voluminator\u2014Approximating the Volume of 3D Buildings to Overcome Topological Errors. AGILE 2015, Springer. Lecture Notes in Geoinformation and Cartography.","DOI":"10.1007\/978-3-319-16787-9"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40965-018-0043-x","article-title":"val3dity: Validation of 3D GIS primitives according to the international standards","volume":"3","author":"Ledoux","year":"2018","journal-title":"Open Geospat. Data Softw. Stand."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.isprsjprs.2012.04.004","article-title":"CityGML\u2014Interoperable semantic 3D city models","volume":"71","year":"2012","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_18","unstructured":"Gr\u00f6ger, G., Kolbe, T.H., Nagel, C., and H\u00e4fele, K.H. (2012). OGC City Geography Markup Language (CityGML) Encoding Standard, Open Geospatial Consortium."},{"key":"ref_19","unstructured":"Cox, S., Daisey, P., Lake, R., Portele, C., and Whiteside, A. (2002). Geography Markup Language (GML) Encoding Specification, Open Geospatial Consortium."},{"key":"ref_20","unstructured":"Foley, J.D., van Dam, A., Feiner, S.K., and Hughes, J.F. (1996). Computer Graphics: Principles and Practice in C, Addison\u2013Wesley Professional. [2nd ed.]."},{"key":"ref_21","unstructured":"Hatcher, A. (2002). Algebraic Topology, Cambridge University Press."},{"key":"ref_22","first-page":"501","article-title":"Diskrete R\u00e4ume","volume":"2","author":"Alexandrov","year":"1937","journal-title":"Matematicheskii Sbornik (N.S.)"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Barmak, J. (2011). Algebraic Topology of Finite Topological Spaces and Applications, Springer. Lecture Notes in Mathematics.","DOI":"10.1007\/978-3-642-22003-6"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"J\u00e4hnich, K. (1984). Topology, Springer. Undergraduate Texts in Mathematics.","DOI":"10.1007\/978-1-4612-1134-1"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/S0195-6698(84)80012-8","article-title":"Posets, Regular CW Complexes and Bruhat Order","volume":"5","year":"1984","journal-title":"Eur. J. Comb."},{"key":"ref_26","unstructured":"Kumar, B. (2018). Topologically Consistent Space, Time, Version, and Scale Using Alexandrov Topologies. Contemporary Strategies and Approaches in 3D, Information Modeling, IGI Global."},{"key":"ref_27","unstructured":"ISO\/TC 211 (2019, June 03). ISO 19107:2003 Geographic Information\u2014Spatial Schema. Available online: https:\/\/www.iso.org\/obp\/ui\/#iso:std:iso:19107:ed-1:v1:en."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"G\u00fcnther, O., and Schek, H.J. (1991). Reasoning about binary topological relations. Advances in Spatial Databases, Springer.","DOI":"10.1007\/3-540-54414-3"},{"key":"ref_29","unstructured":"Giovanella, A. Automatische Redundanzfreie Generierung von Topologie aus Multidimensionalen Geographischen Datenbest\u00e4nden. [Ph.D. Thesis]. in progress."},{"key":"ref_30","unstructured":"3DCityDB (2018, April 25). 3DCityDB Database Schema for CityGML. Available online: https:\/\/www.3dcitydb.org\/3dcitydb\/3dcitydbhomepage\/."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lee, J., and Zlatanova, S. (2009). Making interoperability persistent: A 3D geo database based on CityGML. 3D Geo\u2013Information Sciences, Springer. Chapter 11.","DOI":"10.1007\/978-3-540-87395-2"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1186\/s40965-018-0046-7","article-title":"3DCityDB\u2014A 3D geodatabase solution for the management, analysis, and visualization of semantic 3D city models based on CityGML","volume":"3","author":"Yao","year":"2018","journal-title":"Open Geospat. Data Softw. Stand."},{"key":"ref_33","unstructured":"Chaturvedi, K., Yao, Z., and Kolbe, T. (2015). Web-based Exploration of and Interaction with Large and Deeply Structured Semantic 3D City Models using HTML5 and WebGL. 35. Wissenschaftlich\u2013Technische Jahrestagung der DGPF, Deutsche Gesellschaft f\u00fcr Photogrammetrie, Fernerkundung und Geoinformation e.V."},{"key":"ref_34","unstructured":"Kunde, F. (2012). CityGML in PostGIS\u2014Portierung, Anwendung und Performanz\u2013Analyse am Beispiel der 3DCityDB Berlin. [Master\u2019s Thesis, Universit\u00e4t Potsdam]."},{"key":"ref_35","unstructured":"Kunde, F., Nagel, C., Herrerruela, J., Ross, L., and Kolbe, T.H. (2013, January 12\u201314). 3D-Stadtmodelle in PostGIS mit der 3D City Database. Proceedings of Tagungsband der FOSSGIS-Konferenz, Rapperswil, Switzerland."},{"key":"ref_36","unstructured":"SFCGAL (2018, April 25). Simple Features Wrapper Library for CGAL. Available online: http:\/\/www.sfcgal.org."},{"key":"ref_37","unstructured":"CGAL (2018, April 25). Computational Geometry Algorithms Library. Available online: http:\/\/www.cgal.org\/."},{"key":"ref_38","unstructured":"Eisentraut, P. (2003). PostgreSQL: Das offizielle Handbuch, Verlag Moderne Industrie."},{"key":"ref_39","unstructured":"Herring, J.R. (2010). OpenGIS\u00ae Implementation Standard for Geographic Information\u2014Simple Feature Access\u2014Part 2: SQL Option, Open Geospatial Consortium Inc.. Technical Report OGC 06-104r4."},{"key":"ref_40","unstructured":"Berlin Business Location Center (2018, April 29). Berlin 3D\u2014Download Portal. Available online: http:\/\/www.businesslocationcenter.de\/en\/downloadportal."},{"key":"ref_41","unstructured":"Chair of Geoinformatics, Technical University of Munich (2018, April 30). Cesium-Based 3D Viewer and JavaScript API for the 3D City Database. Available online: https:\/\/github.com\/3dcitydb\/3dcitydb-web-map."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"13","DOI":"10.5194\/isprs-annals-IV-2-W1-13-2016","article-title":"The most common geometric and semantic errors in CityGML datasets","volume":"IV-2\/W1","author":"Biljecki","year":"2016","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. 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