{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:22Z","timestamp":1760242402379,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,6,12]],"date-time":"2017-06-12T00:00:00Z","timestamp":1497225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Cadastral spatial units around the world range from simple 2D parcels to complex 3D collections of spaces, defined at levels of sophistication from textural descriptions to complete, rigorous mathematical descriptions based on measurements and coordinates. The most common spatial unit in a cadastral database is the 2D land parcel\u2014the basic unit subject to cadastral Rights, Restrictions and Responsibilities (RRR). Built on this is a varying complexity of 3D subdivisions and secondary interests. Spatial units may also be subdivided into smaller units, with the remainder being kept as common property for the owners\/tenants of the individual units. This has led to the adoption of hierarchical multi-level schemes. In this paper, we explore the encoding of spatial units in a way that highlights their 2D extent and topology, while fully defining their extent in the third dimension. Obviously, topological encoding itself is not new. However, having mixed a 2D and 3D topological structure is rather challenging. Therefore, despite the potential benefits of mixed 2D and 3D topology, it is currently not used in LandXML, one of the main and best documented formats when representing survey data. This paper presents a multi-level topological encoding for the purposes of survey plan representation in LandXML that is simple and efficient in space requirements, including the question of curved surfaces, (partly) unbounded spatial units, and grouping and division of 2D and 3D spatial units. No \u201coff the shelf\u201d software is available for validating newly lodged surveys and we present our prototype for this. It is further suggested that the conceptual model behind this encoding approach can be extend to the database schema itself.<\/jats:p>","DOI":"10.3390\/ijgi6060171","type":"journal-article","created":{"date-parts":[[2017,6,12]],"date-time":"2017-06-12T10:27:59Z","timestamp":1497263279000},"page":"171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["LandXML Encoding of Mixed 2D and 3D Survey Plans with Multi-Level Topology"],"prefix":"10.3390","volume":"6","author":[{"given":"Rodney","family":"Thompson","sequence":"first","affiliation":[{"name":"Department OTB, GIS Technology Section, Delft University of Technology, P.O. Box 5030, 2600 GA Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3874-4737","authenticated-orcid":false,"given":"Peter","family":"Van Oosterom","sequence":"additional","affiliation":[{"name":"Department OTB, GIS Technology Section, Delft University of Technology, P.O. Box 5030, 2600 GA Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kean","family":"Soon","sequence":"additional","affiliation":[{"name":"Singapore Land Authority, 55 Newton Road, #12-01, Revenue House, Singapore 307987, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,12]]},"reference":[{"unstructured":"Lemmen, C., van Oosterom, P., Thompson, R.J., Hespanha, J., and Uitermark, H. (2010, January 11\u201316). The Modelling of Spatial Units (Parcels) in the Land Administration Domain Model (LADM). Proceedings of the XXIV FIG International Congress, Sydney, Australia.","key":"ref_1"},{"unstructured":"(2017, May 06). ISO TC211. ISO 19152:2012 Geographic Information\u2014Land Administration Domain Model (LADM). Available online: https:\/\/www.iso.org\/standard\/51206.html.","key":"ref_2"},{"unstructured":"Thompson, R.J., van Oosterom, P., Soon, K.H., and Priebbenow, R. (2016, January 2\u20136). A Conceptual Model Supporting a Range of 3D Parcel Representations through all Stages: Data Capture, Transfer and Storage. Proceedings of the FIG Working Week 2016, Christchurch, New Zealand.","key":"ref_3"},{"unstructured":"(2017, May 06). LandXML. Available online: http:\/\/www.landxml.org\/.","key":"ref_4"},{"unstructured":"Scarponcini, P. (2017, May 06). InfraGML Proposal (13\u2013121), OGC Land and Infrastructure Domain Working Group. Available online: https:\/\/portal.opengeospatial.org\/files\/?artifact_id=56299.","key":"ref_5"},{"unstructured":"(2017, May 06). OGC InfraGML 1.0. Available online: https:\/\/portal.opengeospatial.org\/files\/?artifact_id=72352.","key":"ref_6"},{"unstructured":"Thompson, R., and van Oosterom, P. (2011, January 16\u201318). Axiomatic Definition of Valid 3D Parcels, Potentially in a Space Partition. Proceedings of the 2th International FIG 3D Cadastre Workshop, Delft, The Netherlands.","key":"ref_7"},{"unstructured":"Thompson, R., van Oosterom, P., Karki, S., and Cowie, B. (2015, January 17\u201321). A Taxonomy of Spatial Units in a Mixed 2D and 3D Cadastral Database. Proceedings of the FIG Working Week 2015, Sofia, Bulgaria.","key":"ref_8"},{"unstructured":"Thompson, R.J., van Oosterom, P., and Soon, K.H. (2016, January 18\u201320). Mixed 2D and 3D Survey Plans with Topological Encoding. Proceedings of the 5th International FIG 3D Cadastre Workshop, Athens, Greece.","key":"ref_9"},{"unstructured":"(2017, May 06). ICSM. ePlan Data Model Governance, Available online: http:\/\/www.icsm.gov.au\/eplan\/ePlan_Governance_v1.1.pdf.","key":"ref_10"},{"unstructured":"Jane\u010dka, K., and Karki, S. (2016, January 18\u201320). 3D Data Management\u2014Overview Report. Proceedings of the 5th International FIG 3D Cadastre Workshop, Athens, Greece.","key":"ref_11"},{"unstructured":"Dimipoulou, E., Karki, S., Miodrag, R., de Almeida, J.-P.D., Griffith-Charles, C., Thompson, R., Ying, S., and van Oosterom, P. (2016, January 18\u201320). Initial Registration of 3D Parcels: Overview Report. Proceedings of the 5th International FIG 3D Cadastre Workshop, Athens, Greece.","key":"ref_12"},{"unstructured":"Soon, K.H., Tan, D., and Khoo, V. (2016, January 18\u201320). Initial Design to Develop a Cadastral System that Supports Digital Cadastre, 3D and Provenance for Singapore. Proceedings of the 5th International FIG 3D Cadastre Workshop, Athens, Greece.","key":"ref_13"},{"unstructured":"Zeiss, G. (2017, May 06). A Proposal to Replace LandXML with a New Standard: InfraGML. Directions Magazine 11th Dec. Available online: http:\/\/www.directionsmag.com\/entry\/a-proposal-to-replace-landxml-with-a-new-standard-infragml\/371892.","key":"ref_14"},{"doi-asserted-by":"crossref","unstructured":"Stoter, J.E., and van Oosterom, P. (2006). 3D Cadastre in an International Context: Legal, Organizational, and Technological Aspects, CRC Press.","key":"ref_15","DOI":"10.1201\/9781420005677"},{"unstructured":"Oldfield, J., van Oosterom, P., Quak, W., van der Veen, J., and Beetz, J. (2016, January 18\u201320). Can Data from BIMs be Used as Input for a 3D Cadastre? In Proceedings of the 5th International FIG 3D Cadastre Workshop. Athens, Greece.","key":"ref_16"},{"unstructured":"Paulsson, J. (2012, January 25\u201326). Sweedish 3D Property in an International Comparison. Proceedings of the 3rd International FIG 3D Cadastre Workshop: Developments and Practices, Shenzhen, China.","key":"ref_17"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1111\/tgis.12199","article-title":"Building Information Modelling for High-rise Land Administration","volume":"21","author":"Atazadeh","year":"2017","journal-title":"Trans. GIS"},{"doi-asserted-by":"crossref","unstructured":"Richardson, D.E., and van Oosterom, P. (2002). The Balance between Geometry and Topology. Advances in Spatial Data Handling, Springer.","key":"ref_19","DOI":"10.1007\/978-3-642-56094-1"},{"key":"ref_20","first-page":"508","article-title":"Building a Robust Relational Implementation of Topology","volume":"Volume 2750","author":"Hadzilacos","year":"1993","journal-title":"Lecture Notes in Computer Science: Advances in Spatial and Temporal Databases. SSTD 2003"},{"unstructured":"Louwsma, J. H. (2017, May 06). Topology Versus Non-Topology Storage Structures. Available online: http:\/\/www.gdmc.nl\/publications\/2003\/Topology_storage_structures.pdf.","key":"ref_21"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/3-540-57207-4_10","article-title":"Topological Querying of Multiple Map Layers","volume":"Volume 716","author":"Frank","year":"1993","journal-title":"Lecture Notes in Computer Science: Spatial Information Theory A Theoretical Basis for GIS. COSIT 1993"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.compenvurbsys.2006.03.003","article-title":"Simultaneous Storage of Primal and Dual Three-Dimensional Subdivisions","volume":"31","author":"Ledoux","year":"2007","journal-title":"Comput. Environ. Urban Syst."},{"unstructured":"Zlatanova, S., and Lee, J. (2009). Construction Operators for Modelling 3D Objects and Dual Navigation Structures. Lecture Notes in Geoinformation and Cartography: 3D Geoinformation Sciences, Springer. Part II.","key":"ref_24"},{"unstructured":"Baumgart, B.G. (2017, May 06). Winged Edge Polyhedron Representation. Stanfort Artificial Intelligence Project, 1972, 44, Document STAN-CS-72-320 Memo AIM-179. Available online: http:\/\/www.dtic.mil\/dtic\/tr\/fulltext\/u2\/755141.pdf.","key":"ref_25"},{"key":"ref_26","first-page":"18","article-title":"Single Valued Vector Maps\u2014A Concept in Geographic Information Systems","volume":"2","author":"Molenaar","year":"1989","journal-title":"GeoInform. Syst."},{"unstructured":"Van Oosterom, P. (2000). Research Issues in Integrated Querying of Geometric and Thematic Cadastral Information (2), Delft University of Technology. Technical Report.","key":"ref_27"},{"unstructured":"(2017, May 06). DNRM Cadastral Survey Requirements v7.1, Reprint 1, Available online: https:\/\/www.dnrm.qld.gov.au\/?a=105601.","key":"ref_28"},{"unstructured":"(2017, May 06). ICSM. ePlan Protocol LandXML Mapping, Available online: https:\/\/icsm.govspace.gov.au\/files\/2011\/09\/ePlan-Protocol-LandXML-Mapping-v2.1.pdf.","key":"ref_29"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/0010-4485(95)00068-2","article-title":"Determining Intersection Curves Between Surfaces of Two Solids","volume":"28","author":"Yeh","year":"1996","journal-title":"Comput. Aided Des."},{"doi-asserted-by":"crossref","unstructured":"Zlatanova, S., Ledoux, H., Fendel, E., and Rumor, M. (2012). Modelling and Validation of 3D Cadastral Objects. Urban and Regional Data Management: UDMS Annual 2011, CRC Press.","key":"ref_31","DOI":"10.1201\/b11647"},{"doi-asserted-by":"crossref","unstructured":"Thompson, R.J. (2007). Towards a Rigorous Logic for Spatial Data Representation. [Ph.D. Thesis, Delft University of Technology].","key":"ref_32","DOI":"10.54419\/fxkgf8"},{"doi-asserted-by":"crossref","unstructured":"Weinrich, B.E., and Schneider, M. (2005, January 4\u20135). Use of Rational Numbers in the Design of Robust Geometric Primitives for Three Dimensional Spatial Database Systems. Proceedings of the 13th Annual ACM Workshop on GIS, Bremen, Germany.","key":"ref_33","DOI":"10.1145\/1097064.1097088"},{"unstructured":"Lema, J.A.C. (2012). Dual Grid: A Closed Representation Space for Consistent Spatial Databases. [Ph.D. Thesis, Universidade da Coru\u00f1a].","key":"ref_34"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1023\/A:1013768114909","article-title":"Dual grid: A new Approach for Robust Spatial Algebra Implementation","volume":"6","author":"Lema","year":"2002","journal-title":"GeoInformatica"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10707-009-0094-3","article-title":"Connectivity in the Regular Polytope Representation","volume":"15","author":"Thompson","year":"2011","journal-title":"GeoInformatica"},{"doi-asserted-by":"crossref","unstructured":"Belussi, A., Migliorini, S., Negri, M., and Pelagatti, G. (2016). Establishing Robustness of a Spatial Dataset in a Tolerance-Based Vector Model. Trans. GIS.","key":"ref_37","DOI":"10.1111\/tgis.12221"},{"unstructured":"Stolk, P., and Lemmen, C.H.J. (2003, January 2\u20135). Technical aspects of electronics conveyancing. Proceedings of the 2nd FIG Regional Conference, Marrakech, Morocco.","key":"ref_38"},{"unstructured":"Van Oosterom, P., Lemmen, C., Uitermark, H., Boekelo, G., and Verkuijl, G. (2011, January 7\u201313). Land Administration Standardization with focus on Surveying and Spatial Representations. Proceedings of the ACMS Annual Conference Survey Summit 2011, San Diego, CA, USA.","key":"ref_39"}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/6\/6\/171\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:38:51Z","timestamp":1760207931000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/6\/6\/171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,12]]},"references-count":39,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2017,6]]}},"alternative-id":["ijgi6060171"],"URL":"https:\/\/doi.org\/10.3390\/ijgi6060171","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2017,6,12]]}}}