Encyclopedia of GIS

Living Edition
| Editors: Shashi Shekhar, Hui Xiong, Xun Zhou

Topological Relationships and Their Use

  • Sisi ZlatanovaEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-23519-6_1548-1


Topological relations between spatial objects have been widely recognized, implemented, and used in GIS. They provide a notion of the general structure and the interactions of spatial objects. Topology avoids dealing with geometry by introducing topological primitives, namely, boundary, interior, and exterior. The topological primitives allow to define approximate topological relationships between 0D (point), 1D (linestring ), 2D (surface), and 3D (body) spatial objects in 0D, 1D, 2D, and 3D space. The nine-intersection model is the well-known framework for detecting binary topological relationships (Egenhofer and Herring, 1992) and is adopted by the Opengeospatial Consortium as a basic framework for implementation. Suppose two simple spatial objects A and B are defined in the same topological space X and their boundary, interior, and exterior are denoted by ∂ A, A, A, ∂ B, B, and B. The binary relationship R(A, B) between the two objects is then identified by composing...


Topological Space Negative Condition Building Information Model Spatial Object Topological Model 
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  1. Armstrong MA (1983) Basic topology. Springer, New YorkCrossRefzbMATHGoogle Scholar
  2. Billen R, Kurata Y (2008) Refining topological relations between regions considering their shapes. In: Raunbal M, Miller J, Frank AU et al (eds) Geographic information science. Lecture notes in computer science. Heidelberg, Berlin, pp 18–32Google Scholar
  3. Borrman A, Rank E (2009) Topological analysis of 3D building models using a spatial query language. Adv Eng Inform 23(4):370–385CrossRefGoogle Scholar
  4. Breunig M, Zlatanova S (2011) 3D geo-database research: retrospective and future directions. Comput Geosci 37(7):791–803CrossRefGoogle Scholar
  5. Clementini E, di Felice P (1997) Approximate topological relations. Int J Approx Reason 16:173–204MathSciNetCrossRefzbMATHGoogle Scholar
  6. Clementini E, di Felice P, van Oosterom PJM (1993) A small set of formal topological relations suitable for end-user interaction. In: Proceedings of the 3th international symposium on large spatial databases. Springer, Berlin, pp 277–295Google Scholar
  7. de Hoop S, van de Meij L, Molenaar M (1993) Topological relations in 3D vector maps. In: Proceedings of 4th EGIS, Genoa, pp 448–455Google Scholar
  8. Deng M, Cheng T, Chen X et al (2007) Multi-level topological relations between spatial regions based upon topological invariants. Geoinformatica 11:239–267CrossRefGoogle Scholar
  9. Egenhofer MJ (1995) Topological relations in 3D. Technical report, University of MaineGoogle Scholar
  10. Egenhofer MJ, Franzosa RD (1991) Point-set topological spatial relations. Int J Geogr Inf Syst 5:161–174CrossRefGoogle Scholar
  11. Egenhofer MJ, Herring JR (1992) Categorising topological relations between regions, lines and points in geographic databases. In: Egenhofer MJ, Herring IR (eds) A framework for the definition of topological relationships and an approach to spatial reasoning within this framework, Santa Barbara, pp 1–28Google Scholar
  12. Egenhofer MJ, Sharma J, Mark D (1993) A critical comparison of the 4-intersection and 9-intersection models for spatial relations: formal analysis. In: Autocarto 11, Minneapolis, pp 1–11Google Scholar
  13. Egenhofer MJ, Clementini E, di Felice P (1994) Topological relations between regions with holes. Int J Geogr Inf Syst 8(2):129–144CrossRefGoogle Scholar
  14. Ellul C (2013) Can topological pre-culling of faces improve rendering performance of city models in Google Earth. In: Pouliot J, Daniel S, Hubert F, Zamyadi Z (eds) Progress and new trends in 3D geoinformation sciences. Springer, Heidelberg/New York, pp 133–154CrossRefGoogle Scholar
  15. Ellul C, Haklay M (2007) The research agenda for topological and spatial databases. Comput Environ Urban Syst 31:373–378CrossRefGoogle Scholar
  16. Freeman J (1975) The modelling of spatial relations. Comput Graph Image Process 4:156–171CrossRefGoogle Scholar
  17. Gröger G, George B (2012) Geometry and topology. In: Kresse W, Danilo DM (eds) Springer handbook of geographic information. Springer, Berlin/New York, pp 159–177Google Scholar
  18. Herring JR (1991) The mathematical modeling of spatial and non-spatial information in geographic information systems. In: Mark D, Frank A (eds) Cognitive and linguistic aspects of geographic space. Kluwer Academic, Dordrecht, pp 313–350CrossRefGoogle Scholar
  19. Herring JR (2011) OpenGIS implementation specification for geographic information – simple feature access – Part 1: Common architecture: Version: 1.2.1, OGC Doc. No OGC 06-103r3Google Scholar
  20. Kufoniyi O (1995) Spatial coincidence modelling, automated database updating and data consistency in vector GIS. PhD thesis, ITC, The NetherlandsGoogle Scholar
  21. Lee J, Li KJ, Zlatanova S, Kolbe TH, Nagel C, Becker T (2014) IndoorGML, Version 1.0, OGC Doc. No OGC 14-005r3Google Scholar
  22. Louwsma J, Zlatanova S, van Lammeren R, van Oosterom P (2006) Specifying and Implementing Constraints in GIS–with Examples from a Geo-Virtual Reality System. In: GeoInformatica, vol 10, No 4, pp 531–550CrossRefGoogle Scholar
  23. Pullar DV, Egenhofer MJ (1988) Toward the definition and use of topological relations among spatial objects. In: Proceedings of the third international symposium on spatial data handling, Sydney, pp 225–242Google Scholar
  24. Schaap J, Zlatanova S, van Oosterom PJM (2012) Towards a 3D geo-data model to support pedestrian routing in multimodal public transport travel advices, In: Zlatanova S, Ledoux H, Fendel EM, Rumor M (eds) Urban and regional data management. UDMS annual 2011. CRC press/Taylor and Francis Group, Boca Raton/London, pp 63–78Google Scholar
  25. Schneider M, Behr T (2006) Topological relationships between complex spatial objects. ACM Trans Database Syst 31(1):39–81CrossRefGoogle Scholar
  26. Strobl C (2008) Dimensionally extended nine-intersection model (DE-9IM). In: Shekhar S, Xiong H (eds) Encyclopaedia of GIS. Springer, Berlin, pp 240–245CrossRefGoogle Scholar
  27. van Oosterom PJM, Stoter J, Quak W, Zlatanova S (2002) The balance between geometry and topology. In: Richardson D, van Oosterom PJM (eds) Advances in spatial data handling. 10th international symposium on spatial data handling. Springer, Berlin, pp 209–224Google Scholar
  28. Willard S (1970) General topology. Addison-Wesley Publishing Company, ReadingzbMATHGoogle Scholar
  29. Xu D, Zlatanova S (2013) Am approach to develop 3D GeoDBMS topological operators by reducing existing 2D operators, ISPRS annals – volume II-2/W1, 2013, WG II/2, 8th 3D GeoInfo conference & ISPRS WG II/2 workshop, Nov 2013, pp 291–298Google Scholar
  30. Zlatanova S (2000a) 3D GIS for urban development. PhD thesis, Graz University of Technology, ITC, The NetherlandsGoogle Scholar
  31. Zlatanova S (2000b) On 3D topological relationships, In: Proceedings of the 11th international workshop on database and expert system applications (DEXA 2000), 6–8 Sept. Greenwich, London, pp 913–919Google Scholar
  32. Zlatanova S, Tijssen TPM, van Oosterom PJM, Quak WC (2003) Research on usability of Oracle spatial within RWS organisation, GISt No. 21, ISSN:1569–0245, ISBN:90-77029-07-9, AGI-GAG-2003-21, Delft, 75pGoogle Scholar

Recommended Reading

  1. Billen R, Zlatanova S (2003) 3D spatial relationship model: a useful concept for 3D cadastre? Comput Environ Urban Syst 27:411–425CrossRefGoogle Scholar
  2. Clementini E, Sharma J, Egenhofer MJ (1994) Modelling topological spatial relations: strategies for query processing. Comput Graph 18(6):815–822CrossRefGoogle Scholar
  3. de Almeida JP, Morley JG, Dowman IJ (2007) Graph theory in higher order topological analysis of urban scenes. Comput Environ Urban Syst 31:426–440CrossRefGoogle Scholar
  4. Egenhofer MJ, Herring JR (1990) A mathematical framework for the definition of topological relations. In: Proceedings of fourth international symposium on SDH, Zurich, pp 803–813Google Scholar
  5. Escobar-Molano ML, Barret DA, Carson E et al (2007) A representation for databases of 3D objects. Comput Environ Urban Syst 31:409–425CrossRefGoogle Scholar
  6. Hazelton NW, Bennett L, Masel J (1992) Topological structures for 4-dimensional geographic information systems. Comput Environ Urban Syst 16(3):227–237CrossRefGoogle Scholar
  7. Park J, Lee J (2008) Defining 3D spatial neighborhood for topological analyses using a 3D network-based topological data model-CA- building based evacuation simulation. The international archives of the photogrammetry, remote sensing and spatial information sciences, Beijing, vol XXXVII, Part B2, pp 305–310Google Scholar
  8. Whiting E, Battat J, Teller S (2007) Topology of urban environments. In: Dong A, Vande Moere, Gero JS (eds) Computer-aided architectural design futures (CAADFutures). Springer, Berlin, pp 114–128Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.3D GeoinformationFaculty of Architecture and the Built Environment, Delft University of TechnologyDelftThe Netherlands