# Geospatial topology

Geospatial topology studies the rules concerning the relationships between the points, lines, and polygons that represent the features of a geographic region. For example, where two polygons represent adjacent counties, typical topological rules would require that the counties share a common boundary with no gaps and no overlaps. Similarly, it would be nonsense to allow two polygons representing lakes to overlap.

In spatial analysis the topological spatial relations are derived from the DE-9IM model, as spatial predicates about relations between points, lines, and/or areas: Equals, Contains, Covers, CoveredBy, Crosses, Disjoint, Intersects, Overlaps, Touches and Within. In network and graph representations the topology analysis is about topological objects such as faces, edges and nodes.

The ESRI White Paper GIS Topology[1] explains that topology operations are used to manage shared geometry, define and enforce data integrity rules, support topological relationship queries and navigation, and build more complex shapes such as polygons, from primitive ones such as lines. A GIS for Educators worksheet at Linfiniti[2] adds the detection and correction of digitising errors and carrying out network analysis. Topological error correction is explained in more detail in a paper by Ubeda and Egenhofer.[3]

Unlike GML,[4] topologies are not directly represented in ESRI shapefiles which store individual geometric objects in isolation. Topological processing can, however, be undertaken in GIS software such as GRASS GIS[5] or QGIS[6] or could in principle be enforced using integrity constraints in a GIS-enabled DBMS such as PostGIS. However, as Riedemann (2004) explains,[7] topological operators are inherently complex and their implementation requires care to be taken with usability and conformance to standards.

Oracle and PostGIS provide fundamental topological operators allowing applications to test for "such relationships as contains, inside, covers, covered by, touch, and overlap with boundaries intersecting."[8][9] Unlike the PostGIS documentation, the Oracle documentation draws a distinction between "topological relationships [which] remain constant when the coordinate space is deformed, such as by twisting or stretching" and "relationships that are not topological [which] include length of, distance between, and area of." These operators are leveraged by applications to ensure that data sets are stored and processed in a topologically correct fashion.

## References

1. ^ "GIS Topology" (PDF). ESRI. 2005. Retrieved 2011-11-25.
2. ^ "Understanding topology in vector data" (PDF). Department of Land Affairs, Eastern Cape, South Africa. 2009. Retrieved 2011-11-25.
3. ^ Ubeda, Thierry; Egenhofer, Max J. (1997). "Topological error correcting in GIS". Advances in Spatial Databases. pp. 281–297. doi:10.1007/3-540-63238-7_35.
4. ^ Quak, Wilko; de Vries, Marian (2005). "Topological and temporal modelling in GML" (PDF). Delft University of Technology. Retrieved 2011-11-30.
5. ^ GRASS Development Team (2014). "GRASS GIS 7 manual". Retrieved 2014-05-19. "Vector data processing in GRASS GIS"
6. ^ QGIS Development Team (2011). "QGIS User Guide" (PDF). Retrieved 2011-11-25. section 9.5: "A boundary between two adjacent areas is digitized only once, and it is shared by both areas"
7. ^ Riedemann, Catharina (2004). Toppen, F. and P. Prastacos 7th, eds. Towards Usable Topological Operators at GIS User Interfaces (PDF). 7th AGILE Conference on Geographic Information Science. Heraklion, Greece. pp. 669–674. Retrieved 2017-01-11.CS1 maint: Uses editors parameter (link)
8. ^ Oracle (2003). "Topology Data Model Overview". Oracle 10g Part No. B10828-01. Oracle. Retrieved 2011-11-25.
9. ^ "Geometry Relationship Functions". Refractions Research Inc. Retrieved 2011-11-25.