# Geospatial Topology, the Basics

The concept of topology isn’t something that every spatially enabled person fully understands.  That is OK, because I too had to learn (and relearn) how spatial topology works over the years, especially early on back in the ArcView 3.X days.  I think this experience is fairly typical of someone who uses GIS.  If one is taking a GIS course or a course that uses GIS it is not very often that the concept of spatial topology is covered in-depth or at all.  Spatial topology also may not be something that people are overly concerned about during their day-to-day workflow, meaning they may let their geospatial topology skills slide from time to time.  As a public service here is a basic overview of geospatial topology.

First question: What is topology?

You have probably heard the term topology before, whether it was in a GIS course where the instruction lightly glazed over the topic, or in a geometry/mathematics course.

Technically speaking, topology is a field of mathematics/geometry/graph theory, that studies how the properties of a shape remain under a number of different transformations, like bending, stretching, or twisting.   The field of topology is well established within mathematics and far more complicated than I wish to get in this post.

Second question: How does topology relate to GIS and spatial analysis?

Spatial analysis is at its core an analysis of shapes in space.  Geospatial topology is used to determine and preserve the relationships between shapes in the vector data model.

The GIS software we use for analysis and data storage incorporates a set of “topological rules” to define how vector objects are stored and how they can interact with each other.  These rules can dictate how nodes interact within a network, how the edges or faces of polygons coexist, or how points are organized across space.

Back in the “olden-days” (which was before “my time”) GIS users, particularly ArcInfo users, were well versed in geospatial topology because of the coverage.  The coverage data model, a precursor to today’s ubiquitous shapefile format, was unique in that topology was stored within the file.  This data format allowed users a certain set of controls to the spatial relationships within the dataset that later went away with the shapefile.  The shapefile is not a topologically valid dataset, as geometric relationships are not enforced.  For example, how may of you have downloaded (or bought) a shapefile from a data provider and it was FULL of slivers? In the Esri world geospatial topology came back with the geodatabase, and has been incorporated into a number of other geospatial data formats including spatial databases supported by Oracle, PostGIS (2.0) and SpatiaLite.

Today, topology is important in geodatabase design (for those who pay attention to it!), and data creation/editing.  By understanding the set of geospatial topology rules and creating topologically sound data, the user can have a level of trust in their data during analysis.

Esri white paper on GIS topology

PostGIS Topology

PostGIS 2.0 Topology Support

Oracle Topology Data Model

Vector topology in GRASS

Esri Coverage Topology

Esri Geodatabase Topology

Real topology

Vector topology cleaning with Quantum and GRASS – youtube vid