## Topology – A brief introduction

We now want to expand upon our knowledge of spatial feature types and descriptive data for combining them to make up GIS layers. We have talked about how different descriptive data formats such as event themes and generate data can be manipulated to create both spatial features and attribute data. Today we want to separate the spatial elements (vector data – points, line polygons) from the descriptive data (data to be used for attribute information) and get a better understanding of how differing GIS strategies (software driven) provide for relationships amongst these spatial elements. We will then return to the methods of how spatial elements are linked to attribute information.

### Topology defined

In Mathematics

Topology for use in GIS and other Spatial Domains, is borrowed from mathematics. The concept and study of Topology has been around for along time (long for us – maybe new for math). A good description of Topology can be found on Wikipedia. From this page you can see that there are may sub-fields being explored through mathematcs, but we are only interested in the application of toplogical concepts.

The interest in applying topology may have come from the work of Leonhard Euler and his Seven Bridges of Königsberg mathematical problem. Euler’s work defined and area of mathematics called graph theory. Graph theory includes the use of features such as: nodes. edges and faces. These features have been utilized in GIS and other components of spatial data management and modelling.

There are many definitions of this concept, so as in many cases a good start may be to type “GIS topology definition” at the google prompt in your browser.

*Scott’s definition – a spatial feature*

*A bounded geometric object represented in the Cartesian plane*. This may seem to be a simple definition but the spatial elements we use in AGIS are simple (simple features). The manipulation and categorization of these elements is constantly evolving in GIS and this can add to the confusion associated with understanding simple geographic features.

* Scott’s definition – Topology *: I perceive topology as:

*the awareness a spatial feature gains with respect to adjacent features within its layer*. This translates to a structured system by which all spatial elements in a layer are connected in some fashion to each other, and with this connectivity the whole layer can be categorized, queried, manipulated and stored more efficiently (sounds like the Borg Collective).

Building Topology

To build topology, lines are interpreted in such a manner as to give rise to connected, contiguous and possibly filled area features. Follow Scott through the the next sections examples and illustrations on the chalk board to see the relationships between the parts that make up GIS and how topology helps add form and structure. We will look at how older software such as ArcInfo modelled topology and how contemporary GIS desktop software (such QGIS and ArcGIS) make use of data such as shape files (no built in topology) can be used in topological model.

### Examples of topology theory

Older GIS topology was usually held in a GIS through a series of related attribute tables. Each feature, line or polygon, gains a entry for items that relate to topology. For instance a line will have entries in the from node and a to node items in an arc attribute table in an ArcInfo coverage (older ESRI format for GIS data). This arrangement of tables allows the software to determine what lines are connected to another. If the spatial layer has been *built* as a polygon layer a line will index which polygons it contributes to and the direction it navigates around it.

Shape files do not make use of topology rules however, and it is up to GIS user and software to make sure that the data is clean enough to employ mathematical principles to their spatial data.

By working through examples from other universities and ESRI, we will get a better understanding of topology and how we will use it in this class. Scott will go through each one of these links.

Oregon State advanced class

In this example, the topolgical model employed in ArcInfo is explained.

Ordance Survey

In this short example, the Ordance Survery of England illustrates the key factors utilized in many other forms of topology. We have to pay attention to some of these illustrations as understanding them will keep is in check for creating and maintaining clean spatial data.

ESRI description of the evolution of topology

This article is a bit heavy for this class, but by ignoring the references to software and other acronyms, we can get a picture of how and why ArcView shape files were created and used.

David M. Theobald (Colorado State – written for ESRI -Topology and ArcView)

This is a very well written article that gives direction as to how Shape files and ArcView can represent topology.

wiki.gis.com

This is an ESRI site somewhat disguised as a wiki – but has some useful information