2.2. Topology and Topology Rules

 

            In Geographical Information System topology expresses the spatial relationships between adjacent vector features (points, lines, and polygons).  It is the branch of mathematics that deals with geometric properties that remain unchanged during certain transformation, such as stretching or bending. Since topology of a vector object remains fixed as the objects’ geometry is stretched or shrunk, topology is also known as geometry on a rubber sheet. The connections and relationships between objects are described independently of their coordinates.

            Topology, as it relates to spatial data, consists of four elements such as adjacency, containment, connectivity, and coincidence. Adjacency and containment describe the geometric relationships which exist between area features. Adjacency refers to the information about neighbouring spatial objects. Areas can be described as being adjacent when they share a common boundary. Containment is an extension of the adjacency and it refers to the information about inclusion of one spatial object within another spatial object. For example, point with in a polygon. Connectivity is a geometric property used to describe the linkages between linear features. Roads are usually connected together to form a road network. Coincidence defines relationship between spatial objects that occupy same space. For e.g., a forest border might be at the edge of a stream, when one layer is edited, features that are coincident should be updated simultaneously so they continue to share geometry.

Topology Rules

             There are many topology rules that is used to create spatial datasets. Of these rules the important polygon and network topology rules are as follows.

Polygon Topology Rules

1.      Must not have gaps – Polygons within a feature class (layer) should not have gaps. There should not be any gap between the polygons representing two nearby polygons.

2.      Must not overlap - Polygons within a feature class (layer) should not overlap each other. For e.g. Polygon representing Kerala should not overlap the polygon representing Tamil Nadu.

3.      Contains point – Points of a feature class (layer) should fall within the polygon of another feature class(layer). For e.g. Point feature representing the capital of a country should fall within that country.

4.      Must be covered by feature class of – The polygons representing a sub feature class should be covered by another polygon of higher class. For e.g. The boundaries of Palakkad district should be confined within the boundary of Kerala State.

5.      Must cover each other – All polygons in the first feature class and all polygons of second feature class must cover each other. For e.g. The land use polygons and physiography polygons of Palakkad district should lay one over the other.

Network Topology Rules

1.      Must not have dangles – The end of a line must touch any part of another line or part of itself within a feature class. For e.g. All roads in a network should be interconnected

2.      Must not have pseudo nodes – There should not have any inappropriate nodes that may unnecessarily subdivide a line. Such unnecessary nodes should be removed or replaced with vertices.

3.       Must not overlap – Lines must not overlap any part of another line within a feature class. For e.g. The lines representing roads and railway track must not overlap.

4.      Must not self-overlap – Lines must not overlap themselves within a feature class(layer) For e.g. A road should not overlap on itself.

5.      Must not intersect – Lines must not intersect or cross any part of another line within the same feature class(layer) For e.g. A line feature representing a road must not intersect another road within the same dataset.

6.      Must not self-intersect – Lines must not cross or intersect themselves within a feature class(layer). For e.g. A line feature representing a road must not intersect itself.

7.      Must be single part – Lines within a feature class must only have single part. For e.g. A line feature representing a simple road should not be represented by multipart line.

8.      Must not overlap with – Lines in one feature class must not overlap another line in another feature class(layer). For e.g. A line feature representing a road must not overlap with a railway line of another dataset.

9.      Must be covered by feature class of - Lines in one feature class should be covered by lines of another feature class (Layer). For e.g. A line feature representing bus routes should coincide with line feature representing road network.

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