Topology and Spatial Relationships: Adjacency and Incidence, Topological Rules (Especially for GATE-Geospatial 2022)

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The most popular method of retaining spatial relationships among features is to explicitly record adjacency information in what is known as the topologic data model.

What is Topology?

Topology is the study of those properties of geometric objects that remain invariant under certain transformations such as bending or stretching.

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For example, a rubber band can be stretched and bent without losing its intrinsic property of being a closed circuit, if the transformation is within its elastic limits.

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Adjacency and Incidence

  • If a line joins two points, the points are said to be adjacent and incident with the line.
  • The adjacency and incidence relationships can be expressed explicitly in matrices.
  • Node 11 joined node 12 by line 2.
  • Line 5 is incident from node 14, and incident to node 12
This Diagram Shows Adjacency and Incidence Matrix

Topological Rules

A GIS topology is a set of rules and behaviors that model how points, lines, and polygons share coincident geometry. A group of instruction to the geo-database defining the permissible relationships of features within a given feature class or between features in two different feature classes.

Within One-Line Feature Class

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Between Two-Line Feature Classes

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Between a Line and a Point Feature Class

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Between a Line and a Polygon Feature Class

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Between a Point and a Line Feature Class

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Within One Polygon Feature Class

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Between Two Polygon Feature Classes

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Between a Polygon and a Point Feature Class

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Between a Polygon and a Line Feature Class

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Between a Point and a Polygon Feature Class

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All Lines and Polygons

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Many topology rules can be imposed on features in a geodatabase. A well-designed geodatabase will have only those topology rules that define key spatial relationships needed by an organization. Some rules are for within a feature class. Some rules are for between two feature classes.

Examples

  • Adjacent features, such as two counties, will have a common boundary between them. They share this edge.
  • The set of county polygons within each state must completely cover the state polygon and share edges with the state boundary.

The following list shows some examples of where topology rules can be defined for real world features in a vector map:

  • Area edges of a municipality map must not overlap.
  • Area edges of a municipality map must not have gaps.
  • Polygons showing property boundaries must be closed. Undershoots or overshoots of the border lines are not allowed.
  • Contour lines in a vector line layer must not intersect.

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