Vector Topology - Lecture Material - Completely GIS dan Remote Sensing tutorial -
Vector Topology
Topology is the spatial relationships between geographic features. It is not to be confused with topography, the form of the land.

1. The Components of Topology

Topology has three fundamental  components:

    a. Connectivity:
    Arcs are connected to others (at nodes). This identifies possible routes and networks, such as rivers and roads, via the lists of arcs and nodes in the database.

    b.  Containment:
    An enclosed polygon has a measurable area; lists of arcs define boundaries and closed areas.

    c.  Contiguity:
    The adjacency of polygons can be determined by shared arcs.

    Table 6-1

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Polygon Topology: Area
Node Topology: connectivity
Arc Topology: contiguity
Left & Right Polygons
a1, a2, a3
a2, a5, a6
a3, a4, a5
a1, a4, a6
a1, a2, a6
a2, a3, a5
a1, a3, a4
a4, a5, a6
A  D
A  B
A  C
C  D
B  C
B  D

 These are fundamental to GIS analysis and queries, for example:

Diagram explanation:

  • Polygon A is bounded by arcs a1, a2, a3  etc..
  • Polygon D is known as the 'External or Universe Polygon' which describes all areas OUTSIDE the polygons on your map.  It is necessary for reasons of contiguity, all arcs are bounded by two polygons. It would help answer, for example, if you were working in a park: how many areas are adjacent to the park boundary?
  • Node 1 is connected by arcs a1, a2, a6  etc..
  • Each node is connected by at least (and usually) three arcs
  • Arc a1 is bounded either side by polygons A and D  etc..
  • Note: arcs are usually created with a direction, i.e. a 'from' node and a 'to' node. The actual direction may be significant, for example in stream flow, but arbitrary in others, e.g. most roads. Direction determines which polygons are 'left' and 'right'.

GIS vector data can be either constructed with topology (topological data) or without topology : 'spaghetti' data  (see below)

2.  Spaghetti versus Topological data

a. 'Simple' spaghetti data

Vector data that has been created without topology is referred to as 'spaghetti' data for reasons you can imagine (strings of unconnected lines). This is easier to create, but if to be used for GIS, one pays for lack of topology later: a case of "more haste, less speed". Individual features may appear the same, for example:
  • Points:  have  x and y coordinates.
  • Lines (arcs): Strings of x, y vertices.
  • Polygons: Closed set of coordinates.
  • But there is NO spatial relationship between these features:
  • Arcs may not necessarily join and Polygons may not close to form areas.
  • Intersections may not have nodes where two arcs cross.
  • Adjacent digitized polygons may overlap or underlap (leaving an empty wedge).
  • Arcs may consist of many broken segments.

b. 'Complex' topological data

Creating topologically correct data takes longer, but enables GIS queries and analysis.
  • Points: are polygons of zero area and length.
  • Lines (arcs): start and end at nodes.
  • Polygons: given by sets of connected arcs and an interior label point.
 Shared polygon arcs result in:
  • Lower total number of arcs in a database.
  • Adjacent polygons do not enclose overlap wedges or slivers.
  • Cleaner map output (more evident when you zoom in or magnify).
Figure 6-2 : Spaghetti Data versus Topological Data
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This is the raw data. It must be 'cleaned and built' for GIS. There are unacceptable dangling arcs, nodes, and missing intersections.
The data after "clean & build": there are nodes at all intersections, and no dangling arcs.

3. Creation of Topology: 'Clean & Build'

a. Node types

Table 6-3
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At an intersection of 3 or more arcs Always
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At the end of an arc  Arcs (Not polygons) 
e.g. roads, streams 
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 Between 2 arcs    Island polygons, attribute change

b. Arcs

  • Nodes are required at all arc intersections.
  • Dangling arcs can be accepted if the "dangle tolerances" are set.
    • e.g. if tolerance = 5 metres, an arc < 5 is a dangle (error), an arc > 5m is a legitimate arc.

c. Cleaning (moves nodes/arcs)

  • Removes unacceptable dangling arcs and nodes.
  • Joins missing arcs segments (within a special distance).
  • Removes unnecessary pseudo nodes.
  • Adds nodes to all intersections.
  • Label points are added to polygons.

 d. Building topology

  • Does not move any features but 'cements' them into place.
  • Creates a Feature Attribute Table.
  • Builds (again) after new edits including,
    • addition or removal of arcs and points;
    • addition or removal of attribute items.

4. Review

  1. Name & describe the three components of topology.
  2. There is no spatial relationship between points, lines and polygons in spaghetti data. True or false?
  3. When are dangling nodes acceptable?
  4. Define normal node, dangling node & pseudo node.
  5. Name four things that 'clean' does.