Topology
Overview
Topology is the study of the properties of geometric objects that remain unchanged under continuous deformations, such as stretching or bending, often used in GIS to describe spatial relationships between features. Topological relationships include adjacency, connectivity, and containment.
Key Concepts
Adjacency describes features that share a common boundary (neighboring polygons). Connectivity describes features that are linked (road network nodes and edges). Containment describes features that are inside other features (point in polygon). Node is a point where lines meet or end. Arc/Edge is a line segment between two nodes. Face is an area enclosed by arcs (polygon).
Topological Rules
| Rule | Description |
|---|---|
| Must Not Overlap | Polygons cannot share interior space |
| Must Not Have Gaps | Adjacent polygons must share boundaries |
| Must Be Connected | Line features must form a network |
| Must Be Inside | Points must fall within polygons |
| Must Not Self-Intersect | Lines cannot cross themselves |
Applications
- Validating data integrity in vector datasets
- Network analysis (routing, shortest path)
- Polygon operations (union, intersection)
- Error detection and correction
Appendix
Created: 2025-12-13 | Modified: 2025-12-13
See Also
- Geographic Information System (GIS)
- Geometry Engine - Open Source (GEOS)
- Topologically Integrated Geographic Encoding and Referencing (TIGER)
- Vector