Geospatial topology
Encyclopedia
Geospatial topology studies the rules concerning the relationships between the points, lines, and polygons that represent the features of a geographic region. For example, where two polygons represent adjacent counties, typical topological
rules would require that the counties share a common boundary with no gaps and no overlaps. Similarly, it would be nonsense to allow two polygons representing lakes to overlap.
The ESRI
White Paper GIS Topology explains that topology operations are used to manage shared geometry, define and enforce data integrity
rules, support topological relationship queries and navigation, and build more complex shapes such as polygons, from primitive ones such as lines. A GIS for Educators worksheet at Linfiniti adds the detection and correction of digitising errors and carrying out network analysis
. Topological error correction is explained in more detail in a paper by Ubeda and Egenhofer.
Unlike GML
, topologies are not directly represented in ESRI shapefiles which store individual geometric objects in isolation. Topological processing can, however, be undertaken in GIS software such as QGIS or could in principle be enforced using integrity constraints in a GIS-enabled DBMS such as PostGIS
. However, as Riedemann (2004) explains, topological operators are inherently complex and their implementation requires care to be taken with usability and conformance to standards.
Oracle
and PostGIS provide fundamental toplogical operators allowing applications to test for "such relationships as contains, inside, covers, covered by, touch, and overlap with boundaries intersecting." Unlike the PostGIS documentation, the Oracle documentation draws a distinction between "topological relationships [which] remain constant when the coordinate space is deformed, such as by twisting or stretching" and "relationships that are not topological [which] include length of, distance between, and area of." These operators are leveraged by applications to ensure that data is stored an processed in a topologically correct fashion.
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
rules would require that the counties share a common boundary with no gaps and no overlaps. Similarly, it would be nonsense to allow two polygons representing lakes to overlap.
The ESRI
ESRI
Esri is a software development and services company providing Geographic Information System software and geodatabase management applications. The headquarters of Esri is in Redlands, California....
White Paper GIS Topology explains that topology operations are used to manage shared geometry, define and enforce data integrity
Data integrity
Data Integrity in its broadest meaning refers to the trustworthiness of system resources over their entire life cycle. In more analytic terms, it is "the representational faithfulness of information to the true state of the object that the information represents, where representational faithfulness...
rules, support topological relationship queries and navigation, and build more complex shapes such as polygons, from primitive ones such as lines. A GIS for Educators worksheet at Linfiniti adds the detection and correction of digitising errors and carrying out network analysis
Network theory
Network theory is an area of computer science and network science and part of graph theory. It has application in many disciplines including statistical physics, particle physics, computer science, biology, economics, operations research, and sociology...
. Topological error correction is explained in more detail in a paper by Ubeda and Egenhofer.
Unlike GML
Geography Markup Language
The Geography Markup Language is the XML grammar defined by the Open Geospatial Consortium to express geographical features. GML serves as a modeling language for geographic systems as well as an open interchange format for geographic transactions on the Internet...
, topologies are not directly represented in ESRI shapefiles which store individual geometric objects in isolation. Topological processing can, however, be undertaken in GIS software such as QGIS or could in principle be enforced using integrity constraints in a GIS-enabled DBMS such as PostGIS
PostGIS
PostGIS is an open source software program that adds support for geographic objects to the PostgreSQL object-relational database. PostGIS follows the Simple Features for SQL specification from the Open Geospatial Consortium .-Features:...
. However, as Riedemann (2004) explains, topological operators are inherently complex and their implementation requires care to be taken with usability and conformance to standards.
Oracle
Oracle Database
The Oracle Database is an object-relational database management system produced and marketed by Oracle Corporation....
and PostGIS provide fundamental toplogical operators allowing applications to test for "such relationships as contains, inside, covers, covered by, touch, and overlap with boundaries intersecting." Unlike the PostGIS documentation, the Oracle documentation draws a distinction between "topological relationships [which] remain constant when the coordinate space is deformed, such as by twisting or stretching" and "relationships that are not topological [which] include length of, distance between, and area of." These operators are leveraged by applications to ensure that data is stored an processed in a topologically correct fashion.