Geospatial topology
   HOME

TheInfoList



OR:

Geospatial topology is the study and application of qualitative
spatial relation A spatial relationD. M. Mark and M. J. Egenhofer (1994), "Modeling Spatial Relations Between Lines and Regions: Combining Formal Mathematical Models and Human Subjects Testing"PDF/ref> specifies how some object is located in space in relation to s ...
ships between
geographic feature A feature (also called an object or entity), in the context of geography and geographic information science, is a discrete phenomenon that exists at a location in the space and scale of relevance to geography; that is, at or near the surface of Ea ...
s, or between representations of such features in
geographic information Geographic data and information is defined in the ISO/TC 211 series of standards as data and information having an implicit or explicit association with a location relative to Earth (a geographic location or geographic position). It is also cal ...
, such as in
geographic information system A geographic information system (GIS) is a type of database containing Geographic data and information, geographic data (that is, descriptions of phenomena for which location is relevant), combined with Geographic information system software, sof ...
s (GIS). For example, the fact that two regions ''overlap'' or that one ''contains'' the other are examples of topological relationships. It is thus the application of the mathematics of
topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
to GIS, and is distinct from, but complimentary to the many aspects of geographic information that are based on quantitative spatial measurements through
coordinate geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineerin ...
. Topology appears in many aspects of
geographic information science Geographic information science or geographical information science (GIScience or GISc) is the scientific discipline that studies geographic information, including how it represents phenomena in the real world, how it represents the way humans unders ...
and GIS practice, including the discovery of inherent relationships through
spatial query A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most s ...
,
vector overlay Vector overlay is an operation (or class of operations) in a geographic information system (GIS) for integrating two or more vector spatial data sets. Terms such as ''polygon overlay'', ''map overlay'', and ''topological overlay'' are often used ...
and
map algebra Map algebra is an algebra for manipulating geographic data, primarily Field (geography) , fields. Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of primitive operations in a geographic information system (GIS) which allows ...
; the enforcement of expected relationships as validation rules stored in geospatial data; and the use of stored topological relationships in applications such as
network analysis Network analysis can refer to: * Network theory, the analysis of relations through mathematical graphs ** Social network analysis, network theory applied to social relations * Network analysis (electrical circuits) See also *Network planning and ...
. Spatial topology is the generalization of geospatial topology for non-geographic domains, e.g.,
CAD software Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve co ...
.


Topological relationships

In keeping with the definition of
topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
, a ''topological relationship'' between two geographic phenomena is any spatial relation that is not sensitive to measurable aspects of space, including transformations of space (e.g.
map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitud ...
). Thus, it includes most qualitative spatial relations, such as two features being "adjacent," "overlapping," "disjoint," or one being "within" another; conversely, one feature being "5km from" another, or one feature being "due north of" another are ''metric relations''. One of the first developments of
Geographic Information Science Geographic information science or geographical information science (GIScience or GISc) is the scientific discipline that studies geographic information, including how it represents phenomena in the real world, how it represents the way humans unders ...
in the early 1990s was the work of Max Egenhofer, Eliseo Clementini, Peter di Felice, and others to develop a concise theory of such relations commonly called the 9-Intersection Model, which characterizes the range of topological relationships based on the relationships between the interiors, exteriors, and boundaries of features. These relationships can also be classified semantically: * ''Inherent'' relationships are those that are important to the existence or identity of one or both of the related phenomena, such as one expressed in a boundary definition or being a manifestation of a mereological relationship. For example,
Nebraska Nebraska () is a state in the Midwestern region of the United States. It is bordered by South Dakota to the north; Iowa to the east and Missouri to the southeast, both across the Missouri River; Kansas to the south; Colorado to the southwe ...
lies within the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
simply because the former was created by the latter as a partition of the territory of the latter. The Missouri River is adjacent to the state of Nebraska because the definition of the boundary of the state says so. These relationships are often stored and enforced in topologically-savvy data. * ''Coincidental'' relationships are those that are not crucial to the existence of either, although they can be very important. For example, the fact that the
Platte River The Platte River () is a major river in the State of Nebraska. It is about long; measured to its farthest source via its tributary, the North Platte River, it flows for over . The Platte River is a tributary of the Missouri River, which itself ...
passes through
Nebraska Nebraska () is a state in the Midwestern region of the United States. It is bordered by South Dakota to the north; Iowa to the east and Missouri to the southeast, both across the Missouri River; Kansas to the south; Colorado to the southwe ...
is coincidental because both would still exist unproblematically if the relationship did not exist. These relationships are rarely stored as such, but are usually discovered and documented by spatial analysis methods.


Topological data structures and validation

Topology was a very early concern for GIS. The earliest vector systems, such as the
Canadian Geographic Information System {{Unreferenced, date=October 2012 The Canada Geographic Information System (CGIS) was an early geographic information system (GIS) developed for the Government of Canada beginning in the early 1960s. CGIS was used to store geospatial data for th ...
, did not manage topological relationships, and problems such as
sliver polygons Sliver may refer to: Entertainment * ''Sliver'' (novel), a 1991 novel by Ira Levin ** ''Sliver'' (film), a 1993 film adaptation of the novel ** ''Sliver'' (soundtrack), the soundtrack to the 1993 film * "Sliver" (song), a 1990 song by Nirvana *'' ...
proliferated, especially in operations such as
vector overlay Vector overlay is an operation (or class of operations) in a geographic information system (GIS) for integrating two or more vector spatial data sets. Terms such as ''polygon overlay'', ''map overlay'', and ''topological overlay'' are often used ...
. In response, topological vector data models were developed, such as GBF/DIME (U.S. Census Bureau, 1967) and POLYVRT (
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
, 1976). The strategy of the topological data model is to store topological relationships (primarily adjacency) between features, and use that information to construct more complex features. Nodes (points) are created where lines intersect and are attributed with a list of the connecting lines. Polygons are constructed from any sequence of lines that forms a closed loop. These structures had three advantages over non-topological vector data (often called "spaghetti data"): First, they were efficient (a crucial factor given the storage and processing capacities of the 1970s), because the shared boundary between two adjacent polygons was only stored once; second, they facilitated the enforcement of data integrity by preventing or highlighting ''topological errors'', such as overlapping polygons, dangling nodes (a line not properly connected to other lines), and
sliver polygons Sliver may refer to: Entertainment * ''Sliver'' (novel), a 1991 novel by Ira Levin ** ''Sliver'' (film), a 1993 film adaptation of the novel ** ''Sliver'' (soundtrack), the soundtrack to the 1993 film * "Sliver" (song), a 1990 song by Nirvana *'' ...
(small spurious polygons created where two lines should match but do not); and third, they made the algorithms for operations such as
vector overlay Vector overlay is an operation (or class of operations) in a geographic information system (GIS) for integrating two or more vector spatial data sets. Terms such as ''polygon overlay'', ''map overlay'', and ''topological overlay'' are often used ...
simpler. Their primary disadvantage was their complexity, being difficult for many users to understand and requiring extra care during data entry. These became the dominant vector data model of the 1980s. By the 1990s, the combination of cheaper storage and new users who were not concerned with topology led to a resurgence in spaghetti data structures, such as the
shapefile The shapefile format is a geospatial vector data format for geographic information system (GIS) software. It is developed and regulated by Esri as a mostly open specification for data interoperability among Esri and other GIS software product ...
. However, the need for stored topological relationships and integrity enforcement still exists. A common approach in current data is to store such as an extended layer on top of data that is not inherently topological. For example, the Esri
geodatabase A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most spa ...
stores vector data ("feature classes") as spaghetti data, but can build a "network dataset" structure of connections on top of a line feature class. The geodatabase can also store a list of topological rules, constraints on topological relationships within and between layers (e.g., counties cannot have gaps, state boundaries must coincide with county boundaries, counties must collectively cover states) that can be validated and corrected. Other systems, such as
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 (OGC). Technicall ...
, take a similar approach. A very different approach is to not store topological information in the data at all, but to construct it dynamically, usually during the editing process, to highlight and correct possible errors; this is a feature of
GIS software A GIS software program is a computer program to support the use of a geographic information system, providing the ability to create, store, manage, query, analyze, and visualize geographic data, that is, data representing phenomena for which lo ...
such as
ArcGIS ArcGIS is a family of client, server and online geographic information system (GIS) software developed and maintained by Esri. ArcGIS was first released in 1999 and originally was released as ARC/INFO, a command line based GIS system for manipula ...
Pro and
QGIS QGIS is a free and open-source cross-platform desktop geographic information system (GIS) application that supports viewing, editing, printing, and analysis of geospatial data. Functionality QGIS functions as geographic information system (GIS ...
.


Topology in spatial analysis

Several spatial analysis tools are ultimately based on the discovery of topological relationships between features: *
spatial query A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most s ...
, in which one is searching for the features in one dataset based on desired topological relationships to the features of a second dataset. For example, "where are the student locations within the boundaries of School X?" * spatial join, in which the attribute tables of two datasets are combined, with rows being matched based on a desired topological relationship between features in the two datasets, rather than using a stored key as in a normal table join in a relational database. For example, joining the attributes of a schools layer to the table of students based on which school boundary each student resides within. *
vector overlay Vector overlay is an operation (or class of operations) in a geographic information system (GIS) for integrating two or more vector spatial data sets. Terms such as ''polygon overlay'', ''map overlay'', and ''topological overlay'' are often used ...
, in which two layers (usually polygons) are merged, with new features being created where features from the two input datasets intersect. *
transport network analysis A transport network, or transportation network, is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow. Examples include but are not limited to road networks, railways, air routes, ...
, a large class of tools in which connected lines (e.g., roads, utility infrastructure, streams) are analyzed using the mathematics of
graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...
. The most common example is determining the optimal route between two locations through a street network, as implemented in most street web maps.
Oracle An oracle is a person or agency considered to provide wise and insightful counsel or prophetic predictions, most notably including precognition of the future, inspired by deities. As such, it is a form of divination. Description The word '' ...
and
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 (OGC). Technicall ...
provide fundamental topological 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
hich Ij ( fa, ايج, also Romanized as Īj; also known as Hich and Īch) is a village in Golabar Rural District, in the Central District of Ijrud County, Zanjan Province, Iran Iran, officially the Islamic Republic of Iran, and also ...
remain constant when the coordinate space is deformed, such as by twisting or stretching"'' and ''"relationships that are not topological
hich Ij ( fa, ايج, also Romanized as Īj; also known as Hich and Īch) is a village in Golabar Rural District, in the Central District of Ijrud County, Zanjan Province, Iran Iran, officially the Islamic Republic of Iran, and also ...
include length of, distance between, and area of."'' These operators are leveraged by applications to ensure that data sets are stored and processed in a topologically correct fashion. However, topological operators are inherently complex and their implementation requires care to be taken with usability and conformance to standards.


See also

*
Dimensionally Extended 9-Intersection Model The Dimensionally Extended 9-Intersection Model (DE-9IM) is a topological model and a standard used to describe the spatial relations of two regions (two geometries in two-dimensions, R2), in geometry, point-set topology, geospatial topology, ...


References

{{reflist Geographic data and information Cartography Geometric topology Spatial analysis