229:, 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
27:
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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
344:
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.
129:). 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
258:, 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
249:. 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
291:, 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?"
297:, 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
181:
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
241:
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.
559:
Clementini, Eliseo; Di Felice, Paolino; van
Oosterom, Peter (1993). "A small set of formal topological relationships suitable for end-user interaction". In Abel, David; Ooi, Beng Chin (eds.).
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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
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167:
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.
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have gaps, state boundaries must coincide with county boundaries, counties must collectively cover states) that can be validated and corrected. Other systems, such as
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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.
137:
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
85:; the enforcement of expected relationships as validation rules stored in geospatial data; and the use of stored topological relationships in applications such as
245:
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
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to GIS, and is distinct from, but complementary to the many aspects of geographic information that are based on quantitative spatial measurements through
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125:
between two geographic phenomena is any spatial relation that is not sensitive to measurable aspects of space, including transformations of space (e.g.
141:, which characterizes the range of topological relationships based on the relationships between the interiors, exteriors, and boundaries of features.
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relationships are those that are not crucial to the existence of either, although they can be very important. For example, the fact that the
703:
594:
Clementini, Eliseo; Sharma, Jayant; Egenhofer, Max J. (1994). "Modelling topological spatial relations: Strategies for query processing".
307:, in which two layers (usually polygons) are merged, with new features being created where features from the two input datasets intersect.
313:, a large class of tools in which connected lines (e.g., roads, utility infrastructure, streams) are analyzed using the mathematics of
237:(small spurious polygons created where two lines should match but do not); and third, they made the algorithms for operations such as
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Harvard Papers in
Geographic Information Systems: First International Symposium on Data Structures for Geographic Information Systems
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338:"topological relationships remain constant when the coordinate space is deformed, such as by twisting or stretching"
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Several spatial analysis tools are ultimately based on the discovery of topological relationships between features:
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46:
636:
Cooke, Donald F. (1998). "Topology and TIGER: The Census Bureau's
Contribution". In Foresman, Timothy W. (ed.).
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Goodchild, Michael F. (1977). "Statistical
Aspects of the Polygon Overlay Problem". In Dutton, Geoffrey (ed.).
134:
70:
759:
334:"such relationships as contains, inside, covers, covered by, touch, and overlap with boundaries intersecting."
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Advances in
Spatial Databases: Third International Symposium, SSD '93 Singapore, June 23–25, 1993 Proceedings
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simply because the former was created by the latter as a partition of the territory of the latter. The
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the other are examples of topological relationships. It is thus the application of the mathematics of
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233:, such as overlapping polygons, dangling nodes (a line not properly connected to other lines), and
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342:"relationships that are not topological include length of, distance between, and area of."
8:
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Unlike the PostGIS documentation, the Oracle documentation draws a distinction between
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between two locations through a street network, as implemented in most street web maps.
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The ARC/INFO Coverage data structure (1981), a topological data model based on POLYVRT
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574:
565:. Lecture Notes in Computer Science. Vol. 692/1993. Springer. pp. 277–295.
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Topology was a very early concern for GIS. The earliest vector systems, such as the
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Ubeda, Thierry; Egenhofer, Max J. (1997). "Topological error correcting in GIS".
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Peucker, Thomas K.; Chrisman, Nicholas (1975). "Cartographic Data
Structures".
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is the generalization of geospatial topology for non-geographic domains, e.g.,
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The
History of Geographic Information Systems: Perspectives from the Pioneers
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Proceedings 2004: The 7th AGILE Conference on
Geographic Information Science
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provide fundamental topological operators allowing applications to test for
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and GIS practice, including the discovery of inherent relationships through
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532:"A Mathematical Framework for the Definition of Topological Relationships"
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468:. Lecture Notes in Computer Science. Vol. 1262. pp. 281–297.
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782:"Towards Usable Topological Operators at GIS User Interfaces"
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These relationships can also be classified semantically:
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Proceedings of the fourth International Symposium on SDH
625:. Vol. 6: Spatial algorithms. Harvard University.
541:(Extended abstract). pp. 803–813. Archived from
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45:, or between representations of such features in
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441:"7. Topology — QGIS Documentation documentation"
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213:proliferated, especially in operations such as
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53:(GIS). For example, the fact that two regions
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317:. The most common example is determining the
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381:"Topology - GIS Wiki | The GIS Encyclopedia"
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37:is the study and application of qualitative
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758:. Refractions Research Inc. Archived from
187:Topological data structures and validation
30:Examples of topological spatial relations.
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499:"Point-set topological spatial relations"
537:. In Brassel, K.; Kishimoto, H. (eds.).
497:Egenhofer, M.J.; Franzosa, R.D. (1991).
225:(U.S. Census Bureau, 1967) and POLYVRT (
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19:For broader coverage of this topic, see
530:Egenhofer, M.J.; Herring, J.R. (1990).
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787:. In Toppen, F.; P. Prastacos (eds.).
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207:Canadian Geographic Information System
69:. Topology appears in many aspects of
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133:. One of the first developments of
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791:. pp. 669–674. Archived from
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780:Riedemann, Catharina (2004).
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274:Topology in spatial analysis
16:Type of spatial relationship
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474:10.1007/3-540-63238-7_35
221:were developed, such as
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
