Achieving Integrity in Geographic Information Systems—Maps and Nested Maps

• Authors: Lutz Plü/mer;Gerhard Grö/ger
• Venue: Geoinformatica
• Year: 1997

This article provides a formal data model which allows to establishgeometrical-topological integrity of areal objects in a geographicalinformation system (GIS). The data model leads to an automatic tool able tocheck consistency of a given set of data and to avoid inconsistencies causedby updates of the database. To this end we start from the mathematicalnotion of a map which provides an irregular tessellation, i.e., a partitionof the plane which is non-overlapping and covering. From anotherperspective, a map is a plane graph with an explicit representation of facesas its atomic areal components. The concept of nested maps extends thisstandard notion by the specification of a hierarchical structure whichaggregates the set of faces. Such aggregations are common in political andadministrative structures. Whereas the mathematical notion of a map isfamiliar in GIS and the base for many tools supporting topological editing,there was a lack of effectively checkable integrity constraints which arecorrect and complete, i.e., equivalent, for maps. This article provides anaxiomatic, effectively checkable characterization of maps which isequivalent to the standard mathematical one, extends it to nested maps anddiscusses how to use them in order to achieve and maintain integrity in aGIS.