The Mathematical Modeling of Spatial and Non-Spatial Information in Geographic Information Systems

Herring, John R.

doi:10.1007/978-94-011-2606-9_18

Cited by 51 publications

(18 citation statements)

References 5 publications

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“…The need for sound foundation is recognised by many researchers [e,g. Pullar & Egenhofer, 1988, Herring, 1991. First sound models are developed on basis of point-set theory and the notion of boundary, interior and closure op point sets.…”

Section: Historical Backgroundmentioning

confidence: 99%

Topological Relationships and Their Use

Zlatanova

2015

Encyclopedia of GIS

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Section: Historical Backgroundmentioning

confidence: 99%

Topological Relationships and Their Use

Zlatanova

2015

Encyclopedia of GIS

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“…Indeed, intersection operator (\) is perhaps the most expensive one in terms of computation [22]. Set operators of difference and intersection have been used for describing topological relations in different form of combinations, e.g., [20], [22]. This proposed model combines two different operators (i.e., intersection and difference) with three fully subsets of a set (i.e., the interior and boundary of a set and the set itself).…”

Section: The Intersection and Difference Modelmentioning

confidence: 99%

Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants

et al. 2007

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Topological relations have played important roles in spatial query, analysis and reasoning. In a two-dimensional space (IR 2 ), most existing topological models can distinguish the eight basic topological relations between two spatial regions. Due to the arbitrariness and complexity of topological relations between spatial regions, it is difficult for these models to describe the order property of transformations among the topological relations, which is important for detailed analysis of spatial relations. In order to overcome the insufficiency in existing models, a multi-level modeling approach is employed to describe all the necessary details of region-region relations based upon topological invariants. In this approach, a set of hierarchically topological invariants is defined based upon the boundary-boundary intersection set (BBIS) of two involved regions. These topological invariants are classified into three levels based upon spatial set concept proposed, which include content, dimension and separation number at the set level, the element type at the element level, and the sequence at the integrated level. Corresponding to these hierarchical invariants, multi-level formal models of topological relations between spatial regions are built. A practical example is provided to illustrate the use of the approach presented in this paper.

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“…Cell complexes have proven to be of great value in geographic information systems to model vector objects [21], [45]. The suitability of using cell complexes is based on the theoretical results of algebraic topology [1], [36], which provide means to check the consistency of representations defined on the basis of such concepts.…”

Section: Related Workmentioning

confidence: 99%

Multi-VMap: A Multi-Scale Model for Vector Maps

et al. 2006

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Multi-VMap is a compact framework from which plane graphs representing geographic maps at different levels of detail can be extracted. Its main feature is that the scale of the extracted map can be variable through its domain, while each entity maintains consistent combinatorial relations with the rest of entities represented in the map. The model is based on a set of operators, called updates, which modify the level of detail in a small portion of a map. The set of updates is partially ordered, and can therefore be represented as a Directed Acyclic Graph, which defines our multi-scale structure. An algorithm to extract a map at the required resolution is proposed, and a lower bound for the number of different maps which can be extracted from the model is given. The model supports map data processing operations (e.g., querying), as well as progressive and selective transmission of maps over a network.

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The Mathematical Modeling of Spatial and Non-Spatial Information in Geographic Information Systems

Cited by 51 publications

References 5 publications

Topological Relationships and Their Use

Topological Relationships and Their Use

Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants

Multi-VMap: A Multi-Scale Model for Vector Maps

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