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Encyclopedia of GIS pp 1–21Cite as

Topological Relationships and Their Use

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Definition

Topological relations between spatial objects have been widely recognized, implemented, and used in GIS. They provide a notion of the general structure and the interactions of spatial objects. Topology avoids dealing with geometry by introducing topological primitives, namely, boundary, interior, and exterior. The topological primitives allow to define approximate topological relationships between 0D (point), 1D (linestring ), 2D (surface), and 3D (body) spatial objects in 0D, 1D, 2D, and 3D space. The nine-intersection model is the well-known framework for detecting binary topological relationships (Egenhofer and Herring, 1992) and is adopted by the Opengeospatial Consortium as a basic framework for implementation. Suppose two simple spatial objects A and B are defined in the same topological space X and their boundary, interior, and exterior are denoted by ∂ A, A ∘, A −, ∂ B, B ∘, and B −. The binary relationship R(A, B) between the two objects is then identified by...

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Authors and Affiliations

  1. 3D Geoinformation, Faculty of Architecture and the Built Environment, Delft University of Technology, Delft, The Netherlands

    Sisi Zlatanova

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  1. Sisi Zlatanova
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Correspondence to Sisi Zlatanova .

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Editors and Affiliations

  1. Minneapolis, Minnesota, USA

    Shashi Shekhar

  2. Rutgers Business School, Newark, New Jersey, USA

    Hui Xiong

  3. The University of Iowa Tippie College of Business, Iowa City, Iowa, USA

    Xun Zhou

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Zlatanova, S. (2015). Topological Relationships and Their Use. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-23519-6_1548-1

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  • DOI: https://doi.org/10.1007/978-3-319-23519-6_1548-1

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  • Publisher Name: Springer, Cham

  • Online ISBN: 978-3-319-23519-6

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