Conceptual Neighborhoods of Topological Relations Between Lines

  • Rui M.P. Reis
  • Max J. Egenhofer
  • João L.G. Matos
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


Conceptual neighborhood graphs form the foundation for qualitative spatial-relation reasoning as they capture the relations’ similarity. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degrees increases, from the crisp to the broad-boundary lines, roughly at the same degree as it increases for crisp lines that are transformed from R1 into R2.


Spatial Relation Node Degree Directed Line Topological Relation Matrix Difference 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rui M.P. Reis
    • 1
  • Max J. Egenhofer
    • 2
  • João L.G. Matos
    • 3
  1. 1.Instituto Geográfico PortuguêsDirecção de Serviços de Investigação e Gestão de Informação GeográficaPortugal
  2. 2.National Center for Geographic Information and Analysis Department of Spatial Information Science and Engineering Department of Computer ScienceUniversity of MaineOronoUSA
  3. 3.Departamento de Engenharia Civil e Arquitectura Instituto Superior TécnicoPortugal

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