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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)

Abstract

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.

Keywords

Spatial Relation Node Degree Directed Line Topological Relation Matrix Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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