Topological Relationships Between Complex Lines and Complex Regions

  • Markus Schneider
  • Thomas Behr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3716)


Topological relationships between spatial objects in the two-dimensional space have been investigated for a long time in a number of disciplines like artificial intelligence, cognitive science, linguistics, and robotics. In the context of spatial databases and geographical information systems, as predicates they especially support the design of suitable query languages for spatial data retrieval and analysis. But so far, they have only been defined for simplified abstractions of spatial objects like continuous lines and simple regions. With the introduction of complex spatial data types in spatial data models and extensions of commercial database systems, an issue arises regarding the design, definition, and number of topological relationships operating on these complex types. This paper first introduces a formally defined, conceptual model of general and versatile spatial data types for complex lines and complex regions. Based on the well known 9-intersection model, it then formally determines the complete set of mutually exclusive topological relationships between complex lines and complex regions. Completeness and mutual exclusion are shown by a proof technique called proof-by-constraint-and-drawing.


Topological predicate topological constraint rule proof-by-constraint-and-drawing complex spatial data type 9-intersection model 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Markus Schneider
    • 1
  • Thomas Behr
    • 2
  1. 1.Dept. of Computer & Information Science & EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Praktische Informatik IVFern Universität HagenHagenGermany

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