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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)

Abstract

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.

Keywords

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

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References

  1. 1.
    Clementini, E., Di Felice, P.: A Model for Representing Topological Relationships between Complex Geometric Features in Spatial Databases. Information Systems 90(1-4), 121–136 (1996)zbMATHGoogle Scholar
  2. 2.
    Clementini, E., Di Felice, P., Califano, G.: Composite Regions in Topological Queries. Information Systems 20(7), 579–594 (1995)CrossRefGoogle Scholar
  3. 3.
    Egenhofer, M.J., Herring, J.: Categorizing binary topological relations between regions, lines, and points in geographic databases. Technical Report 90-12, National Center for Geographic Information and Analysis, University of California, Santa Barbara (1990)Google Scholar
  4. 4.
    Egenhofer, M.J., Mark, D.: Modeling Conceptual Neighborhoods of Topological Line-Region Relations. Int. Journal of Geographical Information Systems 9(5), 555–565 (1995)CrossRefGoogle Scholar
  5. 5.
    Egenhofer, M.J., Clementini, E., Di Felice, P.: Topological Relations between Regions with Holes. Int. Journal of Geographical Information Systems 8(2), 128–142 (1994)Google Scholar
  6. 6.
    Gaal, S.: Point Set Topology. Academic Press, London (1964)zbMATHGoogle Scholar
  7. 7.
    Güting, R.H.: An Introduction to Spatial Database Systems. VLDB Journal 3(4), 357–399 (1994)CrossRefGoogle Scholar
  8. 8.
    Güting, R.H., Schneider, M.: Realm-Based Spatial Data Types: The ROSE Algebra. VLDB Journal 4, 100–143 (1995)CrossRefGoogle Scholar
  9. 9.
    OGC Abstract Specification, OpenGIS Consortium, OGC (1999), http://www.opengis.org/techno/specs.htm
  10. 10.
    Schneider, M.: Spatial Data Types for Database Systems - Finite Resolution Geometry for Geographic Information Systems. In: Schneider, M. (ed.) Spatial Data Types for Database Systems. LNCS, vol. 1288. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  11. 11.
    Schneider, M.: A Design of Topological Predicates for Complex Crisp and Fuzzy Regions. In: Kunii, H.S., Jajodia, S., Sølvberg, A. (eds.) ER 2001. LNCS, vol. 2224, pp. 103–116. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Tilove, R.B.: Set Membership Classification: A Unified Approach to Geometric Intersection Problems. IEEE Trans. on Computers C-29, 874–883 (1980)CrossRefMathSciNetGoogle Scholar

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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