Conceptual Geometric Modelling

Chapter

Abstract

This chapter starts with a review of existing spatial data models in the literature to show some key problems that need to be addressed by conceptual models to include spatial data and more generally geometric data. Motivated among other things by the need to support spatial modelling for the sustainable land use initiative we present a geometrically enhanced ER model (GERM), which preserves the key principles of ER modelling and at the same time introduces bulk constructions and types that support geometric objects. The model distinguishes between a syntactic level of types and an explicit internal level, in which types give rise to polyhedra that are defined by algebraic varieties. It further emphasises the stability of algebraic operations by means of a natural modelling algebra that extends the usual Boolean operations on point sets.

References

  1. 1.
    AgResearch (2005) Farm plan prototype for SLUI. Retrieved online from the New Zealand Association of Resource Management: http://www.nzarm.org.nz/KinrossWholeFarmPlan_A4_200dpi_secure.pdf
  2. 2.
    Brieskorn E, Knörrer H (1981) Plane algebraic curves. Birkhäuser, BaselGoogle Scholar
  3. 3.
    Balley S, Parent C, Spaccapietra S (2004) Modelling geographic data with multiple representations. Int J Geogr Inf Sci 18(4):327–352CrossRefGoogle Scholar
  4. 4.
    Balley S, Parent C, Spaccapietra S (2004) Modelling geographic data with multiple representations. Int J Geogr Inf Sci 18(4):327–352CrossRefGoogle Scholar
  5. 5.
    Behr T, Schneider M (2001) Topological relationships of complex points and complex regions. In: Kunii HS et al (eds) Conceptual modeling – ER 2001. Lecture notes in computer science, vol 2224. Springer, Berlin, pp 56–69CrossRefGoogle Scholar
  6. 6.
    Chang K-T (2008) Introduction to geographic information systems. McGraw-Hill, New YorkGoogle Scholar
  7. 7.
    Corbett JP (1979) Topological principles in cartography. Technical paper 48, US Bureau of Census, Washington, DCGoogle Scholar
  8. 8.
    Chen CX, Zaniolo C (2000) SQLST: a spatio-temporal data model and query language. In: Laender AHF, Liddle SW, Storey VC (eds) Conceptual modeling – ER 2000. Lecture notes in computer science, vol 1920. Springer, Berlin, pp 96–111CrossRefGoogle Scholar
  9. 9.
    Frank AU (2005) Map algebra extended with functors for temporal data. In: Akoka J et al (eds) Perspectives in conceptual modeling – ER 2005 workshops. Lecture notes in computer science, vol 3770. Springer, Berlin, 194–207Google Scholar
  10. 10.
    Gao XS, Chou SC (1992) Implicitization of rational parametric equations. J Symbol Comput 14:459–470MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Goodchild MF (1992) Geographical data modeling. Comput Geosci 18(4):401–408CrossRefGoogle Scholar
  12. 12.
    Hartwig A (1996) Algebraic 3-D modeling. Peters, WellesleyMATHGoogle Scholar
  13. 13.
    Hull R, King R Semantic database modeling: survey, applications, and research issues. ACM Comput Surv 19(3):201–260Google Scholar
  14. 14.
    Hartmann S, Link S Collection type constructors in entity-relationship modeling. In: Parent C et al. (eds) Conceptual modeling – ER 2007. Lecture notes in computer science, vol 4801. Springer, Berlin, pp 307–322Google Scholar
  15. 15.
    Ishikawa Y, Kitagawa H (2001) Source description-based approach for the modeling of spatial information integration. In: Kunii HS et al (eds) Conceptual modeling – ER 2001. Lecture notes in computer science, vol 2224. Springer, Berlin, pp 41–55CrossRefGoogle Scholar
  16. 16.
    Kösters G, Pagel B-U, Six H-W (1997) Gis-application development with geoooa. Int J Geogr Inf Sci 11(4):307–335CrossRefGoogle Scholar
  17. 17.
    Liu W, Chen J, Zhao R, Cheng T (2005) A refined line-line spatial relationship model for spatial conflict detection. In: Akoka J et al (eds) Perspectives in conceptual modeling – ER 2005 workshops. Lecture notes in computer science, vol 3770. Springer, Berlin, pp 239–248Google Scholar
  18. 18.
    Laurini R, Thompson D (1992) Fundamentals of spatial information systems. Academic, LondonMATHGoogle Scholar
  19. 19.
    Lo CP, Yeung AKW (2006) Concepts and techniques of geographic information systems, 2nd edn. Ph series in geographic information science. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  20. 20.
    Mackay A (2007) Specifications of whole farm plans as a tool for affecting land use change to reduce risk to extreme climatic events. AgResearchGoogle Scholar
  21. 21.
    McKenny M, Schneider M (2007) PLR partitions: a conceptual model of maps. In: Hainaut J-L et al (eds) Advances in conceptual modeling – foundations and applications, ER 2007 workshops. Lecture notes in computer science, vol 4802. Springer, Berlin, 368–377CrossRefGoogle Scholar
  22. 22.
    Ma H, Schewe K-D, Thalheim B (2009) Geometrically enhanced conceptual modelling. In: Laender A et al (eds) Conceptual modeling – ER 2009. Lecture notes in computer science, vol 5829. Springer, Berlin, pp 219–233CrossRefGoogle Scholar
  23. 23.
    Paredaens J (1995) Spatial databases, the final frontier. In: Gottlob G, Vardi MY (eds) Database theory – ICDT’95. Lecture notes in computer science, vol 893. Springer, Berlin, pp 14–32CrossRefGoogle Scholar
  24. 24.
    Paredaens J, Kuijpers B (1998) Data models and query languages for spatial databases. Data Knowl Eng 25(1–2):29–53CrossRefMATHGoogle Scholar
  25. 25.
    Price R, Tryfona N, Jensen CS (2001) Modeling topological constraints in spatial part-whole relationships. In: Kunii HS et al (eds) Conceptual modeling – ER 2001. Lecture notes in computer science, vol 2224. Springer, Berlin, pp 96–111, 27–40CrossRefGoogle Scholar
  26. 26.
    Salomon D (2005) Curves and surfaces for computer graphics. Springer, BerlinGoogle Scholar
  27. 27.
    Schneider M (1997) Spatial data types for database systems, finite resolution geometry for geographic information systems. Lecture notes in computer science, vol 1288. Springer, BerlinGoogle Scholar
  28. 28.
    Schneider M (2009) Spatial and spatio-temporal data models and languages. In: Encyclopedia of database systems, pp 2681–2685Google Scholar
  29. 29.
    Schneider M (2009) Spatial data types. In: Encyclopedia of database systems, pp 2698–2702Google Scholar
  30. 30.
    Stoffel E-P, Lorenz B, Ohlbach H-J (2007) Towards a semantic spatial model for pedestrian indoor navigation. In: Hainaut J-L et al (eds) Advances in conceptual modeling – foundations and applications, ER 2007 workshops. Lecture notes in computer science, vol 4802. Springer, Berlin, pp 328–337CrossRefGoogle Scholar
  31. 31.
    Sali A, Schewe K-D (2009) A characterisation of coincidence ideals for complex values. J Univers Comput Sci 15(1):304–354MathSciNetMATHGoogle Scholar
  32. 32.
    Shekhar S, Xiong H (eds) (2008) Encyclopedia of GIS. Springer, BerlinGoogle Scholar
  33. 33.
    Shekhar S, Vatsavai RR, Chawla S, Burk TE (1999) Spatial pictogram enhanced conceptual data models and their translation to logical data models. In: Agouris P, Stefanidis A (eds) Integrated spatial databases, digital images and GIS. Lecture notes in computer science, vol 1737. Springer, Berlin, pp 77–104CrossRefGoogle Scholar
  34. 34.
    Thalheim B (2000) Entity relationship modeling – foundations of database technology. Springer, BerlinMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Engineering and Computer ScienceVictoria University of WellingtonWellingtonNew Zealand
  2. 2.Software Competence Center HagenbergHagenbergAustria

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