Skip to main content
SpringerLink
Log in

Modelling Higher Dimensional Data for GIS Using Generalised Maps

  • Conference paper
Computational Science and Its Applications – ICCSA 2013 (ICCSA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7971))

Included in the following conference series:

Abstract

Real-world phenomena have traditionally been modelled in 2D/3D GIS. However, powerful insights can be gained by integrating additional non-spatial dimensions, such as time and scale. While this integration to form higher-dimensional objects is theoretically sound, its implementation is problematic since the data models used in GIS are not appropriate. In this paper, we present our research on one possible data model/structure to represent higher-dimensional GIS datasets: generalised maps. It is formally defined, but is not directly applicable for the specific needs of GIS data, e.g. support for geometry, overlapping and disconnected regions, holes, complex handling of attributes, etc. We review the properties of generalised maps, discuss needs to be modified for higher-dimensional GIS, and describe the modifications and extensions that we have made to generalised maps. We conclude with where this research fits within our long term goal of a higher dimensional GIS, and present an outlook on future research.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Frank, A.U.: Spatial concepts, geometric data models, and geometric data structures. Computers & Geosciences 18(4), 409–417 (1992)

    Article  Google Scholar 

  2. Hazelton, N., Leahy, F., Williamson, I.: On the design of temporally-referenced, 3-D geographical information systems: development of four-dimensional GIS. In: Proceedings of GIS/LIS 1990 (1990)

    Google Scholar 

  3. Hansen, H.S.: A quasi-four dimensional database for the built environment. In: Westort, C.Y. (ed.) DEM 2001. LNCS, vol. 2181, pp. 48–59. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. O’Conaill, M.A., Bell, S.B.M., Mason, N.C.: Developing a prototype 4D GIS on a transputer array. ITC Journal (1), 47–54 (1992)

    Google Scholar 

  5. Raper, J.: Multidimensional geographic information science. Taylor & Francis (2000)

    Google Scholar 

  6. Worboys, M.F.: A unified model for spatial and temporal information. The Computer Journal 37(1), 26–34 (1994)

    Article  Google Scholar 

  7. Goodchild, M.F.: Geographical data modeling. Computers & Geosciences 18(4), 401–408 (1992)

    Article  Google Scholar 

  8. Peuquet, D.J.: Representations of Space and Time. Guilford Press (2002)

    Google Scholar 

  9. Oosterom, P.v., Meijers, M.: Towards a true vario-scale structure supporting smooth-zoom. In: Proceedings of the 14th ICA/ISPRS Workshop on Generalisation and Multiple Representation, Paris (2011)

    Google Scholar 

  10. Li, Z.: Reality in time-scale systems and cartographic representation. The Cartographic Journal 31(1), 50–51 (1994)

    Article  Google Scholar 

  11. Karimipour, F., Delavar, M.R., Frank, A.U.: A simplex-based approach to implement dimension independent spatial analyses. Computers & Geosciences 36(9), 1123–1134 (2010)

    Article  Google Scholar 

  12. Albrecht, J.: Universal Analytical GIS Operations. A Task-Oriented Systematization of Data Structure-Independent GIS Functionality Leading Towards a Geographic Modeling Language. PhD thesis, University of Vechta (1995)

    Google Scholar 

  13. Thompson, R.J., van Oosterom, P.: Integrated representation of (potentially unbounded) 2D and 3D spatial objects for rigorously correct query and manipulation. In: Kolbe, T.H., König, G., Nagel, C. (eds.) Advances in 3D Geo-Information Sciences. Lecture Notes in Geoinformation and Cartography, pp. 179–196. Springer (2011)

    Google Scholar 

  14. Basoglu, U., Morrison, J.: The efficient hierarchical data structure for the US historical boundary file. In: Dutton, G. (ed.) Harvard Papers on Geographic Information Systems, vol. 4, Addison-Wesley (1978)

    Google Scholar 

  15. OGC: OpenGIS City Geography Markup Language (CityGML) Encoding Standard. Open Geospatial Consortium. 1.0.0 edn (August 2008)

    Google Scholar 

  16. Peuquet, D.J., Duan, N.: An event-based spatiotemporal data model (ESTDM) for temporal analysis of geographical data. International Journal of Geographical Information Science 9(1), 7–24 (1995)

    Article  Google Scholar 

  17. Claramunt, C., Parent, C., Spaccapietra, S., Thériault, M.: Database modelling for environmental and land use changes. In: Stillwell, J.C.H., Geertman, S., Openshaw, S. (eds.) Geographical Information and Planning. Advances in Spatial Science, pp. 181–202. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  18. van Oosterom, P.: Variable-scale topological data structures suitable for progressive data transfer: The GAP-face tree and GAP-edge forest. Cartography and Geographic Information Science 32(4), 331–346 (2005)

    Article  Google Scholar 

  19. Tøssebro, E., Nygård, M.: Representing topological relationships for spatiotemporal objects. Geoinformatica 15, 633–661 (2011)

    Article  Google Scholar 

  20. van Oosterom, P., Meijers, M.: Vario-scale data structures supporting smooth zoom and progressive transfer of 2D and 3D data. In: Jaarverslag 2011. Nederlandse Commissie voor Geodesie (2012)

    Google Scholar 

  21. Casali, A., Cicchetti, R., Lakhal, L.: Cube lattices: a framework for multidimensional data mining. In: Proceedings of the 3rd SIAM International Conference on Data Mining, pp. 304–308 (2003)

    Google Scholar 

  22. McInerney, T., Terzopoulos, D.: A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image analysis. Computerized Medical Imaging and Graphics 19(1), 69–83 (1995)

    Article  Google Scholar 

  23. Snoeyink, J., van Kreveld, M.: Good orders for incremental (re)construction. In: Proceedings of the 13th ACM Symposium on Computational Geometry, pp. 400–402 (1997)

    Google Scholar 

  24. Blandford, D.K., Blelloch, G.E., Cardoze, D.E., Kadow, C.: Compact representations of simplicial meshes in two and three dimensions. International Journal of Computational Geometry and Applications 15(1), 3–24 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Shewchuk, J.R.: Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations. In: Proceedings of the 16th Annual Symposium on Computational Geometry, pp. 350–359 (2000)

    Google Scholar 

  26. Shewchuk, J.R.: General-dimensional constrained Delaunay and constrained regular triangulations, I: Combinatorial properties. Discrete & Computational Geometry 39(1003), 580–637 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design 23(1), 59–82 (1991)

    Article  MATH  Google Scholar 

  28. Mäntylä, M.: An introduction to solid modeling. Computer Science Press, New York (1988)

    Google Scholar 

  29. Bulbul, R., Frank, A.U.: AHD: The alternate simplicial decomposition of nonconvex polytopes (generalization of a convex polytope based spatial data model). In: Proceedings of the 17th International Conference on Geoinformatics, pp. 1–6 (2009)

    Google Scholar 

  30. Bieri, H., Nef, W.: Elementary set operations with d-dimensional polyhedra. In: Noltemeier, H. (ed.) CG-WS 1988. LNCS, vol. 333, pp. 97–112. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  31. Granados, M., Hachenberger, P., Hert, S., Kettner, L., Mehlhorn, K., Seel, M.: Boolean operations on 3D selective nef complexes: Data structure, algorithms and implementation. In: Proceedings of the 11th Annual European Symposium on Algorithms, pp. 174–186 (September 2003)

    Google Scholar 

  32. Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasi-manifolds. International Journal of Computational Geometry and Applications 4(3), 275–324 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  33. Edmonds, J.: A combinatorial representation of polyhedral surfaces. Notices of the American Mathematical Society 7 (1960)

    Google Scholar 

  34. Brisson, E.: Representing geometric structures in d dimensions: topology and order. In: Proceedings of the 5th Annual Symposium on Computational Geometry, pp. 218–227. ACM, New York (1989)

    Google Scholar 

  35. Hatcher, A.: Algebraic Topology. Cambridge University Press (2002)

    Google Scholar 

  36. Lévy, B., Mallet, J.L.: Cellular modeling in arbitrary dimension using generalized maps. Technical report, ISA-GOCAD (1999)

    Google Scholar 

  37. van Oosterom, P., Stoter, J.: 5D data modelling: Full integration of 2D/3D space, time and scale dimensions. In: Fabrikant, S.I., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds.) GIScience 2010. LNCS, vol. 6292, pp. 310–324. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Delft University of Technology, The Netherlands

    Ken Arroyo Ohori, Hugo Ledoux & Jantien Stoter

Authors
  1. Ken Arroyo Ohori
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hugo Ledoux
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jantien Stoter
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. L-I.S.U.T. - D.A.P.I.t. Facoltà Ingegneria, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano, 10, 85100, Potenza, Italy

    Beniamino Murgante

  2. Covenant University, Canaanland, Ota, Nigeria

    Sanjay Misra

  3. Partimento di Scienze e Tecnologie per LAgricoltura, le Foreste, la Natura e lEnergia, Università degli Studi della Tuscia, Via S. Camillo de Lellis, snc, 01100, Viterbo, Italy

    Maurizio Carlini

  4. Dipartimento di Scienze dell’Ingegneria Civile e dell’Architecttura, Politecnico di Bari, Via Orabona, 4, 70125, Bari, Italy

    Carmelo M. Torre

  5. International University VNU-HCM, Quarter 6, Linh Trung, Thu Duc, Ho Chi Minh City, Vietnam

    Hong-Quang Nguyen

  6. School of Business Systems, Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Arroyo Ohori, K., Ledoux, H., Stoter, J. (2013). Modelling Higher Dimensional Data for GIS Using Generalised Maps. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39637-3_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39637-3_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39636-6

  • Online ISBN: 978-3-642-39637-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation