Representing Three-Dimensional Topography in a DBMS With a Star-Based Data Structure

Chapter
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)

Abstract

For storing and modelling three-dimensional topographic objects (e.g. buildings, roads, dykes and the terrain), tetrahedralisations have been proposed as an alternative to boundary representations. While in theory they have several advantages, current implementations are either not space efficient or do not store topological relationships (which makes spatial analysis and updating slow, or require the use of a costly 3D spatial index). We discuss in this paper an alternative data structure for storing tetrahedralisations in a DBMS. It is based on the idea of storing only the vertices and stars of edges; triangles and tetrahedra are represented implicitly. It has been used previously in main memory, but not in a DBMS—we describe how to modify it to obtain an efficient implementation in a DBMS. As we demonstrate with one real-world example, the structure is around 20 % compacter than implemented alternatives, it permits us to store attributes for any primitives, and has the added benefit of being topological. The structure can be easily implemented in most DBMS (we describe our implementation in PostgreSQL) and we present some of the engineering choices we made for the implementation.

Keywords

Query Point Steiner Point Topological Relationship Vertex Label Constrain Delaunay Triangulation 
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.

Notes

Acknowledgments

This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO) and partly funded by the Dutch Ministry of Economic Affairs, Agriculture and Innovation (project codes: 11300 and 11185).

References

  1. Blandford DK, Blelloch GE, Cardoze DE, Kadow C (2005) Compact representations of simplicial meshes in two and three dimensions. Int J Comput Geom Appl 15(1):3–24CrossRefGoogle Scholar
  2. Carlson E (1987) Three-dimensional conceptual modeling of subsurfaces structures. In: Proceedings 8th international symposium on computer-assisted cartography (Auto-Carto 8), Falls Church, VA, pp 336–345.Google Scholar
  3. Cline AK, Renka RJ (1984) A storage-efficient method for construction of a Thiessen triangulation. Rocky Mountain J Math 14:119–139CrossRefGoogle Scholar
  4. Cohen-Steiner D, Colin de Verdire E, Yvinec M (2004) Conforming delaunay triangulations in 3D. Comput Geom Theor Appl 28:217–233CrossRefGoogle Scholar
  5. Devillers O, Pion S, Teillaud M (2002) Walking in a triangulation. Int J Found Comp Sci 13(2):181–199CrossRefGoogle Scholar
  6. Finnegan DC, Smith M (2010) Managing LiDAR topography using Oracle and open source geospatial software. In: Proceedings GeoWeb 2010, Vancouver, Canada.Google Scholar
  7. Frank A, Kuhn W (1986) Cell graphs: a provable correct method for the storage of geometry. In: Proceedings 2nd international symposium on spatial data handling, Seattle, USA.Google Scholar
  8. Guttman A (1984) R-trees: a dynamic index structure for spatial searching. In: Proceedings 1984 ACM SIGMOD international conference on management of data, ACM Press, pp 47–57.Google Scholar
  9. Ledoux H, Gold CM (2008) Modelling three-dimensional geoscientific fields with the Voronoi diagram and its dual. Int J Geograph Inf Sci 22(5):547–574CrossRefGoogle Scholar
  10. Ledoux H, Meijers M (2011) Topologically consistent 3D city models obtained by extrusion. Int J Geograph Inf Sci 25(4):557–574CrossRefGoogle Scholar
  11. Molenaar M (1990) A formal data structure for three dimensional vector maps. In: Proceedings 4th international symposium on spatial data handling, Zurich, Switzerland, pp 830–843.Google Scholar
  12. Molenaar M (1998) An introduction to the theory of spatial object modelling for GIS. Taylor& Francis, LondonGoogle Scholar
  13. Mücke EP, Saias I, Zhu B (1999) Fast randomized point location without preprocessing in two-and three-dimensional Delaunay triangulations. Comput Geom Theor Appl 12:63–83CrossRefGoogle Scholar
  14. OGC (2006) OpenGIS implementation specification for geographic information-simple feature access. Open Geospatial Consortium inc., document 06–103r3.Google Scholar
  15. OGC (2007) Geography markup language (GML) encoding standard. Open Geospatial Consortium inc., document 07–036, version 3.2.1.Google Scholar
  16. Penninga F (2005) 3D topographic data modelling: Why rigidity is preferable to pragmatism. In: Cohn AG, Mark DM (eds) COSIT-Proceedings international conference on spatial information theory, Lecture Notes in Computer Science, vol 3693. Springer, pp 409–425.Google Scholar
  17. Penninga F (2008) 3D topography: a simplicial complex-based solution in a spatial DBMS. PhD thesis, Delft University of Technology, Delft, The Netherlands.Google Scholar
  18. Pilouk M (1996) Integrated modelling for 3D GIS. PhD thesis, ITC, The Netherlands.Google Scholar
  19. Shewchuk JR (2002) Constrained Delaunay tetrahedralization and provably good boundary recovery. In: Proceedings 11th international meshing roundtable, Ithaca, New York, pp 193–204.Google Scholar
  20. Shewchuk JR (2005) Star splaying: an algorithm for repairing Delaunay triangulations and convex hulls. In: Proceedings 21st annual symposium on computational geometry, ACM Press, Pisa, pp 237–246.Google Scholar
  21. Si H (2008) Three dimensional boundary conforming Delaunay mesh generation. PhD thesis, Berlin Institute of Technology, Berlin.Google Scholar
  22. van Oosterom P, Stoter J, Quak W, Zlatanova S (2002) The balance between geometry and topology. In: Richardson D, van Oosterom P (eds) Advances in Spatial Data Handling-10th International Symposium on Spatial Data Handling, Springer, pp 209–224.Google Scholar
  23. van Oosterom P, Meijers M (2011) Towards a true vario-scale structure supporting smooth-zoom. In: Proceedings of 14th ICA/ISPRS workshop on generalisation and multiple representation, Paris, pp 1–19.Google Scholar
  24. Zlatanova S, Abdul Rahman A, Shi W (2004) Topological models and frameworks for 3D spatial objects. Comp Geosci 30(4):419–428CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Delft University of TechnologyDelftThe Netherlands

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