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Advances in 3D Geo-Information Sciences pp 227–242Cite as

Modelling Three-Dimensional Geoscientific Datasets with the Discrete Voronoi Diagram

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

Abstract

Geoscientific datasets are often formed by scattered samples in 3D space having highly anisotropic distribution. To model the continuity of the phenomena they represent (e.g. temperature of a body of water, or percentage of a chemical in the air) raster structures are in most cases used. To overcome the shortcomings of rasters the Voronoi diagram (VD) has been proposed as an alternative. However, while in theory the VD is a sound solution, its use in practice is hindered by the fact that it is complex to construct and to manipulate (removal of samples, interpolation, etc.), and spatial tools have to be built. We propose in this paper a ‘middle’ solution: the 3D discrete Voronoi diagram (DVD). We investigate the properties of the 3D DVD, we propose algorithms to construct and manipulate it, and we demonstrate its use in practice with a prototype that we have built. Our prototype uses existing tools for visualisation and further analysis of DVDs.

Keywords

  • Graphical Processing Unit
  • Voronoi Diagram
  • Voronoi Cell
  • Moore Neighbourhood
  • Generalise Voronoi Diagram

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.

This work was carried out while the first author was a student in the M.Sc programme Geographical Information Management and Applications (GIMA).

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Notes

  1. 1.

    http://www.grass.itc.it

  2. 2.

    http://www.code.enthought.com/projects/mayavi/

  3. 3.

    http://www.vtk.org

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Author information

Authors and Affiliations

  1. TNO, Geological Survey of the Netherlands, Princetonlaan 6, Utrecht, 3584 CB, The Netherlands

    Tom van der Putte

  2. GIS Technology Group, Delft University of Technology, Delft, 2628 BX, The Netherlands

    Hugo Ledoux

Authors
  1. Tom van der Putte
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  2. Hugo Ledoux
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Corresponding author

Correspondence to Tom van der Putte .

Editor information

Editors and Affiliations

  1. FG Methodik der Geoinformationstechnik, Sekr. H12, TU Berlin, Straße des 17. Juni 135, Berlin, 10623, Germany

    Thomas H. Kolbe

  2. FG Methodik der Geoinformationstechnik, Sekr. H12, TU Berlin, Straße des 17. Juni 135, Berlin, 10623, Germany

    Gerhard König

  3. FG Methodik der Geoinformationstechnik, Sekr. H12, TU Berlin, Straße des 17. Juni 135, Berlin, 10623, Germany

    Claus Nagel

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van der Putte, T., Ledoux, H. (2011). Modelling Three-Dimensional Geoscientific Datasets with the Discrete Voronoi Diagram. In: Kolbe, T., König, G., Nagel, C. (eds) Advances in 3D Geo-Information Sciences. Lecture Notes in Geoinformation and Cartography(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12670-3_14

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