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Integrated Representation of (Potentially Unbounded) 2D and 3D Spatial Objects for Rigorously Correct Query and Manipulation

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Advances in 3D Geo-Information Sciences

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

Abstract

In the search for a rigorous closed algebra for the query and manipulation of the representations of spatial objects, most research, apart from a few exceptions, has focused on defining and refining the mathematical model, whereby the representation is assumed to be defined by real-numbered coordinates in 2D or 3D space. The realization of this theory in the finite precision of a computer implementation is problematic, and frequently leads to unexpected and unwanted results. This paper explores a restricted, but useful representation, which supports a rigorous unsorted logic within the finite precision arithmetic of computer hardware: the regular polytope. This logic allows the derivation of a rich set of computable predicates and spatial functions. It is shown that this approach is readily implementable and is applicable to Cadastral data (with the growing need for integrated 2D and 3D representations and potentially unbounded representations of ownership volume parcels into outer space), and has the potential to support more general spatial data.

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Author information

Authors and Affiliations

  1. Department of Environment and Resource Management, Indooroopilly, Brisbane, Queensland, Australia

    Rodney James Thompson

  2. OTB, GIS Technology, Delft University of Technology, Delft, The Netherlands

    Rodney James Thompson & Peter van Oosterom

Authors
  1. Rodney James Thompson
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  2. Peter van Oosterom
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Corresponding author

Correspondence to Rodney James Thompson .

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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Thompson, R.J., van Oosterom, P. (2011). Integrated Representation of (Potentially Unbounded) 2D and 3D Spatial Objects for Rigorously Correct Query and Manipulation. 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_11

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