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A Triangle-Based Logic for Affine-Invariant Querying of Two-Dimensional Spatial Data

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Constraint Databases (CDB 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3074))

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Abstract

In spatial databases, incompatibilities often arise due to different choices of origin or unit of measurement (e.g., centimeters versus inches). By representing and querying the data in an affine-invariant manner, we can avoid these incompatibilities.

In practice, spatial (resp., spatio-temporal) data is often represented as a finite union of triangles (resp., moving triangles). As two arbitrary triangles are equal up to a unique affinity of the plane, they seem perfect candidates as basic units for an affine-invariant query language.

We propose a so-called “triangle logic”, a query language that is affine-generic and has triangles as basic elements. We show that this language has the same expressive power as the affine-generic fragment of first-order logic over the reals on triangle databases. We illustrate that the proposed language is simple and intuitive. It can also serve as a first step towards a “moving-triangle logic” for spatio-temporal data.

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Author information

Authors and Affiliations

  1. Department WNI, Limburgs Universitair Centrum, Universitaire Campus, B-3590, Diepenbeek, Belgium

    Sofie Haesevoets

Authors
  1. Sofie Haesevoets
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Editor information

Editors and Affiliations

  1. Theoretical Computer Science Group, Hasselt University & Transnational University of Limburg, Belgium

    Bart Kuijpers

  2. University of Nebraska - Lincoln, NE 68588, Lincoln, USA

    Peter Revesz

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Haesevoets, S. (2004). A Triangle-Based Logic for Affine-Invariant Querying of Two-Dimensional Spatial Data. In: Kuijpers, B., Revesz, P. (eds) Constraint Databases. CDB 2004. Lecture Notes in Computer Science, vol 3074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25954-1_4

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  • DOI: https://doi.org/10.1007/978-3-540-25954-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22126-5

  • Online ISBN: 978-3-540-25954-1

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