A Mathematical Tool to Extend 2D Spatial Operations to Higher Dimensions

  • Authors:

  • Farid Karimipour;Mahmoud R. Delavar;Andrew U. Frank

  • Affiliations:

  • Department of Surveying and Geomatics Engineering, College of Engineering, University of Tehran, Tehran, Iran and Institute for Geoinformation and Cartography, Vienna University of Technology, Vie ...;Department of Surveying and Geomatics Engineering, College of Engineering, University of Tehran, Tehran, Iran;Institute for Geoinformation and Cartography, Vienna University of Technology, Vienna, Austria A-1040

  • Venue:
  • ICCSA '08 Proceeding sof the international conference on Computational Science and Its Applications, Part I
  • Year:
  • 2008

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Abstract

3D and temporal objects must be included in GIS to handle real world phenomena. Many have studied extension of spatial operations to these multi-dimensional spaces and suggested technical solutions to extend a spatial operation to a new multi-dimensional space. These technical approaches have led to developments which can not be generalized. One technique used to extend a spatial operation from 2D to a multi-dimensional space is not likely usable for another spatial operation, nor to extend the same spatial operation to another multi-dimensional space. This paper suggested studying spatial operations via their dimension-independent properties. It intends to construct a mathematical framework to integrate spatial operations of different multi-dimensional spaces (3D and time) a GIS should support. The framework will be independent of the space in which the operations are applied using algebraic structures - and more specifically category theory - that ignore those properties of operations which depend on the objects they are applied to. Implementations for some case studies for spatial operations of moving points are presented.