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.
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Karimipour, F., Delavar, M.R., Frank, A.U. (2008). A Mathematical Tool to Extend 2D Spatial Operations to Higher Dimensions. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2008. ICCSA 2008. Lecture Notes in Computer Science, vol 5072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69839-5_12
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DOI: https://doi.org/10.1007/978-3-540-69839-5_12
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