A mathematical tool to extend 2D spatial operations to higher dimensions

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. © 2008 Springer-Verlag Berlin Heidelberg.