A Voronoi-based spatial algebra for spatial relations*

Spatial relation between spatial objects is a very important topic for spatial reasoning, query and analysis in geographical information systems (GIS). The most popular models in current use have fundamental deficiencies in theory. In this paper, a generic algebra for spatial relations is presented, in which (i) appropriate operators from set operators (i. e. union, intersection, difference, difference by, symmetric difference, etc. ) are utilized to distinguish the spatial relations between neighboring spatial objects; (ii) three types of values are used for the computational results of set operations-content, dimension and number of connected components; and (iii) a spatial object is treated as a whole but the Voronoi region of an object is employed to enhance its interaction with its neighbours. This algebra overcomes the shortcomings of the existing models and it can effectively describe the relations of spatial objects.