Spatial Relation Operations on the Basis of V9I

Operations and description for spatial are important to GIS.At the present, investigations about them are mainly based on 9-intersection (9I) model for spatial relations.However, due to the infinity of the complements of objects in the model, it is difficult or impossible to directly capture the complements objects.Therefore, even though most of spatial relations could be defined in the SDTS with aggregates of two or more 9-intersection primitives, it is difficult to calculate these primitives from spatial data, and further operations based on spatial relations are also difficult.A new Voronoi-based 9-intersection (V9I) model can overcome this deficiency by redefining the exterior of spatial object with its Voronoi region instead of its complement in 9-intersection model because the Voronoi region becomes infinitive no more. As one component of the series of investigations about Voronoi and spatial relations, this paper mainly attempts to set up a mapping mechanism and conceptual framework for mainpulating spatial relations on the basis of V9I model for spatial relations in order to provide a theoritical and practical basis for the further deep investigations.The mapping method is composed of three steps close related to each other from the lower level spatial data to higher level spatial relations.The first step is to generate Voronoi diagram on spatial objects with the algorithm based on dynamical distance transform because this algorithm can efficiently reduce the generating error to about a pixel.The second is to compute the V9I model values using a computation rules and logical control flow that is presented to improve the computation speed.The third is to determine spatial relations according to the rules for determining spatial relations from V9I model values.After that, based on the above mapping method, primitive operations on spatial relations are constructed which are available to apply to a GIS system, and formalization of these operations are given by the spatial algebra for the sake of standardization and easy realization of their application to a practical system.With these primitive operations on spatial relations, some more complicated operations of spatial analysis and query can be easy to execute. Finally, in order to examine the above idea and method, an experimental tool for spatial relations is designed and realized using V C ++ on the Windows operation system.Some functions for spatial analysis and query about spatial relations can be executed using the tool.The study and experiment indicate that the new method for spatial relations operations based on V9I model is manipulable and easy to be realized.Moreover, compared with the method based on 9I model, the V9I method can save time and space for spatial query and analysis because the operations are only local but without completeness and complicated topological relations may not be stored permanently since Voronoi digrams can be dynamically constructed through the raster algorithm within the desired precision.