Calculations Based On The Spatial Relationship Of The Voronoi Diagram

Spatial relations are one of the most distinctive aspects of spatial or geographical information, and thus a better understanding of the cognitive aspects of spatial relations, and their formalization in computational models, is critical to the advancement of geographical information science.Currently, 9-intersection method is most popular to be used for the studies and applications of spatial relations in CIS field. However, there are some imperfections and deficiencies in theory and practice in this method, such as the paradox of topological definition, linear dependency of three components of an object and worse computability and so on. To overcome the limitations of this method and other related methods and models and improve the current methods and models for spatial relations, a new method, simply called VW method for the computation of spatial relations is presented in this thesis.In this method, a spatial object is treated as a whole, the Voronoi region of an object is employed to enhance its interaction with its neighbors, and appropriate operators from set operators and several types of values are utilized to compute the spatial relations spatial objects. The new approach can overcome the shortcomings of existing methods and presents a framework for computing different spatial relations.In order to use this method more efficiently, Voronoi diagrams should be generated and maintained dynamically at first. So a new raster based method is described for generating and maintaining Voronoi diagrams dynamically with active region growing technology, and also a method based on virtual four boundaries for conversion of raster Voronoi regions into vector is presented.And then three different types of spatial relations are computed using the new method for spatial relations: for topological relations, a formal computational model called V4T model is presented, and the strategies and steps are developed based on this model; for main direction relations, the distribution of Voronoi regions is used to establish a formal model; for left and right relations, the computation is performed by constructing the directed Voronoi regions; for spatial neighboring relations, the concept of neighbor is extended and Voronoi K order neighbor is introduced to define and compute different neighobring relations within one conceptual framework, also three algorithms are presented to compute the order of neighboring relations.Finally, a tool VTKit for the computation of spatial relations and Voronoi diagram and related applications is developed independently to examine the new method and models for spatial relations using VC++ and COM technology on the platform of Windows 2000. Experimental results with the practical and simulated spatial data show the reasonability and practicability of the new method for spatial relations.