The spatially extended point: A model for defining the qualitative spatial behavior of a point and its scope of influence
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The goal of this dissertation is to provide a formal model for defining the qualitative spatial behavior of a point object. Beyond tracking or indexing the change of the location of a point object, the changes in the relationships between a point object and its environment is considered the main source for the formal model of this dissertation. Specifically, this dissertation focuses on the movement behavior of a point object near the boundary of a region. There are many cases in which a sense of apprehension or resistance is felt when we cross the boundary of a region. Here, the boundary of the region can be described to have a certain threshold with a critical limit needed in order to cross. To cross such a boundary, a minimum level of effort or cost is required. To represent the behaviour of moving objects near the boundary of regions, a new formal approach for integrating an object's scope of influence is described. A scope of influence is defined as the conceptual area where there is a possibility of a phenomenon or event occurring related to the object. Such an object, a spatially extended point (SEP), is considered here by addressing its scope of influence in conjunction with its location. The formalism presented is based on a topological data model and introduces a 12-intersection model to represent the topological relations between a region and the SEP in 2-dimensional space. The fourteen topological relations that can be realized in 2-D are described in the formal model. Compositions of gradual changes between topological relations show how to represent the qualitative spatial behaviors of a SEP objects near the boundary of the region. These qualitative spatial behaviors will hold the potential for enhancing spatial decision support system by providing more refined descriptions of object relations near a known region. To verify and calibrate the SEP concept, a prototype application is provided. This dissertation uses GPS golf cart tracking data from a local public golf course. By using a prototype application with golf course data, it is revealed that there is a clear behavioral pattern to the movement of the golf carts. By applying the concept of the SEP, specific golf carts showing exceptional behavior can be detected. Moreover, region-based analysis shows identifies regions that seriously affect the behavior of golf carts.
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