Qualitative Representation and Reasoning of Combined Direction and Distance Relationships in Three-Dimensional GIS

Qualitative representation and reasoning of combined direction and distance relationships are recognized as one of the promising theoretical themes in 3D GIS which are related to urban information management, planning and services, mining engineering, and so on. The focus of the studies deals with the methodologies on the descriptions of spatial objects and the determinations of their geo-referenced relationships. In this paper, a geometrical projection-based system is applied to divide a 3D space into sub-divisions. Analytical geometry is used as the mathematical tool to represent both distance and direction relationships, which are then integrated to develop a conceptual framework to depict positional relationships. A generalized equation is derived as the result from the integrated reasoning. Empirical examples are provided to show the qualitative reasoning process and results of positional relationships for some classical cases.