Consistent queries over cardinal directions across different levels of detail

Current models for cardinal directions, such as north and northeast, are either point-based or region-based, but no models exist that apply equally, independent of the geometric data types (be it points, lines, or polygons). To allow users to formulate queries such as "Find all towns in Maine that are northeast of Augusta" without pondering about the cities' geometric data types, we extend the model of the model of the direction-relation matrix to handle arbitrary pairs of points, lines, and polygons. This new model, called the deep direction-relation matrix, retains the 3/spl times/3 structure of the direction-relation matrix with empty and non-empty tiles, while it records additionally neighbor codes for empty tiles to capture whether the tiles' boundaries are empty or not. This extension covers all intricacies imposed by line and point objects, yielding a unifying and consistent model for cardinal directions. It enables the use of cardinal directions in spatial query languages independent of the objects' geometric data types.