Oriented Regions for Linearly Conceptualized Features

The typical phenomena in geographic space are 2-dimensional or 3dimensional in nature, yet people often conceptualize some of them as 1dimensional entities embedded in a 2-dimensional space—rivers have widths and depths, and extent across the surface of the Earth, but for some tasks they are thought of as linear objects; likewise, roads as travel paths have widths as they wind through the landscape, but in some scenarios the extent is ignored and only connectivity between points along the path is considered. A critical property that makes these features special is the orientation that is attached (e.g., through the flow of the water or the traffic directions imposed by an authority). Contemporary spatial models capture such features either 1dimensionally as networks of lines or directed lines, or 2-dimensionally simply as regions, each abstracting away one key property—in the case of the network the features’ extents and connections to neighboring areas, and in the case of regions their orientations. This paper introduces oriented regions as a model that preserves the key properties from both abstractions. Key properties of this approach are the sequences in which the boundaries of oriented regions interact, and the placement of objects with respect to the topological hull of a set of oriented regions. This model, dubbed hull+i, is based on topological hulls and the i-notation, a systematic method to capture boundary interactions between oriented regions, and provides a means for representing entire spatial scenes with an arbitrary number of objects, separations, and instances where ensembles of objects surround other objects.