An integrated approach to representing line-line spatial relations in GIS

Spatial relations play an important role in spatial query, analysis and reasoning. However, how to represent various kinds of spatial relations in a unified form is still an open issue. In this paper, an integrated approach is presented for representing line-line spatial relations. In this approach, spatial relations are decomposed into three types, including topological, directional and distance, and topological relation acts as a most basic information chain to carry directional and distance constraints for an integrated representation. At the same time, these three relations are also described based upon the idea of decomposition and combination. At first, a non-disjoint line-line topological relation is decomposed into a set of basic topological relation units, and then these basic relation units are combined by the order of occurrence. In this way, local direction relation and distance relation are defined between two neighboring topological relation units, or between a relation unit and the corresponding endpoints of two lines, where local direction relation is described in a relative terms as left and right, and local distance relation is described by a partially Hausdorff distance. Furthermore, the ordered sets of local direction and local distance relations are constructed and obtained, respectively. Indeed, the integrated approach is very sound to represent the three kinds of spatial relations validly. A simple example is given to illustrate the advantage of the proposed approach in the paper compared to the existing ones.