Splitting Ratios: Metric Details of Topological Line-Line Relations

Within the geographic domain, an important class of relies on geometric abstractions in the form of lines where, for instance, transportation networks and trajectories of movements are typically perceived or modeled at such a generalized geometric level. To support querying and computational comparisons, oftentimes multi-resolution models are needed to guide users from coarser to finer details. Within such a setting topological properties are coarse spatial information, whereas metric refinements offer finer details. The 9-intersection distinguishes 33 topological relations between two lines. This paper develops a model that captures metric details for line-line relations through splitting ratios, which are normalized values of lengths and areas of intersections. These ratios apply to the 9-intersection's nonempty values, thereby providing refinements of topological properties. Three such splitting ratios comprehensively refine 30 of the 33 topological relations: one for the leng...

• Type: Conference
• Year: 2004
• Where: FLAIRS
• Authors: Konstantinos A. Nedas, Max J. Egenhofer
• Keywords: Artificial Intelligence, FLAIRS 2004, Splitting Ratios, Topological Properties, Topological Relations