Abstract
Refined topological relations play an important role in spatial database quality control. Currently, there is no unified and reasonable method to represent refined line/region and line/line topological relations in two-dimensional (2D) space. In addition, the existing independent line/region and line/line models have some drawbacks such as incomplete type discrimination and too many topological invariants. In this paper, a refined line/region and line/line topological relations are represented uniformly by the sequence, dimension, and topological type of the intersection components. To make the relevant definitions conform to the traditional cognitions in 2D Euclidean space, the (simple) spatial object is defined based on manifold topology, and the spatial intersection components are defined based on the whole-whole object intersection set. Then the topological invariant of node degree is introduced, and the adjacent point kinds (e.g., “Null”, “On”, “In”, and “Out”) are defined to distinguish the intersection component types. Excluding impossible and symmetrical types, 29 types of intersection-lines (including 21 between lines/regions and 8 between lines/lines), and 6 types of intersection-points (including 2 between lines/regions and 4 between lines/lines) are classified. On this basis, a node degree-based whole-whole object intersection sets (N-WWIS) model for refined line/region and line/line topological relations is presented, and it can be combined with the Euler number-based whole object intersection and difference (E-WID) model (coarse level) to form a hierarchical representation method of topological relations. Furthermore, a prototype system based on the N-WWIS model for automatic topological integrity checking is developed and some evaluation experiments are conducted with OpenStreetMap (OSM) data is presented based on the classification of intersection components. The experimental results show that the N-WWIS model will enable the geographic information systems (GIS) community to develop automated topological conflict checking and dealing tools for spatial data updates and quality control.
Highlights
Lines and regions are very important spatial objects in two-dimensional (2D) geographic information systems (GIS)
The classification of intersection component types is the key issue in the Eulerrelations number-based whole-whole intersection sets (E-WWIS) model
For the 2D intersection, their types are distinguished by the Euler numbers [29] of the difference between the two regions and the intersection component, i.e., let “IR” denote the intersection component, and the 2D intersection type is distinguished by fE (A\IR) and fE (B\IR) [2]
Summary
Lines and regions are very important spatial objects in two-dimensional (2D) geographic information systems (GIS). In Reference [2], Zhou et al proposed a hierarchical description and calculation coarse relations are represented by the E-WID model, and the refined relations are mainly method of topological between two regions in 2D space. In this method, the represented by the Eulerrelations number-based whole-whole intersection sets (E-WWIS). New topological invariants should be introduced instead of Euler numbers in the E-WWIS model for the discrimination of the types of one-dimensional and zero-dimensional intersection components between lines/regions (and lines/lines).
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