Broad boundary is generally used to replace one-dimensional boundary for spatial objects with vague shape. For regions with broad boundary, this concept should respect both connectedness and closeness conditions. Therefore, some real configurations, like regions with partially broad boundary (e.g. lake with rocky and swamp banks), are considered invalid. This paper aims to represent different levels of shape vagueness and consider them during the identification of topological relations. Then, an object with vague shape is composed by two crisp components: a minimal extent and a maximal extent. Topological relations are identified by applying the 9-Intersection model for the subrelations between the minimal and maximal extents of objects involved. Four subrelations are then represented through a 4-Intersection matrix used to classify the topological relations. For regions with broad boundary, 242 relations are distinguished and classified into 40 clusters. This approach supports an adverbial expression of integrity constraints and spatial queries
Abstract. Topological integrity constraints control the topological properties of spatial objects and the validity of their topological relationships in spatial databases. These constraints can be specified by using formal languages such as the spatial extension of the Object Constraint Language (OCL). Spatial OCL allows the expression of topological constraints involving crisp spatial objects. However, topological constraints involving spatial objects with vague shapes (e.g., regions with broad boundaries) are not supported by this language. Shape vagueness requires using appropriate topological operators (e.g., strongly Disjoint, fairly Meet) to specify valid relations between these objects; otherwise, the constraints cannot be respected. This paper addresses the problem of the lack of terminology to express topological constraints involving regions with broad boundaries. We propose an extension of Spatial OCL based on a geometric model for objects with vague shapes and an adverbial approach for topological relations between regions with broad boundaries. This extension of Spatial OCL is then tested on an agricultural database.
Integrity constraints can control topological relations of objects in spatial databases. These constraints can be modelled using formal languages such as the spatial extension of the Object Constraint Language (Spatial OCL). This language allows the expression of topological integrity constraints involving crisp spatial objects but it does not support constraints involving spatial objects with vague shapes (e.g. forest stand, pollution zone, valley or lake). In this paper, we propose an extension of Spatial OCL based on (1) a geometric model for objects with vague shapes, and (2) an adverbial approach for modelling topological constraints involving regions with broad boundaries. This new language provides an easiness in the formal modelling of these complex constraints. Our approach has been implemented in a code generator. A case study is also presented in the paper in the field of agriculture spreading activities. AOCL OVS takes account of the shape vagueness of spread parcel and improve spatial reasoning about them.
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