Introducing spatial data into multidimensional models leads to the concept of Spatial OLAP (SOLAP). Existing SOLAP models do not completely integrate the semantic component of geographic information (alphanumeric attributes and relationships) or the flexibility of spatial analysis into multidimensional analysis. In this paper, the authors propose the GeoCube model and its associated operators to overcome these limitations. GeoCube enriches the SOLAP concepts of spatial measure and spatial dimension and take into account the semantic component of geographic information. The authors define geographic measures and dimensions as geographic and/or complex objects belonging to hierarchy schemas. GeoCube’s algebra extends SOLAP operators with five new operators, i.e., Classify, Specialize, Permute, OLAP-Buffer and OLAP-Overlay. In addition to classical drill-and-slice OLAP operators, GeoCube provides two operators for navigating the hierarchy of the measures, and two spatial analysis operators that dynamically modify the structure of the geographic hypercube. Finally, to exploit the symmetrical representation of dimensions and measures, GeoCube provides an operator capable of permuting dimension and measure. In this paper, GeoCube is presented using environmental data on the pollution of the Venetian Lagoon.

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.