Some Results on the Modelling of Spatial Data

Abstract. Formal methods based on the mathematical theory of partially ordered sets (i.e., posets) have been used in the database field for the modelling of spatial data since many years. In particular, the use of the lattice completion (or normal completion) of a poset has been shown by Kainz, Egenhofer and Greasley [13] to be a fundamental technique to build meaningful representations of spatial subdivisions. In fact, they proved that the new elements introduced by the normal completion process can (and have to) be interpreted as being the intersection of poset elements. This is fundamental, from a mathematical point of view, since it means that the lattice resulting from the normal completion is the closure of the given poset with respect to the intersection operation. In this paper we precisely clarify the limitations for the use of lattices as models for spatial subdivisions, by proving sufficient and necessary conditions. Our result gives therefore a sound theoretical basis for t...

• Type: Conference
• Year: 1998
• Where: SOFSEM
• Authors: Luca Forlizzi, Enrico Nardelli
• Keywords: Normal Completion, Normal Completion Process, SOFSEM 1998, Spatial Subdivisions, Theoretical Computer Science