Relational Formalism for the Management of Spatial Data

Abstract

Operations on spatial objects have great individuality. As a consequence, the spatial data modelling approaches, which have been proposed, have to consider either data types of the form set of spatial objects or non-1NF data structures or a limited spatial functionality of the operations. The model formalized in this paper overcomes these limitations. In particular, spatial quanta are defined and, based on them, spatial data types are formalized including point, line and surface. All the types consist of connected spatial objects that can be involved in all the spatial operations, which are defined. A relational formalism is developed for the management of spatial data. It considers non-nested relational data structures. The relational algebra consists of a kernel set of operations, the ordinary relational operations and two more. All others are defined in terms of those in the kernel. It is shown that the management of spatial data actually reduces to the management of relational data. The model achieves, and generalizes further, commonly accepted spatial operations. Although the formalism restricts to the management of 2D spatial data, its extension to n-D is straightforward. In conjunction with previous research, the algebraic operations are closed and enable the uniform management of any type of data, i.e. spatial, spatio-temporal, interval and conventional.