Finitely representable spatial objects and efficient computation

Abstract

This paper discusses issues that relate to the finite representation of database entities that may have an infinite size. A first issue concerns the construction of unique representations which support efficient implementations of various procedures. We discuss sorted and unsorted representations of various geometrical entities and show how the sorted representations support more efficient procedures. A second issue concerns the declarative specification of various procedures in terms of the parameters of the finite representation of entities. This issue is of importance in relation to the ease with which a user may express procedures on complex representations. We show how well-defined procedures may be represented in a declarative form in terms of the parameters of the finite representation of the entities.