The projective space has been little explored as a means to characterize spatial objects and their relations. This thesis examines a “projective” approach regarding the modeling of spatial objects and their binary and ternary relations. By providing a formal framework to the qualitative description of the shape of objects and relations such as “object A is left of objects B and C” or “object A is surrounded by object B”, the envisaged models are of great interest in research of geographic information science.
The topological vision of objects in parallel with their representation in a metric space helped to define standards, operators, and data structures that are widely implemented in geographic information systems (GIS) and spatial DBMS. But between the topological and metric space, there are other spaces very little explored. Taking into account such spaces significantly enriches the knowledge on the subject. My research is based on studying the properties of projective space, one of these intermediate spaces. The approach is to consider certain characteristics of this space (its invariants) to describe spatial objects and their relations. These descriptions should make it possible to classify objects following qualitative criteria.