On interval descriptions of spatial relations

In this paper, we propose an extension of the principle of the interval's approach to define new directional and qualitative topological relations where the description is more precise and where an adaptation of the concept of earlier methods based on Ellen's algebra is possible. Thus, for any reference position we want to locate (beginning, middle, between two sets, under, ...), we had only to locate the position by the reference sets and then define the desired spatial relationships by comparing the percentage of the interior parts/exterior parts regarding this reference.