A New Way to Represent the Relative Position between Areal Objects

The fuzzy qualitative evaluation of directional spatial relationships (such as "to the right of", "to the south of"...) between areal objects often relies on the computation of a histogram of angles, which is considered to provide a good representation of the relative position of an object with regard to another. In this paper, the notion of the histogram of forces is introduced. It generalizes and may supersede the histogram of angles. The objects (2-D entities) are handled as longitudinal sections (1-D entities), not as points (0-D entities). It is thus possible to fully benefit from the power of integral calculus and so ensure rapid processing of raster data as well as of vector data, explicitly considering both angular and metric information.