An expressive hybrid model for the composition of cardinal directions

In our previous paper (Kor and Bennett, 2003), we have shown how the nine tiles in the projection-based model for cardinal directions can be partitioned into sets based on horizontal and vertical constraints (called Horizontal and Vertical Constraints Model). In order to come up with an expressive hybrid model for direction relations between two-dimensional single-piece regions (without holes), we integrate the well-known RCC-8 model with the above-mentioned model. From this expressive hybrid model, we derive 8 atomic binary relations and 13 feasible as well as jointly exhaustive relations for the x and y directions respectively. Based on these atomic binary relations, we derive two separate 8x8 composition tables for both the expressive and weak direction relations. We introduce a formula that can be used for the computation of the composition of expressive and weak direction relations between ‘whole or part’ regions. Lastly, we also show how the expressive hybrid model can be used to make several existential inferences that are not possible for existing models.