R3-[Q-Shape] - Research: Qualitative Spatial Reasoning

The Doublecross Calculus

In [Fre92] a ternary calculus based on human cognitive aspects was presented. The observer is situated in position a and looks or moves towards position b and wants to relate object c. Introducing the front/back dichotomy relative to b results in a substantial gain of information. In combination with the left/right dichotomy eight meaningful disjoint orientation relations, namely straight-front (0), right-front (7), right-neutral (6), rightback (5), straight-back (4), left-back (3), left-neutral (2), and left-front (1) are obtained. Also this dichotomy can be applied relative to a seen from b. The following figures show the two different reference systems and the 15 resulting tuples by combining them, which are interpreted as base relations. Additionally a relation i was introduced for the case where a=b, i.e. no orientation information is available.

The two single cross reference systems.
The resulting tuples by combining the two reference systems from above.

Bibliography

[Fre92]: Christian Freksa. Using Orientation Information for Qualitative Spatial Reasoning In Proceedings of the International Conference GIS - From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning in Geographic Space pages 162-178, 1992.