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 on Theories and Methods of Spatio-Temporal Reasoning in Geographic Space pages 162-178, 1992.