Inversing Cardinal Direction Relations

Focusing on the inversing operation of cardinal directions, the current generative method does not always work correctly. According to the given definitions of smallest rectangular direction and original directions, the correlations between cardinal directions and interval algebra are built. Basing on the above analysis, the algorithm to compute the inverse direction and its proof are given. The results show that out of 511*511 possible pairs of basic cardinal directions, there are 757 pairs of inverse relations over simple regions and 1621 pairs over compound regions. Finally the discussion points out the reason why existing generative method works incorrectly and indicates that our method has a quite good dimensional expansibility.