Objectives The modeling of direction relationships between object groups is one of the important research topics in the theory of spatial relationships. However, existing models fail to reasonably classify the direction relationships between object groups, and ignore the impacts of distribution shapes of object groups and distribution density of their sub-objects on direction relationships, making it difficult to accurately determine direction relationships.

Methods To solve the problem, this paper classified the direction relationships between object groups into three categories in the light of different visual cognitive outcomes of object groups; and it was found that the adjacent regions between object groups can reflect the impacts of distribution shapes of object groups and distribution density of their sub-objects on direction relationships. Based on this, a model for quantitatively calculating and qualitatively describing direction relationships between object groups was proposed. First, Delaunay triangulation is used to construct the adjacent region between object groups; then, different types of direction relationships are distinguished by preprocessing the triangles in the adjacent region; after that, the quantitative direction relationships between object groups are separated into the ones between the vertices and the edges of the triangles (i.e. the local quantitative direction relationships) for calculation. Finally, local quantitative direction relationships are transformed and integrated into the qualitative direction relationships between object groups.

Results Experimental results show that:(1) The proposed model can reasonably classify the direction relationships between object groups, and accurately distinguish and describe the direction relationships in some complex situations. (2) It can fully consider the impacts of distribution shapes of object groups and distribution density of their sub-objects on direction relationships, and effectively determine the direction relationships between different geometric types of object groups in map space.

Conclusions The proposed model has good applicability and feasibility, which can overcome the disadvantages of existing models, and improve the accuracy of determining the direction relationships between object groups.