Abstract
Direction relation is an important spatial relation. Descriptions and representations for direction relations have different levels of detail because of the varying dimensions of spatial objects and different scales of the embedding spaces. Based on a direction-relation matrix, the hierarchical frame of spatial direction relations which partitions direction relations orderly and thoroughly is built. Interior direction relations are used to perfect the representation of direction relations and the binary-encoding idea is creatively applied to construct an interior detailed matrix describing multiple interior direction relations by a uniform matrix. The model integrates topological information into the description model for direction relations, which will lay the foundations of spatial compositive reasoning.
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