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Although the definitions of formal models used to represent spatial relations have gained increasing attention over the past 30 years, the linkage between topology and distance has not yet been effectively established. A topological relation model called the distance-based topological relation model (D-TRM) that considers both the topology and distance of spatial regions is proposed. The D-TRM is divided into two subtypes: the actual DTRM (AD-TRM) and the signed DTRM (SD-TRM). The actual distance is based on the distance in a two-dimensional space. The signed distance is based on the sign of the actual distance. Eight topological relations, namely, disjoint, meet, overlap, cover, contain, equal, coveredBy and inside, represented by the AD-TRM and SD-TRM are shown. The mutual exclusiveness among these eight topological relations represented by the SD-TRM is proven. The topological relation …