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Existing binary frameworks such as RCC-8 and the 9-Intersection Model effectively describe relations between two regions but cannot capture the global structure of configurations involving three spatial entities. To overcome this limitation, we propose a formally defined ternary intersection calculus, the Three-Simple-Region Model (3-SRM), for computing topological relations among three simple regions in 2D space. The model is constructed on the basis of three 3x3 matrices\n                    <jats:inline-formula>\n                      <jats:tex-math>$$9I_A$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>$$9I_B$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , and\n                    <jats:inline-formula>\n                      <jats:tex-math>$$9I_C$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . The configuration of\n                    <jats:inline-formula>\n                      <jats:tex-math>$$9I_A$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>$$9I_B$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , and\n                    <jats:inline-formula>\n                      <jats:tex-math>$$9I_C$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    results in a total of 16 topological relations. The identified topological relations in 2D space among three spatial regions are disjoint, meet, covers, covered-by, equal, contain, inside, overlap, between, in-between, outer, inner, meet-inside, inside-meet, exterior meet, and boundary exterior meet. The model characterizes each triadic relation by rigorously evaluating the emptiness patterns of all interior\u2013boundary\u2013exterior intersections among the three regions, providing a natural extension of traditional binary frameworks while maintaining their fundamental topological semantics.\n                  <\/jats:p>","DOI":"10.1038\/s41598-026-35579-2","type":"journal-article","created":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T09:44:37Z","timestamp":1769161477000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computation of topological relations with 3-SRM"],"prefix":"10.1038","volume":"16","author":[{"given":"Nivedita P.","family":"Totad","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Girish M.","family":"Sajjanshettar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Prakash K.","family":"Aithal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,23]]},"reference":[{"issue":"2","key":"35579_CR1","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1016\/S0146-664X(75)80007-4","volume":"4","author":"J Freeman","year":"1975","unstructured":"Freeman, J. 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