Computation of topological relations with 3-SRM
Nivedita P. Totad, Girish M. Sajjanshettar, Prakash K. Aithal
TL;DR
This paper introduces a new model for computing topological relations among three spatial regions in 2D space, extending traditional binary frameworks.
Contribution
The paper proposes the 3-SRM, a formally defined ternary intersection calculus for triadic spatial relations.
Findings
The 3-SRM model identifies 16 distinct topological relations among three spatial regions.
Each relation is characterized by evaluating the emptiness patterns of interior–boundary–exterior intersections.
The model extends binary frameworks while preserving their topological semantics.
Abstract
Topological relation models are fundamental to spatial databases and GIS, providing a basis for reasoning about how spatial objects relate. 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…
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Taxonomy
TopicsConstraint Satisfaction and Optimization · Data Management and Algorithms · Geographic Information Systems Studies