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This paper develops a formal model of topological relations between a directed line segment (DLine) and a region in a two-dimensional space. Such model forms a foundation for characterizing movement patterns of an agent with respect to a region. The DLine-region relations are captured by the 9-intersection for line-region relations with further distinction(More)
Directed line segments are fundamental geometric elements used to model through their spatial relations such concepts as divergence, confluence, and interference. A new model is developed that captures spatial relations between pairs of directed line segments through the intersections of the segments' heads, bodies, and tails. This head-body-tail(More)
Arrows illustrate a large variety of semantics in diagrams. An automated interpretation of arrows would be highly desirable in pen-based interfaces. This paper formalizes the structural patterns of arrows, and identifies three structural properties that contribute to the interpretation of arrows: (1) the assignment of components to three slots, (2) the(More)
This paper explores the applicability of two formal models of spatial relations, Double Cross and RfDL 3-12 , to interpret some typical expressions that people use for describing a route. The relations in these two models allow the qualitative representation of the location and spatial extent of a landmark as seen from a route segment. We explore the(More)