The 9+-Intersection for Topological Relations between a Directed Line Segment and a Region

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 9intersection for line-region relations with further distinction of the line’s boundary into two subparts (starting and ending points). This 9-intersection distinguishes 26 topological DLine-region relations. The relations’ conceptual neighborhood graph takes the shape of a V-shaped tube, whose upper and lower halves are isomorphic to the conceptual neighborhood graph of 19 topological line-region relations. The conceptual neighborhood graph of the 26 DLineregion relations is applied to the iconic representation of movement patterns that satisfy a qualitative condition. By manipulating such iconic representations, the movement patterns that satisfy complex conditions are easily deduced.