Tintersections

Tintersections are a class of junctions in planar networks where three edge segments meet and form a local T shape. In an embedded graph, a T-intersection is typically a degree-3 vertex at which two incident edges are collinear, creating a straight line that is intersected by the third edge at the junction. The concept is used primarily in geographic information systems, road network analysis, and image-based map extraction, where distinguishing T-intersections from other junction types aids in topology, routing, and visualization.

Formal criteria can be stated as follows: a vertex with three incident edges is a candidate T-intersection if two of its edges lie on a common line within a tolerance for measurement error. The remaining edge forms a non-collinear angle with that line. In practice, an angular threshold is applied to account for data noise; variants include a true T with a perpendicular bend or a skewed T where the third edge meets at an acute or obtuse angle.

T-intersections occur frequently in street networks when a street ends at a through road or when data simplification reduces a four-way junction to a T shape. They are also used in modeling utilities and pedestrian networks and can appear in image-derived graphs from road scenes.

Detection and analysis: in GIS and computer vision, T-intersections are identified by examining vertex degrees and local collinearity of incident edges and by applying angle tolerances. Once labeled, they support network routing, traffic simulation, and map generalization. See also X-intersections and Y-intersections.