adjacentsegment

Adjacentsegment is a term used in geometry and related fields to denote a line segment that shares an endpoint with another segment within a given arrangement. The relation is local and is defined with respect to a specified ordering or connectivity of segments.

In a polyline or polygonal chain, adjacent segments are consecutive; they meet at a common vertex. For example, in a sequence of points A, B, C, D, the segments AB and BC are adjacent, as are BC and CD. Adjacent segments influence the local geometry around their joint, including the angle at the shared vertex and any constraints such as collinearity or sharpness.

In graph theoretic or mesh contexts, adjacency of segments is tied to incidence: two segments are adjacent if they share a common endpoint. Adjacent segments may form straight lines when the angle is 180 degrees, or they may bend to create a corner. The concept is used to describe connectivity in various representations, from geometric drawings to computational meshes.

Applications include path simplification, collision detection, rendering of polylines, and mesh processing. When testing for self-intersection in a polyline, adjacent segments typically do not count as intersections, since they share endpoints by construction. Distinguishing adjacent from non-adjacent segments helps in algorithms for simplification, clipping, and geometric reasoning.

See also: polyline, polygon, planar graph, incidence, adjacency, straight angle.