joiningsegmenten

Joiningsegmenten refers to a line segment that connects two points in a Euclidean space. It represents the straight path between those points and is a basic construct in geometry used to define distances, form polylines, and enclose edges of polygons.

Definition and notation: For points A and B in R^2 or R^3, the joiningsegment AB is the set {A + t(B − A) | t ∈ [0,1]}. The length of the joiningsegment AB is d(A,B) = ||B − A||, which in coordinates is sqrt((x2 − x1)^2 + (y2 − y1)^2) in 2D and adds the z-component in 3D.

Construction and properties: There is a unique joiningsegment between distinct points A and B. If A = B, the segment is degenerate with length zero. The joiningsegment lies on the line through A and B, and its midpoint is A + 0.5(B − A). It may intersect other segments at endpoints or interior points depending on the configuration.

Applications: Joiningsegmenten are used in computer graphics to define polygon edges and mesh connections, in geographic information systems to model roads and boundaries, and in computational geometry and robotics as basic connectors in path planning, polyline simplification, and distance calculations.

See also: line segment, distance between points, polyline, edge of a polygon, chord, vector.