Randlänge

Randlänge is a term used in geometry and related fields to denote the length of an edge or boundary. It combines Rand (edge or border) with Länge (length). Depending on context, Randlänge can refer to the length of a single edge in a graph or to the total length of the boundary of a two-dimensional object.

In planar geometry, Randlänge is often synonymous with the perimeter of a polygon or region: the sum of the lengths of all boundary segments. For a polygon with vertices (x_i, y_i) in order, the perimeter P is the sum over i of the Euclidean distance between consecutive vertices, including the edge from the last to the first.

In graph theory, Randlänge can denote the length of an edge; for unweighted graphs the length is commonly taken as 1, while in weighted graphs the Randlänge equals the edge weight. In raster-based image analysis and computer vision, Randlänge may refer to the boundary length of a segmented region and is often approximated by counting boundary pixels or using geometric estimators.

Units depend on context: meters or kilometers in physical layouts, pixels in images. In practice, Randlänge supports shape comparison, boundary quantification, and metrics in design, cartography, and computer vision.

See also: Perimeter, Kantenlänge, boundary length.