kantlængde

Kantlængde is a term used in geometry and graph theory that refers to the length of an edge. In Danish usage, kantlængde describes the distance between the endpoints of a side in a polygon or the weight assigned to an edge in a graph. In most contexts, the distance is measured using a chosen metric, with the Euclidean distance being the most common in geometric settings.

In polygons, the kantlængde of a side is the distance between two consecutive vertices along the boundary. For a polygon with vertices v1, v2, ..., vn in boundary order, the kantlængde of side i is the distance between vi and v(i+1) (with vn+1 = v1). The sum of all kantlængder gives the polygon’s perimeter.

In graphs, each edge has an associated kantlængde or length, often denoted w(e). If all edges have length 1, the graph is unweighted; otherwise the graph is weighted. The length of a path is the sum of the kantlængder of its edges, and the shortest path problem seeks the path with minimal total kantlængde between two vertices. Algorithms such as Dijkstra’s and Bellman–Ford operate on different classes of weight assumptions.

In practice, kantlængde is typically computed using the Euclidean metric for geometric graphs, though other metrics may be used depending on the context, such as Manhattan distance in grid-based layouts. Units depend on the coordinate system or application, and floating-point arithmetic can introduce rounding errors.

See also: distance, perimeter, metric, weighted graph, path length.