In computational geometry, the link distance between two points in a

polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...

is the minimum number of line segments of any

polygonal chain In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points (A_1, A_2, \dots, A_n) called its vertices. The curve itself consists of the line segments co ...

within the polygon that has the two points as its endpoints. The link diameter of the polygon is the maximum link distance of any two of its points. A polygon is a

convex polygon In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is ...

if and only if its link diameter is one. Every

star-shaped polygon In geometry, a star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire polygon boundary is visible. Formally, a polygon is star-shaped if there exists a po ...

has link diameter at most two: every two points may be connected by a polygonal chain that bends once, inside the kernel of the polygon. However, this property does not characterize star-shaped polygons, as there also exist

polygons with holes In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon' ...

in which the link diameter is two.

References

*. Computational geometry Distance {{geometry-stub