Polygonal chain

In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain ⁠

P

{\displaystyle P}

⁠ is a curve specified by a sequence of points

(

A

1

,

A

2

,

…

,

A

n

)

{\displaystyle (A_{1},A_{2},\dots ,A_{n})}

called its vertices. The curve itself consists of the line segments connecting the consecutive vertices.

Variations

Simple

A simple polygonal chain is one in which only consecutive segments intersect and only at their endpoints.

Closed

A closed polygonal chain is one in which the first vertex coincides with the last one, or, alternatively, the first and the last vertices are also connected by a line segment.

A simple closed polygonal chain in the plane is the boundary of a simple polygon. Often the term "polygon" is used in the meaning of "closed polygonal chain", but in some cases it is important to draw a distinction between a polygonal area and a polygonal chain. A space closed polygonal chain is also known as a skew "polygon".

Monotone

A polygonal chain is called monotone if there is a straight line L such that every line perpendicular to L intersects the chain at most once. Every nontrivial monotone polygonal chain is open.