Polygonal curve

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 (A1,A2,…,An){\displaystyle (A_{1},A_{2},\dots ,A_{n})} called its vertices. The curve itself consists of the line segments connecting the consecutive vertices. VariationsSimpleA simple polygonal chain is one in which only consecutive segments intersect and only at their endpoints. ClosedA 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". MonotoneA polygonal chain is called monotone if there is a straight lineL such that every line perpendicular to L intersects the chain at most once. Every nontrivial monotone polygonal chain is open. In comparison, a monotone polyg