Piecewise linear curve

In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain P is a curve specified by a sequence of points ${\displaystyle \scriptstyle (A_{1},A_{2},\dots ,A_{n})}$ called its vertices. The curve itself consists of the line segments connecting the consecutive vertices. A polygonal chain may also be called a polygonal curve,polygonal path,polyline,piecewise linear curve,broken line or, in geographic information systems, a linestring or linear ring.

A simple polygonal chain is one in which only consecutive (or the first and the last) segments intersect and only at their endpoints.

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.

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