# Polygonal chain

A **polygonal chain**, **polygonal curve**, **polygonal path**, or **piecewise linear curve**, is a connected series of line segments. More formally, a polygonal chain *P* is a curve specified by a sequence of points called its **vertices** so that the curve consists of the line segments connecting the consecutive vertices.

In computer graphics a **polygonal chain** is called a **polyline** and is often used to approximate curved paths.

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".

In some cases it is important to draw a distinction between a polygonal area and a polygonal chain.

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 monotone polygonal chain is open. Compare with "Monotone polygon".

## Application and problems

Polygonal curves can be used to approximate other curves and boundaries of real-life objects.

## See also

- Polygon mesh - A 2-dimensional surface created by a connected network of polygons.
- Simplicial complex - a higher dimensional generalization limited to simplex facets
- Maurer rose