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.
- 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