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| [[Image:Chainline.svg|thumb|right|A simple polygonal chain]]
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| [[Image:Self crossed polygonal chain.svg|thumb|right|A self-intersecting polygonal chain]]
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| [[Image:Closed polygonal line.svg|thumb|right|A closed polygonal chain]]
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| A '''polygonal chain''', '''polygonal curve''', '''polygonal path''', or '''piecewise linear curve''', is a connected series of [[line segment]]s. More formally, a polygonal chain ''P'' is a [[curve]] specified by a [[sequence]] of points <math>\scriptstyle(A_1, A_2, \dots, A_n)</math> called its '''vertices''' so that the curve consists of the line segments connecting the consecutive vertices.
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| In [[computer graphics]] a '''polygonal chain''' is called a '''polyline''' and is often used to approximate curved paths.
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| A '''simple polygonal chain''' is one in which only consecutive (or the first and the last) segments intersect and only at their endpoints.
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| 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".
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| In some cases it is important to draw a distinction between a [[polygonal area]] and a polygonal chain.
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| 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. Compare with "[[monotone polygon]]".
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| If that straight line is horizontal, then the polygonal chain is a [[piecewise linear function]].
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| ==Application and problems==
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| [[Image:Euler method.png|left|thumb|Polygonal curve approximation: the unknown curve is in blue, and a polygonal approximation is in red.]]
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| Polygonal curves can be used to approximate other curves and boundaries of real-life objects.
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| == See also == | |
| * [[Polygon mesh]] - A 2-dimensional surface created by a connected network of polygons.
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| * [[Simplicial complex]] - a higher dimensional generalization limited to [[simplex]] facets
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| * [[Maurer rose]]
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| [[Category:Polygons]]
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| [[Category:Curves]]
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