Editing Complex polygon (section)

== Computer graphics ==
{{See also|orbit (dynamics)|winding number}}
[[File:pentagram_with_vertices.svg|thumb|A complex (self-intersecting) pentagon with vertices indicated]]
[[File:regular_star_polygons.svg|thumb|All regular [[star polygon]]s (with fractional [[Schläfli symbol]]s) are complex]]

In computer graphics, a complex polygon is a [[polygon]] which has a boundary comprising discrete circuits, such as a polygon with a hole in it.<ref>Rae Earnshaw, Brian Wyvill (Ed); New Advances in Computer Graphics: Proceedings of CG International ’89, Springer, 2012, page 654.</ref>

Self-intersecting polygons are also sometimes included among the complex polygons.<ref>Paul Bourke; [http://paulbourke.net/geometry/polygonmesh/ Polygons and meshes:Surface (polygonal) Simplification] 1997. (retrieved May 2016)</ref> Vertices are only counted at the ends of edges, not where edges intersect in space.

A formula relating an integral over a bounded region to a closed [[line integral]] may still apply when the "inside-out" parts of the region are counted negatively.

Moving around the polygon, the total amount one "turns" at the vertices can be any integer times 360°, e.g. 720° for a [[pentagram]] and 0° for an [[crossed rectangle|angular "eight"]].