page_title: Complex polygon
section_title: Computer graphics
hierarchical_section_title: Complex polygon / Computer graphics
context_page_description: The term complex polygon can mean two different things:
  In geometry, a polygon in the unitary plane, which has two complex dimensions.
  In computer graphics, a polygon whose boundary is not simple.
context_section_description: 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.
  Self-intersecting polygons are also sometimes included among the complex polygons. 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 angular "eight".
caption: A complex (self-intersecting) pentagon with vertices indicated