Complex polygon
The term complex polygon can mean two different things:
In computer graphics, a polygon which is neither convex nor concave.
In geometry, a polygon in the unitary plane, which has two complex dimensions.
Computer graphics
In the world of computer graphics, a complex polygon is a polygon which is neither convex nor concave. This includes any polygon which:
intersects itself. These include star polygons such as the pentagram:
has a boundary comprising discrete circuits, such as a polygon with a hole in it.
Therefore, unlike simple polygons, a complex polygon may not always be interpreted as a simple polygonal region. 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".
