# Complex polygon

Template:Citations missing The term complex polygon can mean two different things:

## 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:

• 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".

A complex number may be represented in the form $(a+ib)$ , where $a$ and $b$ are real numbers, and $i$ is the square root of $-1$ . A complex number lies in a complex plane having one real and one imaginary dimension, which may be represented as an Argand diagram. So a single complex dimension is really two dimensions, but of different kinds.