Geometric Primitives - 3D Math Primer for Graphics and Game Development - page 333

9.7.1 Simple versus Complex Polygons

A simple polygon does not have any “holes,” whereas a complex polygon
may have holes (see Figure 9.25.) A simple polygon can be described by
enumerating the vertices in order around the polygon. (Recall that in a left-
handed world, we usually enumerate them in clockwise order when viewed
from the “front” side of the polygon.) Simple polygons are used much more
frequently than complex polygons.

Figure 9.25
Simple versus complex polygons

We can turn any complex polygon into a simple one by adding pairs of
“seam” edges, as shown in Figure 9.26. As the close-up on the right shows,
we add two edges per seam. The edges are actually coincident, although
in the close-up they have been separated so you could see them. When
we think about the edges being ordered around the polygon, the two seam
edges point in opposite directions.

Figure 9.26
Turning complex
polygons into
simple ones by
adding pairs of
seam edges