Winding Number
The winding number for a closed curve, is an integer value specified at each point,
off of the curve, but in the plane holding that curve.
It is the net number of times that an
observer, at that point, turns as he observes a bug traversing the curve once.
For vanilla polygons the winding number is 1 inside the polygon and 0 outside.
This assumes that the bug traverses the curve in the correct direction.
The winding number can be 2: 
or
can be negative:
!