Winding Number
The winding number for a closed plane curve, is an integer value specified at each point in the plane, but not on the 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:
!