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MOSIS Technical Notes
Polygons and Winding Numbers
A polygon encloses an area of the plane, thus dividing the plane into
that area which is "inside" the polygon and that which is "outside."
For a simple polygon, the two regions are the obvious ones. However,
when a polygon's boundary intersects itself, then the definition of
inside and outside is not so simple.
A winding number is an attribute of a point with respect to a polygon
that tells us how many times the polygon encloses (or wraps around)
the point. It is an integer, greater than or equal to 0. Regions of
winding number 0 (unenclosed) are obviously outside the polygon, and
regions of winding number 1 (simply enclosed) are obviously inside the
polygon. For a simple polygon, these are the only possible winding
numbers. However, a self-intersecting polygon can create regions with
winding number 2 (or greater), and these regions present a
definitional problem.
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