It is very important to know if a point is inside or outside the polygon before starting to fill the polygon. In this odd even test can help us, but HOW ..? The Answer to that question is answered below in detail with examples.

Lets consider this polygon and a point (above figure) that we need to check for Inside or Outside of polygon. For that we just draw a line from that point in one direction(as drawn in below figure).

Now we need to count the number of intersection of that line with the line segments of the polygon.* “If the number of intersection is odd then we say the point is inside the polygon and if number of intersection is even then we say the point is outside the polygon”*. In our example we can see the number of intersection is 3 which is odd that means the point is inside the polygon.

Now consider the second point and repeat the same procedure as we did for the first one, we got 2 intersections which means the point is outside the polygon.

Sometimes things get a bit complicated as in the case of 3rd point where the line crosses over a vertex of the polygon. Now the question arises – For that vertex how many intersections should we consider(1 or 2). We know that the a vertex can be formed by intersection of endpoints of two line segments, Now we are just interested in the other end point of those line segments. If the end point of those line segment are in the same side of the line drawn from point (3rd point) then we count even(2) intersection and if end point of those line segment are in the opposite side of the line drawn from point (3rd point) then we count odd(1) intersection. In our example for the 3rd point the other ends of both line segments are in same sides so we count even(2) intersection and add 1(normal intersection of line drawn from 3rd point with the line segment of polygon) to it, which gets to a total of 3 which odd that means the 3rd point is inside the polygon.