Geo Fencing - point inside/outside polygon

Question

I would like to determine a polygon and implement an algorithm which would check if a point is inside or outside the polygon.

Does anyone know if there is any exampl

Answer 1

Check if a point is inside a polygon or not -

Consider the polygon which has vertices a1,a2,a3,a4,a5. The following set of steps should help in ascertaining whether point P lies inside the polygon or outside.

Compute the vector area of the triangle formed by edge a1->a2 and the vectors connecting a2 to P and P to a1. Similarly, compute the vector area of the each of the possible triangles having one side as the side of the polygon and the other two connecting P to that side.

For a point to be inside a polygon, each of the triangles need to have positive area. Even if one of the triangles have a negative area then the point P stands out of the polygon.

In order to compute the area of a triangle given vectors representing its 3 edges, refer to http://www.jtaylor1142001.net/calcjat/Solutions/VCrossProduct/VCPATriangle.htm