I am reading this paper http://arxiv.org/pdf/1207.3502.pdf
Given a complex polygon. Its edges may intersect. The algorithm finds out if given point is inside of polygon or not. It draws a line from the point and calculates number of intersections of line and edges of polygon. If the number of intersections is odd the point is inside polygon.
I don't understand how inside or outside of complex polygon are defined? I think there should be definition of it, that doesn't depend on any algorithm. So a polygon is given, what parts are inside of polygon and what part not?