I would go for outlining the polygon with line-to's first, then fill them with pixels, then check if my point is inside them. I know that it may go slower than the algorithm that suppose to run but however I prefer being comfortable with my code when dealing with such problems. To be honest, that algorithm is not something like an idea that comes very quick then implement very clearly.

The line-to is here and fill function is here. Fill will not work with a concave polygon. It may need some update.