Given a simple polygon P with n vertices and a query point q$,$ here is

an algorithm to determine whether q lies in P$.$ Consider the ray :$=$

$\{($qx $+$ $,$ q y$)$ : $>0\}($this is the horizontal ray starting in q and going

rightwards$).$ Determine for every edge e of P whether it intersects $.$ If

the number of intersecting edges is odd, then q in P$,$ otherwise q in P$.$