I thought of one way to do this. Using the algorithm which determines if a point is inside a parallelogram, one can determine if the polygon contains the point within $2N$ steps ($N=2$ for parallelogram) I want to do this for $n$-dimensional parallelotope but I guess it will take $2^N$ check for every vertex of the $n$-parallelotope. Could somebody suggest a better way, which is computationally faster (in a polynomial time, not exponential)?