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 a $2N$ step ($N=2$ 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 can suggest a better way, which is computationally faster (in a polynomial time, not exponential)?

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)?

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

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 a $2N$ step ($N=2$ 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 can suggest a better way, which is computationally faster (in a polynomial time, not exponential)?