I am given a 2D convex polygon ( given in terms of coordinate of the vertices), and I want to lay it on a grid with an undetermined uniform square grid size, $x$.
Now, my task is to choose $x$ such that, regardless of the size and the shape of the polygon, the number of the grid, $G_n$, inside, or intersecting the polygon must remain roughly the same. $G_n$ is a constant that is given.
Some additional info: $x$ should be relatively small compare to the dimension of the polygon, and so, $G_n$ should be quite big ( $>100$)
What is the algorithm to do this? Note that the polygon can be of any size and shape, as long as it is convex.
I understand that the definition is a bit loose here, but I wonder whether anyone has done any research on this, to help to clarify all the concepts?