  We show how to represent a simple polygon $P$ by a grid (pixel-based) polygon
$Q$ that is simple and whose Hausdorff or Fr\'echet distance to $P$ is small.
For any simple polygon $P$, a grid polygon exists with constant Hausdorff
distance between their boundaries and their interiors. Moreover, we show that
with a realistic input assumption we can also realize constant Fr\'echet
distance between the boundaries. We present algorithms accompanying these
constructions, heuristics to improve their output while keeping the distance
bounds, and experiments to assess the output.
