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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 Hausdorffdistance between their boundaries and their interiors. Moreover, we show thatwith a realistic input assumption we can also realize constant Fr\'echetdistance between the boundaries. We present algorithms accompanying theseconstructions, heuristics to improve their output while keeping the distancebounds, and experiments to assess the output.

Mapping polygons to the grid with small Hausdorff and Fr\'echet distance