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We show how to represent a simple polygon by a grid (pixel-based) polygon that is simple and whose Hausdorff or Fr\'echet distance to is small. For any simple polygon , 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.