qreal distance(int width, int height, int desiredWidth, int desiredHeight)
{
    auto targetSamples = desiredWidth * desiredHeight;
    auto xscale = (1.0 * desiredWidth) / width;
    auto yscale = (1.0 * desiredHeight) / height;

    // clamp to the lower of the two scales
    // also clamp to one, as scaling up adds no effective
    // samples, only interpolated samples
    auto sampleScale = min(1, min(xscale, yscale));

    // number of effective source samles in the target
    auto effectiveSamples = width * height * scale * scale;
    // scale down another time, to account for loss of fidelity when
    // using a downscaled image, biases towards smaller downscaling ratios
    effectiveSamples *= scale;

    return targetSamples - effectiveSamples;
}

qreal distance(int width, int height, int desiredWidth, int desiredHeight)
{
    auto targetSamples = desiredWidth * desiredHeight;
    auto xscale = (1.0 * desiredWidth) / width;
    auto yscale = (1.0 * desiredHeight) / height;

    // clamp to the lower of the two scales
    // also clamp to one, as scaling up adds no effective
    // samples, only interpolated samples
    auto sampleScale = std::min(1.0, std::min(xscale, yscale));

    // number of effective source samles in the target
    auto effectiveSamples = width * height * sampleScale * sampleScale;
    // scale down another time, to account for loss of fidelity when
    // using a downscaled image, biases towards smaller downscaling ratios
    effectiveSamples *= sampleScale;

    return targetSamples - effectiveSamples;
}