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It's the minimum distance from that point you are testing to the hyper-rectangle defined by the min and max co-ordinates on each dimension.

So considering dimension x: if the point val is less than the min, the distance is (min - val), if it is between min and max the value is 0 (it is inside the rectangle), if it is more than max the distance is (val - max).

If you are doing Euclidean, square each distance then add them together. I do Manhattan, so just use the absolute value.