How to calculate distance between two rectangles? (Context: a game in Lua.)

Question

Given two rectangles with x, y, width, height in pixels and a rotation value in degrees -- how do I calculate the closest distance of their outlines toward each other?

Answer 1

Pseudo-code:

distance_between_rectangles = some_scary_big_number;
For each edge1 in Rectangle1:
    For each edge2 in Rectangle2:
        distance = calculate shortest distance between edge1 and edge2
        if (distance < distance_between_rectangles)
            distance_between_rectangles = distance

Answer 2

Actually there is a fast mathematical solution.

Length(Max((0, 0), Abs(Center - otherCenter) - (Extent + otherExtent)))

Where Center = ((Maximum - Minimum) / 2) + Minimum and Extent = (Maximum - Minimum) / 2. Basically the code above zero's axis which are overlapping and therefore the distance is always correct.

It's preferable to keep the rectangle in this format as it's preferable in many situations ( a.e. rotations are much easier ).