title: How do I calculate the Minkowski Difference between two AABBs (with no vector math)?
body: <p>I'm implementing the <a href="https://github.com/kikito/bump.lua/tree/2.0">second version of my collision detection library</a>. This particular library should deal with axis-aligned boxes (AABBs). I'd like to start tracking fast-moving boxes on this version. I think calculating the Minkowski Difference between the two would be a good starting point for that.</p>
  
  <p>When I say Minkowsky Difference I mean the geometric operation described in <a href="http://www.wildbunny.co.uk/blog/2011/04/20/collision-detection-for-dummies/#attachment_485">Collision detection for Dummies</a>.</p>
  
  <p>The catch is: The process and algorithm described there is very generic. It uses fairly advanced vector math to calculate the MD of any two polygons.</p>
  
  <p>In my case I have AABBs. Given their numerical simplicity, the library so far has not needed a Vector concept - for example, I have not needed to compute a single dot product. I'd like it to stay that way if at all possible.</p>
  
  <p>So my question is:</p>
  
  <p><strong>Given two AABBs by their top,left,width and height (<code>{t1,l1,w1,h1}</code> and <code>{t2,l2,w2,h2}</code>), how do I calculate their MD, (without getting vector math if possible)?</strong></p>
  
  <p>Just by playing with the widget on Collision detection for Dummies, I'm almost certain that the MD width will be a box of width <code>w1+w2</code> and height <code>h1+h2</code>. But I have no idea about how to calculate its top or left corner.</p>