title: Conservatively cover bitmap with small number of primitives?
body: <p>I'm researching the the possibility of performing occlusion culling in voxel/cube-based games like Minecraft and I've come across a challenging sub-problem. I'll give the 2D version of it.</p>
  
  <p>I have a bitmap, which infrequently has pixels get either added to or removed from it.
  <a href="http://i.imgur.com/Mvxp9Oo.png" rel="nofollow">Image Link</a></p>
  
  <p>What I want to do is maintain some arbitrarily small set of geometry primitives that cover an arbitrarily large area, such that the area covered by all the primitives is within the colored part of the bitmap.
  <a href="http://i.imgur.com/bFnO4cJ.png" rel="nofollow">Image Link</a></p>
  
  <p>Is there a smart way to maintain these sets? Please not that this is different from typical image tracing in that the primitives can not go outside the lines. If it helps, I already have the bitmap organized into a quadtree.</p>