title: Find Voronoi tessellation with area constraints
body: <p>Let's say we want to Voronoi-partition a rectangular surface with N points.
  The Voronoi tessellation results in N regions corresponding to the N points.
  For each region, we calculate its area and divide it by the total area of the whole surface - call these numbers a1, ..., aN. Their sum equals unity.</p>
  
  <p>Suppose now we have a preset list of N numbers, b1, ..., bN, their sum equaling unity.</p>
  
  <p>How can one find a choice (any) of the coordinates of the N points for Voronoi partitioning, such that a1==b1, a2==b2, ..., aN==bN?</p>
  
  <p>Edit:</p>
  
  <p>After a bit of thinking about this, maybe Voronoi partitioning isn't the best solution, the whole point being to come up with a random irregular division of the surface, such that the N regions have appropriate sizes. Voronoi seemed to me like the logical choice, but I may be mistaken.</p>