Drawing borders between an array of objects

I’ve been looking around for this anwser but i’m not quite sucessful wording it for google.

I want to draw mutually excluding 2d borders separating a serie of game objects from one another to do something like this:

44525-original.png

Hence a few questions:

  1. How to detect what objects are the closest to an object from an array of objects (to calculate the midpoint afterward this way)?
  2. How would I proceed to fill those area with a transparent filter?
  3. How to give the whole thing a smooth and round aspect.
  4. Is there an asset that already does all or part of this? Vectrosity maybe?

It is for a Risk-like game, so objects won’t move after startup. There is no need to find a way to optimize this calculation to be done on all frames.

English is not my main language so let me know if anything is unclear, I will gladly try to clarify my questions.

You’re describing a Voronoi tessellation. There are several existing C# libraries that implement Voronoi and Delauney triangulations (a related structure) - try Google.