The plan is to consider the system as a network of springs, and try to jiggle them into a position where they aren't under too much stress. So I'm calculating the "force" each "spring" would apply to each point, and scooting each point a little bit in the direction that the springs are pushing it. Do that over and over, and hopefully the positions will gradually get closer to a reasonable solution.

Neat idea. I specially love the analogy which even a dumb-arse like me can understand :)

Reminds me of some code I wrote back in the late 90's to do a kind of finite element analysis of the signal strengths between multiple base-stations and wireless hand-held terminals (as they were called back then) as they moved around in a shop or warehouse environment. The idea was to try and automate some of the installation process (of the base-stations) which was a time-consuming and tricky operation involving half a dozen people walking round the place with signal strength meters whilst others repositioned base-stations until they eliminated or minimised the blind spots.

It was abandoned in the end. The most powerful workstations we had (SGI something from memory) would take months to process the simplest of scenarios. These days your phone probably does more processing for each frame of a game of Angry Birds!