Path generation for non-intersecting disc movement on a plane

Question

What I\'m looking for

I have 300 or fewer discs of equal radius on a plane. At time 0 each disc is at a position. At time 1 each disc is at a potentially different

Answer 1

The usual solution for this kind of problem is to use what is called a "heat map" (or "influence map"). For every point in the field, you compute a "heat" value. The disks move towards high values and away from cold values. Heat maps are good for your type of problem because they are very simple to program, yet can generate sophisticated, AI-like behavior.

For example, imagine just two disks. If your heat map rule is equi-radial, then the disks will just move towards each other, then back away, oscillating back and forth. If your rule randomizes intensity on different radials, then the behavior will be chaotic. You can also make the rule depend on velocity in which case disks will accelerate and decelerate as they move around.

Generally, speaking the heat map rule should make areas "hotter" at they approach some optimal distance from a disk. Places that are too near a disk, or too far away get "colder". By changing this optimal distance you can determine how close the disks congregate together.

Here are a couple of articles with example code showing how to use heat maps:

http://haufler.org/2012/05/26/beating-the-scribd-ai-challenge-implementing-traits-through-heuristics-part-1/

http://www.gamedev.net/page/resources/_/technical/artificial-intelligence/the-core-mechanics-of-influence-mapping-r2799

Game AI Pro, Volume 2, chapter on Heat Maps