Given a set of points p, I would like to find a point within the space b that bounds the region of p that is as far distant as possible from all points within p.
This is in regards to implementing neighbor avoidance in a flocking simulation as per Craig Reynolds’ Boids – if this isn’t the best way to avoid neighbors I would love suggestions.
EDIT:
In other words, I’d like to find an arbitrary point that is as far from the other points in p as possible, while remaining within the bounding box around p.
By bounding box I mean the solution should be a point that has a y-coordinate that is between the upper and lowermost points, and an x coordinate that is between the left and rightmost points.
To put the question more abstractly, I am looking at this algorithm as a way to find a target for an agent that wants to stay within M units of its nearest neighbors while not getting closer than m units of them. The solution returned by this algorithm should return a point that has the largest distance between it and its closest neighbor.
This is in a 2D plane.
It sounds like the solution must lie on one of the intersections of the Voronoi diagram for the (other) agents. So an algorithmic solution is to construct the Voronoi diagram, iterate the intersections, and pick the one that has greatest shortest distance to a neighbor.