Hi,

I'm trying to create this effect, so that my ants will tend to move away from the central nest if they are not carrying a resource, but tend to move back toward it if they are. My ants are usually controlled by pheramone trails, but they need to be able to act autonomously as well.

Here is my attempt at implementing this: yes, its in javascript.


WorkerAnt.prototype.startRandomDirection = function()
{

// make a new random walk direction with a directional bias
var x = Math.random() * 0.1 + 1
var y = Math.random() * 0.1 + 1;

// create a vector toward the centre of the colony if ant has a resource, and away from it if he doesnt
var dirToNest = Vector2Cache[0];
dirToNest.equalsVectorBetween(this.vPos, Game.World.CentralNest.vPos);

// adjust it by the random amount
dirToNest.X *= x;
dirToNest.Y *= y;

// re-normalise it
dirToNest.normalize();

// invert vector so we are biased to moving back into the nest
if (this.stockType == EnumStockType.None)
{
dirToNest.invert();
}
this.vRoamDir.copyFrom(dirToNest);
}


The code is confounded by the fact that, for performance reasons, I need to avoid creating garbage. This is an ant simulation, with a few thousand ants on screen at once, so ive made a vector class which does all its operations using existing instances.

Yeah, how do I create a random vector which has a bias toward a certain direction, with the constraints I listed?

I needed to do something similar for a BRDF model for my path tracer, I ended up doing this (very similar to jefferytitan's solution):

- calculating a "central" vector which points towards the desired bias
- calculating a random unit vector in the reference sphere
- linearly interpolating the random unit vector with the central vector using a "bias parameter" [eqn]t[/eqn]. If [eqn]t = 0[/eqn], then it's equivalent to just picking a random unit vector, if [eqn]t = 1[/eqn] then the bias is maximal and the central vector is always picked. Values in between give varying amounts of bias.
- normalize the final vector (which will not be of unit length)

Of course, while reasonably fast, it doesn't give a proper bias (it's not cosine weighted) because of the linear interpolation. So it is kind of a hack (and I had to get rid of it eventually because the resulting PDF is nontrivial, but it served me well)