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Handling enemy intersection on splines

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So the enemies of my game are mindlessly animation along pre-generated cutmull-rom splines, interpolating back and forth along the curve. I've set up a volume where these objects can roam and simply calculated a random position for the start of the curve and the end, setting the position of the enemies to the interpolated point along the curve. The problem is, is that obviously these will intersect and I want a way to avoid this. I could I guess have the bounding volume further split into regions where I would know where enemies are located. I could then somehow know at which point two enemies will intersect and temporarily fly away into an empty region and then resume my way onto the curve. Any suggestions?

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