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Collision resolution algorithm

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I'm having difficulties with the algorithm for collision resolution.I'm trying to simulate billiard balls, so finding when they collide is simply checking that the distance between balls is shorter than the sum of their radii.

So I check every pair of balls, and get a list of colliding spheres. My problem is what to do next. I know how to resolve a collision one on one. But in billiards it's normal to have several bodies colliding at the same time.In the very first shot, in fact, every ball should be touching, meaning that the first hit would impact every ball.

My first idea is to get my collisions list, determine which collision happened first in the frame, then roll back time to that moment, apply the results to the balls, advance time again and check for collisions.Then simply loop this way until I come up with no collisions.

My question is if this is the way it is usually done. I imagine that under certain situations it could be expensive to run the collision detection many times, but I can't see how else to deal with the possibility of several collisions, or the case where bouncing off one ball causes the ball to hit another in the same frame (as would happen if the balls are tightly packed).

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You can do something like this:

 

 
remaining=timespan;
 
while(TRUE){
 elapsed=find time of first collision
 resolve that collision (reflection for balls)
 move all other objects by elapsed time
 remaining-=elapsed
 
 if(remaining <= 0)
  break;
}
 

 

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The first thing that comes to mind for me is adding all the collisions to a queue in the order that they occur, then pop each one and have that response put into action.

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