Applying Coefficient of Restitution in a collision resolution method

I have a collision resolution method in my physics engine, that goes like this:

Vector2 n1pos = n1.NonLinearSpace != null ? n1.NonLinearPosition : n1.Position; Vector2 n2pos = n2.NonLinearSpace != null ? n2.NonLinearPosition : n2.Position; Vector2 posDiff = n2pos - n1pos; Vector2 posDiffNormal = posDiff; posDiffNormal.Normalize(); float totalRadius = n1.Radius + n2.Radius; float posDiffLength = posDiff.Length(); float interPenetration = totalRadius - posDiffLength; float averageRestitution = (n1.RestitutionCoefficient + n2.RestitutionCoefficient) / 2; Vector2 forceAmount = Vector2.Multiply(posDiffNormal, interPenetration); Vector2 n1force = ( (n1.Velocity * n1.Mass) + (n2.Velocity * n2.Mass) + n2.Mass * averageRestitution * (n2.Velocity - n1.Velocity) ) / (n1.Mass + n2.Mass); Vector2 n2force = ( (n1.Velocity * n1.Mass) + (n2.Velocity * n2.Mass) + n1.Mass * averageRestitution * (n2.Velocity - n1.Velocity) ) / (n1.Mass + n2.Mass); n1.ApplyForce(???); if (!n1.IsStatic) { n1.Position += ???; } n2.ApplyForce(???); if (!n2.IsStatic) { n2.Position += ???; }

Now, i can't figure out what to apply to the bodies in my engine in order to get proper coefficient of restitution working. (the ??? parts). Can someone help?


Judging by this and your other questions, you are trying to run before you can walk.

<ol> <li>You're trying to code several unfamiliar things at once, when you should be tackling them one at a time. Try setting the coefficient of restituion to 0, so that your objects act like lumps of putty. That'll be easier to code, and once you have that working you can try elastic collisions. <li>No offense, but trying to write a physics engine when you haven't studied basic physics is just masochistic. You can either sit down with a textbook or <strong>experiment</strong>, but there's simply no way to get the engine working without understanding its parts. </ol>


I realize this is an old question, but I ran into the same issue and Google turned up this page. I figured I might share my findings. First, you must realize that the coefficient of restitution is a property of the collision, not of either of the bodies involved in the collision. That is, for n objects, you need to define n(n-1)/2 coefficients of restitution (one for each pair of bodies).

However, the physics engines I have looked into (Bullet, Chipmunk, and Box2d) all define the restitution as a property of the bodies. Upon the time of the collision, they combine the two bodies' coefficients of restitution into a single value and use that in the collision resolution. Obviously, this isn't physically correct. But that doesn't matter much for games: it just needs to behave in an intuitive manner. Here are the restitution functions that those physics engines use:

    <li>Bullet: restitution = body1->restitution * body2->restitution</li> <li>Chipmunk: restitution = body1->restitution * body2->restitution</li> <li>Box2d: restitution = max(body1->restitution, body2->restitution)</li> </ul>

    Box2d allows the users to customize the restitution function in a configuration file. Bullet and Chipmunk do not.

    I recommend you select whatever restitution mixing function feels best. Just play around with it a bit and see what you like.


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