Applying Coefficient of Restitution in a collision resolution method

Question

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?

score 6 · Answer 1 · answered Nov 05 '09 at 22:30

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

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.
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 experiment, but there's simply no way to get the engine working without understanding its parts.

Well see, that's the thing: I learn much more effectively by example than a lot of math equations and rules set down in a book. Now,that said, I did get a chance to study a physics engine and mostly mocked that architecture. The way collisions are calculated right now, all collisions are completely elastic, so I can't start with "putty" collisions. The method I tried for integrating the CoR calculations was incorrect, so your help is much appreciated. — RCIX, Nov 06 '09 at 09:17

score 5 · Answer 2 · answered Jul 25 '10 at 05:42

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:

Bullet: restitution = body1->restitution * body2->restitution
Chipmunk: restitution = body1->restitution * body2->restitution
Box2d: restitution = max(body1->restitution, body2->restitution)

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.

Nice research. I was googling the same problem. I had a feeling that multiplying the material restitution values was the best way, and averaging would be next-best. Using max seems wrong to me, although min might make sense. It doesn't seem to matter too much, so long as you combine them *somehow* (as using separate values in each velocity equation doesn't preserve momentum). Based on this, I'll multiply. — Boann, Sep 09 '13 at 13:46

Applying Coefficient of Restitution in a collision resolution method

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