So, I have been continually working on my physics code, trying to make everything stable. In particular I have been working on the collision response section, this dictates what happens when two bodies touch each other. Things have come a long way from what they were and I'm beginning to pick up on the mathematical concepts. Though, there are a still few things missing before any of this code can actually be used in a game.

There are several different ways to handle collision response in a real time simulation. Some of the more accurate ways work by keeping note of all the forces acting on every object, although these tend to be slow. From what I've learned the easier to implement and more preferred method for collision response is the impulse based. Impulse based collision response works by handling each collision one at a time, figuring out an estimate on the result of the restitution then applying the reaction to both objects as an impulse. This is the type of response that I'm currently trying to get a full grasp on and code correctly.

In a frictionless environment I would use this equation to find the impulse that would be applied to both rigid bodies in the collision.

J = -Vr(1+e) / {1/m1 + 1/m2 + n . [(r1 x n)/I1] x r1 + n . [(r2 x n)/I2] x r2}

J - The scalar impulse
Vr - The relative closing velocity of the two bodies
e - The coefficient of restitution
m1 - The mass of rigid body 1
m2 - The mass of rigid body 2
n - The normal of the collision
r1 - The vector from the center of mass of rigid body 1 to the point of collision
r2 - The vector from the center of mass of rigid body 2 to the point of collision
I1 - Inertia tensor for rigid body 1
I2 - Inertia tensor for rigid body 2

I apply the impulse to the objects as such.

v1 = v1 + (Jn)/m1
v2 = v2 + (-Jn)/m2
w1 = w1 + (r1 x Jn)/I1
w2 = w2 + (r2 x -Jn)/I2

v1 - Velocity of rigid body 1
v2 - Velocity of rigid body 2
w1 - Angular velocity of rigid body 1
w2 - Angular velocity of rigid body 2

I have tested this and everything works correctly. The thing that I'm having issues is when I throw friction into the equation. I have read a few texts on doing this, yet I've been unable to fully understand their method nor correctly implement them.

I know that if I continually work at it I will eventually understand what I'm doing wrong. I'll be happy to make a post when I finally have everything implemented correctly. If anyone is interested in rigid body simulations or if you have any insight on this issue please feel free to e-mail me.

- Chase

"Be excellent to each other" - Bill And Teds Exellent Adventure