Previously, I struggle with the sequential impulse-based method I developed. Thanks to jedediah referring me to this paper, I managed to rebuild the codes and implement the simultaneous impulse based method with Projected-Gauss-Seidel (PGS) iterative solver as described by Erin Catto (mentioned in the reference of the paper as [Catt05]).

So here's how it currently is:

1. The simulation handles 2-dimensional rotating convex polygons.

2. Detection is using separating-axis test, with a SKIN, meaning closest points between two polygons is detected and determined if their distance is less than SKIN.

3. To resolve collision, simultaneous impulse-based method is used. It is solved using iterative solver (PGS-solver) as in Erin Catto's paper. Error-correction is implemented using Baumgarte's stabilization (you can refer to either paper for this) using J V = beta/dt*overlap, J is the Jacobian for the constraints, V the matrix containing the velocities of the bodies, beta an error-correction parameter that is better be < 1, dt the time-step taken by the engine, and overlap, the overlap between the bodies (true overlap, so SKIN is ignored).

However, it is still less stable than I expected :s I tried to stack hexagons (or squares, doesn't really matter), and even with only 4 to 5 of them, they hardly stand still! Also note that I am not looking for a sleeping scheme. But I would settle if you have any explicit scheme to handle resting contacts.

That said, I would be more than happy if you have a way of treating it generally (as continuous collision, instead of explicitly as a special state).

Ideas I have: I would try adding a damping term (proportional to velocity) to the Baumgarte. Is this a good idea in general? If not I would not want to waste my time trying to tune the parameter hoping it magically works.

Ideas I have tried: Using simultaneous position based error correction as described in the paper in section 5.3.2, turned out to be worse than the current scheme.

If you want to know the parameters I used:

• Hexagons, side 50 (pixels)

• gravity 2400 (pixels/sec^2)

• time-step 1/60 (sec)

• beta 0.1

• restitution 0 to 0.2

• coeff. of friction 0.2

• PGS iteration 10

• initial separation 10 (pixels)

• mass 1 (unit is irrelevant for now, i modified velocity directly<-impulse method)

• inertia 1/1000

Thanks in advance! I really appreciate any help from you guys!! :)