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:
The simulation handles 2-dimensional rotating convex polygons.
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.
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!! :)
