>
>
>Hello!
>
>Have anyone figured out how to use the ElastoLab physics package? I would
>like to try it with a simulator I am working on but can't figure out how to
>set things up. Is there any good examples for this somewhere?
>
As Karl said check out the testcases in the class 
SimulatedPhysicsTestcases for examples.

>Do particles collide?
>Can you have objects other than round particles? For example a simple
>square as a physical object?
>
>Thanks! Johannes.
>
<the short answer>

No, no, and no.

<the long answer>

Particles don't collide because the math gets too hard.  Physics is easy 
to solve when the functions are smooth and continuous and there are no 
sudden changes.  With springs and elastics, you can step forward at 0.1 
second intervals and accurately predict where the particle is going to 
be.  With collisions, you (in theory) have to reduce your step size 
suddenly to 100 microseconds or smaller to figure out how the collision 
occurs.  After the collision, you would have to return the step size to 
something bigger in order to calculate quickly enough.

Physics simulators don't try to reduce the step size just to simulate a 
collision.  They determine the time of the collision, add an impulse (a 
force that takes place instantly) and add the impulse to the particle to 
make it change direction and velocity.  Determining the time of the 
collision is hard - it can only be done by guessing when the collision 
might take place, stepping the simulation by that time, and checking to 
see if you're close enough.  This boils down to the "zeros of equations" 
problem with two catches - 1) you want the first zero, not any one and 
2) you want the zero of a minimum of multiple other functions (the 
distances of each particle from each barrier).  ElastoLab does this by a 
bisection algorithm.  Better algorithms would help.

A collision, though, is an easy problem compared to resting contact. 
Consider a particle sitting on the floor.  What is the time of the next 
collision?  Zero.  You can't step forward by zero seconds, apply an 
impulse, and repeat.  You'd think you could just stop the particle.  
This doesn't work either.  A particle rolling down an inclined plane can 
still move - it just can't move into the plane.  It still has gravity 
pulling it down and possibly springs trying to push it into the plane.  
The force you apply to the particle to keep it from penetrating the 
plane can only be calculated by computing the total forces ignoring the 
plane, then by calculating a force normal to the plane that's just 
strong enough to prevent inter-penetration.  This is called dynamic 
constraints.

Dynamic constraints work well when there is only one constraint.  If a 
particle is sitting in a V-shaped valley, it is touching two barriers at 
the same time.  Solving for one barrier creates forces that push it into 
the other.  Your particle will wiggle back and forth and eventually fall 
through.  You have to solve for all constraints simultaneously by 
solving something called an LCP problem (lookup an article by Baraff in 
SIGGRAPH 1984 called "Fast Contact Force Computation for Nonpenetrating 
Rigid Bodies").  The algorithm for solving this involves solving a 
system of linear equations inside a double or triple nested loop.  The 
ElastoLab physics engine does all this.

Now, suppose you have particle-particle collisions.  You can now create 
a V-shaped valley and drop hundreds of particles into it.  If you want 
the particle collisions to be rigid and not squishy,  you have hundreds 
of simultaneous contact points that can quickly change.  In theory, the 
algorithm can handle it, but your performance drops so dramatically that 
it can no longer be calculated in real-time or anything close.

Round particles have the advantage that there are normally a finite 
number of contact points of zero size.  A brick sitting on the floor has 
an infinite number of contact points. You now have to choose which 
contact points you are interested in simulating.  For example, a brick 
sitting on table (2D) has two contact points.  A brick falling off the 
edge of a table has one contact point.  The problem is that as the brick 
falls, the contact point on the brick changes.

Since ElastoLab supports Baraff 1984, it should be possible to handle 
particle-particle collisions and non-sphere particles.  Supporting this 
algorithm is one of the last things I did in ElastoLab and I never had 
the energy to extend it to those areas.

Bottom line - simulated physics is hard.

David Buck
Simberon Inc.
www.simberon.com