I started working on a physically accurate mechanics simulation system,
here is one of the first results.

One feature of this simulation is that it does not use any impact
calculations but simulates collisions with elasticities.  As visible from
the animation i choose quite high elasticity, this makes numerics much
easier, but with small enough integration steps this can be changed. 
Using this method you can completely avoid testing a lot for possible
collisions, even in complex environments.  I just converted the scene
geometry to an iso_rcsg function and this way can check any time how near
the different balls are to the surface.

I also tried modeling the water interaction using the same method as
recently shown by Rune.  In contrast to the other things this is not
physically accurate of course.  What's really difficult about this water
trick is synchronization with the rest of the system, you have the
discrete simulation steps and cannot change the speed continuously.  Apart
from that it's also quite a problem to find the right disturbance from the
balls reaching the surface that creates an appropriate wave.  A lot of
factors have to be taken into account.  Right now the disturbance only
depends on the sign of the ball's speed and not the speed itself meaning
fast balls have the same effect as slow ones, just the direction makes a
difference.

Some more facts about the animation, it's slow-motion 1:2 in fact, the
balls have a density of 5 g/cm^3 and a radius of 0.15-0.45 m.  Stiffness
of the environment is 100000 N/m.  Buoyancy and damping during collisions
is simulated, damping in water is not yet accurate.  

For integration i used simple Euler method, i also implemented 2nd order
(Heun) algorithm, but without calculating the influence of the other balls
twice, this takes most of the time naturally and environment collisions
occur much more often.  For this animation i used 17 steps each 1/1000
second for each frame, but i presume if i use twice as many steps the
final ball arrangement will look quite a bit different... ;-)

But now enough words, here is the animation, a longer and better version
can be found on:

http://www.tu-bs.de/~y0013390/files/ball_sim1.mpg

Christoph

-- 
POV-Ray tutorials, IsoWood include,                 
TransSkin and more: http://www.tu-bs.de/~y0013390/  
Last updated 05 May. 2002 _____./\/^>_*_<^\/\.______

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