Planet SoC

Thanks to my fellow physicist, Oleg Matveychuk, I’ve done with the collision
handler bug I said in the last status report. That was indeed a mistake in the
paper (Collision
Detection and Response for Computer Animation).
One of the collision equation in that paper looks like

Here, is linear and is angular velocity of each of two bodies,
is the vector pointing from center of mass to collision point, and
is normal to collision plane. The expression in parens, let’s call it , is
relative velocity of collision points of two bodies. So, Moore and Wilhelms
propose to set to 0.
It appears that this corresponds to completely unelastic collision (with
restitution coefficient equal to 0), and that’s why it doesn’t look too
realistic.
If we have coefficient of restitution , then proper equation is
, where is taken after collision and before.
Another thing I’ve done is support of generic polyhedra. For example, now we
can experiment not just with cubes, but with parallelepipeds or tetrahedra. And
in future this will help us to handle arbitrary shapes by approximating them
with polyhedra, using point repulsion algorithm which I’m going to implement
(it’s also needed for semi-adjusting BSP trees).