Re[1]: Re[1]: Re[1]: [ODE] Negative penetration depths

[Thomas Harte]

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> hmmm, all should have to be fixed in 1 time step, why 2 time steps?

According to section 3.7, "Joint error and the error reduction parameter (ERP)", 
everyone will only be absolutely fixed in one time step if I set the ERP to 1, but according 
to section 11.5 "Why would you ever want to set ERP less than one?" high values for the 
ERP can result in instability and due to various approximations may not actually resolve 
the problem. So typically the error that corresponds to taking some penetrating bodies 
and making them non-penetrating will not be entirely reduced in the first time step.

> another solution is to make the integration step smaller, or inversely
> proportional to the speed of the moving objects

I didn't even think of this! Don't I feel stupid now. But I'm fairly sure I'd have to be very 
clever about matching erp and time step size if I wanted to be sure all penetrations 
would be fixed during one time step without risking instability.

The advantages of the simple binary search approach is that you can keep your time 
steps quite large and still get only a very small penetration error. In fact you can 
explicitly trade off, to a limit, how much penetration error you want to allow versus 
processing cost for every new collision - the best bit being that I really do mean new 
collisions. Old collisions can correctly be seen to still be occuring at the very start of the 
time step, so no binary search is necessary and the 'large' time step size can be 
resumed.

Besides all of which, to directly quote a limitation from the tri-collider page, 
http://q12.org/cgi-bin/wiki.pl?TriangleCollider, "No mesh-to-mesh collision (penetration 
depth computation is difficult in real-time)". This solution may therefore be the only 
appropriate one for mesh on mesh collisions, since it side steps all complicated 
penetration depth calculations.

-Thomas
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