[Bf-committers] Some Maths / ideas / solutions for Softbodies.

Robert Wenzlaff rwenzlaff at soylent-green.com
Wed Dec 1 05:14:08 CET 2004


On Tuesday 30 November 2004 22:31, Alexander Ewering wrote:
> >> Mabye cloth is not the guideline but people will certainly use it, and
> >> it will crash with forward euler.
> >> Users will think it's a bug, and not a mathematical limitation.
> >
> > If it crashes, it is a bug, even if it is due to a mathimatical
> > limitation.
> >
> > If the mesh explodes because the ODE's are too stiff, that's a
> > mathimatical limitation.
>
> It doesn't crash, it's just too stiff ODEs. Though I must admit I still
> don't understand the mathematical background *why* it "explodes" (after
> slowly building up random noise)

It's called an ill-conditioned system.  It's when a very small change in one 
of the inputs causes a very large change in the output.  The solutions are 
being approximated, so at any time there a certain amount of error in the 
system (difference between the approx result and the true solution).   Each 
iteration of the solution causes a certain amount of coinvergence.  

If the rate of change in convergence is less than the rate of change of the 
error, then the approximation will not converge on a solution.  The residual 
error has more control over the output than the subsiquent inputs do (since 
the output of one itteration is the input to the next).  Thus, anything can 
happen and usually does.

I'd have to look up the exact test for an ill-conditioned system. It's pretty 
obvoius if you look at the system of ODEs as a matrix.  It typically happens 
when you have a mix of very large coefficients and very small coefficients.     
My bet is this mix happens when you want the cloth to be very flexible, but 
not stretchy.
-- 
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  dabis, ad caput tuum saxum immane mittam.
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Robert Wenzlaff    rwenzlaff at soylent-green.com



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