Ageia paper on position based physics (patent)

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Dirk Gregorius
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Joined: Sun Jul 03, 2005 4:06 pm
Location: Kirkland, WA

Ageia paper on position based physics (patent)

Post by Dirk Gregorius » Wed Oct 24, 2007 9:54 pm

Strange that you have these issues. The formulas seem correct. I derived the formulas myself and in the new version it correct now. The derivation is extremely simple (using block vector notation):

We want to find mass weighted displacement (pseudo impulses) where dp is the displacement and P the block vector of impulses and dp = W * P
p' = p + dp = p + W * P

...such that the new positions satisfy the position constraints. That is tricky now since the position constraints are non-linear...
C(p') = 0

...so we linearize while I use the more general Jacobian here instead of limiting myself to 1D constraints as the paper...
C(p') = C(p +dp) = C(p) + J * dp = C(p) + J * W * P = 0

... we also know the direction of our (pseudo) impulses...
P = JT * lambda

... so we arrive at a similar formula as for rigid bodies
J * W * JT * lambda = -C(p)


For particles the Jacobian is basically just the gradient of the constraint function. The effective mass usually just becomes J*W*JT = invM1 + invM2. The paper is so simple that I really can't understand how they got the patent application for this....



HTH,
-Dirk

Antonio Martini
Posts: 135
Joined: Wed Jul 27, 2005 10:28 am
Location: SCEE London

Re: Ageia paper on position based physics

Post by Antonio Martini » Wed Oct 24, 2007 10:06 pm

Dirk Gregorius wrote:For particles the Jacobian is basically just the gradient of the constraint function. The effective mass usually just becomes J*W*JT = invM1 + invM2. The paper is so simple that I really can't understand how they got the patent application for this....
i think it's a really nice paper, but not everything that is very nice is an invention;)

cheers,
Antonio

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