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 nonlinear...
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
Ageia paper on position based physics (patent)

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Re: Ageia paper on position based physics
i think it's a really nice paper, but not everything that is very nice is an invention;)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....
cheers,
Antonio