Help! Require papers about NGS.

[aokman]

I had just read Erin Catto's article on his blog.(http://www.gphysics.com/archives/35)
He mentioned a NGS method for position correction, and used it for his Box2D engine.
I'd like to learn more about NGS method. Could anybody please recommend me some
papers on NGS?

Thanks.

[Dirk Gregorius]

I think there are no particular papers on NGS. The papers that come closest to the method are:

1) Muller: Position Based Dynamics
2) Jacobsen: GDC 2001
3) Cline: PhD (or Master thesis)

NGS stands for Newton-Gauss-Seidel or Non-Linear-Gauss-Seidel. You basically solve a non-linear system of equations with two coupled iterative methods (Newton and Gauss-Seidel).

http://en.wikipedia.org/wiki/Gauss%E2%8 ... del_method
http://en.wikipedia.org/wiki/Newton_method

The gotcha to understand is that satisfying position constraints requires solving a non-linear problem while satisfying velocity constraints requires solving a linear problem. Think of position constraints as a highly non-linear function (e.g. a flying carpet) while for velocity constraints you just look at the tangent space. Also note that Jacobians are a function of the position. So when you change positions you need to update the Jacobian and therefore also the effective mass ( Me = 1/(J*W*JT) )

A good exercise is to generalize the Muller paper to rigid bodies and write it in terms of Jacobians instead of gradients. It is straight forward and I will help you if you have *specific* questions.

http://en.wikipedia.org/wiki/Gradient
http://en.wikipedia.org/wiki/Jacobian_m ... eterminant


HTH,
-Dirk