# Looking for very simple implicit integration example

I am trying to design a robust cloth system. I have no problem at all simulating things like that using forward integration such as euler, midpoint, runge-kutta, verlet, etc. However, I just can't wrap my head around implicit methods.

I don't understand how you formulate the equations in linear algebra terms. I'd really like to see a VERY simple tutorial, and an actual example of how to construct the equations, and then solve for a very simple system (for example, 3 particles connected by 3 springs).

I looked into David Baraff's Large Steps in Cloth Simulation, and I can kind of follow it, but going from equations to code is a weak spot of mine.

I can use a package like eigen to solve, but I'd also really like to see some code for something like conjugate gradient descent. I don't care about efficiency at the moment, I just want to be able to clearly understand what's going on.

Thanks

• I'm also interested in a detailed/step-by-step tutorial on how to properly implement more pretentious integrators. While I tampered a bit with the implicit Euler by solving a nonlinear equation using the Jacobian/Newton's method, it was not good enough. I then found OpenCloth (on google code). You can see the Exact code you requested here: code.google.com/p/opencloth/source/browse/trunk/… . It would be nice to also get a more tutorialish explanation with some figures "and stuff". Apr 16, 2013 at 10:15
• Fantastic! That's exactly the kind of thing I was looking for. I'm going to dig in right now, yummy! Cheers Apr 17, 2013 at 1:50
• It's worth mentioning that OpenCloth encompasses almost all major numerical integration methods for cloth-like objects. This piece of web deserves a lot more attention. I'll try to write a tutorial sometime in the near future (this year), as I also cannot find anything dealing with the implementation details for a not-so mathematical person. Apr 17, 2013 at 6:40
• @teodron: This was a good question, and seems to have been answered. Can one or both of you write up the answer, for the assistance of later members who visit this question? May 4, 2013 at 20:12