### Summary

In this paper, the authors introduce the use of a fast, implicit integration method for cloth simulation. The authors note that the models used for cloth simulation tend to be very stiff, and explicit integration methods are not good at dealing with stiff models. By using an implicit method, they are able to take much larger timesteps when simulating the cloth without the worries of the system numerically blowing up as it likely would using an explicit integrator. More specifically, the authors uses a modified conjugate gradient solver as they identify the matrix as sparse.

The authors also use the idea of mass modification to impose constraints on the system. As an example, if a particle comes in to contact with a solid surface, then its velocity in the direction normal to the surface should be zero. The authors achieve this by giving the particle an infinite mass, thus nullifying the effect of any forces on it in that direction. (Note that the authors represent mass as a 3x3 diagonal matrix and are thus able to constrain forces in arbitrary directions).

The "modified" in modified conjugate gradient comes from the inclusion of a filtering step during iteration. The mass matrix they use is singular, yet the conjugate gradient solver requires the matrices to be symmetric. Thus, the filtering step handles the application of constraints rather than using the mass matrix directly in the solver.

### Problem

Using explicit integrators for cloth simulation is very hard because it is necessary to take very small timesteps. Taking large timesteps leads to the system diverging, yet taking very small timesteps is extraordinarily computationally expensive.

### Solution

To use an implicit integration method (modified conjugate gradient) to simulate cloth.

### Contributions

1. Use of modified conjugate gradient for integration when simulating cloth.

2. Use of mass modification for applying constraints to the system