"Large Steps in Cloth Simulation" - David Baraff and Andrew Witkin

Summary: The major contribution is a system for performing cloth simulation using implicit integration as opposed to explicit integration.
This results in far superior performance compared with previous cloth simulation methods.

Key Contributions/Points

 * Method for performing implicit integration
 * Definition of the various forces involved 
	- stretch
	- shear
	- Bend
	- Damping
	- gravity, etc
 * Framework and methods for applying constraints
 * Modified Conjugate gradient method - based on exploiting modified version of inverse mass matrix used in constraints imposed on cloth particles
In order to maintain the constraints during each iteration, filter a such that the effect is the same as multiplying by the modified mass matrix
but without the multiplying by 1/m;
 

Method for Performing implicit integration

 * The step in the implicit method is calculated based on the conditions at the end of the step 
 * Perform the taylor expansion of f to say f(x0 + deltax, v0 + deltav) = f0 + df_dx*deltax + df_dv*deltav
 * subsitute the taylor series expansion of f into the equation definding deltax and deltav
 * This sets up a linear system which after some rearanging is solvable with a conjugate gradient method.

Questions we hard regarding this paper

 * what is the "trick" that Mike is referring to in the implicit integration - is it just the applying of the taylor series expansion to f
 * Are the definitions of various forces based on the deformation of the triangle any better than a connected grid of masses?




"Interactive Animation of Cloth-Like Objects for Virtual Reality" - Mathieu Desbrun, Mark Meye, Alan H. Barr

Summary

This is a chapter out of the book "Cloth Modeling and Animation".  In this chapter, they address the problem of interactive animation of 
deformable objects in virtual reality systems. 

Problem Solved

The problem that they solve is that both speed of animation and stability of the deformable system regardless of the action of the 
user are important

Method

They base their solution on the implicit integration solution of Baraff and Witkin, but instead of setting up the system of linear equations and
solving it each step, they divide the force from a spring into 2 parts, a linear and a non-linear part.

Key Ideas

This paper provides a method for doing cloth simulation with the large time steps allowed when using implicit integration, while maintaining a low
computation cost per step.  The key idea in this is the dividing of the spring force into a linear component and a non-linear component, then
pre-computing the filter matrix based on only the linear portion of the spring force, and assuming that the non linear component is constant and 
applying a post-correction of angular momentum.

Contributions

A system for simulating cloth in real time in a manner that is robust.  In 1999 this was able to simulate a piece of cloth with up to 800 masses
in real time.  I imagine that today a signifigantly larger piece of cloth would be possible.

Questions

I wonder how this compares to the semi-implicit integration techniques.



"Simulation of Clothing with Folds and Wrinkles" - Section on Semi-Implicit Integration - R. Bridson, S. Marion, R. Fedkiw

Summary

The part of this paper that we examined defines a system for "Mixed Explicit/Implicit Time Integration." The goal of this system is to combine the
advantages of explicit and implicit integration with as few as possible of the disadvantages.

Problem

They wanted to "combine the flexibility and simplicity of explicit methods . . . with the efficiency of backwards schemes"

Methods

In order to gain the advantages of both implicit and explicit integration, they chose to use an explicit "second order accurate leapfrog scheme" 
integration and implicit "trapezoidal rule" integration for performing the velocity update.  They claim that the result of this is that the elastic
forces that are independent of velocity can be update using explicit integration and implicit integration on the damping forces that are dependent 
on velocity. Specifically the steps are as follows

 * vtemp(n +1/2) v(n) + deltat/2*a(t(n), x(n), v(n+1/2))
 * modification of vtemp in place to limit strain etc
 * modify position based on v(n+1/2)
 * v(n+1/2) = v(n) + deltat/2 * a(t(n), x(n), v(n))
 * v(n+1) = v(n + 1/2) + deltat/2*a(t(n+1), x(n+1), v(n+1))
 * modify v in place to limit strain etc . . 

Key ideas

Using implicit integration for the forces that are dependent on velocity and explicit for the forces that are dependent on position allows the
system of equations to be solved more quickly than otherwise because the forces are typically linear with respect to velocity.  Additionally
the use of explicit integration to update position allows constraints to be enforced by simply modifying the velocities, rather than requring
a more complicated procedure in order to enforce the constraints.

Contributions

The primary contribution of this paper is a semi-implicit integration method for cloth simulation.  They also discuss the use of level sets
for handling collisions and we did not understand this section very well at all.

Questions

 * What exactly is going in the steps they listed for the semi-implicit integration, this is not quite clear to us yet.