"Cloth animation, Time Integrations and Constraints"


Animation tools should computer effective while still physically acceptable 
for the eye. This our aim in the domain of cloth simulation. 
Most of the existing models ignored the fact 
that textiles are in general "nearly inextensibles". 
Considering this constarint in the principal directions only , we developped
 time integration algorithm. Based on Lagrangian formulation over 
equality constraints and a fast projection ( back to tha constained "space"),
 we get a time stepping "filter"
easy to integrate in existing software. 

Next we deal with unilateral ( contact) constraints. We want to get
 a robust method with accurate detection and handling of the collisions.

We treat the contact-constraints implicitly .To make the problem
tractable, we approximate the inequality-constraints as
equality-constraints.
 For rigid obstacles, we introduce a method
related to slack variables. The choice of these (pseudo) slack
variables relies on the local contact geometry and can be viewed as an
offsetting constraint.
 Our equality-constraints also avoid potential
locking artifacts related to mesh-discretization.
We design the
self-collisions constraints to be rigid-body transformation-invariant
and prove they are pairwise linearly independent. This important
feature contributes to the robustness of our dynamic
simulations. Using an implicit scheme in time and an augmented
Lagrangian formulation leads to larger time steps and does not
introduce artificial forces such as in penalty methods.


We will give some animated illustrations and discuss the remaining problems.

This is based on Rony Goldenthal's PhD , and is done in collaboration with
 E. Grinspun, Columbia./