This paper presents a method to deal with tangling, where cloth gets pinched between two intersecting surfaces. Though this situation might seem like a problem itself to be remedied, the authors note that in production studios like Pixar, animators routinely allow models to self-intersect. To not do so, the authors say, would both inhibit their creative freedom and force them to endlessly tweak their scenes.

All previous methods for dealing with collisions were history-based: they decide whether cloth has interpenetrated a surface (or itself) by looking at where it was before and seeing if it crossed the surface. This has the obvious issue that if the simulator guesses wrong, then the cloth can become permanently tangled.

In contrast, their method does not use history, but rather what they call a "global intersection analysis" step to decide if an intersection happened -- before it's too late. In this step, they first find intersection curves between pairs of meshes, and then use a flood-fill algorithm on each curve -- choosing the smaller one if any ambiguities arise. 

For each one of these curves, they then take the set of particles (vertices) within this curve and make sure that it can't move while its pinched. If pinching surfaces are in motion, they alpha weight between the movements (an artist-configurable parameter). The end result is cloth that doesn't tangle.