How it holds together

This is a mass-spring system solved with two moves each frame, a technique from Thomas Jakobsen's work on the physics in Hitman: Codename 47:

• Verlet integration moves each point by storing its previous position instead of an explicit velocity, which is simple and very stable.
• Constraint relaxation then nudges the two ends of every spring back toward their rest length, repeated several times a frame. Enough passes and the sheet behaves like it barely stretches at all.

Tearing is almost free: once a spring is pulled past a threshold, just delete it. Do that to enough neighbours and the fabric splits, no special case required.