[meheleventyone]

Paper for the extended version here, linking to this one because the extension solves some issues and isn't that much more complex: https://matthias-research.github.io/pages/publications/XPBD....

For a more lay explanation you solve constraints directly by moving elements around and using the difference between their current position and previous position as their velocity. If you've some experience of numerical integration it's quite similar to verlet integration. This approach is good because it lets you have constraints with infinite stiffness without the simulation exploding.

The original papers consider points (like a mass-spring system) but it's also been extended to rigidbodies.

[naillo]

Good survey on many other extensions too: http://mmacklin.com/2017-EG-CourseNotes.pdf

[zokier]

How does PBD compare to IPC[1] derived methods, like affine body dynamics[2] that I happened to notice in the latest siggraph papers?

[1] https://ipc-sim.github.io/ (see related projects section at bottom)

[2] https://arxiv.org/abs/2201.10022