I've always loved this sort of cloth animation. I think the first one I saw was dissimulate's tearable cloth demo on Codepen - I can't believe they wrote that code 9 years ago!
These cloth simulators always feel somewhat unstable - try generating a Grid cloth, and see it start bouncing and moving randomly. Is this due to accumulating IEEE 754 floating point errors?
From what I understand it's not just floating point errors, but due to the nature of approximating continues function as simple discrete steps. Linked wikipedia article has a graph demonstrating that with large steps the error accumulates way before floating point precision is a concern.
There are different numeric integration techniques with different tradeoffs. Stuff like Eulers method, Verlet, Runge-Kutte. In some of them overall energy tends to accumulate in others it gets lost both of which is wrong. Some of the more complex ones tend to behave a bit better, but then you get into the problem whether gains from each individual step being more complex outweighs what you would get from running more iterations of simpler/faster algorithm.
I've got a demo[1] where people can play with (my interpretation of) various calculation engines, adjust variables, etc. But seeing this comment made me realise I've never heard of Verlet integration[2] before - not surprising given that I got an F in Maths (and got thrown out of Physics before I could take the exam). So ... how efficient and accurate is Verlet compared to Euler/Runge-Kutte/etc? And what other methods are out there for this sort of calculation?
Would be interesting to know what integrator they use. Verlet schemes can be implemented with very little effort and they don't suffer from this issue (see e.g. the leap frog method).
But in general you would nearly always add some sort of damping mechanism, particularly for CG applications.
Energy preservation doesn't work by default in physics simulations unless you specifically code for it (e.g. by periodic explicit adjustment).
It's not only the rounding error, it's also quantisation of time and other minor errors coming from the mathematical model itself.
If the error is on the damping side, you get the real life effect of motion eventually stopping due to energy dissipation. If it's on the acceleration side you get a runaway simulation.
Simulating cloth for instance with spray damper models it’s quite old. Even older than robotics research on folding cloths—and it has progressed pretty far. See for a recent survey:
https://youtu.be/wSSqx-Dh6ko
[1] - https://codepen.io/dissimulate/pen/eZxEBO
[2] - https://github.com/Dissimulate/Tearable-Cloth
It's very simple to implement a basic setup like this, and I agree that the results are super cool.
From what I understand it's not just floating point errors, but due to the nature of approximating continues function as simple discrete steps. Linked wikipedia article has a graph demonstrating that with large steps the error accumulates way before floating point precision is a concern.
There are different numeric integration techniques with different tradeoffs. Stuff like Eulers method, Verlet, Runge-Kutte. In some of them overall energy tends to accumulate in others it gets lost both of which is wrong. Some of the more complex ones tend to behave a bit better, but then you get into the problem whether gains from each individual step being more complex outweighs what you would get from running more iterations of simpler/faster algorithm.
[1] - https://scrawl-v8.rikweb.org.uk/demo/particles-008.html
[2] - https://en.wikipedia.org/wiki/Verlet_integration
It's not only the rounding error, it's also quantisation of time and other minor errors coming from the mathematical model itself.
If the error is on the damping side, you get the real life effect of motion eventually stopping due to energy dissipation. If it's on the acceleration side you get a runaway simulation.
https://arxiv.org/abs/2407.01361