raigan

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1. Physics behind briddge constructor

I meant the *original* Bridge Builder game https://en.wikipedia.org/wiki/Bridge_Builder It's quite possible Bridge Constructor is using FEM! Gish also uses penalty-method + really tiny steps, since it's by the same author.
2. Physics behind briddge constructor

I know that the original Bridge Builder uses particles + springs with very small timesteps to keep things stable, similar to this paper: http://www.uni-weimar.de/~caw/papers/p7-kacic-alesic.pdf Other games have used a similar approach, for example I would bet that Rigs of Rods works the same way since they've mentioned that their simulator runs at 1000hz. The game is open source so you can poke around and see how it works: https://github.com/RigsOfRods/rigs-of-rods
3. Problems in [Cloth Simulation] with Verlet Integration

Thanks raigan, I tried something like below: FindCollisionParticles();  // if found one, then mark this particle isActive = false; which makes it also not movable by its physical update or constraints.  for (num_iterations) {     SolveDistanceConstraints(); } // at the end of the update RecoverDeactivatedParticles();    // Reactive particles that are marked deactive in FindCollisionParticles();   Somehow this doesn't work for me.     Sorry, maybe I didn't explain very well: you need to handle collision *just like a constraint*, i.e you need to solve both collisions and other constraints together in the loop, otherwise the solver won't converge nicely. Something like: for (num_iterations) {     SolveDistanceConstraints();     SolveCollisionConstraints(); } This way the constraint forces can "talk" to each other and find a mutually acceptable equilibrium state. Of course: what does SolveCollisionConstraints() look like? There are many ways of implementing this; the un-optimized version is to run a full broad+narrow phase collision in here, but that gets slow. Instead you can cache the pairs returned by the broadphase before solving, and re-run narrow phase (i.e calculate the vert-face or edge-edge penetration depth and project out of collision if the two features are penetrating). JoeJ's approach also works, AFAICT it's Jacobi iterations instead of Gauss-Seidel -- see the paper "Mass Splitting for Jitter-Free Parallel Rigid Body Simulation" for more info: IIRC you shouldn't be scaling by some arbitrary number but instead averaging all particle displacements based on relative mass. The paper has more details. The downside to Jacobi is that it converges more slowly.
4. Problems in [Cloth Simulation] with Verlet Integration

This isn't as complicated a problem as you think -- you just need to remember that collision constraints are a type of constraint, and solve them *together* with the distance constraints in your solving loop. eg something like: for(num_solver_iterations) { SolveDistanceConstraints(); SolveCollisionConstraints(); } Of course, this moves collision detection to inside your solver loop, which is bad for performance. Typically people cache the broadphase and update the narrow phase, i.e your collision data knows the face+vertex that are colliding, and when solving the collision constraint you first check if collision is happening (which you have to do anyway to calculate the error term) and if not you skip solving it this iteration. I hope this makes sense!
5. Orientation and angular velocity of particle cloud

AFAICT this still requires some idea of a "rest pose"/starting configuration (the a_i unit vectors in the stackexchange reply). (Thanks so much btw, I hadn't realized there were approaches to this besides Muller's! Very interesting.) The OP wanted to know if there are any approaches that *don't* require some sort of initial state/rest pose.
6. Orientation and angular velocity of particle cloud

I'm not an expert but I don't think that your conclusion necessarily follows. It just doesn't make sense to me: particles only have a defined position, not an orientation. You can aggregate their positions to get a COM, which helps you define all the other properties you listed (eg angular momentum doesn't make sense for a particle in isolation, but does relative to the COM), but AFAICT the COM doesn't help define an orientation. I'm struggling to see how you could define orientation without some sort of frame of reference similar to that provided by a rest pose.
7. Orientation and angular velocity of particle cloud

I am using this method to analyze and control deformable soft bodies in a physics engine. When creating an object of a particular, well defined shape, like for instance a truss or girder with the orientation vector pointing along the length of the body, I can see on screen how the orientation (visualized by a point and a line) drifts away from the physical shape. This happens slowly by simply adding angular velocity and letting it rotate unconstrained by external forces. When influencing it through collision or by constraining it to other bodies, the orientation quickly drifts away from the correct value.   This seems like the exact use-case for shape matching -- i.e you start with a particular arrangement of particles. Why exactly do you want to avoid having to define a "rest pose"?
8. Orientation and angular velocity of particle cloud

This seems related to "shape matching"; this recent paper should have lots of useful references (and itself presents a method to extract rotation from a point cloud): http://matthias-mueller-fischer.ch/publications/stablePolarDecomp.pdf Note that AFAICT you'll need some sort of "rest pose" defined for the points or the concept of orientation doesn't make a lot of sense.
9. Help understanding term in XPBD (position based dynamics) paper

Awesome! I'm glad that works :)   Thanks for letting me know about those details -- I wonder if it's an error in the paper or what.   Do normalized constraints offer any benefits? I've never come across them before.
10. Help understanding term in XPBD (position based dynamics) paper

I'm a bit rusty but IIRC in PBD gradC is a vector, which means gradC(xi - x^n) might be a dot product, projecting the approximate velocity (xi - x^n) onto the constraint gradient gradC.   This is just a guess! Please let me know if you work it out, because I'd like to try implementing this too. :)
11. Motor control redux

hey -- no worries, it's a hard problem!   One thing that might have slipped under your radar is the physics-based locomotion R&D that Cryptic Sea are doing (in conjunction with their games Sub Rosa and A New Zero): https://twitter.com/crypticsea/status/796871092438605824
12. Motor control redux

awesome!    One thing I thought of, have you read any of Michiel van de Panne's papers? He does a lot of research into control of physics-driven characters:  https://www.cs.ubc.ca/~van/papers/Simbicon.htm https://www.cs.ubc.ca/~van/papers/2010-TOG-gbwc/index.html https://www.cs.ubc.ca/~van/papers/2013-TOG-MuscleBasedBipeds/index.html http://www.cs.mcgill.ca/~kry/pubs/abc/index.html https://www.cs.ubc.ca/~van/papers/2015-CGF-multiskilled/index.html
13. Motor control redux

Bullet forums maybe? (they're mostly dead lately though): http://bulletphysics.org/Bullet/phpBB3/viewforum.php?f=4   I really like this project/idea :)
14. Using Physics to Generate Sound

This is definitely something that has been presented in siggraph papers and some GDC lectures IIRC.   Here's a presentation that might be of interest: https://www.cs.princeton.edu/~prc/ChucKU/PerryCookPhysicalModelingGameSoundCon2014.pdf