Hello! I have read some stuff on the web, but still couldn't get a clear answer/solution.

So i try to ask here. What would be the best approach for simulating game world consisting out of static mesh (tris) and not rotating spheres and capsules/cylinders

the requirements:

1) very stable, in sense no tunneling should occur at all (very fast moving objects will be present)

2) spheres should be able to slide around on mesh (and collide between each other) and behave like rigid physical objects should.

3) fast algorithms/approaches, cause i need to code it in lua. (some solves/algorithms may be simplified, the most important is to prevent tunneling)

from what i have found i tend to implement speculative contacts, but for now i have some issues with contact solver (i mean the right way to implement it, cause most papers etc cover more complicated cases with rotations etc, and it may be an overdo for my case)

appreciate any helpful input!

If you want CCD for a player or character controller the Conservative Advancement (CA) algorithm works very well. If you want to simulate many shapes doing CCD with the static environment then I recommend looking into Catto's GDC presentation on CCD. He makes some comments about the case where you can do linear casts without any rotation, and this simple approach may be good enough for you since you have no rotation, and you might get away with CA in this case too.

If you want CCD between all the moving objects with one another... Well be prepared for an N^2 algorithm. To do CCD between moving things and then resolve the collision you need to find the first time of impact, resolve, and continue until you exhaust the entire timestep, which means you run an N^2 algorithm an unknown number of times. I'm sure you can see why games don't really do this.

Thanks for the replies! Ok, so i will try first to impelement speculative contacts, if it will work sufficient/well probably will stay with it, otherwise i will give a try to Conservative Advancement.

but you will lose the ability to control the bounce.

recommend looking into Catto's GDC presentation on CCD