How to resolve collision when both of the intersecting bodies were moving?

Question

Suppose there are two quadrilaterals A and B. A is stationary but B is moving. They collided. Now B is inside A.

To check if they are intersecting I can use 2d separating axis theorem (SAT). To push B out of A so that they are not intersecting anymore, I can again use SAT to get the Minimum Translation Vector(MTV) and project B out of A using it.

My problem is, what should I do when both A and B were moving, and then they collided? I can't project A out of B or B out of A alone since both of them were moving. How should I separate them?

Answer 1

If you seperate along the Minimum Translation Vector, you could be getting some very jerky behaviour.

I think you should do your projection backwards along the movement path, which lead to the collision.

Then you can resolve your collision physics (change of movement direction ...) and move the object that collided the rest of it's new movement for the partial timestep still missing.

If you do that, then 2 moving objects is straightforward:

You subtract their velocity vectors and calculate how far you would have to move the first of the two backwards along this combined velocity to avoid the collision. Then you calculate the timelength that represents and actually move both of them backwards along their orginal velocities.

edit for clarity:

For two moving object if the first moves with a velocity of v1 and the second with v2, then resolve the collision hypothetically with a velocity of v=v1-v2 (vector valued) for the first object and 0 for the second objects velocity. You get a negative timestep dt, which you would have to move the first obeject backwards. Multiply this timestep with the actual velocities, v1 and v2, to move both object backwards.

Answer 2

Not completely sure if this answer is 100% correct, but i can't comment yet :/

First a question, is it completely necesary to have objects get inside another object and then pushing it out?

What i mean is, maybe you can avoid movement in a certain direction in case there is "going to be" a collision.

im not sure how modern engines handle collisions, but what if when you detect a collision you instance a collision handler, who knows both colliders and can correct the positionning of both?