(I've just found about this forum). I hope it is ok to repost my question again here. I posted this question at stackoverflow, but it looks like I might get better help here.

Here is the question:

I've implemented basic particles motion simulation with continuous collision detection.

But there is small issue in display.

Assume simple case of circles moving inside square. All elastic collisions. no firction. All motion is constant speed. No forces are involved, no gravity. So when a particle is moving, it is always moving at constant speed (in between collisions)

What I do now is this:

Let the simulation time step be 1 second (for example). This is the time step simulation is advanced before displaying the new state (unless there is a collision sooner than this).

At start of each time step, time for the next collision between any particles or a particle with a wall is determined. Call this the TOC time; let’s say TOC was .5 seconds in this case.

Since TOC is smaller than the standard time step, then the system is moved by TOC and the new system is displayed so that the new display shows any collisions as just taking place (say 2 circles just touched each other’s, or a circle just touched a wall)

Next, the collision(s) are resolved (i.e. speeds updated, changed directions etc..).

A new step is started. The same thing happens. Now assume there is no collision detected within the next 1 second (those 2 circles above will not be in collision any more, even though they are still touching, due to their speeds showing they are moving apart now), Hence, simulation time is advanced now by the full one second, the standard time step, and particles are moved on the screen using 1 second simulation time and new display is shown.

You see what has just happened: One frame ran for .5 seconds, but the next frame runs for 1 second, may be the 3rd frame is displayed after 2 seconds, may be the 4th frame is displayed after 2.8 seconds (because TOC was .8 seconds then) and so on.

What happens is that the motion of a particle on the screen appears to speed up or slow down, even though it is moving at constant speed and was not even involved in a collision.

i.e. Looking at one particle on its own, I see it suddenly speeding up or slowing down, becuase another particle had hit a wall.

This is because the display tick is not uniform. i.e. the frame rate update is changing, giving the false illusion that a particle is moving at non-constant speed while in fact it is moving at constant speed. The motion on the screen is not smooth, since the screen is not updating at constant rate.

I am not able to figure how to fix this. If I want to show 2 particles at the moment of the collision, I must draw the screen at different times. Drawing the screen always at the same tick interval, results in seeing 2 particles before the collision, and then after the collision, and not just when they colliding, which looked bad when I tried it.

So, how do real games handle this issue? How to display things in order to show collisions when it happen, yet keep the display tick constant? These 2 requirements seem to contradict each other’s.