How to pre-calculate the trajectories in a billiard (pool) game?

Question

Most collision detection algorithm in billiard uses a naive approch, where the balls' positions are incremented and then checked for collisions. This method dosen't work well when the speed are really high because we might "skip" collisions.

I have been searching for a way to pre-calculate the trajectories of the balls in a billiard game. Once the trajectories are know, I can animate the balls until they stop moving. And I don't have to worry about the speed, because the collisions are mathematically detected and resolved.

Do you know if anyone has done that? I don't want to reinvent the wheel. Thank you.

Answer 1

Start with quadtrees and make your sampling interval smaller. If your billiard balls are moving so fast that they pass through other balls, however, you're modeling the game incorrectly. Have you ever played a game of billiards where the balls ACTUALLY moved that fast?

Alternatively

Between your time steps, model the ball's previous position and current position as a 2-Dimensional cylinder. If any two cylinders collide, make the time step smaller and try again. In this fashion, you get very quick general calculations, and you can still handle super high velocities.