2d collision response between circles

Question

I\'m trying to calculate new velocities for 2 colliding balls, but can\'t really do that before I solve another problem.

Since in digital world a real collision alm

Answer 1

Whether your strategy of move-then-collide makes sense depends on what kind of thing you are trying to simulate, and on the trade-off between accuracy and speed. If you are, say, writing a snooker simulator, or Super Monkey Ball, then move-then-collide is probably not good enough, for three reasons.

First, the balls will have the wrong velocities after collision. The differences will be subtle, but will feel wrong to players:

On the left, velocities at the end of a time-step when balls are allowed to intersect before collision is detected. On the right: velocities immediately after a collision at the correct time and place.

Second, objects moving fast enough may pass through each other without colliding. Or even if you detect the collision, you may eject the objects in the wrong way, causing some kind of illegal motion. (See tasvideos.org for a collection of collision bugs in the Super Mario Bros games that are caused by this move-then-eject strategy.)

Third, objects may end up intersecting at the end of your time step, with no room to move them apart (because other objects get in the way). So you end up having to draw the objects in intersecting position, which looks wrong.

In applications where these issues matter, then it's better to determine the point of collision before moving the balls. See this article of mine for a basic introduction to this collide-then-move approach.