Collision Handling Between Circle and Line Segments

Question

I'm implementing a small game and am having trouble getting the physics working properly. In this game, there is one ball (a circle which moves from frame to frame, and may change radius) and several walls (line segments which also change and move from frame to frame). I can detect collisions properly, and making the ball bounce off in the correct direction is no problem.

Difficulties arise in situations where the ball intersects a line in one frame, then intersects it again in the subsequent frame, causing a double bounce. I could move the ball back along the normal of the line until it is in a valid position, but this causes really weird behaviour when the line in question is being hit along its axis (imagine a ping pong ball falling down on an upright toothpick and suddenly shifting aside so that it is on one side of the toothpick...). There are also a few issues when the ball intersects more than one line in a given frame (imagine four lines together making a rectangle and the ball intersecting the corner of said rectangle) -- which direction should it bounce off? In which direction should it shift?

I don't really have a specific question, but am looking for tips or some useful tutorials. All the 2D ones I've managed to find so far only cover rectangle intersections.

I'm using XNA if it makes any difference.

Thanks,
Cameron

Answer 1

This is an universal problem with most physics libraries. If you google for "penetration depth" (together with "physics", I suggest, or you might find something entirely different :D) you will find that even these libraries use tricks like yours.

There are two solutions to this:

The cheap one is to increase your update frequency. Move objects in 10 smaller steps instead of a single big one and you will have less penetration, so fixing it by offsetting the ball away from the wall will be less visible.

The expensive one is continuous collision detection. There are algorithms that can tell you, given a moving and a stationary object, the exact point in time both will will intersect. Google "swept sphere rectangle intersection" to find some of these.

You can then update like this: ball needs to move by 1.0 units. Check for collision. Collision occurs after 0.25 units, so move ball by 0.25 units, calculate reflection vector (so the ball bounces off the wall), repeat collision check with remaining 0.75 units (until you know the final position of the ball). This avoids penetrations entirely and even if your ball is moving so fast that it would normally skip over the wall in a single update, the collision will be detected.

Answer 2

It's generally accepted that, because of the timestep your collisions will intersect past an acceptable point in between updates.

Basically, you have to interpolate back to the point in between the last and current frame where the collision truly happened, move the object back to that point, and then calculate the forces, etc.