How to rotate circle in response to collision?

Question

I am in the process of developing a very simple physics engine. The only non-static objects in it will be circles and the only collision detection I will be performing is between circles and line pieces.

For the purpose I am utilizing the principals described in Advanced Character Physics. That is, I do integration by using a simple Verlet integrator. I perform collision detection and response simply by calculating the distance between the circles and the line pieces and in case that the distance is less than the cirles radius I project the circle out of the line piece.

This works very well and the result is a practically perfect moving circle. The current state of the engine can be seen here: http://jsfiddle.net/8K4Wj/. This however, also shows the one major problem I am facing: The circle does not rotate at all.

As far as I can figure out there is three different collision cases that will have to be dealt with seperately:

1. When the circle is colliding with a line vertex and is not rolling along the line.
2. When the circle has just hit or rolled of a line. Then the exact point of impact will have to be calculated (how?) and the circle is rotated according to the distance between the impact position and the projected position.
3. When the circle is rolling along a line. Then is it simply rotated according to the distance traveled since last frame.

Here is the closest I have got to solving the problem: http://jsfiddle.net/vYjzt/. But as the demo shows it doesn't handle the edge cases probably.

I have searched for a solution online but I can not find any material that deals with the given problem specifically (as I said the physics engine is relatively simple and I do not want to bother with complex physic simulation concepts).

Answer 1

What looks wrong in your demo is that you're not considering angular moment and energy when determining the motion.

For the easy case, when the wheel is dropping to the floor in your demo, it stops spinning while in free fall. Angular momentum should keep it going.

A more complicated situation is when the wheel finally lands on the floor, it moves with the same horizontal velocity it had before hitting floor. This would be correct if it wasn't rolling but since it is rolling, some of the kinetic energy will have to go into the spinning motion, and this should slow it down. As a more clear example of this, consider the opposite case where the wheel is spinning quickly but has no linear momentum. When this wheel is set on the floor, it should take off and the spinning should slow. Also, for example, as the wheel rolls down a hill, it accelerates more slowly because the energy needs to go into both linear and circular motion.

It's not too hard to do, but to show a rolling object in a way that looks intuitively correct, I think you'll need to consider the kinetic energy and angular momentum associated with rolling. By "not too hard", I mean that all of your equations will essentially but twice as long, with one term for linear motion and another for angular. I won't recite all of the equations, it's basically just the chapter in rotational motion from any physics text.

(Nice demo, btw!)