private void HandleCollision(MoveBall b1, MoveBall b2)
{ //collision detected: the collision has happened anytime between the previous frame and this one.
//find how much time has past since the the collision
MyVector3 relVelocity = MoveBall.RelativeVelocity(b2, b1); // V° rel velocity (const)
MyVector3 relPosition = MoveBall.RelativePosition(b2, b1); // P° rel position at t=0
// relative position P(t) = P° - V° * t
// the collision happens when |P(t)| = 2 * radius
// <P(t)|P(t)> = <(P° - V° * t)|(P° - V° * t)> = 4 * radius^2
// solve the above quadratic eq. for t
float term1 = MyVector3.Dot(relVelocity, relPosition);
float term2 = MyVector3.Dot(relPosition, relPosition);
float term3 = MyVector3.Dot(relVelocity, relVelocity);
float rootSquared = term1 * term1 - term3 * (term2 - 4 * SnookerBall.radius * SnookerBall.radius);
if (rootSquared < 0)
{
rootSquared = 0;
}
float timeAfterCollision = (term1 + Mathf.Sqrt(rootSquared)) / term3;
b1.MoveByVector(b1.GetVelocity().Scale(-timeAfterCollision)); //minus sign because we are moving the ball back in time
b2.MoveByVector(b2.GetVelocity().Scale(-timeAfterCollision)); //minus sign because we are moving the ball back in time
relPosition = MoveBall.RelativePosition(b2, b1); //vector joining the centers of the 2 balls
MyVector3 b1_parallel = b1.GetLinearMomentum().ParallelComponent(relPosition);
MyVector3 b1_perpendicular = b1.GetLinearMomentum().NormalComponent(relPosition);
MyVector3 b2_parallel = b2.GetLinearMomentum().ParallelComponent(relPosition);
MyVector3 b2_perpendicular = b2.GetLinearMomentum().NormalComponent(relPosition);
//the two ball exchange the parallel components of their linear momenta
//this is only valid in the case of the masses being the same
b1.SetLinearMomentum(MyVector3.Add(b1_perpendicular, b2_parallel));
b2.SetLinearMomentum(MyVector3.Add(b2_perpendicular, b1_parallel));
}