Question

Colliding balls and reflection angles

Asked by: vroksjab

Hi!

I'm writing a game(c#) based on the old one called "Jezzball". My problem is the ball physics.

I have a class for the balls

class Ball
{
      Point pos;
      Vector speed;
      int diameter;
      . . .
      static public void Collide(Ball a, Ball b)
      {
            //How do I calculate the new angles and velocities
      }
}

struct Vector
{
      float x,y;
      . . .
      public static double DotProduct( Vector v1, Vector v2)
      {
            return v1.x*v2.x + v1.y*v2.y;
      }
}

I know when the balls collide and then the static Collide-method is called passing the two colliding balls as parameters.
So how do i calculate the ball-reflection angles. I've read something about the Dot(or was i Cross) product but I don't know more about it than the methoid above . . .

I havn't read anything about vectors in school yet so please explain the calculations.

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Asked On
2004-12-13 at 08:27:39ID21240523
Tags

physics

Topic

Physics & Artificial Intelligence in Game Programming

Participating Experts
4
Points
50
Comments
9

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Answers

 

by: ozoPosted on 2004-12-13 at 17:28:10ID: 12815480

In the center of gravity frame, see if the balls approach close enough to collide.
If so, reflect their velocities across the point of contact

 

by: nielsboldtPosted on 2004-12-14 at 04:39:36ID: 12818555

 static public void Collide(Ball a, Ball b)
     {
          //How do I calculate the new angles and velocities
         ///we compute the  contact normal first
         vec2 normal = (a.position - b.position).normalized()
         ///then the contact velocity is given by
         vec2 cVel = dot( a.speed - b.speed , normal );
         ///we can use a restituition coefficient e to model a collision
        /// e is between 0 and 1 where 1 means an elastic collision and 0 an nonelastic collision
       ///and we alter the velocity as
      a.speed += -0.5 *(1+e) *cVel * normal;
      b.speed -= -0.5 *(1+e) * cVel * normal;

     ///all calculations are done in the world frame  
     }

 

by: ozoPosted on 2004-12-14 at 04:51:05ID: 12818640

This assumes that abs(a.position - b.position) <= a.diameter+b.diameter

 

by: nielsboldtPosted on 2004-12-14 at 05:14:49ID: 12818826

yeah, i know: He wrote that he knew when the balls where colliding so no need to treat this.

IHowever it should be abs(a.position - b.position) <= 0.5*(a.diameter+b.diameter)

 

by: jhshuklaPosted on 2004-12-14 at 09:47:14ID: 12821871

did we forget mass somewhere?

 

by: vroksjabPosted on 2004-12-14 at 10:21:11ID: 12822211

As I said I don't know much about vectors . . . What is the code for the Vector.Normalized() method . . . It would also be nice if someone wrote anything about the masses as well . . . but it is not critical

 

by: ozoPosted on 2004-12-15 at 03:56:48ID: 12828856

    public static Vector normalized( Vector v)
     {
         float s = sqrt(dot(v,v));
         v.x /= s;  v.y /= s;
         return v;
     }

if we have a.mass and b.mass, then
 
    float cVel = dot( a.speed - b.speed , normal );
    Vector aspeed=a.speed;
     a.speed += b.mass/(a.mass+b.mass) * ((1+e) * -cVel * normal + (1-e)*b.speed);
      b.speed += a.mass/(a.mass+b.mass) * ((1+e) * cVel * normal + (1-e)*aspeed);

(though the usage of "speed" and "Vel" are swaped from their meanings)

 

by: nielsboldtPosted on 2004-12-15 at 04:40:01ID: 12829153

A minor correction is needed for the collision law

- float cVel = dot( a.speed - b.speed , normal );
-    Vector aspeed=a.speed;
 -    a.speed += b.mass/(a.mass+b.mass) * ((1+e) * -cVel * normal + (1-e)*b.speed);
 -     b.speed += a.mass/(a.mass+b.mass) * ((1+e) * cVel * normal + (1-e)*aspeed);

just consider two spheres colliding each having a velocity 2 in opposite directions

should be

 -    a.speed += (a.mass+b.mass)/a.mass * ((1+e) * -cVel * normal);
 -     b.speed += (a.mass+b.mass)/b.mass * ((1+e) * cVel * normal);

as the impulse in the collision is J = (a.mass+b.mass) * ((1+e) * -cVel * normal);

and then the change in velocity of an object is given by J/mass


 

by: DanMacDonaldPosted on 2005-03-15 at 17:41:11ID: 13550693

I tired this solution and if a ball in motion strikes a ball at rest it imparts 2x the velocity to the ball at rest.

20120131-EE-VQP-002

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