Physics algorithm

Ok... After a bit of research and effort, I think I have some code that will calculate the velocities of two pool balls after collision.

Code:

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                VECTOR a( myPoolBall[collision.GetObject1()].GetVelocity() );
                VECTOR b( myPoolBall[collision.GetObject2()].GetVelocity() );
                VECTOR n( myPoolBall[collision.GetObject2()].GetPosition(),
                                  myPoolBall[collision.GetObject1()].GetPosition() );
                VECTOR t(n);
                swap(t[0], t[1]);
                t[0] *= -1;

                assert( abs( pow(a.Magnitude(), 2) + pow(b.Magnitude(), 2) - pow(a.Magnitude(), 2)
                                - pow(b.Magnitude(), 2) ) < DBL_MIN);

                VECTOR af = proj(b, n) + proj(a, t);
                VECTOR bf = proj(a, n) + proj(b, t);

                assert( abs( pow(a.Magnitude(), 2) + pow(b.Magnitude(), 2) - pow(af.Magnitude(), 2)
                                - pow(bf.Magnitude(), 2) ) < DBL_MIN);

                VECTOR axf = proj(af, n);
                VECTOR bxf = proj(bf, n);
                VECTOR ayf = proj(af, t);
                VECTOR byf = proj(bf, t);

                myPoolBall[collision.GetObject1()].SetVelocity(axf+ayf);        // Set New Velocity Vectors
                myPoolBall[collision.GetObject2()].SetVelocity(bxf+byf);        // To The Colliding Balls

                assert( abs( pow(a.Magnitude(), 2) + pow(b.Magnitude(), 2) - pow(VECTOR(axf + ayf).Magnitude(), 2)
                                - pow(VECTOR(bxf + byf).Magnitude(), 2) ) < DBL_MIN);

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Does this look correct?

Does it work?

The problem with this algorithm is that I conserve momentum, but I do not conserve kinetic energy. I am thinking that this is caused by the inaccuracies of the floating point primitive, but I am not totally sure.

I was wondering if the math is correct. If it is, then the problem is the floating-point errors, a problem which I cannot resolve. If its the math, then I could change the algorithm.

who said that kinetic energy is conserved ? ..........
only momentum is conserved.

e=(difference in speed of seperation)\(difference in speed of aproach)

KE(new) = e*KE(old)

i am recalling these two equations from my mecanics lessons,
so they might not be actually acurate, as i am starting to forget.

Perfectly elastic collision:

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html

There's no such thing as a perfectly elastic collision.

Quote:

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Originally posted by Darkwraith
Ok... After a bit of research and effort, I think I have some code that will calculate the velocities of two pool balls after collision.

Code:

---

                VECTOR a( myPoolBall[collision.GetObject1()].GetVelocity() );
                VECTOR b( myPoolBall[collision.GetObject2()].GetVelocity() );
                VECTOR n( myPoolBall[collision.GetObject2()].GetPosition(),
                                  myPoolBall[collision.GetObject1()].GetPosition() );
                VECTOR t(n);
                swap(t[0], t[1]);
                t[0] *= -1;

                assert( abs( pow(a.Magnitude(), 2) + pow(b.Magnitude(), 2) - pow(a.Magnitude(), 2)
                                - pow(b.Magnitude(), 2) ) < DBL_MIN);

                VECTOR af = proj(b, n) + proj(a, t);
                VECTOR bf = proj(a, n) + proj(b, t);

                assert( abs( pow(a.Magnitude(), 2) + pow(b.Magnitude(), 2) - pow(af.Magnitude(), 2)
                                - pow(bf.Magnitude(), 2) ) < DBL_MIN);

                VECTOR axf = proj(af, n);
                VECTOR bxf = proj(bf, n);
                VECTOR ayf = proj(af, t);
                VECTOR byf = proj(bf, t);

                myPoolBall[collision.GetObject1()].SetVelocity(axf+ayf);        // Set New Velocity Vectors
                myPoolBall[collision.GetObject2()].SetVelocity(bxf+byf);        // To The Colliding Balls

                assert( abs( pow(a.Magnitude(), 2) + pow(b.Magnitude(), 2) - pow(VECTOR(axf + ayf).Magnitude(), 2)
                                - pow(VECTOR(bxf + byf).Magnitude(), 2) ) < DBL_MIN);

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Does this look correct?

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What are the vector, pow, assert, setvelocity etc... subs doing?

Quote:

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Originally posted by Darkwraith
Perfectly elastic collision:

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html

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Can't really help with the actual problem as i dont understand algorithms (i dont even have vb only joined this forum for the maths lol) but it depends if you are taking into acount friction in your calculations. Because in reality it is Energy that is conserved, rather than kinetic energy. Some energy is lost to friction (otherwise the ball would never stop rolling). But if you aren't taking friction into account then yes KE should be conserved.

Quote:

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There's no such thing as a perfectly elastic collision.

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A perfectly elastic collision is where kinetic energy and momentum is conserved. I know it does not exist in reality, but I really do not want to deal with friction.

Quote:

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vector, pow, assert, setvelocity

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VECTOR: The name of the data object (which is a three dimensional vector of type double)
pow(x, y): x ^ y
assert: This is a debugging statement that gives the user the option to kill the program if the statement is false.
Poolball::SetVelocity: sets the velocity of the pool ball

I didn't even know of the assert command... this is in VB right?

Nope. C++

assert() is in the <cassert> library.