Incorrect impulse calculation in ParticleContact::resolveVelocity

[snickerbockers]

resolveVelocity calculates impulse using the sum of the inverse mass of two particles:

real totalInverseMass = particle[0]->getInverseMass();
if (particle[1]) totalInverseMass += particle[1]->getInverseMass();

This is not correct because (1 / x) + (1 / y) != (1 / (x + y)). A more correct implementation would be:

real totalInverseMass = 1.0 / particle[0]->getInverseMass();
if (particle[1]) totalInverseMass += 1.0 / particle[1]->getInverseMass();
totalInverseMass = 1.0 / totalInverseMass

[LucasCampos]

@jayelliott at first, I agreed with you, but taking a more careful look at the code, I noticed one thing, totalInverse mass is not, as you pointed

1.0/(ma+mb)

but

ma*mb/(ma+mb)

This is correct, as reading the formulae on page 124

\Delta p_a = \frac{m_b}{m_a+m_b}
\Delta p_b = \frac{-m_a}{m_a+m_b}

and comparing with lines 112

particleMovement[0] = movePerIMass * particle[0]->getInverseMass();

and 114

particleMovement[1] = movePerIMass * particle[1]->getInverseMass();

we notice that they indeed are the same equation. Yet choosing totalInverseMass as the name of such variable was indeed an unfortunate choice.

P.S.: The latex code can be rendered here: http://www.codecogs.com/latex/eqneditor.php

[lch32111]

Edit ver 4. I think what @LucasCampos says is right on the case of resolveInterpenetration method.

In the code, Line 109 of the resolveInterpenetration Vector3 movePerIMass = contactNormal * (penetration / totalInverseMass); idmillington uses the division with totalInverseMass.

it means that totalInverseMass before this code was (m_a + m_b)/ m_a * m_b. because the code of totalInverseMass is

// The movement of each object is based on their inverse mass, so
// total that.
real totalInverseMass = particle[0]->getInverseMass();
if (particle[1]) totalInverseMass += particle[1]->getInverseMass();

which is 1/m_a + 1/m_b == (m_a + m_b) / m_a * m_b in the case of particle[1] existing. and then with the movePerlMass variable using division with totalInverseMass, the equation becomes m_a * m_b / (m_a + m_b).

and then if you multiply 1 /m_a(the inverse mass of object a) with this new equation, you can get the delta(p_a).

As LucasCampos pointed out, I think the variable name should be modified for the better understandings of the codes.

However, In the case of resolveVelocity method, the situation is a little different.

At first, I thought what @snickerbockers says is right.

However, I wrote all the code of bridge demo, and tested it. and the code was not working properly. I saw the particle suddenly bounce extremely over the sky. After removing snickerbockers' thought, the code is working well.

So, I searched for some detail of physics in impulse equation. And I think the point is on the real equation of impulse calculation. Actually, I don't fully understand the equation, but Someone who is interested in this can search for it more.

Anyway, All the codes in pcontacts.cpp is working well.