# Essential Math WeblogThoughts on math for games

## 5/15/2011

### Collision Response errata

Filed under: Erratical — Jim @ 8:38 pm

On page 636 of the second edition, the second paragraph begins as follows:

Each object will have its own value of epsilon. […]

On page 637, equation 13.18 contains a term epsilon_a, and below it is written

The equation for j_b is similar, except that we substitute epsilon_b for epsilon_a.

The code on page 638 follows this by referring to m_Elasticity and other->m_Elasticity.

These assertions are incorrect. The coefficient of restitution is not a property of an individual object — it is a property of the collision itself. This can be seen clearly in equation 13.15, which applies to both objects. So if we are considering four materials A, B, C, and D, there would be six possible coefficients of restitution: A colliding with B, A colliding with C, A colliding with D, B colliding with C, B colliding with D, and C colliding with D.

Many thanks to James McGovern of the Art Institute of Vancouver for pointing this out.

An error that was corrected in the second edition, but is not noted in the errata for the first is in the equation for the impulse magnitude for rotational collision (Equation 12.24, page 618). The sum of cross products in the denominator should be dotted with the normalized collision normal.

And in both editions, the moments of inertia tensors used in the collision response equations (on pages 617-618 in the first edition, and page 639 in the second edition) are referred to as I_a and I_b. These should be J_a and J_b to match the previous notation used. The intent of this was to separate the notation for the identity matrix from the notation for the inertia tensor. However, standard convention is to use I for the inertia tensor, hence the typo.

Thanks for Johnny Newman, also of Vancouver, for discovering the latter two errors.

Apologies for any confusion any of this may have caused readers.