# Calculating impulse with multiple collision points

In my amateur 2D rigid body physics engine for a game I react on collisions between two bodies with an impulse j (formula 11) as explained here.

To calculate this impulse I need one contact point P between the two colliding bodies and the perpendicular normal n of the edge the contact point of A is colliding with.

That works wonderful. At least as far as I don't have multiple contact points. But what to do if this is not the case?

Should I calculate an impulse for each of the contact points or is there a way to reduce multiple contact points to a single one if this is a correct solution?

As an example I have following two situations, where two bodies collide. The x denotes the center of mass and the tips of each triangle pointing down an vertice of A that is colliding with the edge underneath:

    _____________________                        _____________________
|                     |                      |                     |
A  |          x          |                   A  |                     |
|    _____________    |                      |         x  ______   |
\  /             \  /                       |           /      \  /
\/               \/                        |    __    /        \/
_____________________                        \  /  \  / ___________
|                     |                        \/    \/ /           |
B  |          x          |                   B   _________/    x       |
|_____________________|                      |______________________|


In the left situation its intuitively pretty clear that I can reduce the two collision points to one exactly in the middle between both since the this would be collinear to both centers of mass. Also as normal n the perpendicular vector of the edge both vertices are colliding with can be chosen.

But what to do in the right situation?