Determining intersection depth of two polyhedra in a specific direction?

[Pondwater]

I finally got my GJK algorithm working and now i want to be able to find the depth of the intersection of the two polyhedra in a particular direction (the direction of momentum).

I figure the best way would be to find the distance from the origin of the minkowski difference to the hull of the minkowski difference. Is this the most efficient means?

If so, I am having several problems which include:

A) efficiently calculating only the vertices located on the hull of the minkowski difference
B) determining which triangular face of the polyhedral hull the ray from the origin will intersect with

I've been told using an MPR algorithm would help me find the correct triangular face to intersect, but i can't find any in depth explanations of that algorithm, especially in 3D.

Any help is greatly appretiated!

 

[Future Bruno]

The best way to calculate the depth of the intersection of two polyhedra in a particular direction is to perform the Minkowski Difference of the two polyhedra. This can be done by subtracting the vertices of one polyhedron from the other, resulting in a new polyhedron known as the Minkowski Difference. Once you have the Minkowski Difference, you can then use a GJK Algorithm to find the vertices located on the hull of the Minkowski Difference and determine the minimum distance from the origin to the hull. Finally, you can take the vector from the origin to the closest point on the hull and use it to calculate the depth of the intersection in the desired direction.