# Find the point of intersection between two convex polyhedrons

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So basically I'm writing a 3D physics algorithm. I'm using the separating axis theorem to determine when two convex polyhedrons (fancy term for 3D objects without dents,holes, or any concave areas) have collided. I've gotten this to work perfectly however I'm having a little trouble in programming what the objects should do once they've collided. The problem is I can't find the point of intersection between the objects which I need to have them rotate properly. By point of intersection I mean the point that is on the normal of the collision halfway between the penetration depth of the objects. It's really hard to define in words but it's a pretty intuitive point. Imagine for instance two cubes who are the same size and oriented (rotated) the same way in 3D space. If these two cubes where to intersect on the x axis then the point of intersection would be the point that shared the two cube's y and z values and was halfway between their x values.

Now I know the translation, orientation, and dimensions of the objects as well as the location of all their vertices. I've also worked out the collision normal and penetration depth between them. Can anyone tell me a simple (as simple as this stuff gets anyway) method of finding the point of intersection? I'm a fan of numbered steps

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Rutin
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