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How do you get the intersection point between a capsule and an AABB?

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That is, the point where they touch?

I'm using this code: http://www.gamasutra.com/view/feature/3383/simple_intersection_tests_for_games.php

It is, so far as I know, the only thing stopping me from having swept sphere-box collision physics. And my brains currently feels like silly putty. Help! The equations are eating me alive!!!

...See what I mean?

Edit: Correction: Capsule and AABB. I have Capsule and Plane.

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