Suppose you are given a wooden board with both big and small nails spread over it. Two of the big nails are red. Now you're given a roll of wire. You're only allowed to tie the wire at the red nails. Your goal is to connect the big nails, passing through each of them exactly once, and you may pass through the small nails at most once, if necessary. You want to do so such that you spend the least amount of wire.
That's what I have to do, in a nutshell.
EDIT> Actually, come to think of it, I don't NEED the convex hull. I'm a COMPLETE, utter idiot. Kill me.