If I'm hearing you, you're essentially hoping to recreate the tube w/ miters in paper?
Just lay something like a small piece of aluminum angle along the tube to mark a center line w/ a fine sharpie. The patterns have the 90* markings, so you should be able to line them up in phase. Play around with the tube size because I've found that at the tube-size, the patterns are a bit to short to go all the way around. Try an extra .1-.2mm.