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7 months agoMy condolences, buddy.
My condolences, buddy.
You may be interested to know that these kinds of paper adhesives are usually intentionally designed so that the substrate (paper) tears before the adhesive does. This is meant to ensure robust packing and to give proof that the package has not been tampered with. Couple this with ever thinner and shittier substrates, and, well…
♪ How 'bout I do ANYWAY ♪
So many solver solutions that day, either Z3 or Gauss-Jordan lol. I got a little obsessed about doing it without solvers or (god forbid) manually solving the system and eventually found a relatively simple way to find the intersection with just lines and planes:
It’s a suboptimal solution in that it uses 4 hailstones instead of the theoretical minimum of 3, but was a lot easier to wrap my head around. Incidentally, it is not too hard to adapt the above algorithm to not need C (i.e., to use only 3 hailstones) by using line intersections. Such a solution is not much more complicated than what I gave and still has a simple geometric interpretation, but I’ll leave that as an exercise for the reader :)