I was hoping they’d discuss CNC Lasers, but it was more about the bin packing.
The ever-elusive riddle: What's the best way to cut Christmas cookies?
21–27 of 27 posts
Re: The ever-elusive riddle: What's the best way to cut Christmas cookies?
#22The article doesn't really make it clear that there's an actual result, showing that many two-dimensional packing problems are equivalent to finding real roots of multivariate polynomials, and many problems are ∃ℝ-complete. (∃ℝ-complete is kind of like NP-complete for real numbers. The ∃ℝ complexity class lies between NP and PSPACE.)
The paper shows that various specific problems are ∃ℝ-complete. One such problem is packing simple polygons with at most 8 corners into a square, with rotation and translation. (E.g. cutting polygonal cookies out of dough.) Another is packing objects bounded by segments and hyperbolic curves into a square with translation but not rotation.
Random fact from the paper: there's no agreement on how to pronounce ∃ℝ-complete.
The "Existential Theory of the Reals" is (ambiguiously) the ∃ℝ complexity class, a formal language, and an algorithmic problem. More info: https://en.wikipedia.org/wiki/Existential_theory_of_the_real...
Disclaimer: I didn't know anything about ∃ℝ before looking into this, but thought others might be interested in a bit of background.
Re: The ever-elusive riddle: What's the best way to cut Christmas cookies?
#23Ironically (or perhaps fittingly?), the entire article is blocked by a cookie wall on mobile that I have to click through before reading.
The article, as is typical in my experience, loads fine with javascript disabled. Browsing with javascript off by default is the only way to stay sane on the modern web I think. Most sites work better with javascript disabled.
Re: The ever-elusive riddle: What's the best way to cut Christmas cookies?
#24Ironically (or perhaps fittingly?), the entire article is blocked by a cookie wall on mobile that I have to click through before reading.
That would be fittingly. Irony refers to a counter-intuitive result (and yes I know that some one more grammar nerd than me can probably tell me its more complicated). In this case, a giant cookie pop-up on an article about cookies could be described as fitting or coincidental but not ironic. It could be ironic if there was a giant cookie pop-up on an article about why one should never eat cookies.
Re: The ever-elusive riddle: What's the best way to cut Christmas cookies?
#25Re: The ever-elusive riddle: What's the best way to cut Christmas cookies?
#26This is amusing but IRL you'd just roll up the extra dough and cut more cookies out of it until you can only get one cookie, then eat the rest of the dough. This is your reward.
Agreed. minimizing waste is an important goal but this is a bad example.
A real life example of a related problem I know is cutting leather, say to make shoes. There, the shape to be cut is constant, but the surfaces they have to cut from (hide shapes and their defects) are different for each hide.
Cutting cigar wrappers (https://en.wikipedia.org/wiki/Cigar#Wrapper) out of tobacco leaves is a similar problem (https://patents.google.com/patent/US4275627 has a good description). I once read about software for doing that, but can’t find that.
Re: The ever-elusive riddle: What's the best way to cut Christmas cookies?
#27I've discovered that an area is most easily filled when the shapes of the individual components used to fill the area are similar.
So, rectangles with rectangles and ellipses with ellipses.
That's how I increase packing density but I can't prove it works.