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It’s interesting they’re using the FFT.

I’m guessing they’re using it for convolutions to increase the computation speed for calculating whether a given object placement and orientation interfere but my small brain wouldn’t really know.

If so, is that a common technique in optimization problems?

Funny coincidence, I happened to see this just yesterday in SIGGRAPH technical papers trailer[1]. Seeing the videos of SIGGRAPH is one of the highlights of science year to me; even though I don't understand the stuff basically at all, I can enjoy the pretty pictures and appreciate the intricacies/complexity of trying to simulate/model some seemingly mundane things. In some ways it makes me look at the world in new light and recognize just how much detail there is around me all the time.

[1] https://youtu.be/VBZ2sDxvZQE

It's very fun to go watch the presentations from years past. Stuff we now take for granted (e.g. rendering glass using ray tracing) used to be bleeding edge not too long ago.
On the flip side, there is tons of stuff that never escaped academia and only existed on a proof-of-concept level, with no code available and for casual observer like me no way to play around with.
For a lot of those papers in the trailer it is not at all clear to me why they are at SIGGRAPH. They seemed more about figuring out the state of a simulated physical system than about how to draw that system.
Fun, and interesting. But the illustration is highly misleading.

The article explains that the researchers are pleased when they can achieve a 35-40% packing density.

That illustration is directly from the paper and has a packing density of 35.77%.
You are absolutely right! Thanks for the correction.

It seems that I didn't know what a 35% packing looked like.

Please show us an algorithm with better packing density for this problem if you know one.
>In one demonstration, the new algorithm efficiently placed 670 objects in just 40 seconds, achieving a packing density of about 36%. It took two hours to arrange 6,596 objects with a packing density of 37.30%. "The densities we're getting, close to 40%, are significantly better than those obtained by traditional algorithms," Matusik says, "and they're also faster."

Faster and better than alternatives sounds good to me.

Using this as the basis for a SASS offering for the e-commerce industry might be interesting… how to pack a box most efficiently in order to save on materials and shipping costs
It doesn't seem to be anything they are very worried about, considering the number of items I receive in vastly oversized boxes stuffed with paper or bubble pack to fill the empty space.
Bruteforce is a new method now?
"They do something with FFT for bin packing." The whole article could have been that sentence.