It would seem like this can be done by solving various optimization formulas via plane geometry? The radicals arise from solving maximization polynomials assuming it's a constructable solution.
Depends on the shape. Irregular shape packing and optimisation is still being advanced. Newer approaches are using ai. Lots of GitHub repositories with different approaches.
Early in my generative art, I spent a lot of time packing various small shapes together, it was a fun process to figure out how to maximize the coverage without leaving large gaps. For example, a piece with almost every shape I was using: https://digcon.art/details.html?key=river-in-the-woods
One I can think of is circles-in-circles where you are bundling wires or optical fibre cores into cables. (And probably for tensile cables used in bridges and so on)
Communications theory is largely about how to pack circles/spheres efficiently in multiple dimensions. So arguably pretty much all of the modern society is based on efficient packing.
Great site, thanks! Improvement idea: please use SVGs instead (or in addition to) GIFs. It should be relatively easy, much better quality, probably smaller image file sizes.
I've been pondering what an algorithm would look like that does this. Given a bunch of boxes of various sizes and weights, and a room of a given dimension, what's the most efficient arrangement to make sure they all fit?
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[ 3.6 ms ] story [ 56.5 ms ] threadHowever, Multi dimensional bin packing problems are the some of the hardest non linear optimization problems.
Minimizing maximum to minimum ratio for structural stability.
Erich's Packing Center - https://news.ycombinator.com/item?id=29529130 - Dec 2021 (16 comments)
https://medium.com/the-chain/solving-the-box-selection-algor...