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# bin_packer_3d

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This crate solves the problem of "fitting smaller boxes inside of a larger box" using a three
dimensional fitting algorithm.

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The algorithm orthogonally packs the all the items into a minimum number of bins by leveraging a [First Fit
Decreasing](https://en.wikipedia.org/wiki/Bin_packing_problem#First_Fit_Decreasing_(FFD)) greedy
strategy, along with rotational optimizations.

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# Usage:

```rust
    use bin_packer_3d::bin::Bin;
    use bin_packer_3d::item::Item;
    use bin_packer_3d::packing_algorithm::packing_algorithm;

    let deck = Item::new("deck", [2, 8, 12]);
    let die = Item::new("die", [8, 8, 8]);
    let items = vec![deck, deck, die, deck, deck];

    let packed_items = packing_algorithm(Bin::new([8, 8, 12]), &items);
    assert_eq!(packed_items, Ok(vec![vec!["deck", "deck", "deck", "deck"], vec!["die"]]));
```

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# Limitations:

This algorithm solves a constrained version of the 3D bin packing problem. As such, we have the
following limitations:

 * The items we are packing, and the bins that we are packing them into, are limited to cuboid
   shapes.

 * The items we are packing can be rotated in any direction, with the limitation that each edge must
   be parallel to the corresponding bin edge.

 * As an NP-Hard problem, this algorithm does not attempt to find the optimal solution, but instead
   uses an approximation that runs with a time complexity of *O(n^2)*

# Acknowledgements:

The algorithm leverages a rotational optimization when packing items which are less than half the
length of a bin's side, as proposed in the paper titled "The Three-Dimensional Bin Packing Problem"
(Martello, 1997), page 257:
[https://www.jstor.org/stable/pdf/223143.pdf](https://www.jstor.org/stable/pdf/223143.pdf)