# Shapes In A Box -- Disassembling 3D objects for efficient packing and fabrication

arXiv: https://arxiv.org/abs/2104.05281 · HTML: https://mlsanity.com/paper/2104.05281/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2021.

## Built on by (most cited first, 5 of 5)

- [Learning based 2D Irregular Shape Packing](https://mlsanity.com/paper/2309.10329/) (2023)
- [Learning Gradient Fields for Scalable and Generalizable Irregular Packing](https://mlsanity.com/paper/2310.19814/) (2023)
- [An overview of some mathematical techniques and problems linking 3D vision to 3D printing](https://mlsanity.com/paper/2309.10549/) (2023)
- [Introducing Resizable Region Packing Problem in Image Generation, with a Heuristic Solution](https://mlsanity.com/paper/2509.16363/) (2025)
- [Differentiable Packing of Irregular 3D Objects with Adaptive Container Estimation](https://mlsanity.com/paper/2606.16333/) (2026)

## Abstract (arXiv)

Modern 3D printing technologies and the upcoming mass-customization paradigm call for efficient methods to produce and distribute arbitrarily-shaped 3D objects. This paper introduces an original algorithm to split a 3D model in parts that can be efficiently packed within a box, with the objective of reassembling them after delivery. The first step consists in the creation of a hierarchy of possible parts that can be tightly packed within their minimum bounding boxes. In a second step, the hierarchy is exploited to extract the (single) segmentation whose parts can be most tightly packed. The fact that shape packing is an NP-complete problem justifies the use of heuristics and approximated solutions whose efficacy and efficiency must be assessed. Extensive experimentation demonstrates that our algorithm produces satisfactory results for arbitrarily-shaped objects while being comparable to ad-hoc methods when specific shapes are considered.