# Learning based 2D Irregular Shape Packing

arXiv: https://arxiv.org/abs/2309.10329 · HTML: https://mlsanity.com/paper/2309.10329/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 54 references that are in the map.
- First posted on arXiv 19 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Learning Practically Feasible Policies for Online 3D Bin Packing](https://mlsanity.com/paper/2108.13680/) (2021)
- [TAP-Net: Transport-and-Pack using Reinforcement Learning](https://mlsanity.com/paper/2009.01469/) (2020)
- [PackIt: A Virtual Environment for Geometric Planning](https://mlsanity.com/paper/2007.11121/) (2020)
- [Mononizing Binocular Videos](https://mlsanity.com/paper/2009.01424/) (2020)
- [Shapes In A Box -- Disassembling 3D objects for efficient packing and fabrication](https://mlsanity.com/paper/2104.05281/) (2021)

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

- [DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems](https://mlsanity.com/paper/2406.19705/) (2024)
- [GFPack++: Improving 2D Irregular Packing by Learning Gradient Field with Attention](https://mlsanity.com/paper/2406.07579/) (2024)
- [Optimizing 2D+1 Packing in Constrained Environments Using Deep Reinforcement Learning](https://mlsanity.com/paper/2503.17573/) (2025)
- [Geometry-Aware Reinforcement Learning for 2D Irregular Nesting](https://mlsanity.com/paper/2606.10611/) (2026)
- [DreamUV: Unwrap Artist-like UV by End-to-End Flow Matching](https://mlsanity.com/paper/2606.22445/) (2026)

## Abstract (arXiv)

2D irregular shape packing is a necessary step to arrange UV patches of a 3D model within a texture atlas for memory-efficient appearance rendering in computer graphics. Being a joint, combinatorial decision-making problem involving all patch positions and orientations, this problem has well-known NP-hard complexity. Prior solutions either assume a heuristic packing order or modify the upstream mesh cut and UV mapping to simplify the problem, which either limits the packing ratio or incurs robustness or generality issues. Instead, we introduce a learning-assisted 2D irregular shape packing method that achieves a high packing quality with minimal requirements from the input. Our method iteratively selects and groups subsets of UV patches into near-rectangular super patches, essentially reducing the problem to bin-packing, based on which a joint optimization is employed to further improve the packing ratio. In order to efficiently deal with large problem instances with hundreds of patches, we train deep neural policies to predict nearly rectangular patch subsets and determine their relative poses, leading to linear time scaling with the number of patches. We demonstrate the effectiveness of our method on three datasets for UV packing, where our method achieves a higher packing ratio over several widely used baselines with competitive computational speed.