# Patchwork: A compact representation for 3D polygonal shapes

arXiv: https://arxiv.org/abs/2605.16266 · HTML: https://mlsanity.com/paper/2605.16266/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Builds on (most cited first, 24 of 24)

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- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
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- [On the Decision Boundaries of Neural Networks: A Tropical Geometry Perspective](https://mlsanity.com/paper/2002.08838/) (2020)
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- [Piecewise Linear Regression via a Difference of Convex Functions](https://mlsanity.com/paper/2007.02422/) (2020)
- [Intuitive and Efficient Roof Modeling for Reconstruction and Synthesis](https://mlsanity.com/paper/2109.07683/) (2021)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
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- [Understand the Effectiveness of Shortcuts through the Lens of DCA](https://mlsanity.com/paper/2412.09853/) (2024)
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## Abstract (arXiv)

We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds and the ability to approximate arbitrary shapes with arbitrary precision in any dimension. We propose an efficient gradient-based optimization scheme to fit Patchwork representations to 2D and 3D data, along with a novel regularization loss that progressively prunes redundant elements, yielding high compactness after convergence. Our approach offers fast fitting performance, a fraction of the required parameters compared to existing alternatives, and native support for inside-outside classification, making it a versatile and compact representation for geometric learning and reconstruction tasks, with future potential for 3D generation. Our implementation is available at: https://github.com/Ankbzpx/patchwork-experiment.