# UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree

arXiv: https://arxiv.org/abs/2006.09102 · HTML: https://mlsanity.com/paper/2006.09102/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 30 of 78)

- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [Decomposing 3D Scenes into Objects via Unsupervised Volume Segmentation](https://mlsanity.com/paper/2104.01148/) (2021)
- [Hierarchical Neural Coding for Controllable CAD Model Generation](https://mlsanity.com/paper/2307.00149/) (2023)
- [CAD-MLLM: Unifying Multimodality-Conditioned CAD Generation With MLLM](https://mlsanity.com/paper/2411.04954/) (2024)
- [SolidGen: An Autoregressive Model for Direct B-rep Synthesis](https://mlsanity.com/paper/2203.13944/) (2022)
- [SketchGen: Generating Constrained CAD Sketches](https://mlsanity.com/paper/2106.02711/) (2021)
- [CAD-Recode: Reverse Engineering CAD Code from Point Clouds](https://mlsanity.com/paper/2412.14042/) (2024)
- [CAD-SIGNet: CAD Language Inference from Point Clouds using Layer-wise Sketch Instance Guided Attention](https://mlsanity.com/paper/2402.17678/) (2024)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders](https://mlsanity.com/paper/2112.09329/) (2021)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [Engineering Sketch Generation for Computer-Aided Design](https://mlsanity.com/paper/2104.09621/) (2021)
- [Text-to-CAD Generation Through Infusing Visual Feedback in Large Language Models](https://mlsanity.com/paper/2501.19054/) (2025)
- [SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations](https://mlsanity.com/paper/2303.10613/) (2023)
- [Reconstructing editable prismatic CAD from rounded voxel models](https://mlsanity.com/paper/2209.01161/) (2022)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [ExtrudeNet: Unsupervised Inverse Sketch-and-Extrude for Shape Parsing](https://mlsanity.com/paper/2209.15632/) (2022)
- [Img2CAD: Conditioned 3D CAD Model Generation from Single Image with Structured Visual Geometry](https://mlsanity.com/paper/2410.03417/) (2024)
- [Img2CAD: Reverse Engineering 3D CAD Models from Images through VLM-Assisted Conditional Factorization](https://mlsanity.com/paper/2408.01437/) (2024)
- [Can Large Language Models Understand Symbolic Graphics Programs?](https://mlsanity.com/paper/2408.08313/) (2024)
- [FlexCAD: Unified and Versatile Controllable CAD Generation with Fine-tuned Large Language Models](https://mlsanity.com/paper/2411.05823/) (2024)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [HoLa: B-Rep Generation using a Holistic Latent Representation](https://mlsanity.com/paper/2504.14257/) (2025)
- [TransCAD: A Hierarchical Transformer for CAD Sequence Inference from Point Clouds](https://mlsanity.com/paper/2407.12702/) (2024)
- [CADDreamer: CAD Object Generation from Single-view Images](https://mlsanity.com/paper/2502.20732/) (2025)
- [CPFN: Cascaded Primitive Fitting Networks for High-Resolution Point Clouds](https://mlsanity.com/paper/2109.00113/) (2021)
- [ShapeCoder: Discovering Abstractions for Visual Programs from Unstructured Primitives](https://mlsanity.com/paper/2305.05661/) (2023)
- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)

## Abstract (arXiv)

Signed distance field (SDF) is a prominent implicit representation of 3D meshes. Methods that are based on such representation achieved state-of-the-art 3D shape reconstruction quality. However, these methods struggle to reconstruct non-convex shapes. One remedy is to incorporate a constructive solid geometry framework (CSG) that represents a shape as a decomposition into primitives. It allows to embody a 3D shape of high complexity and non-convexity with a simple tree representation of Boolean operations. Nevertheless, existing approaches are supervised and require the entire CSG parse tree that is given upfront during the training process. On the contrary, we propose a model that extracts a CSG parse tree without any supervision - UCSG-Net. Our model predicts parameters of primitives and binarizes their SDF representation through differentiable indicator function. It is achieved jointly with discovering the structure of a Boolean operators tree. The model selects dynamically which operator combination over primitives leads to the reconstruction of high fidelity. We evaluate our method on 2D and 3D autoencoding tasks. We show that the predicted parse tree representation is interpretable and can be used in CAD software.