# CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing

arXiv: https://arxiv.org/abs/2108.11305 · HTML: https://mlsanity.com/paper/2108.11305/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 37 references that are in the map.
- First posted on arXiv 25 Aug 2021.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation](https://mlsanity.com/paper/1908.01491/) (2019)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [BAE-NET: Branched Autoencoder for Shape Co-Segmentation](https://mlsanity.com/paper/1903.11228/) (2019)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree](https://mlsanity.com/paper/2006.09102/) (2020)
- [Image2Mesh: A Learning Framework for Single Image 3D Reconstruction](https://mlsanity.com/paper/1711.10669/) (2017)

## Built on by (most cited first, 30 of 51)

- [Semantic-Aware Implicit Neural Audio-Driven Video Portrait Generation](https://mlsanity.com/paper/2201.07786/) (2022)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [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)
- [Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders](https://mlsanity.com/paper/2112.09329/) (2021)
- [SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations](https://mlsanity.com/paper/2303.10613/) (2023)
- [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)
- [FlexCAD: Unified and Versatile Controllable CAD Generation with Fine-tuned Large Language Models](https://mlsanity.com/paper/2411.05823/) (2024)
- [HoLa: B-Rep Generation using a Holistic Latent Representation](https://mlsanity.com/paper/2504.14257/) (2025)
- [ShapeCoder: Discovering Abstractions for Visual Programs from Unstructured Primitives](https://mlsanity.com/paper/2305.05661/) (2023)
- [ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation](https://mlsanity.com/paper/2205.14573/) (2022)
- [cadrille: Multi-modal CAD Reconstruction with Reinforcement Learning](https://mlsanity.com/paper/2505.22914/) (2025)
- [BrepGPT: Autoregressive B-rep Generation with Voronoi Half-Patch](https://mlsanity.com/paper/2511.22171/) (2025)
- [Pointer-CAD: Unifying B-Rep and Command Sequences via Pointer-based Edges & Faces Selection](https://mlsanity.com/paper/2603.04337/) (2026)
- [Improving Unsupervised Visual Program Inference with Code Rewriting Families](https://mlsanity.com/paper/2309.14972/) (2023)
- [Text2CAD: Text to 3D CAD Generation via Technical Drawings](https://mlsanity.com/paper/2411.06206/) (2024)
- [Learning to Edit Visual Programs with Self-Supervision](https://mlsanity.com/paper/2406.02383/) (2024)
- [DiffCSG: Differentiable CSG via Rasterization](https://mlsanity.com/paper/2409.01421/) (2024)
- [Don't Mesh with Me: Generating Constructive Solid Geometry Instead of Meshes by Fine-Tuning a Code-Generation LLM](https://mlsanity.com/paper/2411.15279/) (2024)
- [Revisiting CAD Model Generation by Learning Raster Sketch](https://mlsanity.com/paper/2503.00928/) (2025)
- [Parametric Point Cloud Completion for Polygonal Surface Reconstruction](https://mlsanity.com/paper/2503.08363/) (2025)
- [CADReasoner: Iterative Program Editing for CAD Reverse Engineering](https://mlsanity.com/paper/2603.29847/) (2026)
- [DPA-Net: Structured 3D Abstraction from Sparse Views via Differentiable Primitive Assembly](https://mlsanity.com/paper/2404.00875/) (2024)
- [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024)
- [ShapeLib: Designing a library of programmatic 3D shape abstractions with Large Language Models](https://mlsanity.com/paper/2502.08884/) (2025)
- [MiCADangelo: Fine-Grained Reconstruction of Constrained CAD Models from 3D Scans](https://mlsanity.com/paper/2510.23429/) (2025)
- [Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation](https://mlsanity.com/paper/2209.10191/) (2022)

## Abstract (arXiv)

Generating an interpretable and compact representation of 3D shapes from point clouds is an important and challenging problem. This paper presents CSG-Stump Net, an unsupervised end-to-end network for learning shapes from point clouds and discovering the underlying constituent modeling primitives and operations as well. At the core is a three-level structure called em CSG-Stump, consisting of a complement layer at the bottom, an intersection layer in the middle, and a union layer at the top. CSG-Stump is proven to be equivalent to CSG in terms of representation, therefore inheriting the interpretable, compact and editable nature of CSG while freeing from CSG's complex tree structures. Particularly, the CSG-Stump has a simple and regular structure, allowing neural networks to give outputs of a constant dimensionality, which makes itself deep-learning friendly. Due to these characteristics of CSG-Stump, CSG-Stump Net achieves superior results compared to previous CSG-based methods and generates much more appealing shapes, as confirmed by extensive experiments. Project page: https://kimren227.github.io/projects/CSGStump/