# BSP-Net: Generating Compact Meshes via Binary Space Partitioning

arXiv: https://arxiv.org/abs/1911.06971 · HTML: https://mlsanity.com/paper/1911.06971/

## Key facts

- Cited by 206 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2019.

## Built on by (most cited first, 30 of 206)

- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [InstantMesh: Efficient 3D Mesh Generation from a Single Image with Sparse-view Large Reconstruction Models](https://mlsanity.com/paper/2404.07191/) (2024)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [MonoScene: Monocular 3D Semantic Scene Completion](https://mlsanity.com/paper/2112.00726/) (2021)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [DreamGaussian4D: Generative 4D Gaussian Splatting](https://mlsanity.com/paper/2312.17142/) (2023)
- [NEAT: Neural Attention Fields for End-to-End Autonomous Driving](https://mlsanity.com/paper/2109.04456/) (2021)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [NeSF: Neural Semantic Fields for Generalizable Semantic Segmentation of 3D Scenes](https://mlsanity.com/paper/2111.13260/) (2021)
- [Capturing, Reconstructing, and Simulating: the UrbanScene3D Dataset](https://mlsanity.com/paper/2107.04286/) (2021)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [MeshXL: Neural Coordinate Field for Generative 3D Foundation Models](https://mlsanity.com/paper/2405.20853/) (2024)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)
- [ShaRF: Shape-conditioned Radiance Fields from a Single View](https://mlsanity.com/paper/2102.08860/) (2021)
- [NDC-Scene: Boost Monocular 3D Semantic Scene Completion in Normalized Device Coordinates Space](https://mlsanity.com/paper/2309.14616/) (2023)
- [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)
- [LOLNeRF: Learn from One Look](https://mlsanity.com/paper/2111.09996/) (2021)
- [OmniSeg3D: Omniversal 3D Segmentation via Hierarchical Contrastive Learning](https://mlsanity.com/paper/2311.11666/) (2023)
- [Scaling Mesh Generation via Compressive Tokenization](https://mlsanity.com/paper/2411.07025/) (2024)
- [Towards Implicit Text-Guided 3D Shape Generation](https://mlsanity.com/paper/2203.14622/) (2022)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [PolyDiff: Generating 3D Polygonal Meshes with Diffusion Models](https://mlsanity.com/paper/2312.11417/) (2023)

## Abstract (arXiv)

Polygonal meshes are ubiquitous in the digital 3D domain, yet they have only played a minor role in the deep learning revolution. Leading methods for learning generative models of shapes rely on implicit functions, and generate meshes only after expensive iso-surfacing routines. To overcome these challenges, we are inspired by a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core ingredient of BSP is an operation for recursive subdivision of space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition. Importantly, BSP-Net is unsupervised since no convex shape decompositions are needed for training. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built on a set of planes. The convexes inferred by BSP-Net can be easily extracted to form a polygon mesh, without any need for iso-surfacing. The generated meshes are compact (i.e., low-poly) and well suited to represent sharp geometry; they are guaranteed to be watertight and can be easily parameterized. We also show that the reconstruction quality by BSP-Net is competitive with state-of-the-art methods while using much fewer primitives. Code is available at https://github.com/czq142857/BSP-NET-original.