# Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning

arXiv: https://arxiv.org/abs/2406.05261 · HTML: https://mlsanity.com/paper/2406.05261/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 7 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [ParSeNet: A Parametric Surface Fitting Network for 3D Point Clouds](https://mlsanity.com/paper/2003.12181/) (2020)
- [BRepNet: A topological message passing system for solid models](https://mlsanity.com/paper/2104.00706/) (2021)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree](https://mlsanity.com/paper/2006.09102/) (2020)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Inferring CAD Modeling Sequences Using Zone Graphs](https://mlsanity.com/paper/2104.03900/) (2021)
- [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)
- [HPNet: Deep Primitive Segmentation Using Hybrid Representations](https://mlsanity.com/paper/2105.10620/) (2021)
- [NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud](https://mlsanity.com/paper/2303.16465/) (2023)
- [Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram](https://mlsanity.com/paper/2210.13676/) (2022)
- [VoronoiNet: General Functional Approximators with Local Support](https://mlsanity.com/paper/1912.03629/) (2019)
- [A Survey of Methods for Converting Unstructured Data to CSG Models](https://mlsanity.com/paper/2305.01220/) (2023)
- [Variational Shape Approximation of Point Set Surfaces](https://mlsanity.com/paper/2005.01003/) (2020)

## Built on by (most cited first, 18 of 18)

- [CAD-MLLM: Unifying Multimodality-Conditioned CAD Generation With MLLM](https://mlsanity.com/paper/2411.04954/) (2024)
- [Img2CAD: Reverse Engineering 3D CAD Models from Images through VLM-Assisted Conditional Factorization](https://mlsanity.com/paper/2408.01437/) (2024)
- [HoLa: B-Rep Generation using a Holistic Latent Representation](https://mlsanity.com/paper/2504.14257/) (2025)
- [AutoBrep: Autoregressive B-Rep Generation with Unified Topology and Geometry](https://mlsanity.com/paper/2512.03018/) (2025)
- [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)
- [CMT: A Cascade MAR with Topology Predictor for Multimodal Conditional CAD Generation](https://mlsanity.com/paper/2504.20830/) (2025)
- [CADReasoner: Iterative Program Editing for CAD Reverse Engineering](https://mlsanity.com/paper/2603.29847/) (2026)
- [DualBrep: A Dual-Field Continuous Representation for B-rep Modelling](https://mlsanity.com/paper/2606.31579/) (2026)
- [Autoregressive B-Rep Shape Generation with Parametric Surfaces](https://mlsanity.com/paper/2607.17093/) (2026)
- [View2CAD: Reconstructing View-Centric CAD Models from Single RGB-D Scans](https://mlsanity.com/paper/2504.04000/) (2025)
- [B-Rep Distance Functions (BR-DF): How to Represent a B-Rep Model by Volumetric Distance Functions?](https://mlsanity.com/paper/2511.14870/) (2025)
- [CADENA: Stepwise CAD Reverse Engineering](https://mlsanity.com/paper/2608.00799/) (2026)
- [SharpNet: Enhancing MLPs to Represent Functions with Controlled Non-differentiability](https://mlsanity.com/paper/2601.19683/) (2026)
- [BrepGaussian: CAD reconstruction from Multi-View Images with Gaussian Splatting](https://mlsanity.com/paper/2602.21105/) (2026)
- [Learning From Design Procedure To Generate CAD Programs for Data Augmentation](https://mlsanity.com/paper/2603.06894/) (2026)
- [CGGT: Curve-Grounded Geometry Transformer for 3D Parametric Curve Reconstruction](https://mlsanity.com/paper/2609.14521/) (2026)
- [UniBRep: Learning Unified Geometry and Topology for Image-conditioned B-Rep Generation](https://mlsanity.com/paper/2610.04092/) (2026)

## Abstract (arXiv)

We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning, referred to as the ``split``, followed by a ``fit`` operation to derive a single primitive within each partition. Specifically, our partitioning aims to produce the classical Voronoi diagram of the set of ground-truth (GT) B-Rep primitives. In contrast to prior B-Rep constructions which were bottom-up, either via direct primitive fitting or point clustering, our Split-and-Fit approach is top-down and structure-aware, since a Voronoi partition explicitly reveals both the number of and the connections between the primitives. We design a neural network to predict the Voronoi diagram from an input point cloud or distance field via a binary classification. We show that our network, coined NVD-Net for neural Voronoi diagrams, can effectively learn Voronoi partitions for CAD models from training data and exhibits superior generalization capabilities. Extensive experiments and evaluation demonstrate that the resulting B-Reps, consisting of parametric surfaces, curves, and vertices, are more plausible than those obtained by existing alternatives, with significant improvements in reconstruction quality. Code will be released on https://github.com/yilinliu77/NVDNet.