# B-Rep Distance Functions (BR-DF): How to Represent a B-Rep Model by Volumetric Distance Functions?

arXiv: https://arxiv.org/abs/2511.14870 · HTML: https://mlsanity.com/paper/2511.14870/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [NeuralRecon: Real-Time Coherent 3D Reconstruction from Monocular Video](https://mlsanity.com/paper/2104.00681/) (2021)
- [TripoSG: High-Fidelity 3D Shape Synthesis using Large-Scale Rectified Flow Models](https://mlsanity.com/paper/2502.06608/) (2025)
- [MVDiffusion: Enabling Holistic Multi-view Image Generation with Correspondence-Aware Diffusion](https://mlsanity.com/paper/2307.01097/) (2023)
- [Atlas: End-to-End 3D Scene Reconstruction from Posed Images](https://mlsanity.com/paper/2003.10432/) (2020)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [ScanComplete: Large-Scale Scene Completion and Semantic Segmentation for 3D Scans](https://mlsanity.com/paper/1712.10215/) (2017)
- [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)
- [SolidGen: An Autoregressive Model for Direct B-rep Synthesis](https://mlsanity.com/paper/2203.13944/) (2022)
- [Engineering Sketch Generation for Computer-Aided Design](https://mlsanity.com/paper/2104.09621/) (2021)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation, Inversion, and Manipulation](https://mlsanity.com/paper/2302.00190/) (2023)
- [Make-A-Shape: a Ten-Million-scale 3D Shape Model](https://mlsanity.com/paper/2401.11067/) (2024)
- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)

## Built on by (most cited first, 1 of 1)

- [CADENA: Stepwise CAD Reverse Engineering](https://mlsanity.com/paper/2608.00799/) (2026)

## Abstract (arXiv)

This paper presents a novel geometric representation for CAD Boundary Representation (B-Rep) based on volumetric distance functions, dubbed B-Rep Distance Functions (BR-DF). BR-DF encodes the surface mesh geometry of a CAD model as signed distance function (SDF). B-Rep vertices, edges, faces and their topology information are encoded as per-face unsigned distance functions (UDFs). An extension of the Marching Cubes algorithm converts BR-DF directly into watertight CAD B-Rep model (strictly speaking a faceted B-Rep model). A surprising characteristic of BR-DF is that this conversion process never fails. Leveraging the volumetric nature of BR-DF, we propose a multi-branch latent diffusion with 3D U-Net backbone for jointly generating the SDF and per-face UDFs of a BR-DF model. Our approach achieves comparable CAD generation performance against SOTA methods while reaching the unprecedented 100% success rate in producing (faceted) B-Rep models.