# NeuroNURBS: Learning Efficient Surface Representations for 3D Solids

arXiv: https://arxiv.org/abs/2411.10848 · HTML: https://mlsanity.com/paper/2411.10848/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 16 Nov 2024.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Predicting Depth, Surface Normals and Semantic Labels with a Common Multi-Scale Convolutional Architecture](https://mlsanity.com/paper/1411.4734/) (2014)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [MultiMAE: Multi-modal Multi-task Masked Autoencoders](https://mlsanity.com/paper/2204.01678/) (2022)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [Multimodal Deep Learning](https://mlsanity.com/paper/2301.04856/) (2023)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2209.08725/) (2022)
- [Diffusion-SDF: Text-to-Shape via Voxelized Diffusion](https://mlsanity.com/paper/2212.03293/) (2022)
- [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)
- [SolidGen: An Autoregressive Model for Direct B-rep Synthesis](https://mlsanity.com/paper/2203.13944/) (2022)
- [JoinABLe: Learning Bottom-up Assembly of Parametric CAD Joints](https://mlsanity.com/paper/2111.12772/) (2021)
- [OctFusion: Octree-based Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2408.14732/) (2024)
- [Reconstructing editable prismatic CAD from rounded voxel models](https://mlsanity.com/paper/2209.01161/) (2022)
- [Geometric Deep Learning for Computer-Aided Design: A Survey](https://mlsanity.com/paper/2402.17695/) (2024)
- [NURBS-Diff: A Differentiable Programming Module for NURBS](https://mlsanity.com/paper/2104.14547/) (2021)
- [On the Noise Scheduling for Generating Plausible Designs with Diffusion Models](https://mlsanity.com/paper/2311.11207/) (2023)
- [Adversarial Latent Autoencoder with Self-Attention for Structural Image Synthesis](https://mlsanity.com/paper/2307.10166/) (2023)
- [UVStyle-Net: Unsupervised Few-shot Learning of 3D Style Similarity Measure for B-Reps](https://mlsanity.com/paper/2105.02961/) (2021)

## Built on by (most cited first, 8 of 8)

- [AutoBrep: Autoregressive B-Rep Generation with Unified Topology and Geometry](https://mlsanity.com/paper/2512.03018/) (2025)
- [FoV-Net: Rotation-Invariant CAD B-rep Learning via Field-of-View Ray Casting](https://mlsanity.com/paper/2602.24084/) (2026)
- [Autoregressive B-Rep Shape Generation with Parametric Surfaces](https://mlsanity.com/paper/2607.17093/) (2026)
- [BrepLLM: Enabling Large Language Models to Understand Boundary Representations](https://mlsanity.com/paper/2512.16413/) (2025)
- [Draw it like Euclid: Teaching transformer models to generate CAD profiles using ruler and compass construction steps](https://mlsanity.com/paper/2601.09428/) (2026)
- [AutoRegressive Generation with B-rep Holistic Token Sequence Representation](https://mlsanity.com/paper/2601.16771/) (2026)
- [NURBS Splatting: A Unified Differentiable Rendering Framework for Vector Graphics](https://mlsanity.com/paper/2606.31764/) (2026)
- [CANTO: CAD-Native Transformer Operators for AI-Aided Engineering](https://mlsanity.com/paper/2609.36806/) (2026)

## Abstract (arXiv)

Boundary Representation (B-Rep) is the de facto representation of 3D solids in Computer-Aided Design (CAD). B-Rep solids are defined with a set of NURBS (Non-Uniform Rational B-Splines) surfaces forming a closed volume. To represent a surface, current works often employ the UV-grid approximation, i.e., sample points uniformly on the surface. However, the UV-grid method is not efficient in surface representation and sometimes lacks precision and regularity. In this work, we propose NeuroNURBS, a representation learning method to directly encode the parameters of NURBS surfaces. Our evaluation in solid generation and segmentation tasks indicates that the NeuroNURBS performs comparably and, in some cases, superior to UV-grids, but with a significantly improved efficiency: for training the surface autoencoder, GPU consumption is reduced by 86.7%; memory requirement drops by 79.9% for storing 3D solids. Moreover, adapting BrepGen for solid generation with our NeuroNURBS improves the FID from 30.04 to 27.24, and resolves the undulating issue in generated surfaces.