# NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature

arXiv: https://arxiv.org/abs/2404.13420 · HTML: https://mlsanity.com/paper/2404.13420/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 65 references that are in the map.
- First posted on arXiv 20 Apr 2024.

## Builds on (most cited first, 30 of 33)

- [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)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [ParSeNet: A Parametric Surface Fitting Network for 3D Point Clouds](https://mlsanity.com/paper/2003.12181/) (2020)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [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)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations](https://mlsanity.com/paper/2205.02825/) (2022)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders](https://mlsanity.com/paper/2112.09329/) (2021)
- [SA-ConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networks](https://mlsanity.com/paper/2105.03582/) (2021)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Critical Regularizations for Neural Surface Reconstruction in the Wild](https://mlsanity.com/paper/2206.03087/) (2022)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [Iso-Points: Optimizing Neural Implicit Surfaces with Hybrid Representations](https://mlsanity.com/paper/2012.06434/) (2020)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [Fusion 360 Gallery: A Dataset and Environment for Programmatic CAD Construction from Human Design Sequences](https://mlsanity.com/paper/2010.02392/) (2020)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)

## Built on by (most cited first, 12 of 12)

- [HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition](https://mlsanity.com/paper/2411.14628/) (2024)
- [FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models](https://mlsanity.com/paper/2506.16627/) (2025)
- [A Survey of AI Methods for Geometry Preparation and Mesh Generation in Engineering Simulation](https://mlsanity.com/paper/2512.23719/) (2025)
- [Autoregressive B-Rep Shape Generation with Parametric Surfaces](https://mlsanity.com/paper/2607.17093/) (2026)
- [Masked Extended Attention for Zero-Shot Virtual Try-On In The Wild](https://mlsanity.com/paper/2406.15331/) (2024)
- [Joint Neural SDF Reconstruction and Semantic Segmentation for CAD Models](https://mlsanity.com/paper/2510.03837/) (2025)
- [Scheduling the Off-Diagonal Weingarten Loss of Neural SDFs for CAD Models](https://mlsanity.com/paper/2511.03147/) (2025)
- [Neural Octahedral Field: Octahedral prior for simultaneous smoothing and sharp edge regularization](https://mlsanity.com/paper/2408.00303/) (2024)
- [Towards Understanding 3D Vision: the Role of Gaussian Curvature](https://mlsanity.com/paper/2508.11825/) (2025)
- [A Finite Difference Approximation of Second Order Regularization of Neural-SDFs](https://mlsanity.com/paper/2511.08980/) (2025)
- [SharpNet: Enhancing MLPs to Represent Functions with Controlled Non-differentiability](https://mlsanity.com/paper/2601.19683/) (2026)
- [CGGT: Curve-Grounded Geometry Transformer for 3D Parametric Curve Reconstruction](https://mlsanity.com/paper/2609.14521/) (2026)

## Abstract (arXiv)

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon, is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points. Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.