# Neural Parametric Surfaces for Shape Modeling

arXiv: https://arxiv.org/abs/2309.09911 · HTML: https://mlsanity.com/paper/2309.09911/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2023.

## Built on by (most cited first, 5 of 5)

- [Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2401.12946/) (2024)
- [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024)
- [Parameterization-driven Neural Surface Reconstruction for Object-oriented Editing in Neural Rendering](https://mlsanity.com/paper/2310.05524/) (2023)
- [NESI: Shape Representation via Neural Explicit Surface Intersection](https://mlsanity.com/paper/2409.06030/) (2024)
- [Blended Chart Surfaces: A Seamless Explicit Representation for Smooth Surface Fitting](https://mlsanity.com/paper/2606.18069/) (2026)

## Abstract (arXiv)

The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the capabilities of parametric surfaces, which are the prevalent surface representations in product design, CAD/CAM, and computer animation. We present Neural Parametric Surfaces, the first piecewise neural surface representation that allows coarse patch layouts of arbitrary n-sided surface patches to model complex surface geometries with high precision, offering greater flexibility over traditional parametric surfaces. By construction, this new surface representation guarantees G0 continuity between adjacent patches and empirically achieves G1 continuity, which cannot be attained by existing neural patch-based methods. The key ingredient of our neural parametric surface is a learnable feature complex C that is embedded in a high-dimensional space ℝD and topologically equivalent to the patch layout of the surface; each face cell of the complex is defined by interpolating feature vectors at its vertices. The learned feature complex is mapped by an MLP-encoded function f:C rightarrow S to produce the neural parametric surface S. We present a surface fitting algorithm that optimizes the feature complex C and trains the neural mapping f to reconstruct given target shapes with high accuracy. We further show that the proposed representation along with a compact-size neural net can learn a plausible shape space from a shape collection, which can be used for shape interpolation or shape completion from noisy and incomplete input data. Extensive experiments show that neural parametric surfaces offer greater modeling capabilities than traditional parametric surfaces.