# NASM: Neural Anisotropic Surface Meshing

arXiv: https://arxiv.org/abs/2410.23109 · HTML: https://mlsanity.com/paper/2410.23109/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 69 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [MeshCNN: A Network with an Edge](https://mlsanity.com/paper/1809.05910/) (2018)
- [Adaptive O-CNN: A Patch-based Deep Representation of 3D Shapes](https://mlsanity.com/paper/1809.07917/) (2018)
- [A Survey on Deep Geometry Learning: From a Representation Perspective](https://mlsanity.com/paper/2002.07995/) (2020)
- [HodgeNet: Learning Spectral Geometry on Triangle Meshes](https://mlsanity.com/paper/2104.12826/) (2021)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [Learning the Geodesic Embedding with Graph Neural Networks](https://mlsanity.com/paper/2309.05613/) (2023)
- [CWF: Consolidating Weak Features in High-quality Mesh Simplification](https://mlsanity.com/paper/2404.15661/) (2024)
- [Learning Mesh Representations via Binary Space Partitioning Tree Networks](https://mlsanity.com/paper/2106.14274/) (2021)

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

- [Learning Manifolds in High-D Point Embedding for Anisotropic Surface Approximation from Unstructured Point Clouds](https://mlsanity.com/paper/2607.28855/) (2026)

## Abstract (arXiv)

This paper introduces a new learning-based method, NASM, for anisotropic surface meshing. Our key idea is to propose a graph neural network to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve curvature-based anisotropic metric by using a dot product loss between high-d edge vectors. This can dramatically reduce the computational time and increase the scalability. Then, we propose a novel feature-sensitive remeshing on the generated high-d embedding to automatically capture sharp geometric features. We define a high-d normal metric, and then derive an automatic differentiation on a high-d centroidal Voronoi tessellation (CVT) optimization with the normal metric to simultaneously preserve geometric features and curvature anisotropy that exhibit in the original 3D shapes. To our knowledge, this is the first time that a deep learning framework and a large dataset are proposed to construct a high-d Euclidean embedding space for 3D anisotropic surface meshing. Experimental results are evaluated and compared with the state-of-the-art in anisotropic surface meshing on a large number of surface models from Thingi10K dataset as well as tested on extensive unseen 3D shapes from Multi-Garment Network dataset and FAUST human dataset.