# Learning Delaunay Surface Elements for Mesh Reconstruction

arXiv: https://arxiv.org/abs/2012.01203 · HTML: https://mlsanity.com/paper/2012.01203/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2020.

## Built on by (most cited first, 23 of 23)

- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [VisCo Grids: Surface Reconstruction with Viscosity and Coarea Grids](https://mlsanity.com/paper/2303.14569/) (2023)
- [SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes](https://mlsanity.com/paper/2409.20562/) (2024)
- [PU-Flow: a Point Cloud Upsampling Network with Normalizing Flows](https://mlsanity.com/paper/2107.05893/) (2021)
- [Deep Point Cloud Reconstruction](https://mlsanity.com/paper/2111.11704/) (2021)
- [Differentiable Surface Triangulation](https://mlsanity.com/paper/2109.10695/) (2021)
- [Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction](https://mlsanity.com/paper/2109.04398/) (2021)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2301.13656/) (2023)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [Spectrum AUC Difference (SAUCD): Human-aligned 3D Shape Evaluation](https://mlsanity.com/paper/2403.01619/) (2024)
- [TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2505.04590/) (2025)
- [Point2Quad: Generating Quad Meshes from Point Clouds via Face Prediction](https://mlsanity.com/paper/2504.19545/) (2025)
- [MASH: Masked Anchored SpHerical Distances for 3D Shape Representation and Generation](https://mlsanity.com/paper/2504.09149/) (2025)
- [NeuralMeshing: Differentiable Meshing of Implicit Neural Representations](https://mlsanity.com/paper/2210.02382/) (2022)
- [A Review of Deep Learning-Powered Mesh Reconstruction Methods](https://mlsanity.com/paper/2303.02879/) (2023)
- [CircNet: Meshing 3D Point Clouds with Circumcenter Detection](https://mlsanity.com/paper/2301.09253/) (2023)
- [Self-Supervised Dual Contouring](https://mlsanity.com/paper/2405.18131/) (2024)
- [OffsetOPT: Explicit Surface Reconstruction without Normals](https://mlsanity.com/paper/2503.15763/) (2025)
- [Isomorphic mesh generation from point clouds with multilayer perceptrons](https://mlsanity.com/paper/2210.14157/) (2022)
- [PRS: Sharp Feature Priors for Resolution-Free Surface Remeshing](https://mlsanity.com/paper/2311.18494/) (2023)
- [Delaunay Canopy: Building Wireframe Reconstruction from Airborne LiDAR Point Clouds via Delaunay Graph](https://mlsanity.com/paper/2604.02497/) (2026)

## Abstract (arXiv)

We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties of 2D Delaunay triangulations to construct a mesh from manifold surface elements. Our method first estimates local geodesic neighborhoods around each point. We then perform a 2D projection of these neighborhoods using a learned logarithmic map. A Delaunay triangulation in this 2D domain is guaranteed to produce a manifold patch, which we call a Delaunay surface element. We synchronize the local 2D projections of neighboring elements to maximize the manifoldness of the reconstructed mesh. Our results show that we achieve better overall manifoldness of our reconstructed meshes than current methods to reconstruct meshes with arbitrary topology. Our code, data and pretrained models can be found online: https://github.com/mrakotosaon/dse-meshing