# PointTriNet: Learned Triangulation of 3D Point Sets

arXiv: https://arxiv.org/abs/2005.02138 · HTML: https://mlsanity.com/paper/2005.02138/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2020.

## Built on by (most cited first, 30 of 32)

- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [The Power of Points for Modeling Humans in Clothing](https://mlsanity.com/paper/2109.01137/) (2021)
- [SCALE: Modeling Clothed Humans with a Surface Codec of Articulated Local Elements](https://mlsanity.com/paper/2104.07660/) (2021)
- [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)
- [SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes](https://mlsanity.com/paper/2409.20562/) (2024)
- [Deep Point Cloud Reconstruction](https://mlsanity.com/paper/2111.11704/) (2021)
- [Differentiable Surface Triangulation](https://mlsanity.com/paper/2109.10695/) (2021)
- [A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2301.13656/) (2023)
- [Deep Surface Reconstruction from Point Clouds with Visibility Information](https://mlsanity.com/paper/2202.01810/) (2022)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [TetGAN: A Convolutional Neural Network for Tetrahedral Mesh Generation](https://mlsanity.com/paper/2210.05735/) (2022)
- [Scalable Surface Reconstruction with Delaunay-Graph Neural Networks](https://mlsanity.com/paper/2107.06130/) (2021)
- [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)
- [Procedural Generation of 3D Maize Plant Architecture from LIDAR Data](https://mlsanity.com/paper/2501.13963/) (2025)
- [Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networks](https://mlsanity.com/paper/2508.19071/) (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)
- [MergeNet: Explicit Mesh Reconstruction from Sparse Point Clouds via Edge Prediction](https://mlsanity.com/paper/2407.11610/) (2024)
- [OffsetOPT: Explicit Surface Reconstruction without Normals](https://mlsanity.com/paper/2503.15763/) (2025)
- [Multi-view Geometry: Correspondences Refinement Based on Algebraic Properties](https://mlsanity.com/paper/2205.01634/) (2022)
- [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)
- [PolyFlow: Continuous Topology Embedding Flow Matching for Artist-style Mesh Generation](https://mlsanity.com/paper/2606.30673/) (2026)
- [From a few Accurate 2D Correspondences to 3D Point Clouds](https://mlsanity.com/paper/2206.08749/) (2022)
- [Point Cloud to Mesh Reconstruction: Methods, Trade-offs, and Implementation Guide](https://mlsanity.com/paper/2412.10977/) (2024)
- [PolycubeNet: A Dual-latent Diffusion Model for Polycube-Based Hexahedral Mesh Generation](https://mlsanity.com/paper/2605.20274/) (2026)

## Abstract (arXiv)

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D learning pipelines. The method iteratively applies two neural networks: a classification network predicts whether a candidate triangle should appear in the triangulation, while a proposal network suggests additional candidates. Both networks are structured as PointNets over nearby points and triangles, using a novel triangle-relative input encoding. Since these learning problems operate on local geometric data, our method is efficient and scalable, and generalizes to unseen shape categories. Our networks are trained in an unsupervised manner from a collection of shapes represented as point clouds. We demonstrate the effectiveness of this approach for classical meshing tasks, robustness to outliers, and as a component in end-to-end learning systems.