# Multi-chart Generative Surface Modeling

arXiv: https://arxiv.org/abs/1806.02143 · HTML: https://mlsanity.com/paper/1806.02143/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2018.

## Built on by (most cited first, 26 of 26)

- [Advances in 3D Generation: A Survey](https://mlsanity.com/paper/2401.17807/) (2024)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [Neural Template: Topology-aware Reconstruction and Disentangled Generation of 3D Meshes](https://mlsanity.com/paper/2206.04942/) (2022)
- [An Object is Worth 64x64 Pixels: Generating 3D Object via Image Diffusion](https://mlsanity.com/paper/2408.03178/) (2024)
- [Learning to Generate 3D Shapes from a Single Example](https://mlsanity.com/paper/2208.02946/) (2022)
- [Multi-modal Machine Learning in Engineering Design: A Review and Future Directions](https://mlsanity.com/paper/2302.10909/) (2023)
- [Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstruction](https://mlsanity.com/paper/2106.03135/) (2021)
- [Surrogate Modeling of Car Drag Coefficient with Depth and Normal Renderings](https://mlsanity.com/paper/2306.06110/) (2023)
- [FakeNews: GAN-based generation of realistic 3D volumetric data -- A systematic review and taxonomy](https://mlsanity.com/paper/2207.01390/) (2022)
- [MV-DeepSDF: Implicit Modeling with Multi-Sweep Point Clouds for 3D Vehicle Reconstruction in Autonomous Driving](https://mlsanity.com/paper/2309.16715/) (2023)
- [Deep Generative Model for Efficient 3D Airfoil Parameterization and Generation](https://mlsanity.com/paper/2101.02744/) (2021)
- [Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks](https://mlsanity.com/paper/2303.01978/) (2023)
- [3inGAN: Learning a 3D Generative Model from Images of a Self-similar Scene](https://mlsanity.com/paper/2211.14902/) (2022)
- [MVControl: Adding Conditional Control to Multi-view Diffusion for Controllable Text-to-3D Generation](https://mlsanity.com/paper/2311.14494/) (2023)
- [ET3D: Efficient Text-to-3D Generation via Multi-View Distillation](https://mlsanity.com/paper/2311.15561/) (2023)
- [Range-GAN: Range-Constrained Generative Adversarial Network for Conditioned Design Synthesis](https://mlsanity.com/paper/2103.06230/) (2021)
- [Learning Mesh Representations via Binary Space Partitioning Tree Networks](https://mlsanity.com/paper/2106.14274/) (2021)
- [Neural Rendering of Humans in Novel View and Pose from Monocular Video](https://mlsanity.com/paper/2204.01218/) (2022)
- [Test-Time Augmentation for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2311.13152/) (2023)
- [Learning Effective NeRFs and SDFs Representations with 3D Generative Adversarial Networks for 3D Object Generation](https://mlsanity.com/paper/2309.16110/) (2023)
- [Optimizing 3D Geometry Reconstruction from Implicit Neural Representations](https://mlsanity.com/paper/2410.12725/) (2024)
- [Deep Generative Models on 3D Representations: A Survey](https://mlsanity.com/paper/2210.15663/) (2022)
- [Towards AI-Architecture Liberty: A Comprehensive Survey on Design and Generation of Virtual Architecture by Deep Learning](https://mlsanity.com/paper/2305.00510/) (2023)
- [3D Shape Generation: A Survey](https://mlsanity.com/paper/2506.22678/) (2025)
- [Recent Advances and Trends in Learning-based 3D Representations](https://mlsanity.com/paper/2606.04871/) (2026)

## Abstract (arXiv)

This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well represented by multiple parameterizations (charts), each focusing on a different part of the shape. The new tensor data representation is used as input to Generative Adversarial Networks for the task of 3D shape generation. The 3D shape tensor representation is based on a multi-chart structure that enjoys a shape covering property and scale-translation rigidity. Scale-translation rigidity facilitates high quality 3D shape learning and guarantees unique reconstruction. The multi-chart structure uses as input a dataset of 3D shapes (with arbitrary connectivity) and a sparse correspondence between them. The output of our algorithm is a generative model that learns the shape distribution and is able to generate novel shapes, interpolate shapes, and explore the generated shape space. The effectiveness of the method is demonstrated for the task of anatomic shape generation including human body and bone (teeth) shape generation.