# TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes

arXiv: https://arxiv.org/abs/2405.20283 · HTML: https://mlsanity.com/paper/2405.20283/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 90 of its 119 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 90)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [MVDream: Multi-view Diffusion for 3D Generation](https://mlsanity.com/paper/2308.16512/) (2023)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation](https://mlsanity.com/paper/2309.16653/) (2023)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [LGM: Large Multi-View Gaussian Model for High-Resolution 3D Content Creation](https://mlsanity.com/paper/2402.05054/) (2024)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Wonder3D: Single Image to 3D using Cross-Domain Diffusion](https://mlsanity.com/paper/2310.15008/) (2023)
- [Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation](https://mlsanity.com/paper/2303.13873/) (2023)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [SyncDreamer: Generating Multiview-consistent Images from a Single-view Image](https://mlsanity.com/paper/2309.03453/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)

## Built on by (most cited first, 21 of 21)

- [Architect: Generating Vivid and Interactive 3D Scenes with Hierarchical 2D Inpainting](https://mlsanity.com/paper/2411.09823/) (2024)
- [Dynamic Scene Reconstruction: Recent Advance in Real-time Rendering and Streaming](https://mlsanity.com/paper/2503.08166/) (2025)
- [Radiance Meshes for Volumetric Reconstruction](https://mlsanity.com/paper/2512.04076/) (2025)
- [Bezier Splatting for Fast and Differentiable Vector Graphics Rendering](https://mlsanity.com/paper/2503.16424/) (2025)
- [2D Triangle Splatting for Direct Differentiable Mesh Training](https://mlsanity.com/paper/2506.18575/) (2025)
- [Neural Geometry Image-Based Representations with Optimal Transport (OT)](https://mlsanity.com/paper/2511.18679/) (2025)
- [Inverse Rendering for High-Genus Surface Meshes from Multi-View Images](https://mlsanity.com/paper/2511.18680/) (2025)
- [Splatwizard: A Benchmark Toolkit for 3D Gaussian Splatting Compression](https://mlsanity.com/paper/2512.24742/) (2025)
- [PAS3R: Pose-Adaptive Streaming 3D Reconstruction for Long Video Sequences](https://mlsanity.com/paper/2603.21436/) (2026)
- [Benchmarking PhD-Level Coding in 3D Geometric Computer Vision](https://mlsanity.com/paper/2603.30038/) (2026)
- [Shape from Semantics: 3D Shape Generation from Multi-View Semantics](https://mlsanity.com/paper/2502.00360/) (2025)
- [DensiCrafter: Physically-Constrained Generation and Fabrication of Self-Supporting Hollow Structures](https://mlsanity.com/paper/2511.09298/) (2025)
- [Med-PU: Point Cloud Upsampling for High-Fidelity 3D Medical Shape Reconstruction](https://mlsanity.com/paper/2501.16716/) (2025)
- [VoroLight: Learning Voronoi Surface Meshes via Sphere Intersection](https://mlsanity.com/paper/2512.12984/) (2025)
- [PUFM++: Point Cloud Upsampling via Enhanced Flow Matching](https://mlsanity.com/paper/2512.20988/) (2025)
- [Inverse Rendering for High-Genus 3D Surface Meshes from Multi-view Images with Persistent Homology Priors](https://mlsanity.com/paper/2601.12155/) (2026)
- [Vector Scaffolding: Inter-Scale Orchestration for Differentiable Image Vectorization](https://mlsanity.com/paper/2605.11913/) (2026)
- [HoloTetSphere: Unified TetSphere Mesh Reconstruction for Physical Simulations](https://mlsanity.com/paper/2607.08398/) (2026)
- [CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxation](https://mlsanity.com/paper/2608.20803/) (2026)
- [From Surfaces to Volumes: Registered Geometry for Protein Representation Learning](https://mlsanity.com/paper/2609.36277/) (2026)
- [Physics-based Sphere Packing for Lagrangian Mesh Morphing](https://mlsanity.com/paper/2610.08880/) (2026)

## Abstract (arXiv)

We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents 3D shapes by deforming a collection of tetrahedral spheres, with geometric regularizations and constraints that effectively resolve common mesh issues such as irregular triangles, non-manifoldness, and floating artifacts. Experimental results on multi-view and single-view reconstruction highlight TetSphere splatting's superior mesh quality while maintaining competitive reconstruction accuracy compared to state-of-the-art methods. Additionally, TetSphere splatting demonstrates versatility by seamlessly integrating into generative modeling tasks, such as image-to-3D and text-to-3D generation.