# Triangle Splatting+: Differentiable Rendering with Opaque Triangles

arXiv: https://arxiv.org/abs/2509.25122 · HTML: https://mlsanity.com/paper/2509.25122/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 37 references that are in the map.
- First posted on arXiv 29 Sep 2025.

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

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation](https://mlsanity.com/paper/2404.15506/) (2024)
- [Gaussian Grouping: Segment and Edit Anything in 3D Scenes](https://mlsanity.com/paper/2312.00732/) (2023)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [Gaussian Opacity Fields: Efficient Adaptive Surface Reconstruction in Unbounded Scenes](https://mlsanity.com/paper/2404.10772/) (2024)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [Segment Any 3D Gaussians](https://mlsanity.com/paper/2312.00860/) (2023)
- [RaDe-GS: Rasterizing Depth in Gaussian Splatting](https://mlsanity.com/paper/2406.01467/) (2024)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis](https://mlsanity.com/paper/2402.12377/) (2024)
- [MILo: Mesh-In-the-Loop Gaussian Splatting for Detailed and Efficient Surface Reconstruction](https://mlsanity.com/paper/2506.24096/) (2025)
- [Sparse Voxels Rasterization: Real-time High-fidelity Radiance Field Rendering](https://mlsanity.com/paper/2412.04459/) (2024)
- [Radiant Foam: Real-Time Differentiable Ray Tracing](https://mlsanity.com/paper/2502.01157/) (2025)
- [Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation](https://mlsanity.com/paper/2407.09497/) (2024)
- [Beyond Gaussians: Fast and High-Fidelity 3D Splatting with Linear Kernels](https://mlsanity.com/paper/2411.12440/) (2024)
- [LinPrim: Linear Primitives for Differentiable Volumetric Rendering](https://mlsanity.com/paper/2501.16312/) (2025)
- [Deformable Radial Kernel Splatting](https://mlsanity.com/paper/2412.11752/) (2024)
- [DMesh++: An Efficient Differentiable Mesh for Complex Shapes](https://mlsanity.com/paper/2412.16776/) (2024)
- [DMesh: A Differentiable Mesh Representation](https://mlsanity.com/paper/2404.13445/) (2024)
- [HaloGS: Loose Coupling of Compact Geometry and Gaussian Splats for 3D Scenes](https://mlsanity.com/paper/2505.20267/) (2025)

## Built on by (most cited first, 5 of 5)

- [Nexels: Neurally-Textured Surfels for Real-Time Novel View Synthesis with Sparse Geometries](https://mlsanity.com/paper/2512.13796/) (2025)
- [DiffSoup: Direct Differentiable Rasterization of Triangle Soup for Extreme Radiance Field Simplification](https://mlsanity.com/paper/2603.27151/) (2026)
- [Radiant Foam Rendering on a Graph Processor](https://mlsanity.com/paper/2601.04382/) (2026)
- [Iterative Motion Compensation for Canonical 3D Reconstruction from UAV Plant Images Captured in Windy Conditions](https://mlsanity.com/paper/2510.15491/) (2025)
- [TRON: Tracing Rays to Orchestrate a Neural Renderer for 3D Gaussian Reconstructions](https://mlsanity.com/paper/2606.11314/) (2026)

## Abstract (arXiv)

Reconstructing 3D scenes and synthesizing novel views has seen rapid progress in recent years. Neural Radiance Fields demonstrated that continuous volumetric radiance fields can achieve high-quality image synthesis, but their long training and rendering times limit practicality. 3D Gaussian Splatting (3DGS) addressed these issues by representing scenes with millions of Gaussians, enabling real-time rendering and fast optimization. However, Gaussian primitives are not natively compatible with the mesh-based pipelines used in VR headsets, and real-time graphics applications. Existing solutions attempt to convert Gaussians into meshes through post-processing or two-stage pipelines, which increases complexity and degrades visual quality. In this work, we introduce Triangle Splatting+, which directly optimizes triangles, the fundamental primitive of computer graphics, within a differentiable splatting framework. We formulate triangle parametrization to enable connectivity through shared vertices, and we design a training strategy that enforces opaque triangles. The final output is immediately usable in standard graphics engines without post-processing. Experiments on the Mip-NeRF360 and Tanks & Temples datasets show that Triangle Splatting+achieves state-of-the-art performance in mesh-based novel view synthesis. Our method surpasses prior splatting approaches in visual fidelity while remaining efficient and fast to training. Moreover, the resulting semi-connected meshes support downstream applications such as physics-based simulation or interactive walkthroughs. The project page is https://trianglesplatting2.github.io/trianglesplatting2/.