# Quadratic Gaussian Splatting: High Quality Surface Reconstruction with Second-order Geometric Primitives

arXiv: https://arxiv.org/abs/2411.16392 · HTML: https://mlsanity.com/paper/2411.16392/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 30 of 39)

- [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)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (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)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [DrivingGaussian: Composite Gaussian Splatting for Surrounding Dynamic Autonomous Driving Scenes](https://mlsanity.com/paper/2312.07920/) (2023)
- [GaussianEditor: Swift and Controllable 3D Editing with Gaussian Splatting](https://mlsanity.com/paper/2311.14521/) (2023)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [Differentiable Surface Splatting for Point-based Geometry Processing](https://mlsanity.com/paper/1906.04173/) (2019)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [VastGaussian: Vast 3D Gaussians for Large Scene Reconstruction](https://mlsanity.com/paper/2402.17427/) (2024)
- [CityGaussian: Real-time High-quality Large-Scale Scene Rendering with Gaussians](https://mlsanity.com/paper/2404.01133/) (2024)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [StopThePop: Sorted Gaussian Splatting for View-Consistent Real-time Rendering](https://mlsanity.com/paper/2402.00525/) (2024)
- [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)
- [GSDF: 3DGS Meets SDF for Improved Rendering and Reconstruction](https://mlsanity.com/paper/2403.16964/) (2024)
- [GaMeS: Mesh-Based Adapting and Modification of Gaussian Splatting](https://mlsanity.com/paper/2402.01459/) (2024)

## Built on by (most cited first, 20 of 20)

- [Geometry-Grounded Gaussian Splatting](https://mlsanity.com/paper/2601.17835/) (2026)
- [Universal Beta Splatting](https://mlsanity.com/paper/2510.03312/) (2025)
- [PLANING: A Loosely Coupled Triangle-Gaussian Framework for Streaming 3D Reconstruction](https://mlsanity.com/paper/2601.22046/) (2026)
- [Confidence-Based Mesh Extraction from 3D Gaussians](https://mlsanity.com/paper/2603.24725/) (2026)
- [ObjSplat: Geometry-Aware Gaussian Surfels for Active Object Reconstruction](https://mlsanity.com/paper/2601.06997/) (2026)
- [ExMesh: Explicit Mesh Reconstruction with Topology Adaptation](https://mlsanity.com/paper/2606.07288/) (2026)
- [Spectral Defense Against Resource-Targeting Attack in 3D Gaussian Splatting](https://mlsanity.com/paper/2603.12796/) (2026)
- [3D Gaussian Splatting with Self-Constrained Priors for High Fidelity Surface Reconstruction](https://mlsanity.com/paper/2603.19682/) (2026)
- [Fourier Splatting: Generalized Fourier encoded primitives for scalable radiance fields](https://mlsanity.com/paper/2603.19834/) (2026)
- [Splaxel: Efficient Distributed Training of 3D Gaussian Splatting for Large-scale Scene Reconstruction via Pixel-level Communication](https://mlsanity.com/paper/2606.18588/) (2026)
- [A Mixed-Primitive-based Gaussian Splatting Method for Surface Reconstruction](https://mlsanity.com/paper/2507.11321/) (2025)
- [Fast Converging 3D Gaussian Splatting for 1-Minute Reconstruction](https://mlsanity.com/paper/2601.19489/) (2026)
- [GVGS: Gaussian Visibility-Aware Multi-View Geometry for Accurate Surface Reconstruction](https://mlsanity.com/paper/2601.20331/) (2026)
- [Analysis of Converged 3D Gaussian Splatting Solutions: Density Effects and Prediction Limit](https://mlsanity.com/paper/2602.08909/) (2026)
- [From ex(p) to poly: Gaussian Splatting with Polynomial Kernels](https://mlsanity.com/paper/2603.18707/) (2026)
- [Deformable Triangle Splatting: Flexible Primitives for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2607.22446/) (2026)
- [TopoSurfel: Closing the Loop between Gaussian Surfels and Meshes for Surface Reconstruction](https://mlsanity.com/paper/2608.20687/) (2026)
- [ExMesh++: From Multi-View Images to Relightable UV-PBR Mesh Assets via Topology-Adaptive Reconstruction and Decomposition](https://mlsanity.com/paper/2608.24109/) (2026)
- [Non-Uniform Quantisation for 3DGS Compression](https://mlsanity.com/paper/2608.28272/) (2026)
- [ToCo-Mesh: Topology-Consistent Dynamic Mesh Reconstruction via Adaptive Tessellation and Surface-Aligned 2DGS](https://mlsanity.com/paper/2609.29529/) (2026)

## Abstract (arXiv)

We propose Quadratic Gaussian Splatting (QGS), a novel representation that replaces static primitives with deformable quadric surfaces (e.g., ellipse, paraboloids) to capture intricate geometry. Unlike prior works that rely on Euclidean distance for primitive density modeling--a metric misaligned with surface geometry under deformation--QGS introduces geodesic distance-based density distributions. This innovation ensures that density weights adapt intrinsically to the primitive curvature, preserving consistency during shape changes (e.g., from planar disks to curved paraboloids). By solving geodesic distances in closed form on quadric surfaces, QGS enables surface-aware splatting, where a single primitive can represent complex curvature that previously required dozens of planar surfels, potentially reducing memory usage while maintaining efficient rendering via fast ray-quadric intersection. Experiments on DTU, Tanks and Temples, and MipNeRF360 datasets demonstrate state-of-the-art surface reconstruction, with QGS reducing geometric error (chamfer distance) by 33% over 2DGS and 27% over GOF on the DTU dataset. Crucially, QGS retains competitive appearance quality, bridging the gap between geometric precision and visual fidelity for applications like robotics and immersive reality.