# Spherical Voronoi: Directional Appearance as a Differentiable Partition of the Sphere

arXiv: https://arxiv.org/abs/2512.14180 · HTML: https://mlsanity.com/paper/2512.14180/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 28 of 28)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [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)
- [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)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [GaussianShader: 3D Gaussian Splatting with Shading Functions for Reflective Surfaces](https://mlsanity.com/paper/2311.17977/) (2023)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [Shape, Light, and Material Decomposition from Images using Monte Carlo Rendering and Denoising](https://mlsanity.com/paper/2206.03380/) (2022)
- [NeRO: Neural Geometry and BRDF Reconstruction of Reflective Objects from Multiview Images](https://mlsanity.com/paper/2305.17398/) (2023)
- [3D Gaussian Ray Tracing: Fast Tracing of Particle Scenes](https://mlsanity.com/paper/2407.07090/) (2024)
- [RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPS](https://mlsanity.com/paper/2403.13806/) (2024)
- [ENVIDR: Implicit Differentiable Renderer with Neural Environment Lighting](https://mlsanity.com/paper/2303.13022/) (2023)
- [EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis](https://mlsanity.com/paper/2410.01804/) (2024)
- [Neural Microfacet Fields for Inverse Rendering](https://mlsanity.com/paper/2303.17806/) (2023)
- [Deformable Beta Splatting](https://mlsanity.com/paper/2501.18630/) (2025)
- [EnvGS: Modeling View-Dependent Appearance with Environment Gaussian](https://mlsanity.com/paper/2412.15215/) (2024)
- [Radiant Foam: Real-Time Differentiable Ray Tracing](https://mlsanity.com/paper/2502.01157/) (2025)
- [NeRF-Casting: Improved View-Dependent Appearance with Consistent Reflections](https://mlsanity.com/paper/2405.14871/) (2024)
- [Ref-GS: Directional Factorization for 2D Gaussian Splatting](https://mlsanity.com/paper/2412.00905/) (2024)
- [NerfBaselines: Consistent and Reproducible Evaluation of Novel View Synthesis Methods](https://mlsanity.com/paper/2406.17345/) (2024)
- [Neural Directional Encoding for Efficient and Accurate View-Dependent Appearance Modeling](https://mlsanity.com/paper/2405.14847/) (2024)
- [3iGS: Factorised Tensorial Illumination for 3D Gaussian Splatting](https://mlsanity.com/paper/2408.03753/) (2024)
- [VoronoiNet: General Functional Approximators with Local Support](https://mlsanity.com/paper/1912.03629/) (2019)
- [NeLF-Pro: Neural Light Field Probes for Multi-Scale Novel View Synthesis](https://mlsanity.com/paper/2312.13328/) (2023)

## Built on by (most cited first, 11 of 11)

- [Neural Harmonic Textures for High-Quality Primitive Based Neural Reconstruction](https://mlsanity.com/paper/2604.01204/) (2026)
- [Confidence-Based Mesh Extraction from 3D Gaussians](https://mlsanity.com/paper/2603.24725/) (2026)
- [Power Foam: Unifying Real-Time Differentiable Ray Tracing and Rasterization](https://mlsanity.com/paper/2604.24994/) (2026)
- [Tessellating The Earth](https://mlsanity.com/paper/2606.27514/) (2026)
- [Beyond Spherical Harmonics: Rethinking Appearance Models for Radiance Reconstruction](https://mlsanity.com/paper/2606.09794/) (2026)
- [Soft Anisotropic Diagrams for Differentiable Image Representation](https://mlsanity.com/paper/2604.21984/) (2026)
- [MooMIns -- Monocular 3D Reconstruction and Object Pose Estimation from Multiple Instances](https://mlsanity.com/paper/2606.14389/) (2026)
- [Bake It Till You Make It: Ultrafast Spatial Texture-Atlas Splatting](https://mlsanity.com/paper/2607.13808/) (2026)
- [Compact Neural Appearance Models for Efficient Gaussian Splatting](https://mlsanity.com/paper/2609.05255/) (2026)
- [Chronosphere: Space-Time Tessellation of Local Climate Experts](https://mlsanity.com/paper/2609.21872/) (2026)
- [Efficient Confidence-Aware Densification for 3DGS](https://mlsanity.com/paper/2610.13541/) (2026)

## Abstract (arXiv)

Radiance field methods (e.g. 3D Gaussian Splatting) have emerged as a powerful paradigm for novel view synthesis, yet their appearance modeling often relies on Spherical Harmonics (SH), which impose fundamental limitations. SH struggle with high-frequency signals, exhibit Gibbs ringing artifacts, and fail to capture specular reflections - a key component of realistic rendering. Although alternatives like spherical Gaussians offer improvements, they add significant optimization complexity. We propose Spherical Voronoi (SV) as a unified framework for appearance representation in 3D Gaussian Splatting. SV partitions the directional domain into learnable regions with smooth boundaries, providing an intuitive and stable parameterization for view-dependent effects. For diffuse appearance, SV achieves competitive results while keeping optimization simpler than existing alternatives. For reflections - where SH fail - we leverage SV as learnable reflection probes, taking reflected directions as input following principles from classical graphics. This formulation attains state-of-the-art results on synthetic and real-world datasets, demonstrating that SV offers a principled, efficient, and general solution for appearance modeling in explicit 3D representations. Project page: https://sphericalvoronoi.github.io/